A general framework for using Monte Carlo methods in dynamic systems is provided and its wide applications indicated. Under this framework, several currently available techniques are studied and generalized to accommodate more complex features. All of these methods are partial combinations of three ingredients: importance sampling and resampling, rejection sampling, and Markov chain iterations. We deliver a guideline on how they should be used and under what circumstance each method is most suitable. Through the analysis of differences and connections, we consolidate these methods into a generic algorithm by combining desirable features. In addition, we propose a general use of Rao-Blackwellization to improve performances. Examples from econometrics and engineering are presented to demonstrate the importance of Rao-Blackwellization and to compare different Monte Carlo procedures. Keywords: Blind deconvolution; Bootstrap filter; Gibbs sampling; Hidden Markov model; Kalman filter; Markov...

. In this report, we present an overview of sequential simulationbased methods for Bayesian filtering of nonlinear and non-Gaussian dynamic models. It includes in a general framework numerous methods proposed independently in various areas of science and proposes some original developments. Keywords: Bayesian estimation, optimal filtering, nonlinear non-Gaussian state space models, hidden Markov models, sequential Monte Carlo methods. 1. Introduction 1 Many problems in statistical signal processing, automatic control, applied statistics or econometrics can be stated as follows. A transition equation describes the prior distribution of the Markovian hidden signal of interest fx k ; k 2 Ng, the so-called hidden state process, and an observation equation describes the likelihood of the observations fy k ; k 2 Ng, k being the discrete time index. The aim is to estimate the hidden state process using the observations. In the Bayesian framework, all relevant information on fx 0 ; x ...

In this paper, we propose a new particle filter based on sequential importance sampling. The algorithm uses a bank of unscented filters to obtain the importance proposal distribution. This proposal has two very "nice" properties. Firstly, it makes efficient use of the latest available information and, secondly, it can have heavy tails. As a result, we find that the algorithm outperforms standard particle filtering and other nonlinear filtering methods very substantially. This experimental finding is in agreement with the theoretical convergence proof for the algorithm. The algorithm also includes resampling and (possibly) Markov chain Monte Carlo (MCMC) steps.

Jump Markov linear systems (JMLS) are linear systems whose parameters evolve with time according to a finite state Markov chain. In this paper, our aim is to recursively compute optimal state estimates for this class of systems. We present efficient simulation-based algorithms called particle filters to solve the optimal filtering problem as well as the optimal fixed-lag smoothing problem. Our algorithms combine sequential importance sampling, a selection scheme, and Markov chain Monte Carlo methods. They use several variance reduction methods to make the most of the statistical structure of JMLS.

A framework for positioning, navigation and tracking problems using particle filters (sequential Monte Carlo methods) is developed. It consists of a class of motion models and a general non-linear measurement equation in position. A general algorithm is presented, which is parsimonious with the particle dimension. It is based on marginalization, enabling a Kalman filter to estimate all position derivatives, and the particle filter becomes low-dimensional. This is of utmost importance for highperformance real-time applications. Automotive and airborne applications illustrate numerically the advantage over classical Kalman filter based algorithms. Here the use of non-linear models and non-Gaussian noise is the main explanation for the improvement in accuracy. More specifically, we describe how the technique of map matching is used to match an aircraft's elevation profile to a digital elevation map, and a car's horizontal driven path to a street map. In both cases, real-time implementations are available, and tests have shown that the accuracy in both cases is comparable to satellite navigation (as GPS), but with higher integrity. Based on simulations, we also argue how the particle filter can be used for positioning based on cellular phone measurements, for integrated navigation in aircraft, and for target tracking in aircraft and cars. Finally, the particle filter enables a promising solution to the combined task of navigation and tracking, with possible application to airborne hunting and collision avoidance systems in cars.

