Probability hypothesis density filter with adaptive parameter estimation for tracking multiple maneuvering targets

AbstractThe probability hypothesis density (PHD) filter has been recognized as a promising technique for tracking an unknown number of targets. The performance of the PHD filter, however, is sensitive to the available knowledge on model parameters such as the measurement noise variance and those associated with the changes in the maneuvering target trajectories. If these parameters are unknown in advance, the tracking performance may degrade greatly. To address this aspect, this paper proposes to incorporate the adaptive parameter estimation (APE) method in the PHD filter so that the model parameters, which may be static and/or time-varying, can be estimated jointly with target states. The resulting APE-PHD algorithm is implemented using the particle filter (PF), which leads to the PF-APE-PHD filter. Simulations show that the newly proposed algorithm can correctly identify the unknown measurement noise variances, and it is capable of tracking multiple maneuvering targets with abrupt changing parameters in a more robust manner, compared to the multi-model approaches

Commande robuste pour une gestion énergétique fonction de l'état de santé de la batterie au sein des véhicules hybrides

Un des enjeux actuels de la réduction des émissions polluantes pour les véhicules automobiles concerne l'utilisation de moyens de propulsion hybride (électrique+thermique). Les problématiques principales, pour l'automatique, sont alors d'optimiser l'efficacité énergétique globale du véhicule, mais aussi d'améliorer les performances du véhicule hybride. Nous envisageons ici de développer des méthodes de commande robuste dans cet objectif, tout en prenant en compte les contraintes liées à la mise en oeuvre pratique.In the recent years, growing public concern has been given both on the energy problem and on the environment problem resulted from dramatically increased vehicles equipped with Internal Combustion Engine (ICE). Subsequently, intensive contributions have been made by the automotive industries and research institutes on vehicles that depend less on the fossil fuels, and introduce less pollutant emissions. This has led to the emergence of environment-friendly and energy-saving vehicles such as the Hybrid Electric Vehicle (HEV) that is usually equipped with one or more additional electric motors and the associated power battery compared with the Conventional vehicles (CVs) propelled solely by the ICE. The key point of an HEV is to design a proper Energy Management Strategy (EMS) that decides how to split the demanded power between the engine and the motor (battery). As the most important and expensive part of an HEV, it is important to take into account battery states, such as battery State of Charge (SOC) and battery ageing, aiming at maintain the optimality of the achieved EMS, as well as prolonging the battery life. In this dissertation, an HEV of parallel structure, which is equipped with a Lithiumion battery is considered. This dissertation is focused on accounting for battery related items, i.e. battery SOC and SOH indicated by battery parameters, in the EMS developments leading to a kind of fault tolerant EMS. Some brief introduction on the control methods and realization approaches involved in this work is presented first, followed by two big parts: the first part is focused on the battery modeling and estimation, while the second part is concerned by the vehicle modeling and few kinds of EMS development methods.SAVOIE-SCD - Bib.électronique (730659901) / SudocGRENOBLE1/INP-Bib.électronique (384210012) / SudocGRENOBLE2/3-Bib.électronique (384219901) / SudocSudocFranceF

Systems and control : 21th Benelux meeting, 2002, March 19-21, Veldhoven, The Netherlands

