Multilane traffic density estimation with KDE and nonlinear LS and tracking with Scalar Kalman filtering

Tezin basılısı, İstanbul Şehir Üniversitesi Kütüphanesi'ndedir.With increasing population, the determination of traffic density becomes very critical in managing the urban city roads for safer driving and low carbon emission. In this study, Kernel Density Estimation is utilized in order to estimate the traffic density more accurately when the speeds of the vehicles are available for a given region. For the proposed approach, as a first step, the probability density function of the speed data is modeled by Kernel Density Estimation. Then, the speed centers from the density function are modeled as clusters. The cumulative distribution function of the speed data is then determined by Kolmogorov-Smirnov Test, whose complexity is less when compared to the other techniques and whose robustness is high when outliers exist. Then, the mean values of clusters are estimated from the smoothed density function of the distribution function, followed by a peak detection algorithm. The estimation of variance values and kernel weights, on the other hand, are found by a nonlinear Least Square approach. As the estimation problem has linear and non-linear components, the nonlinear Least Square with separation of parameters approach is adopted, instead of dealing with a high complexity nonlinear equation. Finally, the tracking of former and latter estimations of a road is calculated by using Scalar Kalman Filtering with scalar state - scalar observation generality level. Simulations are carried out in order to assess theperformanceoftheproposedapproach. Forallexampledatasets, theminimummean square error of kernel weights is found to be less than 0.002 while error of mean values is found to be less than 0.261. The proposed approach was also applied to real data from sample road traffic, and the speed center and the variance was accurately estimated. By using the proposed approach, accurate traffic density estimation is realized, providing extra information to the municipalities for better planning of their cities.Declaration of Authorship ii Abstract iii Öz iv Acknowledgments vi List of Figures ix List of Tables x Abbreviations xi 1 Introduction 1 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Methods to Find Probability Density Function and Cumulative Distribution Function . . . . . . . . . . . . . . . . . . . . . . . . . . . .3 1.3 Traffic Density Estimation with Kernel Density Estimation . . . . . . . . 4 1.4 The Approaches for Determination of Key Parameters of Traffic Density Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . .5 1.5 Tracking between Estimated Data and New Data . . . . . . . . . . . . . . 6 1.6 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2 Literature Review 7 2.1 Methodologies Used for Estimation of Traffic Density . . . . . . . . . . . . 7 2.2 An Example Study of Traffic Density Estimation with KDE and CvM . . 9 2.3 Three Complementary Studies for Traffic Density Estimation and Tracking 9 2.4 Comparison of Three Different Nonlinear Estimation Techniques on the Same Problem . . . . . . . . . . . . . . . . . . . . . . . . .10 2.4.1 A Maximum Likelihood Approach for Estimating DS-CDMA Multipath Fading Channels . . . . . . . . . . . . . . . . . . . . . . . . 12 2.4.2 Channel Estimation for the Uplink of a DS-CDMA System . . . . 12 2.4.3 A Robust Method for Estimating Multipath Channel Parameters in the Uplink of a DS-CDMA System. . . . . . . . . . . . . . .13 3 The Model 16 3.1 Finding Density Distribution with KDE . . . . . . . . . . . . . . . . . . . 16 3.2 Finding Empirical CDF with KS Test . . . . . . . . . . . . . . . . . . . . 18 3.3 Determination of Speed Centers via PDA . . . . . . . . . . . . . . . . . . 20 3.4 Estimation of Variance and Kernel Weights with Nonlinear LS Method . . 21 3.5 Tracking of Traffic Density Estimation with Scalar Kalman Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 4 Numerical Calculations for Traffic Density Estimation 26 4.1 An Example Traffic Scenario with Five Speed Centers . . . . . . . . . . . 26 4.2 The Estimation of A Real Time Data . . . . . . . . . . . . . . . . . . . . . 29 4.3 Traffic Density Estimation with Different Kernel Numbers . . . . . . . . . 29 5 Examples to Test Tracking Part of the Model 31 5.1 Tracking with the Change only in Mean Values . . . . . . . . . . . . . . . 32 5.2 Tracking with the Change only in Kernel Weights . . . . . . . . . . . . . . 35 5.3 Tracking with the Change in All Three Parameters . . . . . . . . . . . . . 36 6 Assesment 38 7 Conclusion 41 A Derivation of Newton-Raphson Method for the Estimation of Variance Values and Kernel Weights 43 Bibliography 4

Generalized multivariate analysis of variance - A unified framework for signal processing in correlated noise

