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## Simulation Results

Figure 2.6 is the simulation result for the comparison of Bayesian PDP-F described in [26] and the time-domain PDDP-F over a range of SNR values for different n. The simulation environment is the same as for the frequencydomain PDDP-F simulations. We see three curves in the plot where n = 1

corresponds to the Bayesian PDP-F case. It is obvious that time-domain PDDP-F outperforms Bayesian PDP-F. Increasing n (number of consecutive channel estimates) also increases the success rate. If we also compare with the frequency-domain PDDP-F algorithm, we see that the time-domain PDDP-F is more robust and success rate is higher for n ≥ 3. Also one drawback of the frequency-domain PDDP-F is that its non-parametric spectrum might suffer from limited resolution. In these simulations, we assumed that the speed vector is known beforehand.

As was the case in the frequency-domain PDDP-F, simulations for the case when the speed vector is estimated jointly was carried out for n = 2. However to reduce the simulation time, we had to reduce the ray tracing points (K = 5 now). Apart from that, simulation environment and the system parameters are the same. Joint speed vector estimation was carried out by maximizing the likelihood with respect to the speed vector in every ray tracing point. Hence it is again an exhaustive search over the possible values of the speed magnitude and the direction of motion. The results are demonstrated in figure 2.7. As expected, there is a loss of performance when compared to the case of known speed vector.

The time-domain PDDP-F approach can be seen as an elegant method

for localization. Instead of trying to match only the PDPs (diagonal elements of the covariance matrices for the same time instant), the whole covariance matrices are compared, also by taking into account the Doppler information.

However, there are some important things to note. First of all, DO and FO problems are also present here. So care must be taken for them. The advantage of the time-domain PDDP-F over its frequency-domain version lies in the weighting matrix (inverse of the covariance matrix) used. If we consider the noiseless case, the weighting matrix tries to balance the weak and strong rays. In other words, strong rays (rays with high power) are weighted by small coefficients whereas weak rays are weighted by higher coefficients. As a result, this gives the advantage of observing even very little details which would be mostly ignored in the frequency-domain case. However if we consider noise, this could also lead to noise amplification when the path contribution is below the noise level.

### Localization Performance for Deterministic Path Amplitudes and Rayleigh Fading Cases

The purpose of this section is to evaluate the localization performance of fingerprinting algorithms for different path amplitude modeling we have investigated so far. However we will not pass through all the cases we have investigated before. For all the cases, we assume that pulse shape is either real or symmetric.

#### Anisotropic Case for Non-overlapping Pulses with LoS and NLoS Paths

We will now talk about another interesting and a quite frequent scenario in wireless communications. In this situation, there is a direct LoS path between BS and MT and the rest of the paths are NLoS. It is more reasonable to model the LoS path with a deterministic path amplitude and a deterministic phase. For the NLoS paths, Rayleigh fading modeling is more realistic. Consequently J1,1 is given by (3.90) and Ji,i ’s are given by (3.26) for i ∈ [2,Np]. Derivation of Ekr − ˆrk2 is again carried out via equations (3.139), (3.140), (3.141).

**Table of contents :**

Abstract

Acknowledgements

Contents

List of Figures

Acronyms

Notation

**1 Introduction **

1.1 Fundamentals of Geometrical Localization Methods

1.1.1 Angle of Arrival Methods

1.1.2 Time of Arrival Methods

1.1.3 Time Difference of Arrival Methods

1.1.4 Received Signal Strength Methods

1.1.5 Hybrid Methods

1.2 Fingerprinting Methods

1.3 Identifiability Issues and Performance Bounds

**2 Power Delay Doppler Profile Fingerprinting **

2.1 Introduction

2.2 Frequency-Domain PDDP-F

2.2.1 Obtaining PDDP from Ray Tracing Data

2.2.2 Obtaining PDDP from Measurement Data and The Fingerprinting Operation

2.2.3 Simulation Results

2.3 Time-Domain PDDP-F

2.3.1 Simulation Results

2.4 Conclusion

**3 Performance Analysis of Power Delay Profile Fingerprinting **

3.1 Introduction

3.2 CRB Analysis of PDP-F

3.2.1 Rayleigh Fading Case

3.2.2 Deterministic Path Amplitude Case

3.2.3 Rician Fading Case

3.3 Discussion

3.3.1 Localization Performance for Deterministic Path Amplitudes and Rayleigh Fading Cases

3.4 Conclusion

**4 Performance Analysis of Power Delay Doppler Profile Fingerprinting**

4.1 Introduction

4.2 CRB Analysis of PDDP-F

4.2.1 Rayleigh Fading Case

4.2.2 Deterministic Path Amplitude Case

4.3 Conclusion

**5 Pairwise Error Probability Analysis for Power Delay Profile Fingerprinting **

5.1 Introduction

5.2 PEP of the LS Technique for Deterministic Path Amplitudes

5.2.1 Simulation Results

5.3 PEP of the GML Technique for Rayleigh Fading

5.3.1 Simulation Results

5.4 Conclusion

**6 Mobile Terminal Tracking based on Kalman Filtering**

6.1 Introduction

6.2 Adaptive Kalman Filtering based Tracking

6.2.1 Adaptive Kalman Filtering Approaches

6.2.2 State-Space Models for Position Tracking

6.2.3 Adaptive EM-KF with Fixed-Lag Smoothing for Position Tracking

6.2.4 Non-Linear Measurements

6.3 Fitting of State Space Mobility Models to M3 Measurements

6.4 Conclusion

**7 Conclusions and Future Work **

Appendices

**A CRB of the Position Vector for Non-overlapping Case **

**B Distribution of the Summation of Non-identical Exponential RVs **

**C R´esum´e ´Etendu en Fran¸cais **

C.1 Abstract en fran¸cais

C.2 Contributions et Cadre de cette Th`ese

C.3 R´esum´e du Chapitre

C.3.1 Questions d’identifiabilit´e et Bornes de Performance .

C.4 R´esum´e du Chapitre

C.4.1 Domaine de Fr´equence PDDP-F

C.4.2 Domaine Temporel PDDP-F

C.5 R´esum´e du Chapitre

C.5.1 Conclusions

C.6 R´esum´e du Chapitre

C.6.1 Conclusions

C.7 R´esum´e du Chapitre

C.7.1 PEP de la Technique LS pour des Amplitudes de Chemin D´eterministes

C.7.2 PEP de la Technique de GML pour Rayleigh Fading .

C.7.3 Conclusions

C.8 R´esum´e du Chapitre

C.9 Futures travaux