NON-LINE-OF-SIGHT ERROR MITIGATION TECHNIQUES FOR RADIOLOCATION (Ph.D. Thesis Proposal) Jose Manuel Huerta

Table of Contents LIST OF ACRONYMS............................................................................................................... 3 1

FOREWORD AND GENERAL OBJECTIVES................................................................ 4

2

STATE OF THE ART .......................................................................................................... 6

2.1 PARAMETERS ...................................................................................................................... 6 2.1.1 TIMING METHODS.............................................................................................................. 7 2.1.2 ANGULAR METHODS ......................................................................................................... 7 2.2 STATIC POSITIONING ......................................................................................................... 8 2.3 DYNAMIC POSITIONING ..................................................................................................... 9 2.3.1 UNSCENTED KALMAN FILTER........................................................................................... 9 2.3.1.1 Form of the sigma set................................................................................................... 10 2.3.1.2 Obtain the statistics from a sigma set........................................................................... 10 2.3.1.3 Pass through a non-linear function .............................................................................. 10 2.3.1.4 UKF iteration ............................................................................................................... 11 2.3.1.5 The Square-Root-UKF................................................................................................. 12 2.3.2 PARTICLE FILTER ............................................................................................................ 12 2.3.3 COMPARISON .................................................................................................................. 13 2.4 NLOS MITIGATION TECHNIQUES ................................................................................... 13 2.4.1 HYPOTHESIS BASED APPROACHES .................................................................................. 14 2.4.2 STATISTICAL ANALYSIS .................................................................................................. 15 2.4.3 TRACKING OF THE BIAS ................................................................................................... 15 2.4.4 MODELLING THE ERROR INTRODUCED BY THE NLOS.................................................... 16 2.4.5 MITIGATING THE NLOS AT THE PARAMETER ESTIMATION STAGE ................................. 17 2.4.6 SUMMARY OF NLOS MITIGATION TECHNIQUES ............................................................. 18 3

PRELIMINARY RESULTS .............................................................................................. 19

2 3.1 3.2 3.3 3.3.1 3.3.2 3.3.3 3.4 3.5 3.6 3.6.1 3.6.2 3.6.3 3.7 3.8 3.9 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5

EXTENDED MODEL ........................................................................................................... 19 OBSERVATION NOISE ........................................................................................................ 20 LOS-NLOS ESTIMATION ................................................................................................. 21 TRANSITION PROBABILITIES EVOLUTION ........................................................................ 22 SITUATION EVENTS ......................................................................................................... 23 PROBABILITY DENSITY FUNCTION OF THE SITUATION EVENTS ....................................... 25 IMPROVED UKF................................................................................................................ 25 SIMULATION RESULTS ...................................................................................................... 27 EXPERIMENTAL RESULTS ................................................................................................ 28 TESTING ENVIRONMENT .................................................................................................. 28 LOS-NLOS SITUATION ESTIMATOR EVALUATION ......................................................... 30 EVALUATION OF THE IMPROVED UKF ............................................................................ 31 CONVERGENCE SPEED ...................................................................................................... 32 PRELIMINARY CONCLUSIONS .......................................................................................... 32 LIST OF PUBLICATIONS .................................................................................................... 33

WORK PLAN ..................................................................................................................... 34 NLOS ERROR MODELLING .............................................................................................. 34 NLOS PROBABILITY ......................................................................................................... 34 JOINT LOS-NLOS ESTIMATION ...................................................................................... 34 BLIND PROBABILITIES ESTIMATION ................................................................................ 34 USE OF MT SENSORS ........................................................................................................ 35 RAO-BACKWELLIZATION ................................................................................................ 35 EXTENSION TO COOPERATIVE SYSTEMS ........................................................................ 35 UPGRADING OF THE TEST-BED ........................................................................................ 36 WORK CALENDAR ............................................................................................................. 37 REFERENCES.................................................................................................................... 38

3

List of Acronyms 2G

2nd Generation

PC

Personal Computer

3G

3rd Generation

PCF

BS

Base Station

Positioning Calculation Function

BW

Bandwidth

Probability Density Function

CDF

Cumulative Density Function

PF

Particle Filter

RB

Rao-Backwellization

DL

Down-Link

RSS

Received Signal Strength

DOA

Direction of Arrival

RTOA

Relative Time of Arrival

DSP

Digital Signal Processor

RTT

Round Trip Time

EKF

Extended Kalman Filter

SINR

FPGA

Field Programmable Grid Array

Signal to Interference and Noise Ratio

SNR

Signal to Noise Ratio

GPS

Global Positioning System

GSM

Global Standard for Mobile Communications

SRUKF Square Root Unscented Kalman Filter TA

Time Advance

HMM

Hidden Markov Model

TDOA

Time Difference of Arrival

KF

Kalman Filter

TOA

Time of Arrival

LOS

Line of Sight

UKF

Unscented Kalman Filter

LUT

Look Up Table

UMTS

MIMO Multiple Input Multiple Output

Universal Mobile Telecommunication System

UP

Up-Link

ML

Maximum Likelihood

UPC

MT

Mobile Terminal

Technical University of Catalonia

NLOS

Non Line of Sight

UT

Unscented Transform

NMV

Normalized Minimum Variance

VHDL

VHSIC Hardware Description Language

4

1 Foreword and General Objectives A field of growing importance in cellular networks is the geographical location of a Mobile Terminal (MT) [Sil95][Dra98][Caf98][Gus05]. In fact, most of the short calls in these networks are related to the speaker’s position with sentences like “I’m at home”, “I will arrive in two minutes”, etc. It is well known that today’s cellular networks provide not only voice or data communication. Value-add services became an important part of the communication business. Extra value-add services can be developed to exploit the location necessity if enough accuracy is achieved [Sil95]. “Where am I?”, “Map of the surrounding area”, “How to arrive?”, “Where’s the nearest restaurant?” are few examples of this kind of services. Also, this will be mandatory for 911 services [FCC96][FCC02]. That explains the interest to this topic in the recent years. The pass from 2nd Generation (2G) to 3rd Generation (3G) cellular systems offer us a new set of possibilities, in location terms, due to the higher bandwidth and the use of antenna arrays. Better accuracy that GPS is theoretically achievable. The location can be performed at Up-Link (UP), where the Base Stations (BS) estimate the position of the MT from the received MT signals, or Down-Link (DL), where is the MT who locate itself from the BS’s signals. In both cases, the location is normally based on parameter estimation. Thus, some parameters related to the MT position are estimated from the radio signals, and combined in a Position Calculation Function (PCF). Examples of these parameters are Time of Arrival (TOA) and Direction of Arrival (DOA). An estimation error in these parameters is propagated to the positioning estimation. The greatest impairments to the parameter estimation are the multipath and the NonLine-of-Sight (NLOS), being the last the worst of the two, which is usually referred as a “killer” effect. Both of them bias the parameter estimation. For instance, the NLOS effect can degrade the TOA measurements with a bias higher than 500 meters [Woo00] in regular urban conditions. The multipath can be mitigated in the parameter estimation stage. High resolution methods provide an unbiased estimation under severe multipath conditions [Vid02]. It is considered that the NLOS can not be avoided on the parameter estimation stage. Thus, the only solution is to develop a PCF capable of mitigate the effect of the bias in the final positioning. Several solutions have appeared in the recent year in that direction, which will be reviewed in the state-of-the-art chapter. Two major frameworks can be considered: static and dynamic positioning. Static positioning uses the set of measures related with some time instant for the position estimation. Dynamic positioning uses also the past measures. The NLOS mitigation strategies include statistical analysis, geographical properties and signal quality measures. Almost all solutions present in literature are based on detecting the parameters contaminated with NLOS bias and give a lesser (or none) influence in the PCF.