Generalized multivariate analysis of variance (GMANOVA) and related reduced-rank regression are general statistical models that comprise versions of regression, canonical correlation, and profile analyses as well as analysis of variance (ANOVA) and covariance in univariate and multivariate settings. It is a powerful and, yet, not very well-known tool. We develop a unified framework for explaining, analyzing, and extending signal processing methods based on GMANOVA. We show the applicability of this framework to a number of detection and estimation problems in signal processing and communications and provide new and simple ways to derive numerous existing algorithms. Many of the methods were originally derived from scratch , without knowledge of their close relationship with the GMANOVA model. We explicitly show this relationship and present new insights and guidelines for generalizing these methods. Our results could inspire applications of the general framework of GMANOVA to new problems in signal processing. We present such an application to flaw detection in nondestructive evaluation (NDE) of materials. A promising area for future growth is image processing

Channel estimation and signal enhancement for DS-CDMA systems

This dissertation focuses on topics of Bayesian-based multiuser detection, space-time (S-T) transceiver design, and S-T channel parameter estimation for direct-sequence code-division multiple-access (DS-CDMA) systems. Using the Bayesian framework, various linear and simplified nonlinear multiuser detectors are proposed, and their performances are analyzed. The simplified non-linear Bayesian solutions can bridge the performance gap between sub-optimal linear multiuser detectors and the optimum multiuser detector. To further improve the system capacity and performance, S-T transceiver design approaches with complexity constraint are investigated. Novel S-T receivers of low-complexity that jointly use the temporal code-signature and the spatial signature are proposed. Our solutions, which lead to generalized near-far resistant S-T RAKE receivers, achieve better interference suppression than the existing S-T RAKE receivers. From transmitter side, we also proposed a transmit diversity (TD) technique in combination with differential detection for the DS-CDMA systems. It is shown that the proposed S-T TD scheme in combination with minimum variance distortionless response transceiver (STTD+MVDR) is near-far resistant and outperforms the conventional STTD and matched filter based (STTD+MF) transceiver scheme. Obtaining channel state information (CSI) is instrumental to optimum S-T transceiver design in wireless systems. Another major focus of this dissertation is to estimate the S-T channel parameters. We proposed an asymptotic, joint maximum likelihood (ML) method of estimating multipath channel parameters for DS-CDMA systems. An iterative estimator is proposed to further simplify the computation. Analytical and simulation results show that the iterative estimation scheme is near-far resistant for both time delays and DOAs. And it reaches the corresponding CRBs after a few iterations

Optimisation des performances de réseaux de capteurs dynamiques par le contrôle de synchronisation dans les systèmes ultra large bande

The basic concept of Impulse-Radio UWB (IR-UWB) technology is to transmit and receive baseband impulse waveform streams of very low power density and ultra-short duration pulses (typically at nanosecond scale). These properties of UWB give rise to fine time-domain resolution, rich multipath diversity, low power and low cost on-chip implementation facility, high secure and safety, enhanced penetration capability, high user capacity, and potential spectrum compatibility with existing narrowband systems. Due to all these features, UWB technology has been considered as a feasible technology for WSN applications. While UWB has many reasons to make it a useful and exciting technology for wireless sensor networks and many other applications, it also has some challenges which must be overcome for it to become a popular approach, such as interference from other UWB users, accurate modelling of the UWB channel in various environments, wideband RF component (antennas, low noise amplifiers) designs, accurate synchronization, high sampling rate for digital implementations, and so on. In this thesis, we will focus only on one of the most critical issues in ultra wideband systems: Timing Synchronization.Dans cette thèse nous nous sommes principalement concentrés sur les transmissions impulsion radio Ultra Large Bande (UWB-IR) qui a plusieurs avantages grâce à la nature de sa bande très large (entre 3.1GHZ et 10.6GHz) qui permet un débit élevé et une très bonne résolution temporelle. Ainsi, la très courte durée des impulsions émises assure une transmission robuste dans un canal multi-trajets dense. Enfin la faible densité spectrale de puissance du signal permet au système UWB de coexister avec les applications existantes. En raison de toutes ces caractéristiques, la technologie UWB a été considérée comme une technologie prometteuse pour les applications WSN. Cependant, il existe plusieurs défis technologiques pour l'implémentation des systèmes UWB. A savoir, une distorsion différente de la forme d'onde du signal reçu pour chaque trajet, la conception d'antennes très larges bandes de petites dimensions et non coûteuses, la synchronisation d'un signal impulsionnel, l'utilisation de modulation d'onde d'ordre élevé pour améliorer le débit etc. Dans ce travail, Nous allons nous intéresser à l'étude et l'amélioration de la synchronisation temporelle dans les systèmes ULB