Book of abstract

Restless bandit index policies for dynamic sensor scheduling optimization

This dissertation addresses two complex stochastic and dynamic resource allocation problems, with application in modern sensor systems: (i) hunting multiple elusive hiding targets and (ii) tracking multiple moving targets. These problems are naturally formulated as Multi-armed Restless Bandit Problems (MARBPs) with real-state variables, which introduces technical difficulties that cause its optimal solution to be intractable. Hence, in this thesis we focus on designing tractable and well-performing heuristic policies of priority-index type. We consider the above MARBPs as Markov Decision Processess (MDPs) with special structure, and we deploy recent extensions to the unifying principle to design a dynamic priority index policy based on a Lagrangian relaxation and decomposition approach. This approach allows to design an index rule based on a structural property of the optimal solution to the decomposed parametric-optimization subproblems. The resulting index is a measure of the Marginal Productivity (MP) of resources invested in the subproblems, and it is then used to define a heuristic priority rule for the original intractable problems. For each of the problems under consideration we perform such a decomposition, to analyze the conditions under which the index recovering the optimal policies for the subproblems exists. We further obtain formulae for the indices which do not admit a closed form expression, but which are approximately computed by a tractable evaluation method. Apart from the practical contribution of deriving the tractable sensor scheduling polices which improve on existing heuristics, the main contributions of this thesis are the following: (i) deploying the recent extensions of Sufficient Indexability Conditions (SIC) to the real state case, for two problems in which direct verification of the SIC and obtaining a closed-form index formula are not possible, (ii) addressing the technical difficulties to analyze PCL-indexability introduced by the uncountable state space of the MARBPs of concern, and the state evolution over it given by non-linear dynamics by exploiting the special structure of the trajectories of the state and the action processes under a threshold policy using properties of M¨obius Transformations, and (iii) providing with a tractable approximate evaluation method for the resulting index policies._________________________________________________________________________________________________________________________________Esta tesis estudia dos problemas dinámicos y estocásticos de asignación de recursos, con aplicación a sistemas modernos de sensores: (i) localización de múltiples objetivos evasivos que se ocultan y (ii) el rastreo de múltiples objetivos que se mueven. Estos problemas son modelizados naturalmente como problemas de “Multi-armed Restless Bandit” con variable de estado real, lo que introduce dificultades técnicas que causan que su solción óptima no sea computacionalmente tratable. Debido a esto, en esta tesis nos concentramos en cambio en diseñar políticas heurísticas de prioridad que sean computacionalmente tratables y cuyo rendimento sea casi óptimo. Modelizamos los problemas arriba mencionados como problemas de decisión Markovianos con estructura especial y les aplicamos resultados existentes en la literatura, los que constituyen un principio unificador para el diseño de políticas de índices de prioridad basadas en la relajación Lagrangiana y la descomposición de esos problemas. Este enfoque nos permite considerar una propiedad de los subproblemas: la indexabilidad, por la cual podemos resolverlos de manera óptima mediante una política índice. El índice resultante es una medida de productividad de los recursos invertidos en los subproblemas, y es usado luego como medidad de la prioridad dinámica para los problemas originales intratables. Para cada uno de los problemas bajo estudio realizamos tal descomposición, y analizamos las condiciones bajo las que una política índice que recupere la solución óptima de los subproblemas existe. Además obtenemos fórmulas para los índices, las que a pesar de no admitir una expresión cerrada, son calculadas aproximadamente de manera eficiente meadiante un método tratable. Aparte de la contribución práctica de obtener reglas heurísticas de índices de prioridad para el funcionamiento de sistemas de múltiples sensores en el contexto de los dos problemas analizados, las principales contribuciones teóricas son las siguientes: (i) la aplicación de las extensiones recientes de las condiciones suficientes de indexabilidad para el caso de variable de estado real, para dos problemas en los que tanto la verificación directa de ellas como la obtención de fórmulas cerradas no son posibles, (ii) el tratamiento de las dificultades técnicas para establecer la indexabilidad introducidas por el espacio de estado infinito de los problemas bajo consideración, y por la evolución sobre este estado dada por dinámicas no lineales, explotando propiedades estructurales de los procesos de la variable de estado y trabajo bajo políticas de umbral como recursiones de Transformaciones de Möbius, and (iii) un método aproximado de evaluación de las políticas de índices resultantes

Trajectory optimization for target localization using small unmanned aerial vehicles

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2008.Includes bibliographical references (p. 189-197).Small unmanned aerial vehicles (UAVs), equipped with navigation systems and video capability, are currently being deployed for intelligence, reconnaissance and surveillance missions. One particular mission of interest involves computing location estimates for targets detected by onboard sensors. Combining UAV state estimates with information gathered by the imaging sensors leads to bearing measurements of the target that can be used to determine the target's location. This 3-D bearings-only estimation problem is nonlinear and traditional filtering methods produce biased and uncertain estimates, occasionally leading to filter instabilities. Careful selection of the measurement locations greatly enhances filter performance, motivating the development of UAV trajectories that minimize target location estimation error and improve filter convergence. The objective of this work is to develop guidance algorithms that enable the UAV to fly trajectories that increase the amount of information provided by the measurements and improve overall estimation observability, resulting in proper target tracking and an accurate target location estimate. The performance of the target estimation is dependent upon the positions from which measurements are taken relative to the target and to previous measurements. Past research has provided methods to quantify the information content of a set of measurements using the Fisher Information Matrix (FIM). Forming objective functions based on the FIM and using numerical optimization methods produce UAV trajectories that locally maximize the information content for a given number of measurements. In this project, trajectory optimization leads to the development of UAV flight paths that provide the highest amount of information about the target, while considering sensor restrictions, vehicle dynamics and operation constraints.(cont.) The UAV trajectory optimization is performed for stationary targets, dynamic targets and multiple targets, for many different scenarios of vehicle motion constraints. The resulting trajectories show spiral paths taken by the UAV, which focus on increasing the angular separation between measurements and reducing the relative range to the target, thus maximizing the information provided by each measurement and improving the performance of the estimation. The main drawback of information based trajectory design is the dependence of the Fisher Information Matrix on the true target location. This issue is addressed in this project by executing simultaneous target location estimation and UAV trajectory optimization. Two estimation algorithms, the Extended Kalman Filter and the Particle Filter are considered, and the trajectory optimization is performed using the mean value of the target estimation in lieu of the true target location. The estimation and optimization algorithms run in sequence and are updated in real-time. The results show spiral UAV trajectories that increase filter convergence and overall estimation accuracy, illustrating the importance of information-based trajectory design for target localization using small UAVs.by Sameera S. Ponda.S.M