5 The objective of the present work is to develop a PCF using new strategies in order to have better NLOS mitigation than previous approaches. The approach is intended to be used in real 3G urban scenarios with severe NLOS conditions. A test-bed is used to prove the reliability of the techniques with real measures. The localization model considered is depicted at Figure 1. The different antennas depicted at this figure symbolize different signals receiver, but not necessary different antennas. Thus, they can reflect several receivers spread over the BS’s receiving the signal from the MT (UL), or the signals from several BS’s arriving at the MT (DL). Channel estimation is performed using the known pseudo-random sequences (like a midamble). Using the channel estimation, the parameters (TOA, DOA, …) are estimated. Also a LOS-NLOS probability is estimated. Finally, a PCF uses all parameters from all BS and all LOS-NLOS estimations to perform the positioning estimation. It is assumed that there are enough BS’s to obtain a closed positioning solution. That means at least 2 DOA or 3 TOA. The scenario is mainly urban, with a high probability to be at NLOS (more than 50 %). There is no minimum number of BS’s at LOS. In fact, more than 90 % of the time there will be not enough BS at LOS to have a close solution. The system performs 100 parameter estimations per second. The clocks from all BS are synchronized between them, but not with the mobile clock.

RF receiver

Channel estimation

Parameters estimation LOS/NLOS estimation

LOS/NLOS estimation RF receiver

Figure 1. Complete localization model

Channel estimation

Parameters estimation

PCF

6

2 State of the art 2.1 Parameters As stated in the introduction, the positioning is usually based on parameters. There are two families of parameters, the range based and angle based parameters. The range based parameters can be obtained from the study of propagation time or propagation attenuation. Regarding to time, we can consider the next parameters: •

Round Trip Time (RTT): The propagation time between a transmission from the BS to the MT and the answer from the MT to the BS. This is a measure currently estimated at GSM (2G) and UMTS (3G) as the Time Advance (TA).

•

Received Signal Strength (RSS): The received signal power. It allows estimating the range between transmitter and receiver when the transmission power is known.

•

Time of Arrival (TOA): The propagation time between the BS and the MT. The estimation of the TOA requires synchronization between both BS and MT. Synchronization error translates into TOA estimation error.

•

Time Difference of Arrival (TDOA): Time difference between two arrivals that come from the same transmission (or at least, two transmissions, transmitted at the same time).

•

Relative Time of Arrival (RTOA): The time instant where the signal is received at BS or MT (depending of if an UL or DL situation is considered). Some RTOA measures of different BS’s can be considered if the transmission time of all is the same.

Figure 2. TOA and DOA location examples.

7 Direction of Arrival (DOA) is the only parameter based on angle. An antenna array is needed at the receiver in order to estimate the DOA. The estimation of this parameter is different, depending of the nature of it. But RTT, TOA, TDOA and RTOA are estimated in the same way, since all of them need to estimate the time instant where the signal arrives at the receiver.

2.1.1 Timing methods We know as Timing methods the set of approaches giving an estimation of the signal reception time. Different solutions have appeared in literature, with a different trade off between complexity and resolution. The multipath problem can lead to a biased timing measure, in the same way that the NLOS effect. A high resolution timing estimator is required to avoid this effect. [Vid02] describes a high resolution, normalized minimum variance (NMV) algorithm applied to the timing estimation. It is a spectral estimator based on [Lag84] first designed to DOA estimation problems. The resolution of this estimator is better than a sample, allowing us to detect the first arrival (which bears the range information) without influence of delayed taps. At Figure 3 it is depicted a comparison between a standard low resolution timing estimation and the NMV technique. This will be the estimator used for all timing parameters in order to avoid the multipath problem. At this point we will consider that the multipath effect has been completely solved by the NMV estimator. If the multipath effect at one time instant is high enough to provoke a biased estimation, we will consider it as a NLOS situation.

2.1.2 Angular methods After a study of different angle estimator [D641] we conclude that the [Bes00] has the best trade-off between complexity and accuracy for our scenario.

Figure 3. Left: The TOA is computed as the maximum of the channel impulse response estimation. Right: From the same channel estimation, the NMV technique allows a better resolution estimation of the taps, allowing an easy determination of the first arrival. (true arrivals are denoted by crosses).

8

2.2 Static Positioning The Static Positioning problem can be formulated in the following fashion. Let be y(t) a vector containing all the measured parameters at time t. Let be p(t) the MT position at t. Thus, we can state that:

y (t ) = g f ( p(t ) ) + n(t )

(1)

where g f (·) is the noise free observation function and n(t) the observation noise. Let be N its covariance matrix. If n(t) is assumed Gaussian and E {n(t )} = 0 , a general ML estimator of p(t) is [Tor84]: pˆ (t ) = arg min ( y (t ) − g f ( pˆ (t ) ) ) N −1 ( y (t ) − g f ( pˆ (t ) ) ) T

(2)

And if N is diagonal with equal entries ( N = σ n I ), the ML estimator of p(t) can be simplified: pˆ (t ) = arg min y (t ) − g f ( pˆ (t ) )

(3)

This equation can not be solved in an easy way since g f (·) is not linear, resulting in a non convex problem. If all measured parameters are DOA, then the expression in (3) is near to be convex, and a sub-optimal closed-form solution can be derived [Pag02]. One common solution is the linearization of y(t) by expanding it in a second order Taylor series about a reference point p 0 (expected to be close to p(t)): g f ( p(t ) )

g f ( p 0 ) + G ′f

p0

( p(t ) − p0 )

(4)

is the derivate matrix of g f (·) evaluated at p 0 . But this linearization is where G ′f p0 highly dependent of the election of p 0 . A bad choose of p 0 results in a biased estimator [Tor84] as expected from a non convex problem. [Abe87][Abe89][Abe90] offer different sub-optimal solutions to the static positioning with TDOA measures, with accuracy close to the ML solution (in LOS conditions). At [Abe87] a closed form solution is presented. The set of TDOA measures is interpolated to a circle, centred at the MT position. At [Abe89][Abe90] a divide & conquer strategy is presented to simplify the ML estimator, thus obtaining a trade-off between accuracy and complexity. [Aso01] is one of the most used solutions. Based on the log-likelihood, it finds a simpler approach, also very close to the ML solution. [Caf00] proposes a very elegant geometric approach. 2 TOA measures are translated to a norm to a line solution. The result is a convex problem, with a closed form solution. It is important to mention the work at [Rib04][Urr04], which not only present a closed form solution for the TDOA parameter case, but also has NLOS mitigation capabilities.

9

2.3 Dynamic Positioning Two major tracking techniques are used for positioning: Kalman Filter (KF) and Particle Filter (PF). Due to the non-linearity of the model, the Kalman Filter is not a suitable solution. Instead of it, the Extended Kalman Filter [Kay93] is used. But the behaviour of the EKF in the positioning framework is not as good as desired, although it is the most commonly used solution [Hel99]. Recently the Unscented Kalman Filter (UKF) has been presented [Jul97]. The UKF is based on the Unscented Transform (UT) and allows obtaining the statistics of random variables that pass through non-linear functions. The particle filter is a more complex approach in computational cost sense, but with better accuracy. So, a trade-off between complexity and accuracy is available and the selection of one or another must be done according to the requirements of the system. The positioning estimation can be summarized in the state-observation model: xt = f ( xt −1 , u t )

(5)

y t = g ( xt , n t )

where xt is the state, y t the observation, ut the state noise and nt the observation noise. f ( ·) is the state function and g ( ·) is the observation function. Normally the state contains the estimated position and speed of the mobile. But can also contain other parameters like the transmission time when RTOA measures are used.

2.3.1 Unscented Kalman Filter The UKF is an extension of the KF, which uses the UT to solve the non-linearity of the system [Wan00][Jul04][Jul04b]. This algorithm was first presented at [Jul97]. Let the extended state be: z t = ⎡⎣ xTt

uTt

nTt ⎤⎦

T

(6)

All random variables included in ut and nt must be Gaussian. This is not a restriction in the sense that any f(·) and g(·) functions are allowed, and the real distribution of the variables can be obtained from Gaussian distributions. The unscented transform is an approach that allows calculating the statistics of random variables that undergoes non-linear transformations (the state and observation functions). The method consist on calculating a set of sigma points Zt associated with z t ; obtain the observation sigma set from Yt = g ( Zt ) ; and finally obtain an estimation of y t from Yt .

