There are many multiple-model (MM) target-tracking algorithms that are available but there has yet to be a comparison that includes all of them. This work compares seven of the currently most popular MM algorithms in terms of performance, credibility, and computational complexity. The algorithms to be considered are the autonomous multiple-model algorithm, generalized pseudo- Bayesian of first order, generalized pseudo-Bayesian of second order, interacting multiple-model algorithm, B-Best algorithm, Viterbi algorithm, and reweighted interacting multiple-model algorithm. The algorithms were compared using three scenarios consisting of maneuvers that were both in and out of the model set. Based on this comparison, there is no clear-cut best algorithm but the B-best algorithm performs best in terms of tracking errors and the IMM algorithm has the best computational complexity among the algorithms that have acceptable tracking errors.

De nombreux travaux de recherches sont menés depuis quelques années dans le but de fournir une solution précise et intègre au problème de la localisation de véhicules routiers. Ces recherches sont en majorité fondées sur la théorie probabiliste de l’estimation. Elles utilisent la fusion multi-capteurs et le filtrage de Kalman mono-modèle, au travers de variantes adaptées aux systèmes non linéaires ; l’unique modèle complexe étant supposé décrire toute la dynamique du véhicule. Nous proposons dans cette thèse une approche multi-modèles. Cette étude dérive d’une analyse modulaire de la dynamique du véhicule, c’est-à-dire que l’espace d’évolution est pris comme un espace discret : plusieurs modèles simples et dédiés chacun à une manœuvre particulière sont générés, ce qui améliore la robustesse face aux défauts de modélisation du système. Il s’agit d’une variante de l’algorithme IMM, qui prend en compte l’asynchronisme des capteurs embarqués dans le processus d’estimation de l’état du véhicule. Pour cela, une nouvelle modélisation sous contraintes est développée, ce qui permet de mettre à jour la vraisemblance des modèles intégrés même en l’absence de mesures provenant de capteurs extéroceptifs. Toutefois, la performance d’un tel système nécessite d’utiliser des données capteurs de bonne qualité. Plusieurs opérations sont présentées, illustrant la correction du biais des capteurs, des bruits de mesures ainsi que la prise en compte de l’angle de dévers de la chaussée. La méthodologie développée est validée à travers une comparaison avec les algorithmes de fusion probabilistes EKF, UKF, DD1, DD2 et le filtrage particulaire. Cette comparaison est fondée sur des mesures courantes de précision et de confiance, puis sur l’utilisation de critères statistiques de consistance et de crédibilité, à partir de scénarios synthétiques et ensuite des données réelles. / Many research works have been devoted in the last years in order to provide an accurate and high integrity solution to the problem outdoor vehicles localization. These research efforts are mainly based on the probability estimation theory. They use multi-sensor fusion approach and a single-model based Kalman filtering, through some variants adapted to nonlinear systems. The single complex model that is used is assumed to describe the dynamics of the vehicle. We rather propose a multiple model approach in this thesis. The presented study derives from a modular analysis of the dynamics of the vehicle, ie the evolution of the vehicle is considered as a discrete process, which combines several simple models. Each model is dedicated to a particular manoeuvre of the vehicle. This evolution space discretizing will improves the system robustness to modelling defects. Our approach is a variant of the IMM algorithm, which takes into account the asynchronism of the embedded sensors. In order to achieve this goal, a new system constrained modelling is developed, which allows to update the various models likelihood even in absence of exteroceptive sensors. However, the performance of such a system requires the use of good quality data. Several operations are presented, illustrating the corrections on the sensors bias, measurements noise and taking into account the road bank angle. The developed methodology is validated through a comparison with the probabilistic fusion algorithms EKF, UKF, DD1, DD2 and particle filtering. This comparison is based on measurements of accuracy and confidence, then the use of statistical consistency and credibility measures, from simulation scenarios and then real data.

In modern systems for air surveillance, it is important to have a high quality situationassessment. SAAB has a system for air surveillance, and in this thesis possibleimprovements of the tracking performance of this system are explored. The focushas been on improving the tracking of highly maneuverable targets observed withlow sampling rate. To evaluate improvements of the tracking performance, a componentthat is similar to the one used in SAAB’s present tracker was implementedin an Interacting Multiple Model (IMM) structure. The use of an Auxiliary ParticleFilter for improving the tracking performance is explored, and a way to fita particle filter into SAAB’s existing IMM framework is proposed. The differentfilters were implemented in Matlab, and evaluation was done by the meansof Monte Carlo simulations. The results from Monte Carlo simulations show significantimprovement when tracking in two dimensions. However, the results inthree dimensions do not display any substantial overall improvement when usingthe particle filter compared to using SAAB’s present filter. It is therefore notworthwhile to switch the filter used in SAAB’s present tracker for a particle filter,at least not under the high SNR circumstances presented in this thesis. However,further studies within this area are recommended before any final decisions aremade.

