Increasingly, for many application areas, it is becoming important to include elements of nonlinearity and non-Gaussianity in order to model accurately the underlying dynamics of a physical system. Moreover, it is typically crucial to process data on-line as it arrives, both from the point of view of storage costs as well as for rapid adaptation to changing signal characteristics. In this paper, we review both optimal and suboptimal Bayesian algorithms for nonlinear/non-Gaussian tracking problems, with a focus on particle filters. Particle filters are sequential Monte Carlo methods based on point mass (or "particle") representations of probability densities, which can be applied to any state-space model and which generalize the traditional Kalman filtering methods. Several variants of the particle filter such as SIR, ASIR, and RPF are introduced within a generic framework of the sequential importance sampling (SIS) algorithm. These are discussed and compared with the standard EKF through an illustrative example.

/pdf/a-tutorial-on-particle-filters-for-online-nonlinear-non-1rzkwgk2pp.pdf

A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking

This is the first part of a comprehensive and up-to-date survey of the techniques for tracking maneuvering targets without addressing the so-called measurement-origin uncertainty. It surveys various mathematical models of target motion/dynamics proposed for maneuvering target tracking, including 2D and 3D maneuver models as well as coordinate-uncoupled generic models for target motion. This survey emphasizes the underlying ideas and assumptions of the models. Interrelationships among models and insight to the pros and cons of models are provided. Some material presented here has not appeared elsewhere.

Survey of maneuvering target tracking. Part I. Dynamic models

In this paper, we introduce three novel distributed Kalman filtering (DKF) algorithms for sensor networks. The first algorithm is a modification of a previous DKF algorithm presented by the author in CDC-ECC '05. The previous algorithm was only applicable to sensors with identical observation matrices which meant the process had to be observable by every sensor. The modified DKF algorithm uses two identical consensus filters for fusion of the sensor data and covariance information and is applicable to sensor networks with different observation matrices. This enables the sensor network to act as a collective observer for the processes occurring in an environment. Then, we introduce a continuous-time distributed Kalman filter that uses local aggregation of the sensor data but attempts to reach a consensus on estimates with other nodes in the network. This peer-to-peer distributed estimation method gives rise to two iterative distributed Kalman filtering algorithms with different consensus strategies on estimates. Communication complexity and packet-loss issues are discussed. The performance and effectiveness of these distributed Kalman filtering algorithms are compared and demonstrated on a target tracking task.

Distributed Kalman filtering for sensor networks

Increasingly, for many application areas, it is becoming important to include elements of nonlinearity and non-Gaussianity in order to model accurately the underlying dynamics of a physical system. Moreover, it is typically crucial to process data on-line as it arrives, both from the point of view of storage costs as well as for rapid adaptation to changing signal characteristics. In this paper, we review both optimal and suboptimal Bayesian algorithms for nonlinear/non-Gaussian tracking problems, with a focus on particle filters. Particle filters are sequential Monte Carlo methods based on point mass (or “particle”) representations of probability densities, which can be applied to any state-space model and which generalize the traditional Kalman filtering methods. Several variants of the particle filter such as SIR, ASIR, and RPF are introduced within a generic framework of the sequential importance sampling (SIS) algorithm. These are discussed and compared with the standard EKF through an illustrative example.

/pdf/a-tutorial-on-particle-filters-for-on-line-nonlinear-non-43lm33c5mj.pdf

A tutorial on particle filters for on-line nonlinear/non-Gaussian Bayesian tracking

Now in its second edition, this accessible text presents a unified Bayesian treatment of state-of-the-art filtering, smoothing, and parameter estimation algorithms for non-linear state space models. The book focuses on discrete-time state space models and carefully introduces fundamental aspects related to optimal filtering and smoothing. In particular, it covers a range of efficient non-linear Gaussian filtering and smoothing algorithms, as well as Monte Carlo-based algorithms. This updated edition features new chapters on constructing state space models of practical systems, the discretization of continuous-time state space models, Gaussian filtering by enabling approximations, posterior linearization filtering, and the corresponding smoothers. Coverage of key topics is expanded, including extended Kalman filtering and smoothing, and parameter estimation. The book's practical, algorithmic approach assumes only modest mathematical prerequisites, suitable for graduate and advanced undergraduate students. Many examples are included, with Matlab and Python code available online, enabling readers to implement algorithms in their own projects.

Yakov Bar-Shalom

Papers

Multitarget-Multisensor Tracking: Principles and Techniques