10

2.3.1.1 Form of the sigma set Assume that a random vector a has mean a and covariance Pa . The associated sigma set A is a ( 2 La + 1) × La matrix, where La is the size of the vector a . The columns of A , Ai are called sigma points, and are calculated according to: A0 = a

( A = a −(

( L + λ ) Pa )

Ai = a +

( L + λ ) Pa )

i

i = 1,… , L

(7)

i

i−L

i = 1,… , L

where λ = α 2 L − L is a spreading of the sigma points parameter. A standard value is α = 10−3 . The pass from the mean and covariance to the sigma set is called unscented transform and represented by: UT a , Pa ⎯⎯ →A

(8)

2.3.1.2 Obtain the statistics from a sigma set The mean and covariance associated to the sigma set A are computed from the sigma points according to: 2L

a = ∑ Wi ( m ) Ai i =0

2L

Pa = ∑ Wi i =0

( m ,c )

( Ai − a )( Ai − a )

(9)

T

where the weights are: W0( m ) = λ ( L + λ ) W0( c ) = λ ( L + λ ) + 3 − α 2 Wi

( m ,c )

(10)

= 1 ( 2 L + 2λ ) , i ≠ 0

This operation is the inverse unscented transform and is represented by: −1

UT A ⎯⎯⎯ → a , Pa

(11)

2.3.1.3 Pass through a non-linear function The main ability of the unscented transform is to compute the statistic of a random variable through a non-linear function. Assume that we want to compute the statistics of b = f ( a ) from the statistics of a , being f ( ·) a non-linear function. First we transform the a vector: UT a , Pa ⎯⎯ →A

(12)

11 Then obtain the B sigma set from A by:

Bi = f ( Ai )

i = 0… 2 L

(13)

Also expressed by:

B = f (A )

(14)

Then, applying the inverse unscented transform, we can obtain the statistics of b : −1

UT B ⎯⎯⎯ → b, Pb

(15)

2.3.1.4 UKF iteration The UKF itself is a Kalman Filter where the non linearities are avoided using the unscented transform. Let’s see how it works. First, we compute the sigma set associated with the previous iteration extended state (6) : UT zt −1 , Pzt −1 ⎯⎯ → Zt −1

(16)

This sigma set can be represented as: ⎡Ztx−1 ⎤ ⎢ ⎥ Zt −1 = ⎢Ztu−1 ⎥ ⎢Ztn−1 ⎥ ⎣ ⎦

(17)

separating the parts of the state and noises. Notice that Ztx−1 ≠ Xt −1 . Second, we predict the next state: Z tx|t −1 = f ( Z tx−1 , Z tu−1 ) −1

UT → xt|t −1 , Pxt|t −1 Z tx|t −1 ⎯⎯⎯

(18)

Third, predict the observation: Yt|t −1 = g ( Z tx|t −1 , Z tn−1 ) −1

UT → y t|t −1 , Pyt|t −1 Yt|t −1 ⎯⎯⎯

Fourth, compute the Kalman gain matrix:

(19)

12 2L

Pxyt|t −1 = ∑ Wi ( c ) ( Ztx|t −1 − xt|t −1 )( Yt|t −1 − y t|t −1 )

T

i =0

(20)

−1 y t|t −1

K = Pxyt|t−1 P

Finally, obtain the statistics of the state: xt = xt|t −1 + K ( y t − y t|t −1 ) T

zt = ⎡⎣ xtT 0 0 ⎤⎦ Pxt = Pxt|t −1 − KPyt|t −1 K T ⎡ Pxt ⎢ Pzt = ⎢ 0 ⎢0 ⎣

0 Pu 0

(21)

0⎤ ⎥ 0⎥ Pn ⎥⎦

2.3.1.5 The Square-Root-UKF First appeared in [Wan01] a new approach to the UKF has been presented to avoid some minor problems. The computation of the square-root of the matrix continuously in time can lead to a non positive defined state covariance matrix. Using the Cholesky factorization the numerical stability and positive definiteness are guaranteed.

2.3.2 Particle Filter When trying to analytically solve the state and observation equation model from a Bayesian point of view, the final objective is to find a closed expression for p(x0..t | y 0..t ) . One solution is to follow the Bayes rule: p ( x 0..t | y 0..t ) =

p ( y t | xt ) p ( xt | xt −1 ) p ( x 0..t −1 | y 0..t −1 ) p ( y t | y 0..t −1 )

(22)

But for non-linear and non-Gaussian systems this expression is analytically intractable. The Monte Carlo solution consists on approximating a PDF as a sum of Dirac deltas (called particles). Then, all integrations can be computed as summations. The particle filter solution consists on transform the state and all random variables to particle sets [Dju03][Gus02][Liu01]. The number of particles must be high enough in order to characterize the behaviour of the variables correctly. Then all the functions are computed for each particle as if they were a deterministic value. All the results form a particle set that defines the PDF of the solution. Two extra ideas are applied in the particle filters:

•

Importance sampling: That means to put more particles in the areas of most interest of the PDF. This technique allows reducing the number of particles needed to characterize the PDF.

13

Figure 4. Differences between the behaviour of proposed trackers

•

Resampling: The solution of a particle filter iteration is the input of the next. One undesired effect is the degradation of the spread of particles. That means that a lot of light particles concentrate in a small area, with the characterization of the function is carried by a low number of particles. In order to avoid this effect, the particles are redistributed at each iteration.

The computational cost of the PF is very high. We do not consider the PF as a possible solution, because this computational cost. In our work we will use the PF as a benchmark to compare the proposed approaches.

2.3.3 Comparison At Figure 4 there is an example of the behaviour of the UKF compared with a Particle Filter (PF) and an Extended Kalman Filter (EKF). The first row is the distribution of a Gaussian variable, the second row is the distribution of that variable after passing through a non linear function. In the first column, a particle filter with enough number of particles can completely describe the distribution of the output, and thus, the mean and covariance. At the second column, the EKF fails to obtain a good estimation of both mean and covariance. At the third column the UKF can approximate the result by a smart choose of five sigma points. The computational cost of both Kalman Filters is similar, but the performance of the UKF under high non linearities is much higher.

2.4 NLOS Mitigation Techniques As stated in the introduction, the NLOS situation is the major contributor to the positioning error when it is present. In fact, all other contributions to the positioning error are masked by the NLOS effect. Urban environments are characterized by a high

14 probability of NLOS situation. Since urban environment is the most common situation of a cellular communication, the study of the NLOS error mitigation is of vital importance. Several approaches have been presented in the recent years regarding to the NLOS mitigation. Let’s take a review of them.