Probabilistic Methods for Model Validation

This dissertation develops a probabilistic method for validation and verification (V&V) of uncertain nonlinear systems. Existing systems-control literature on model and controller V&V either deal with linear systems with norm-bounded uncertainties,or consider nonlinear systems in set-based and moment based framework. These existing methods deal with model invalidation or falsification, rather than assessing the quality of a model with respect to measured data. In this dissertation, an axiomatic framework for model validation is proposed in probabilistically relaxed sense, that instead of simply invalidating a model, seeks to quantify the "degree of validation". To develop this framework, novel algorithms for uncertainty propagation have been proposed for both deterministic and stochastic nonlinear systems in continuous time. For the deterministic flow, we compute the time-varying joint probability density functions over the state space, by solving the Liouville equation via method-of-characteristics. For the stochastic flow, we propose an approximation algorithm that combines the method-of-characteristics solution of Liouville equation with the Karhunen-Lo eve expansion of process noise, thus enabling an indirect solution of Fokker-Planck equation, governing the evolution of joint probability density functions. The efficacy of these algorithms are demonstrated for risk assessment in Mars entry-descent-landing, and for nonlinear estimation. Next, the V&V problem is formulated in terms of Monge-Kantorovich optimal transport, naturally giving rise to a metric, called Wasserstein metric, on the space of probability densities. It is shown that the resulting computation leads to solving a linear program at each time of measurement availability, and computational complexity results for the same are derived. Probabilistic guarantees in average and worst case sense, are given for the validation oracle resulting from the proposed method. The framework is demonstrated for nonlinear robustness veri cation of F-16 flight controllers, subject to probabilistic uncertainties. Frequency domain interpretations for the proposed framework are derived for linear systems, and its connections with existing nonlinear model validation methods are pointed out. In particular, we show that the asymptotic Wasserstein gap between two single-output linear time invariant systems excited by Gaussian white noise, is the difference between their average gains, up to a scaling by the strength of the input noise. A geometric interpretation of this result allows us to propose an intrinsic normalization of the Wasserstein gap, which in turn allows us to compare it with classical systems-theoretic metrics like v-gap. Next, it is shown that the optimal transport map can be used to automatically refine the model. This model refinement formulation leads to solving a non-smooth convex optimization problem. Examples are given to demonstrate how proximal operator splitting based computation enables numerically solving the same. This method is applied for nite-time feedback control of probability density functions, and for data driven modeling of dynamical systems

On the non-linear dynamics of financial market risk and liquidity.

This thesis provides a novel empirical treatment of the dynamics of financial market risk and liquidity, two very important areas both for financial research as well as to practitioners in the financial markets: We devise empirical non-linear time series models of the two concepts that specifically take into account 'explosive', self-reinforcing dynamic patterns. While 'conventional' empirical models are often 'linear' and tend to neglect these effects, real-life evidence such as e.g. the 1987 crash, the large stock market drops on February 27th, 2007 or the huge losses posted by investment banks and hedge funds during July and August 2007, suggest that such an approach is warranted: In the first part of the thesis we extend a time series model of Value-at-Risk (VaR) with non-linear multiplicative features and endogenous regime thresholds. When estimated with a Markov Chain Monte Carlo (MCMC) method against real data, the resulting 'Self- Exciting Threshold CAViaR' (Conditional Autoregressive Value-at- Risk) model is able to detect trigger thresholds for explosive market risk as well as the scale of such a possible expansion in risk. The second part of the thesis is dedicated to the 'Conditional Autoregressive Liquidity' (CARL) model, a multiplicative time series approach to the empirical modelling of market liquidity. The newly con-ceptualised model is capable of picking up self-reinforcing dynamics, i.e. autoregressive patterns in liquidity, which is in accordance with theoretical research on the topic. Moreover, by incorporating a multidimensional liquidity proxy, the model CARL is explicitly designed to take into account the fact that liquidity is a concept with many facets, unlike other empirical treatments that often view liquidity only along a single dimension (e.g. the bid-ask spread, volume, trade duration). In this thesis, we demonstrate the empirical versatility of the model using both fixed interval data (daily and weekly) as well as tick-by-tick intraday data, for which we propose a filtering technique in order to be able to use the model in such a data environment. We note that the model is able to pick up autocorrelation structures in liquidity rather well and find the forecast performance very encouraging for practical use