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<p> This thesis investigates the application of multiple model estimation algorithms to the problem of channel equalization for digital data transmission and channel tracking for space-time block coded systems with non-Gaussian additive noise. Recently, a network of Kalman filters (NKF) has been reported for the equalization of digital communication channels based on the approximation of the a posteriori probability density function of a sequence of delayed symbols by a weighted Gaussian sum. A serious drawback of this approach is that the number of Gaussian terms in the sum increases exponentially through iterations. In this thesis, firstly, we have shown that the NKF-based equalizer can be further improved by considering the interactions between the parallel filters in an efficient way. To this end, we take resort to the Interacting Multiple Model (IMM) estimator widely used in the area of multiple target tracking. The IMM is a very effective approach when the system exhibits discrete uncertainties in the dynamic or measurement model as well as continuous uncertainties in state values. A computationally feasible implementation based on a weighted sum of Gaussian approximation of the density functions of the data signals is introduced. Next, we present an adaptive multiple model blind equalization algorithm based on the IMM estimator to estimate the channel and the transmitted sequence corrupted by intersymbol interference and noise. It is shown through simulations that the proposed IMM-based equalizer offers substantially improved performance relative to the blind equalizer based on a (static or non-interacting) network of extended Kalman filters. It obviates the exponential growth of the state complexity caused by increasing channel memory length. The proposed approaches avoid the exponential growth of the number of terms used in the weighted Gaussian sum approximation of the plant noise making it practical for real-time processing.</p> <p> Finally, we consider the problem of channel estimation and tracking for space-time block coded systems contaminated by additive non-Gaussian noise. In many practical wireless channels in which space-time block coding techniques may be applied, the ambient noise is likely to have an impulsive component that gives rise to larger tail probabilities than is predicted by the Gaussian model. Although Kalman filters are often used in practice to track the channel variation, they are notoriously sensitive to heavy-tailed outliers and model mismatches resulting from the presence of impulsive noise. Non-Gaussian noise environments require the modification of standard filters to perform acceptably. Based on the coding/decoding technique, we propose a robust IMM algorithm approach in estimating time-selective fading channels when the measurements are perturbed by the presence of impulsive noise. The impulsive noise is modeled by a two terms Gaussian mixture distribution. Simulations demonstrate that the proposed method yields substantially improved performance compared to the conventional Kalman filter algorithm using the clipping or localization approaches to handle impulses in the observation. It is also shown that IMM-based approach performs robustly even when the prior information about the impulsive noise is not known exactly.</p> / Thesis / Master of Applied Science (MASc)

Yes / A rigorous model for automatic modulation classification (AMC) in cognitive radio (CR) systems is proposed in this paper. This is achieved by exploiting the Kalman filter (KF) integrated with an adaptive interacting multiple model (IMM) for resilient estimation of the channel state information (CSI). A novel approach is proposed, in adding up the squareroot singular values (SRSV) of the decomposed channel using the singular value decompositions (SVD) algorithm. This new scheme, termed Frobenius eigenmode transmission (FET), is chiefly intended to maintain the total power of all individual effective eigenmodes, as opposed to keeping only the dominant one. The analysis is applied over multiple-input multiple-output (MIMO) antennas in combination with a Rayleigh fading channel using a quasi likelihood ratio test (QLRT) algorithm for AMC. The expectation-maximization (EM) is employed for recursive computation of the underlying estimation and classification algorithms. Novel simulations demonstrate the advantages of the combined IMM-KF structure when compared to the perfectly known channel and maximum likelihood estimate (MLE), in terms of achieving the targeted optimal performance with the desirable benefit of less computational complexity loads.

Hybrid systems have been identified as one of the main directions in control theory and attracted increasing attention in recent years due to their huge diversity of engineering applications. Multiplemodel (MM) estimation is the state-of-the-art approach to many hybrid estimation problems. Existing MM methods with fixed structure usually perform well for problems that can be handled by a small set of models. However, their performance is limited when the required number of models to achieve a satisfactory accuracy is large due to time evolution of the true mode over a large continuous space. In this research, variable-structure multiple model (VSMM) estimation was investigated, further developed and evaluated. A fundamental solution for on-line adaptation of model sets was developed as well as several VSMM algorithms. These algorithms have been successfully applied to the fields of fault detection and identification as well as target tracking in this thesis. In particular, an integrated framework to detect, identify and estimate failures is developed based on the VSMM. It can handle sequential failures and multiple failures by sensors or actuators. Fault detection and target maneuver detection can be formulated as change-point detection problems in statistics. It is of great importance to have the quickest detection of such mode changes in a hybrid system. Traditional maneuver detectors based on simplistic models are not optimal and are computationally demanding due to the requirement of batch processing. In this presentation, a general sequential testing procedure is proposed for maneuver detection based on advanced sequential tests. It uses a likelihood marginalization technique to cope with the difficulty that the target accelerations are unknown. The approach essentially utilizes a priori information about the accelerations in typical tracking engagements and thus allows improved detection performance. The proposed approach is applicable to change-point detection problems under similar formulation, such as fault detection.