2.4.1 Hypothesis based approaches One solution is to discard the BS’s at NLOS. In that direction, it is possible to make hypothesis about whose BS’s are in LOS. Given some kind of reliability measure it is possible to select the better hypothesis. With this idea one of the most famous solutions is the Chen’s approach [Che99]. It is a high computational cost solution for the static positioning case using TOA measures. Let’s define the observations as:

yi (t ) = p(t ) − p BSi

2

+ ni (t )

(23)

where yi (t ) is the ith TOA measure taken from the ith BS, which is at position p BSi , and the mobile is at p(t). If the measurement noise ni (t ) is considered Gaussian with zero mean, a Maximum Likelihood (ML) estimator of the position is the one who minimizes the residual:

R ( pˆ (t ) ) =

1 nBS

∑ ( y − pˆ (t ) − p ) i

i

BSi

2

(24)

pˆ (t ) = arg min R ( pˆ (t ) ) This expression is equivalent to (3) plus the 1 nBS factor, used to compare between solutions obtained with a different number of measures. The Gaussianity of ni (t ) depends of the TOA estimator used and the propagation conditions, but we can assume it is Gaussian for LOS conditions with no multipath. It is expected a lower residual for the case of all LOS measures than for the case of any NLOS measure is present. In that sense R ( pˆ (t ) ) is related to the LOS-NLOS situation, as a NLOS measure tends to raise the residual. Let’s assume that we have a number of available TOA measures greater than 3, the minimum number needed to obtain a closed solution; and inside these measures at least 3 of them have been taken in LOS. The Chen’s approach is based on estimating the position for all possible combinations of 3 (the hypothesis) or more TOA measures, and combining them using the inverse of the associated residual (the reliability measure). Let be Bi a set of 3 or more TOA measures, and { B1 ,… , BNB } all possible sets of measures among the available TOA measures. Let be pˆ i (t ) the position estimated using the ML estimator of (24) over the measures of Bi . Then the estimated position is computed as:

15

∑ pˆ (t ) ( R (pˆ (t ), B )) pˆ (t ) = ∑ ( R (pˆ (t ), B )) i

i

i

−1

i

−1

i

(25)

i

i

This is the weighted mean of the estimated positions. The sets with no NLOS measures are expected to have a bigger weight than the ones with NLOS measures. Chen also proposed to select a percent of the sets (the ones with lower residual) to be considered in (25), thus rejecting the hypothesis with higher residual. One of the flaws of this approach is the high computational cost associated with (24). The residual is not a convex function. Grid-based methods, Taylor series linearization or simulated annealing can be used to solve this equation. Another flaw is the assumption of 3 LOS measures. In a real urban environment this assumption is very restrictive. The last flaw is on the residual study. The bias introduced by the NLOS is always positive. If yi (t ) − pˆ (t ) − p BSi is negative, it is less likely that this base station is at NLOS. But the square operation of (24) removes this information. In the same line as [Che99], we can find [Rib04][Urr04]. The hypothesis idea present in [Che99] is combined with a closed form estimator, leading to a reduced cost solution. At [Urr05] the work is extended to a dynamical location framework where a trellis search is performed over the set of hypothesis.

2.4.2 Statistical Analysis The statistical analysis among the time of the observations can detect the NLOS situation. At [Wyl96] this information is used to estimate the introduced bias by the NLOS situation. It assumes constant bias, which is a very restrictive assumption that can only be taken in stopped mobiles. [Ven02] studies the detection of NLOS using statistical information, in order to discard them. [Ven04] combines the statistical information with geometrical information. The BS’s nearer to the MT are considered more probable to be al LOS.

2.4.3 Tracking of the bias One solution is to track the bias introduced by the NLOS. [Wyl96][Naj04][Gir05] are a few examples of this idea. But all of them share that the system must perform a LOSNLOS situation estimator prior to the tracking of the bias, to provoke more freedom on the bias associated with the NLOS measures. More freedom means less memory and higher variance of the bias random variable in the state equation. A lower time correlation of the bias and a higher bias variance are translated in a lower weight of the associated measure. This is because the bias only affects the observation equation associated with its measure, and the freedom of this variable is directly related to the influence of the measure in the rest of the state vector. [Wyl96] consider constant bias, as stated in 2.4.2. [Naj04] models the bias as a random walk as described in [Fri69] and uses this model in an EKF. The state-observation model is:

16

x(t ) = Ax(t − 1) + n x (t ) b(t ) = B(t )b(t − 1) + nb (t )

(26)

y (t ) = g f ( x(t ) ) + b(t ) + u(t )

where b(t) is the bias vector and nb (t ) the state noise of the bias. B is a diagonal matrix whose elements control the memory of the bias variable. The covariance of the bias Qb (t ) is a diagonal matrix whose elements control the variance of each bias. Using some parallel measures like delay spread, the LOS-NLOS probability is estimated. This probability is used to control the values at B and Qb (t ) . [Gir05] is designed for GPS and consider that the bias can only change on some random events, which follow a Poisson statistic. Uses a PF to track the evolution of the bias variation events and an EKF similar to [Naj04] that only allow changes in b(t) at these events. The major flaw of these approaches is that the bias evolution in time is chaotic and all of the proposed models are simplifications of it.

2.4.4 Modelling the error introduced by the NLOS One of the possibilities is not to discard the NLOS or weight them, but to model the observation in a different way depending of the LOS-NLOS situation. In that way [Con01] and [Con05] are two papers that follow this idea. Basically, [Con01] used TDOA measures contaminated with NLOS, and develops an ML estimator under the assumption of Gaussian noise when in LOS, and exponential noise when in NLOS. [Con05] considers the case of a CDMA cellular system. The MT is assigned to one BS, called the home BS. TDOA measures are taken at the mobile where the home BS is always one of the two used for each measure. The home BS is considered in LOS. It develops an estimator for three different cases about the a priori knowledge of the NLOS error: •

To know the extant distribution of the NLOS noise: they first develop an ML estimator based on the known PDF’s, but without knowing which are in LOS or NLOS. Then uses the estimated position to determine the NLOS situation of all measures. Finally the position estimator is rerun with the previous estimation of LOS-NLOS.

•

To have limited prior information of the NLOS noise: Assumes that the mean of the NLOS bias and the probability of being at NLOS situation are known. A similar approach is developed.

•

No information about this noise is available: Assumes a Gaussian distribution of the LOS noise. Because the home BS is in LOS, the sign of yi − g fi (pˆ (t )) is less likely to be negative for NLOS BS. It defines a new concept of residual that considers the sign:

17 Ri ( pˆ (t ) ) =

1 1 + erf 2 2

⎛ yi − g fi ( pˆ (t ) ) ⎞ ⎜⎜ ⎟⎟ 2σ i ⎝ ⎠

(27)

being σ i the variance of the ith measure noise. If this residual is greater than a threshold the measure is considered NLOS and discarded. After discarding, if there are not enough LOS measures, the NLOS measures with lesser residual are considered, but its PDF is not Gaussian. An asymmetric Gaussian PDF is chosen for the final position estimation like Figure 5. The side variances relation is a tuning constant. Bigger values on the NLOS case offer protection against NLOS error but less accuracy in LOS cases.

2.4.5 Mitigating the NLOS at the parameter estimation stage As far as we know, there is only one paper regarding to the NLOS mitigation in the TOA estimator stage. [Alj02][Alj02b] presents an unbiased TOA estimator for NLOS situations. Assuming that all the arrival times from all scatters are known, it is possible to estimate the unbiased TOA using a scattering model. Three different scattering models are considered (see Figure 6): •

Ring of scatters: All reflections are uniformly distributed over a circumference.

•

Disk of scatters: All reflections are uniformly distributed inside a circle.

•

Gaussian scatters; All reflections are distributed following a two dimensional Gaussian distribution.

All scatters distributions are defined by its centre and its radius (or variance). Using the set of arriving times, both parameters are estimated. Two algorithms are developed, one using the Minimum Mean Square Error criterion, and other using the ML Expectation Maximization algorithm.

Figure 5. Asymmetric PDF for NLOS error distribution. Figure extracted from [CON05].

18

Figure 6. Ring of scatters and Disk of scatters models. Figures extracted from [Alj02b].

Although this document is very original, has a major flaw: to know all arrival times is a very hard problem.

2.4.6 Summary of NLOS mitigation techniques Two error sources are considered that include the Gaussian measure error, always present, and the NLOS error, only present when in NLOS situation. Most of the existing techniques assume that NLOS measurements represent a small portion of the total. Since NLOS measures are biased and differ from the measure expectations, they can be considered as outliers. Statistical techniques like least square residuals or prediction error can be used to determine if measures are taken under NLOS conditions. These approaches fail when multiple NLOS BS’s are present and the number of remaining LOS BS is not enough to determine the solution. Ericsson field studies had shown that typically only 4 or 5 BS’s are heard by the MT [Eri99]. One cannot assume than the majority of BS’s is in LOS, because the communication between the MT and a far BS is usually modelled as NLOS [Con05]. A few number of approaches [Alj02][Ven02][Con05] are designed for scenarios with a majority of NLOS measures, mainly based on the positive sign of the bias. But the field is still open and new and better approaches are expected to arrive soon.