Abstract—The classical particle filter deals with the estimation of one state process conditioned on a realization of one observation process. We extend it here to the estimation of multiple state processes given realizations of several kinds of observation processes. The new algorithm is used to track with success multiple targets in a bearings-only context, whereas a JPDAF diverges. Making use of the ability of the particle filter to mix different types of observations, we then investigate how to join passive and active measurements for improved tracking. Index Terms—Bayesian estimation, bearings-only tracking, Gibbs sampler, multiple receivers, multiple targets tracking,

We address the problem of multitarget tracking encountered in many situations in signal or image processing. We consider stochastic dynamic systems detected by observation processes. The difficulty lies on the fact that the estimation of the states requires the assignment of the observations to the multiple targets. We propose an extension of the classical particle filter where the stochastic vector of assignment is estimated by a Gibbs sampler. This algorithm is used to estimate the trajectories of multiple targets from their noisy bearings, thus showing its ability to solve the data association problem. Moreover this algorithm is easily extended to multireceiver observations where the receivers can produce measurements of various nature with different frequencies.

The problem of tracking multiple targets with multiple sensors in the presence of interfering measurements is considered. A new hybrid bootstrap filter is proposed. The bootstrap filter is an approach where random samples are used to represent the target posterior distributions. By using this approach, we circumvent the usual problem of an exponentially increasing number of association hypotheses as well as allowing the use of any nonlinear/non-Gaussian system and/or measurement models. I. INTRODUCTION This paper concerns the problem of tracking multiple targets using the information from multiple sensors. The sensors produce measurements as a result of random noise, clutter, countermeasures and interference, in addition to those from the required targets. Hence, it is usually not possible to distinguish with certainty the origin of the sensor measurements. In the Bayesian approach to target tracking, the aim is to construct the probability density function (pdf) of the targets conditi...

In this paper we present Monte Carlo methods for multi-target tracking and data association. The methods are applicable to general non-linear and non-Gaussian models for the target dynamics and measurement likelihood. We provide efficient solutions to two very pertinent problems: the data association problem that arises due to unlabelled measurements in the presence of clutter, and the curse of dimensionality that arises due to the increased size of the state-space associated with multiple targets. We develop a number of algorithms to achieve this. The first, which we will refer to as the Monte Carlo Joint Probabilistic Data Association Filter (MC-JPDAF), is a generalisation of the strategy proposed in [1], [2]. As is the case for the JPDAF, the distributions of interest are the marginal filtering distributions for each of the targets, but these are approximated with particles rather than Gaussians. We also develop two extensions to the standard particle filtering methodology for tracking multiple targets. The first, which we will refer to as the Sequential Sampling Particle Filter (SSPF), samples the individual targets sequentially by utilising a factorisation of the importance weights. The second, which we will refer to as the Independent Partition Particle Filter (IPPF), assumes the associations to be independent over the individual targets, leading to an efficient componentwise sampling strategy to construct new particles. We evaluate and compare the proposed methods on a challenging synthetic tracking problem.

Abstract—Sequential Bayesian estimation for nonlinear dynamic state-space models involves recursive estimation of filtering and predictive distributions of unobserved time varying signals based on noisy observations. This paper introduces a new filter called the Gaussian particle filter1. It is based on the particle filtering concept, and it approximates the posterior distributions by single Gaussians, similar to Gaussian filters like the extended Kalman filter and its variants. It is shown that under the Gaussianity assumption, the Gaussian particle filter is asymptotically optimal in the number of particles and, hence, has much-improved performance and versatility over other Gaussian filters, especially when nontrivial nonlinearities are present. Simulation results are presented to demonstrate the versatility and improved performance of the Gaussian particle filter over conventional Gaussian filters and the lower complexity than known particle filters. The use of the Gaussian particle filter as a building block of more complex filters is addressed in a companion paper. Index Terms—Dynamic state space models, extended Kalman filter, Gaussian mixture, Gaussian mixture filter, Gaussian particle filter, Gaussian sum filter, Gaussian sum particle filter, Monte Carlo filters, nonlinear non-Gaussian stochastic systems, particle filters, sequential Bayesian estimation, sequential sampling methods, unscented Kalman filter. I.