This thesis presents a comprehensive example framework on how current multiple model state estimation algorithms for jump Markov linear systems can be improved. The possible improvements are categorized as: -Design of multiple model state estimation algorithms using new criteria. -Improvements obtained using existing multiple model state estimation algorithms. In the first category, risk-sensitive estimation is proposed for jump Markov linear systems. Two types of cost functions namely, the instantaneous and cumulative cost functions related with risk-sensitive estimation are examined and for each one, the corresponding multiple model estate estimation algorithm is derived. For the cumulative cost function, the derivation involves the reference probability method where one defines and uses a new probability measure under which the involved processes has independence properties. The performance of the proposed risk-sensitive filters are illustrated and compared with conventional algorithms using simulations. The thesis addresses the second category of improvements by proposing -Two new online transition probability estimation schemes for jump Markov linear systems. -A mixed multiple model state estimation scheme which combines desirable properties of two different multiple model state estimation methods. The two online transition probability estimators proposed use the recursive Kullback-Leibler (RKL) procedure and the maximum likelihood (ML) criteria to derive the corresponding identification schemes. When used in state estimation, these methods result in an average error decrease in the root mean square (RMS) state estimation errors, which is proved using simulation studies. The mixed multiple model estimation procedure which utilizes the analysis of the single Gaussian approximation of Gaussian mixtures in Bayesian filtering, combines IMM (Interacting Multiple Model) filter and GPB2 (2nd Order Generalized Pseudo Bayesian) filter efficiently. The resulting algorithm reaches the performance of GPB2 with less Kalman filters.

In solving target tracking problems, the Kalman filter (KF) is a systematic estimation algorithm. Whether the state of a moving target adapts to the changes in the observations depends on the model assumptions. The interacting multiple model (IMM) algorithm uses interaction of a bank of parallel KFs by updating associated model probabilities. Every parallel KF has its model probability adjusted by the dynamic system. For moving targets of different dynamic linear models, an IMM with two KFs generally performs well. In this thesis, in order to improve the performance of target tracking and state estimation, multi-sensor data fusion technique will be used. Same types of IMMs can be incorporated in the cooperative IMM-based algorithm. The IMM-based estimators exchange with each other the estimates, model robabilities and model transition probabilities. A distributed algorithm for multi-sensor tracking usually needs a fusion center that integrates decisions or estimates, but the proposed cooperative IMM-based algorithm does not use the architecture. Cooperative IMM estimator structures exchange weights and estimates on the platforms to avoid accumulation of errors. Performance of data fusion may degrade due to different kinds of undesirable environmental effects. The simulations show that an IMM estimator with smaller measurement noise level can be used to compensate the other IMM, which is affected by larger measurement noise. In addition, failure of a sensor will cause the problem that model probabilities can not be updated in the corresponding estimator. Kalman filters will not be able to perform state correction for the moving target. To tackle the problem, we can use the estimates from other IMM estimators by adjusting the corresponding weights and model probabilities. The simulations show that the proposed cooperative IMM structure effectively improve the tracking performance.

As part of the processing of tracking targets, surveillance radars detect the presence of targets and estimate their locations. This dissertation re-examines some of the often ignored practical considerations of radar tracking. With the advent of digital computers, modern radars now use sampled versions of received signals for processing. Sampling rates used in practice result in the bin-straddling phenomenon, which is often treated as an undesired loss in signal power. Here, a signal model that explicitly models the sampling process is used in the derivation of the average loglikelihood ratio test (ALLRT), and its detection performance is shown to defeat the bin-straddling losses seen in traditional radar detectors. In monopulse systems, data samples are taken from the sum and difference channels, by which a target direction-of-arrival (DOA) estimate can be formed. Using the same signal model, we derive new estimators for target range, strength, and DOA and show performance benefits over traditional monopulse techniques that are predominant in practice. Since tracking algorithms require an error variance report on target parameter estimates, we propose using the generalized Cramer-Rao lower bound (GCRLB), which is the CRLB evaluated at estimates rather than true values, as an error variance report. We demonstrate the statistical efficiency and variance consistency of the new estimators. With several parameter estimates collected over time, tracking algorithms are used to compute track state estimates and predict future locations. Using agile- beam surveillance radars with programmable energy waveforms, optimal scheduling of radar resources is a topic of interest. In this dissertation, we focus on the energy management considerations of tracking highly maneuverable aircraft. A comparison between two competing interacting multiple model (IMM) filter configurations is made, and a recently proposed unbiased mixing procedure is extended to the case of three modes. Finally, we introduce the radar management operating curve (RMOC), which shows the fundamental tradeoff in radar time and energy, to aid radar designers in the selection of an overall operating signal-to-noise level.