19

3 Preliminary results After a review of the state-of-the art we propose to develop a location estimator without making any assumption about the number of BS at NLOS, because the assumptions made in most of then are not applicable to real environments. In order to achieve it we propose to use a tracking system to take profit of the variable condition of the LOSNLOS situation. That is, there is an enough number of BS that at some moment are at LOS. This doesn’t be necessary the same time for all of them, but is not so restrictive to consider that a sufficient number of BS will be at LOS at different moments. The tracking system will correct the measure using the available information. But a NLOS measure is not useless, because although its variance is big, it gives information that must be considered. At a first stage of the study we consider using a priori information about the statistics of the NLOS error and the probabilities of being at NLOS. All preliminary results are taken under this assumption. Future work will try to solve the problem without a priori information. After a review of the tracking algorithms we state that the better results without a prohibitive cost come from the UKF. We will adapt the UKF for the LOS-NLOS behaviour. First a Bayesian estimator is developed based on parallel measures and statistical data (not the residual like [Che99], but the error prediction) to estimate the probability of being at LOS or NLOS. Then this information is used in the modified UKF. Like in [Con05] we propose to use different error probability distribution for the observation noise in LOS and NLOS. The NLOS effect is not considered as a bias, but as an error with a non Gaussian non zero mean PDF. Solutions to the NLOS problem in the parameter stage like [Alj02] are not considered because the difficulty associated with the determination of all arrivals.

3.1 Extended Model The state-observation model presented in (5) does not contemplate the LOS-NLOS situation. We can extend the model to: xt = f ( xt −1 , u t ) y t = g f (xt ) + g st (n t )

(28)

where g f ( xt ) is the ideal noise-free measure and g st (n t ) is the observation noise, that depends on the situation st (the LOS-NLOS situation for each BS). This model allows a different behaviour of the observation function depending of the LOS-NLOS situation. Also the LOS-NLOS situation evolves in time according to: st = h ( st −1 , v t ) ot = l ( st , w t )

(29)

20

Switch

g LOS ( ·) Observation

State State

g NLOS ( ·) 1 Situation Event

l ( ·)

2 3 Situation Situation

Figure 7. Observation drive by situation.

where h(·) is the situation function; vt is the situation noise; ot is a set of observations (called situation events) related to the LOS-NLOS situation (like signal quality indicators); and l(·) is the event function, driven by the event noise wt . The situation vector st take discrete values from S , where S = 2nBS , and nBS is the number of BS. This model is summarized in Figure 7 where the situation switches between two different observation functions. This problem can be summarized in estimating the probability of the state given the observations and situation events:

(

p(xt y1:t , o1:t ) = p xt y1:t , p ( st | y1:t , o1:t )

)

(30)

Thus the problem is divided into two steps: •

Estimate the LOS-NLOS probabilities p(st | y1:t , o1:t ) .

•

Estimate the position from these probabilities and the observations.

3.2 Observation noise The behaviour of the g st (n t ) function is different depending of the current situation. In that sense, the PDF of the output of this function (the PDF of the observation noise) is different depending of the situation. In order to model these PDF we have done a measurement campaign using real measures. We have measured the range estimation error of the MVN estimator for LOS and NLOS cases [Hue05]. At Figure 8 there are depicted the results. For LOS case we have selected a Gaussian distribution with mean 0 and a variance that depends on the SNR. For the NLOS we have selected a Rayleigh distribution:

21 Comparisson of error PDF between empirical error and ideal model

Comparisson of error PDF between empirical error and ideal model for NLOS 0.04 Error from real data Ideal Rayleigh PDF 0.035

0.09 Error from real data Ideal Gaussian pdf

0.08

0.03

0.06

Probability Density

Probability Density

0.07

0.05 0.04 0.03

0.02 0.015 0.01

0.02

0.005

0.01 0 -40

0.025

-30

-20

-10 0 10 Equivalent meters

20

30

0

40

0

20

40

60 80 Equivalent meters

100

120

140

Figure 8. Comparison between TOA error histogram and model in LOS and NLOS cases. −τ 2

Pg NLOS ( nt ) (τ ) =

τ e 2s

2

(31)

s2

and the parameter s depends of the propagation scenario. For our scenario we selected s = 42 . These functions have been determined for our scenario (urban) and our estimator. Other scenarios or other scenarios could probably have different PDF of the observation noise. But the LOS-NLOS estimator will provide a probability of being at each situation. The probability of the observation, known the situation probabilities can be derived as: 1

) ∑ p( y

(

p yti y1:t −1 , o1:t −1 =

i t

) (

y1:t −1 , sti = k p sti = k o1:t −1

)

(32)

k =0

The first term of the summatory is the observation expectation for both LOS and NLOS, the second term is the estimated situation probability. Thus, the result is a weighted mean between both PDF’s according to the estimated situation probability.

3.3 LOS-NLOS estimation Let’s consider, for simplicity, that the LOS-NLOS situation probability is independent between different BS: nBS

(

p ( st y1:t , o1:t ) = ∏ p sti y1:t , o1:t i =1

where st = ⎡⎣ st1

st2

)

(33)

stnBS ⎤⎦ .

Let’s consider that the o1:i t is a vector composed by all the situation events for the BS i. To simplify further formulation, we allow situation events that are dependent of the result of the UKF (and thus dependent of y1:t ). Then, equation (33) can be rewritten as:

22 nBS

(

p ( st y1:t , o1:t ) = ∏ p sti o1:i t i =1

)

(34)

Because sti can only take two possible values (LOS and NLOS) the optimal solution is the grid-based method [Aru02]. Let γ it = ⎡⎣γ ti ,1 γ ti ,2 ⎤⎦ be a vector containing the probabilities for both situations at time t for BS i. The prediction equation of this probability is obtained from the Chapman-Kolmogorov equation:

(

1

γ ti|,tk−1 = ∑ γ ti−,m1|t −1 p sti = k sti−1 = m m=0

)

(35)

The update equation is obtained from the Bayes’ rule:

γ

i,k t

=

(

γ ti|,tk−1 p oti sti = k 1

∑γ

m=0

i ,m t |t −1

(

)

p o s =m i t

i t

(36)

)

The computed probability at (36) is the second term of the summatory at (32). Using (35) and (36) we can compute the γ it vector. The transition probability p sti sti−1 is obtained from the set { pLL , pNL , pLN , p NN } , where:

(

( = p(s

) = 0)

pLL = p sti = 1 sti−1 = 1 pNL

i t

= 1 sti−1

( = p(s

) = 0)

pLN = p sti = 0 sti−1 = 1 pNN

i t

= 0 sti−1

)

(37)

In fact, this approach is the same as considering a two-states Hidden Markov Model (HMM) [Rab86][Eph02], one state per situation. If the HMM is solved using forward iteration [Rab86], the result is equivalent to equations (35) and (36).

