Miroslav Flídr

Nonlinear estimation framework in target tracking

The goal of the article is to describe a software framework designed for nonlinear state estimation of discrete-time dynamic systems. The framework was designed with the aim to facilitate implementation, testing and use of various nonlinear state estimation methods. The main strength of the framework is its versatility due to the possibility of either structural or probabilistic model description. Besides the well-known basic nonlinear estimation methods such as the extended Kalman filter, the divided difference filters and the unscented Kalman filter, the framework implements the particle filter with advanced features. As the framework is designed on the object oriented basis, further extension by user-specified nonlinear estimation algorithms is extremely easy. The paper describes the individual components of the framework, their key features and use. The paper demonstrates easy and natural application of the framework in target tracking which is illustrated in two examples - tracking a ship with unknown control and tracking three targets based on raw data.

A Software Framework and Tool for Nonlinear State Estimation

Abstract The goal of the article is to describe a software framework designed for nonlinear state estimation of discrete time dynamic systems. The framework was designed with the aim to facilitate implementation, testing and use of various nonlinear state estimation methods in mind. The main strength of the framework is its versatility due to the possibility of either structural or probabilistic description of the problem. Besides the well-known basic nonlinear estimation methods such as the extended Kalman filter, the divided difference filters and the unscented Kalman filter, the framework implements particle filter with advanced features as well. As the framework is designed on the object oriented basis, further extension by user-specified nonlinear estimation algorithms is extremely easy. The paper provides a brief introduction into nonlinear state estimation problem and describes the individual components of the framework, their key features and use. The strengths of the framework are presented in two examples.

Nonlinear Nonnormal Dynamic Models: State Estimation and Software

The purpose of this paper is to formulate and to solve recursive Bayesian state estimation problems for nonlinear non-Gaussian models and to introduce software for model and filter design. The initial a priori density of the state vector, state and measurement noise are always represented in the form of a discrete normal density mixture and a posteriori density of state vector has the same form. A software package was developed for solving Bayesian nonlinear filtering problems. The software package is based on MATLAB and the Symbolic Math Toolbox with an aim to create an easy-to-use tool for model and filter design. This tool can be used for state estimation of general nonlinear non-Gaussian systems or for many special problems like tracking time-varying parameters, fault detection, hypothesis testing, robustification of filters due to outliers and so on.

Bicriterial dual control for stochastic systems with unknown variable parameters

Abstract A suboptimal dual controller for discrete stochastic systems with unknown parameters is proposed. Two criteria are designed and used to ensure both aspects of dual control - caution and active learning. The optimization procedure consists of minimization of a quadratic cost function and maximization of the one-step prediction error on certain domain. Extended Kalman filter and Gaussian sum method were used for simultaneous state and parameter estimation of systems with Gaussian and non-Gaussian disturbances, respectively. A comparison of the proposed dual controller with caution and certainty equivalent controllers is shown in numerical examples.

Dual Adaptive Controllers Based on Partial Certainty Equivalence

Abstract The article deals with the optimal control of a linear discrete stochastic state space system with uncertain parameters. The solution of this optimization problem leads to design of controllers with dual features. Because the closed-form solution is hardly attainable a suitable suboptimal approaches has to be used. Many of the simpler approaches restrict the control horizon only to one step ahead and thus suffer from the myopic behavior. One way how to overcome this restriction is to use the partial certainty equivalence approximation of the joint probability density functions. The goal of this paper is to present a comparison of suboptimal adaptive dual control methods employing this approximation.

Non-myopic innovations dual controller

Abstract Optimal control of a linear discrete stochastic state space system with uncertain parameters is treated. The problem statement leads to design of a dual controllers. Unfortunately, except for few special cases it is not possible to obtain closed-form solution for such controller. Many suboptimal approaches were proposed to overcome this obstacle, however, mostly they restrict the control horizon only to one step ahead and thus suffer from myopic behaviour. This paper presents technique that makes it possible to derive suboptimal dual controller in closed-form for arbitrarily long control horizon. The design of the presented controller is based on the innovations dual controller and use of the partial certainty equivalence principle. The proposed dual controller is compared to other non-dual controllers in a numerical example.

Application of estimation techniques on queue lengths estimation in traffic network

The paper deals with the application of the state and parameter estimation techniques in the area of traffic control. The most important properties of the traffic system are described and the model of the traffic system, based on the traffic flow conservation principle, is presented. Various estimation and identification techniques are briefly introduced and applied for three types of roads and micro-regions, namely for city ring road, peripheral road, and city centre. Performance of estimation techniques is validated, using the derived models on real and synthetic data coming from Prague, with respect to accuracy and complexity.

FRAMEWORK FOR IMPLEMENTING AND TESTING NONLINEAR FILTERS

Abstract The aim of this paper is to present a software framework facilitating implementation, testing and use of various nonlinear estimation methods. This framework is designed to offer an easy to use tool for state estimation of discrete time dynamic stochastic systems. Besides implementation of various local and global state estimation methods it contains procedures for system design and simulation. Its strength is in the fact that it provides means that help students get acquainted with nonlinear state estimation problem and to be able to test features of various estimation methods. Another considerable advantage of proposed framework is its high modularity and extensibility. The paper briefly describes nonlinear estimation problem and its general solution using the Bayesian approach leading to the Bayesian recursive relations. Then it presents key features of the software framework designed in MATLAB environment that supports straightforward implementation of estimation methods based on the Bayesian approach. The strengths of the framework are demonstrated on implementation of the Divided difference filter 1st order.

Nonlinear Estimation Software Framework in Optimal and Adaptive Control Problems

Abstract The paper presents the use of a MATLAB based software framework designed for nonlinear state estimation of discrete-time dynamic systems in optimal and adaptive control problems. The main focus of the framework is to facilitate implementation, testing and use of various nonlinear state estimation methods. Nevertheless, due to its versatility, the framework is also suitable for adaptive control purposes. The designer of the controller can utilize any of the large number of offered estimators which provide the necessary state and parameter estimates in the form of conditional probability density function. The paper presents the possibilities of the toolbox usage in optimal and adaptive control problems. It will be demonstrated how easily and naturally an estimation problem can be described by means provided by the framework and how easily it can be fitted into and controller.

Nonlinear estimation framework: A versatile tool for state estimation

The paper presents MATLAB based software framework designed for nonlinear state estimation of discrete-time dynamic systems. The framework is designed to facilitate implementation, testing and use of various nonlinear state estimation methods. It allows simple description of the problem, specification of estimation experiment and processing the resulting data in order to simply compare various estimators. The main strength of the framework is its versatility. The framework provides means for description of the problem by either structural or probabilistic model. The user has a wide variety of classic and contemporary estimation methods at hand, which can be easily parametrized. Besides the well-known basic nonlinear estimation methods such as the extended Kalman filter, the divided difference filters and the unscented Kalman filter, the framework implements the particle filter with advanced features. The framework offers tools for straightforward evaluation of many well known metrics used for estimate quality assessment. And as the framework is designed on the object oriented basis, further extension by user-specified nonlinear estimation algorithms is extremely easy. The aim of the paper is to get acquainted with the possibilities of the toolbox. It will demonstrate the easy and natural way in which the estimation problem can be described within the means provided by the framework. Two examples of target tracking will be demonstrated with the estimation experiment setup using the presented framework.