3.3.1 Transition probabilities evolution A deeper analysis of this model reveals that the transition probabilities { pLL , pNL , pLN , pNN } are closely related to the MT speed and the propagating conditions of the environment. In fact the probability of transition depends on the distance travelled by the MT (for a still MT the state remains equal all the time). Known the transition probabilities, it is possible to evaluate the time of remaining at a certain state. Give that a terminal is in NLOS situation, the probability of remaining k time instants in NLOS is: f (k | NLOS ) = pNL (1 − pNL ) k

(38)

The average number of time instants a terminal remains in NLOS is given by: ∞

E {nNLOS } = ∑ kf ( k | NLOS ) = k =0

1 − pNL pNL

(39)

23 Distribution of length of LOS situations

0

Distribution of length of NLOS situations

0

10

10 PDF of experimental results Exponential PDF

PDF of experimental results Exponential PDF

-1

-1

10 Probability

Probability

10

-2

-2

10

10

-3

10

-3

0

5

10

15

10

0

meters

5

10

15

meters

Figure 9. PDF’s of the length of LOS (left) and NLOS (right) situations

Note that the duration of remaining at NLOS state (in seconds) is related to the length of the NLOS state (in meters) through the speed of the MT, v: nNLOS ∆t =

LNLOS v

(40)

where ∆t is the reference time interval at which transitions may occur (typically the sampling time when positioning). Combining (39) with (40) we get: E {nNLOS } =

pNL =

E { LNLOS } 1 − pNL = v∆t pNL

v∆t v∆t + E { LNLOS }

(41)

a probability which is clearly time-varying if the speed of the MT is changing. Therefore, if this model is to be used in a positioning environment, the average length (in meters) of the NLOS situations E { LNLOS } characterize the environment (rural, suburban, urban, etc. and assumed known from a previous field campaign), while this can be related to the transition probabilities through the speed of the terminal v(t). In order to proof that the proposed model is valid, the probability density function (PDF) of LOS and NLOS length situations is evaluated from real measurements. The histograms are plotted in Figure 9, as well as the exponential fitting.

3.3.2 Situation events Among the possible candidates to be a situation event to be included in vector ot , a few of them have revealed important about the LOS-NLOS situation. These are:

24 •

Delay spread indicator: In this context is measured as the relation between Signal to Interference and Noise Ratio (SINR) of the detected arrival (computed as the relation between the power of the associated ray and the noise floor) and the SINR at the RAKE receiver. In fact this is a relation between the selected ray and the total received signal power, and thus a multipath measure.

•

Prediction error: This is the relation between the observed measure and the predicted value of this observation using previous state. This is a measure of the variance of the estimator. Normally great variances are not associated with a noisy environment but with a NLOS situation.

•

Geographical information: Some zones have more obstacles than others, and thus a higher NLOS probability. Then the probability of the last estimated location is applied for the next. This information can be as simple as a function of the range between the MT and the BS (greater range, greater the chances of obstacles between the MT and the BS) or as complex as possible. [Geo02] demonstrates that the study of the propagation conditions at all positions has a non prohibitive cost. For simplicity we only consider the range measure as an observation in order to have a non-constrained result.

We assume that we have the distribution of each observation parameters associated with both LOS and NLOS cases. We will consider, for simplicity, that the three observations are independent. PDF associated with Delay spread indicator

PDF associated with prediction error

3

0.05 LOS case NLOS case

LOS case NLOS case

0.045

2.5

0.04 0.035

2 Probability

Probability

0.03 1.5

1

0.025 0.02 0.015 0.01

0.5

0.005 0

0

0.1

0.2

0.3

0.4 0.5 0.6 NMV quality

0.7

0.8

0.9

1

0

0

10

20

30

40 50 60 70 Prediction error in meters

80

90

PDF associated with Geographic observation LOS case NLOS case

0.01 0.009 0.008

Probability

0.007 0.006 0.005 0.004 0.003 0.002 0.001 0

50

100

150 200 Range in meters

250

300

Figure 10. PDF of the delay spread indicator of RTOA measures for LOS and NLOS states

100

25

3.3.3 Probability density function of the situation events In a realistic setting, the determination of the PDF of the observations requires a training phase, where every observation is classified as taken in LOS or NLOS. By comparing the estimated observations with the known LOS-NLOS situation it is possible to define the behaviour of each observation parameter associated with each situation, and represented by its PDF. At Figure 10 it is depicted the PDF for all three parameters under real urban conditions. In order to get a smoothed solution a Gaussian low-pass filter has been used among the PDF’s. These results will be used as a Look-Up-Table (LUT) when computing the observation probability.

3.4 Improved UKF One of the hottest topics in the Unscented Transform field is the spreading distribution of the sigma points. The presented spreading rules are the most used, but other possibilities exist. The standard UKF is not well suited for our application as we will see. Some modification according to the spreading of the sigma points are proposed to ensure a low computational cost while enhancing the accuracy. In the standard UKF the computation of the observation noise must be done at step (19). But these observation noise must follow the PDF obtained according to (32). Since this function is dependent of the LOS-NLOS estimation, the computation of the associated sigma points is a hard problem. Also, we have determined empirically that the random variable is not well represented by only three sigma points. These two characteristic leads to a bad accuracy and a high computational cost. In order to solve this problem we propose to change the spreading of the sigma points at step (19). The expected observation will be computed two times, for both situations. Then both sigma sets will be combined into a double sized sigma set, weighted by the situation probability. Let’s define the operation A ± b as the operation of adding the vector b to each column of A; and the operation A as the square root matrix of A. The modified algorithm can be summarized in Algorithm 1. Notice the change in the step (42), that lead to a double sized sigma set at (43). The advantages of this approach are: •

The computation of step (42) is very simple, since g ( si = j ) ( Ztn|t −1 ) does not t change. The three sigma points associated with both situations can be previously calculated.

•

The use of six sigma points gives a better representation of the observation function, leading in a better accuracy.

26 Initialize with: ⎡ Px0 ⎢ Pz0 = ⎢ 0 ⎢0 ⎣

z 0 = E {z 0 }

0 Pu 0

0⎤ ⎥ T 0 ⎥ = E ( z 0 − z0 )( z 0 − z0 ) Pn ⎥⎦

{

}

For t = 1,… , ∞ : Calculate the sigma set: ⎡Ztx−1 ⎤ ⎢ ⎥ Zt −1 = ⎢Ztu−1 ⎥ = ⎣⎡ zt −1 ⎢Ztn−1 ⎥ ⎣ ⎦

zt −1 + η Pzt −1

zt −1 − η Pzt −1 ⎦⎤

State prediction: Ztx|t −1 = f ( Ztx−1 , Ztu−1 ) 2L

xt|t −1 = ∑ Wi ( m )Ztx|t −1 i =0 2L

Pxt|t −1 = ∑ Wi ( c ) ( Zix,t|t −1 − xt|t −1 )( Zix,t|t −1 − xt|t −1 )

T

i =0

Update:

Yt|it,−j1 = g if ( Ztx|t −1 ) + γ ti|,t −j 1 g( si = j ) ( Ztn|t −1 )

i = 1,… , nBS

t

⎡ Yt|1,1 ⎤ Yt|1,2 t −1 t −1 ⎢ ⎥ Yt |t −1 = ⎢ ⎥ = ⎣⎡Y0,t|t −1 nBS ,1 nBS ,1 ⎢ Yt |t −1 Yt|t −1 ⎥ ⎣ ⎦ 1

j = 1, 2

Y4 L +1,t|t −1 ⎦⎤

(43)

2L

y t|t −1 = ∑∑ Wi ( m ) Y( i + (2 L +1) j ),t|t −1 j =0 i =0 1

2L

(

)(

Pyt|t−1 = ∑∑ Wi ( c ) Y(i + (2 L +1) j ),t|t −1 − y t|t −1 Y( i + (2 L +1) j ),t|t −1 − y t|t −1 j =0 i =0 2L

1

(

Pxyt|t−1 = ∑ Wi ( c ) ( Zix,t|t −1 − xt|t −1 )∑ Y(i + (2 L +1) j ),t|t −1 − y t|t −1 i =0

j =0

−1 y t|t −1

K t = Pxyt|t −1 P

xt = xt|t −1 + K t ( y t − y t ) Pxt = Pxt|t −1 − K t Pyt|t −1 K Tt Algorithm 1. Improved UKF

(42)

)

T

)

T

27 LOS NLOS Combined

Sigma point

(b)

(a) LOS Sigma point

LOS Sigma point

NLOS Sigma point

NLOS Sigma point

(c)

(d)

Figure 11. Example of using an extended sigma set. a) The distribution of an observation variable, under two situations weighted by the probability of each situation, and the combination of both. b) Characterization of the result variable with three sigma points c) Characterization of the result with six weighted sigma points d) Another example.

These ideas are represented at Figure 11. The subfigure a) represents the PDF for both situations and the weighted combination of both. At b) there is the characterization of this function with three sigma points; this is the standard UKF case. Otherwise at c) it is depicted the result when using six sigma points. Compare the results between c) and d), obtained with a different situation probability. Notice that the position of the sigma points is the same, only changes the weight.

3.5 Simulation results We simulate two different environments to compare the results of the proposed approach with other classical approaches. The Table 1 describes both scenarios. The BS are placed in a circle of 4000 meters. The MT moves with variable direction and speed between 0 and 100 Km/h and does not move beyond the 4 Km circle. All BS’s perform 100 RTOA measures per second. The positioning estimators used are: •

PA: The proposed approach. That is, estimate the LOS-NLOS situation, and use this estimation in the improved UKF.

•

UKF: A classical approach with UKF, but with no estimation of the LOS-NLOS situation.

•

ML: A static Maximum likelihood estimator based on (3) by exhaustive search on the possible positions grid with 0.1 meters between points.

•

CHEN: The approach presented in [Che99], adapted to RTOA measures. 50 % of rejected combinations.

28 Environment E { LLOS } E { LNLOS } Variance of RTOA measure at LOS Rayleigh parameter at NLOS Nº of available BS

Urban 5m 10 m 12 m 3.5 8

Sub-urban 20 m 7m 6m 2 4

Table 1. Simulated scenarios parameters. 8 BS - Urban Environment 1

0.9

0.9

0.8

0.8

0.7

0.7

0.6

0.6 Probability

Probability

4 BS - Sub-urban Environment 1

0.5 0.4 0.3

0.4 0.3

0.2

0.2

PA UKF ML

0.1 0

0.5

0

50

100 Positioning Error (m)

CHEN PA UKF ML

0.1

150

0

0

20

40

60

80 100 120 Positioning Error (m)

140

160

180

200

Figure 12. Simulation results.

The EKF is not included because it diverging probability. It is important to notice that the computational cost of the ML and Chen estimators is very high. At Figure 12 it is depicted the result of the simulations.

3.6 Experimental Results 3.6.1 Testing environment We have a test-bed composed by a MT and a BS, working at the 1.8 GHz band, with a Band Width (BW) of 5 MHz. This test-bed is capable to estimate the channel 200 times per second, and can store 2 minutes per experiment. The estimated channels are sent to a PC for further processing. The test-bed core is based on the C40 and C67 Texas Ins. DSP’s, and they are currently programmed. The BS has 4-antennas arrays, which allow us to perform DOA estimations. In order to avoid synchronization hazards, we use a rubidium clock at both the MT and the BS. The error introduced by the clocks inside the 2 minutes window is insignificant. A GPS placed at the mobile give us a confident location measure to compare. There are photos of the equipment at Figure 13. The test-bed scenario is at the UPC facilities of Barcelona. See Figure 14 for a satellite view of the area. The zone allows us to select between all LOS, sub-urban or urban scenario.

29

Figure 13. Left: The MT equipment. The Rack contains the base band processor and the modulator. Upper the rack there is an amplifier. Right: The BS equipment. At the right there is a rack with the demodulator and processing unit.

Figure 14. Satellite view of the test-bed scenario.

The following results are tested using the test-bed as close as possible to real urban UMTS conditions. Four BS’s are emulated from four different measurement campaigns. The MT is moving at a variable speed between 0 and 40 Km/h (a car in a city), and arbitrary direction. Depending on the location strategy, different channels may be used. The Dedicated Physical Channel (DPCH) is used in UL and DL for DOA and RTT estimation. At this channel the power is strictly controlled every slot, so the SINR is fixed for the serving BS. The fixed SINR depends on the communication bit rate. Table 2 shows typical SINR values for different bit rates. The rest of BS’s will observe a SINR that depends of the propagation channel between them and the mobile.

30 Bit Rate (kbps) SINR (dB)

12.2 4.10

16 4.28

32 6.29

64 8.30

144 11.32

384 15.08

Table 2. Typical SINR for different bit rates at DL.

The Common Pilot Channel (CPICH) is used in DL for RTOA estimation. It consists of a broadcast channel with fixed power. The SINR observed at the mobile depends of the propagation channel. But, for the channel estimation a different number of slots can be used, resulting in different accuracy channel estimation, and thus different accuracy in RTOA estimation. The intracellular and intercellular interference is emulated adding white noise prior to the channel estimation

3.6.2 LOS-NLOS situation estimator evaluation We consider three different estimators: •

Fixed probability: That is, consider γ (t ) = a0 for all t. In fact this is like no predict the LOS-NLOS, but to consider a general situation for all t.

•

Direct Function: This is to compute γ(t) vector only from the situation events of the same time, but not from previous instants. This is the same as to obtain the maximum information from the current observations, but without tracking.

•

HMP: The proposed LOS-NLOS estimator.

•

Clairvoyant estimation: To perfectly know the actual situation. Of course it is not possible to obtain this result in a real system, but it allows to ghuess how close the estimation is from the actual LOS-NLOS situation. Final positioning error for different LOS-NLOS situation estimators 26

Positioning RMSE (meters)

24 22 20 18 16 14 Direct Function LOS-NLOS estimator Clairvoyant Estimation Fixed Probability

12 10

1/4

1/2 1 2 Slots used for timing estimation

4

Figure 15. Positioning error using different LOS-NLOS situation estimators.

31 At Figure 15 there is the effect of the LOS-NLOS on the location accuracy when using the proposed UKF and four BS’s. With these results on the hand we recommend to use the proposed approach because although its gain is not very big (1 to 2 meters), the added computational cost is very low (compared with the rest of the algorithm).

3.6.3 Evaluation of the improved UKF At this point we want to evaluate the tracking capability of the improved UKF in front of other solutions. We consider two different positioning techniques: •

Location performed at the MT, using RTOA measures from 4 BS’s.

•

Location performed at 2 BS’s using TOA and DOA measures.

For the LOS-NLOS estimator the proposed approach is used. The three trackers feed from the same parameters and the same LOS-NLOS estimator, but not from the same LOS-NLOS estimates, since them depend of the previous position estimates. The scenario is a heavy NLOS environment as described previously. The probability of being in LOS situation at one base station is less than 40 %. Considering that a close solution requires four RTOA measures, almost all published approaches need all four BS’s at LOS for correct operating. In these results this condition is fulfilled only the 2.4% of the time. We have three different captures of 30 seconds, with 200 snapshots per second, of the first location schema, with four RTOA measures. These results are combined with the taken from four captures of one minute of the second scenario, with 2 TOA and 2 AOA. Comparison between trackers 35

RMSE (meters)

30

25

20

15

10

5 1/4

Particle Filter RMSE + Std. deviation UKF RMSE + Std. Deviation EKF RMSE + Std. deviation Particle filter RMSE UKF RMSE EKF RMSE 1/2

1 Slots used for channel estimation

Figure 16. Positioning error using different position trackers.

2

4

32 Convergence speed 250 UKF Particle Filter

Postioning error (meters)

200

150

100

50

0

0

5

10

15

Time (sec.)

Figure 17. Evolution of the positioning error with a system initialized with 200 meters error.

The system is initialized with a correct estimation, in order to ensure a convergence situation. If the error goes beyond one thousand meters, then the experiment is declared divergent and discarded from the result. At Figure 16 is depicted the positioning error obtained. No UKF or Particle Filter experiment has been discarded due to divergence, but more than 35 % of the EKF experiments have been discarded because this reason. PF has a better accuracy that the UKF, but a much high computational cost. So UKF seems to be the reasonable selection.

3.7

Convergence speed

The previous experiment started with the first estimation obtained from the GPS. But, normally the system does not know were to start. A static location algorithm is normally used, but with such kind of environment (50 % of BS at NLOS) the expected error is very high. In this experiment we a UE locating itself from 4 BS’s signals performing RTOA measures. The introduced initial error is 200 meters, to emulate the effect of a bad initial static localization. The UE is moving at a speed between 10 and 30 Km/h. Like the rest of experiments, where is a very intense NLOS environment. At Figure 17 is depicted the evolution of the positioning error. This result has been obtained combining five realizations of 15 seconds. The EKF has not been represented because of its divergence. The particle filter initial distribution is Gaussian, centred at the 200 meters error initial position with a 200 meters standard deviation.

3.8 Preliminary Conclusions At this point a new localization estimator has been developed and evaluated in a real UMTS scenario. This filter is composed by two parts: a LOS-NLOS situation estimator, and an improved UKF, which is capable to adapt itself to take profit of the situation estimation. The proposed approach gives a substantial gain when compared to classical EKF solutions both in accuracy and stability, in a hard NLOS framework.

33

3.9 List of publications i.

J. M. Huerta, J. A. Castro, J. Vidal, “Analysis of experimental data of location based services”, SATURN project deliverable D641, December 2002, http://gpstsc.upc.es/comm/saturn

ii.

M. Najar, J.M. Huerta, J. Vidal, J.A. Castro, “Mobile location with bias tracking in non-line-of-sight”, Acoustics, Speech, and Signal Processing, 2004. Proceedings. (ICASSP '04). IEEE International Conference on, Volume 3, 1721 May 2004 Page(s):iii - 956-9 vol.3

iii.

J.M. Huerta, J. Vidal, “Mobile Tracking Using UKF, Timing Measures and LOS-NLOS Expert Knowledge”, Acoustics, Speech, and Signal Processing, 2005. Proceedings. (ICASSP '05). IEEE International Conference on, Volume 4, March 18-23, 2005 Page(s):901 – 904

iv.

J.M. Huerta, J. Vidal, “LOS-NLOS Situation Tracking for Positioning Systems”, submitted to Signal Processing and Wireless Communications, 2006 (SPAWC’06), IEEE International Conference on.

34

4 Work Plan Following the lines presented in this document, the future work will be focused in better fit the model of the NLOS situation in order to develop more accurate position estimation.

4.1 NLOS error modelling To model the NLOS observation error with a Rayleigh distribution seems not to be the best solution since it has been derived from a low number of real realizations. Using the observations of a ray tracing simulator it could be possible to better model this distribution. It is reasonable to think that the distribution of the NLOS error depends of the density of reflecting items, the range, or other possible parameters. Then, the results can be checked using the measurements of the new test-bed. Also, the parameters regarding the NLOS error distribution could be include in the UKF. In this direction it would be a good idea to develop a realistic TOA model that includes the LOS-NLOS situation for further simulations.

4.2 NLOS probability The choice of the situation events has been done empirically (see 3.3.2). There is a high probability of finding better situation events that could help in the determination of LOS-NLOS situation. In that sense, the Kalman Gain and MSE expectation matrices need to be studied in order to consider them as situation events. Other possibilities are the study of geometrical influence over the probability of NLOS. We are currently using the range, but maybe the transversal speed is related to the transition probability.

4.3 Joint LOS-NLOS estimation In the present work it is assumed independency between BS in terms of LOS-NLOS. This assumption has been made for simplicity. But the dependence between BS seems to be reasonable. Can a joint estimation of the LOS-NLOS situation improve the final accuracy? We think yes, because the estimation of LOS-NLOS situation is vital for the goodness of the algorithm. Estimate the situation for all measures in a joint fashion can probably enhance the LOS-NLOS estimation, and this improvement will propagate to the final accuracy.

4.4 Blind probabilities estimation In present work it is assumed that the transition probabilities between situations are known. Baum-Welch method [Bau70][Bau72] can be used to determine these probabilities during the position estimation (see 3.3.1), and thus relaxing this assumption. But no only the transition probabilities, all a priori knowledge can be estimated during the algorithm, including:

35 •

The statistics of the noise in LOS and NLOS situations: LOS error is Gaussian, but the variance depends of the SINR. NLOS error function can be parameterized and its parameters estimated during the algorithm.

•

The kinetics of the mobile: The state equation of (5) can be expressed as: xt = Axt −1 + nt

(44)

being Qn the covariance matrix of nt . This assumption can be taken in localization since the evolution of position, Cartesian speed and transmission time is linear. A and Qn can be estimated during the algorithm. •

and The probabilities of situation events: In the same way as for the NLOS error distribution, the probabilities function of situation events can be parameterized and its parameters estimated during the algorithm.

All of these parameters are considered constant during the tracking.

4.5 Use of MT sensors Another possibility is to combine the radiolocation parameters (like TOA or DOA) with the estimates of sensors mounted on the MT. An inertiometer, speed meter or compass are few examples of sensors that can provide useful information to the PCF. The best of using this kind of information is that they are never affected by the NLOS situation, which can be very useful for detecting the NLOS situation in the radio parameters.

4.6 Rao-Backwellization The same concepts from [Gir05] can be applied to our case. The Rao-Backwellization (RB) allows combining a KF with a PF in order to better fit the non-linearities, at a low computational cost. In that direction we propose to develop a PF that follows the LOS-NLOS situation of all BS. An UKF is run per each possibility. Using the RB, the PF can use the UKF outputs to select the most probable particle (the set of LOS-NLOS situations). As demonstrated in this document a good estimation of the situation can improve the accuracy of the estimator.

4.7 Extension to Cooperative systems Another topic is to study the case where two or more MT’s are to be located. In cooperative systems the MT’s also communicate between them. The measures derived from these communications can be useful if the location systems of MT’s are joined. The final state-observation model will be composed by all state equations from MT’s and all observations between MT’s and the BS plus the observation derived from measures between the MT’s.

36

Figure 18. Localization in cooperative systems.

4.8 Upgrading of the Test-bed New equipment has been acquired and needs to be programmed. Two new mobile units with two antennas per MT are now available. These units can operate in the 1.8 GHz band, with a BW of 5 MHz, and are compatible with the existing BS. But the mobiles are modular and the RF part can be changed and upgraded to a 5 GHz, 100 MHz BW signal. The core of these units is a Virtex-II FPGA. So a complete Transmitter must be programmed in VHDL. Because of the two antennas per mobile, localization over MIMO communications can be studied. Also a new receiver is expected to arrive by the end of 2006. It is expected that this new receiver could process data without losing packets at a sample rate of 300 MHz. The core of the receiver is a heterogeneous system composed by three Virtex-4 FPGA’s and four C67x DSP. An embedded PC is included in the receiver. At a first stage, we will try to set up the new test bed in the 1.8 GHz, with a BW of 5 MHz. The receiver is intended to store the signal for future processing. If successful, higher BW will be tested, and real-time processing at the receiver will be programmed. The major advantages of this new test-bed are: •

FPGA architecture, allows a high speed processing. 100 MHz BW signals can be considered.

•

Processing capabilities at the receiver allows processing all the receiving data without discarding any packet.

•

MIMO communications.

•

Cooperative framework can be useful in a localization system.

37 After the test-bed work is finished an extensive measurement campaign must be done, in order to have a big database to test the proposed algorithms. Current database is not big enough to definitely check the approaches.

4.9 Work calendar We are currently working on the Rao-Backwellization and the Joint LOS-NLOS estimation. This research is assumed to finish on May 2006. We also have started the software programming of the test-bed. The new MT’s are expected to be finished on summer 2006, and the BS must be finished before the summer of 2007. The most important topic, under our point of view, is the blind parameter estimation. As soon as we finish the RB and Joint LOS-NLOS estimation we will start with this topic. Is very soon to give an expectation for the finishing date for this topic, but a reasonable date could me January 2007. Extension to Cooperative systems can be then started. The rest of the topics will be studied when appropriate, depending on the time requirements of the cited ones. We assume the end of 2007 as the date of the Ph. D. dissertation.

38

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