Bernoulli Particle/Box-Particle Filters for Detection and Tracking in the Presence of Triple Measurement Uncertainty

Abstract

This work presents sequential Bayesian detection and estimation methods for nonlinear dynamic stochastic systems using measurements affected by three sources of uncertainty: stochastic, set-theoretic and data association uncertainty. Following Mahler's framework for information fusion, the paper develops the optimal Bayes filter for this problem in the form of the Bernoulli filter for interval measurements. Two numerical implementations of the optimal filter are developed. The first is the Bernoulli particle filter (PF), which turns out to require a large number of particles in order to achieve a satisfactory performance. For the sake of reduction in the number of particles, the paper also develops an implementation based on box particles, referred to as the Bernoulli Box-PF. A box particle is a random sample that occupies a small and controllable rectangular region of nonzero volume in the target state space. Manipulation of boxes utilizes the methods of interval analysis. The two implementations are compared numerically and found to perform remarkably well: the target is reliably detected and the posterior probability density function of the target state is estimated accurately. The Bernoulli Box-PF, however, when designed carefully, is computationally more efficient.Index Terms-Bernoulli filter, box particle filters, interval measurements, particle filters, random sets, sequential Bayesian estimation.

Particle filtering with applications in networked systems: a survey

“…Various methods have been put forward to robustify the particle filtering algorithm for systems with unknown statistics. The box particle filtering, which combines sequential Monte Carlo method with interval analysis, has been introduced in [41][42][43]. Unlike the standard particle filtering method where particles are points in the state space and likelihood functions are defined by a statistical model, the box particle filter uses multidimensional intervals in the state space as particles and a bounded error model to evaluate the likelihood functions.…”

An Introduction to Box Particle Filtering [Lecture Notes]

“…The box-PF algorithm is presented through the prism of the Bayesian inference using mixtures of uniform pdfs with boxed supports. More details about the box-PF and its implementation can be found in [3]- [5].…”

“…Indeed, in some applications where the sampling importance resampling (SIR) PF may require thousands of particles to achieve accurate and reliable performance, the box-PF can reach the same level of accuracy with just a few dozen box particles. Recent developments [4] also show that a box-PF can be interpreted as a Bayes' filter approximation allowing the application of box-PF to challenging target tracking problems [5].…”

Box-Particle Implementation and Comparison of Cardinalized Probability Hypothesis Density Filter

“…The box-particle filter was studied and explained through the Bayesian perspective by interpreting each box particle as a uniform probability density function (PDF) [10]. A single target box-particle Bernoulli filter with box measurements was presented in [11]. The box-particle PHD filter for multi-target tracking with an unknown number of targets, clutter and false alarms was derived in [12].The box-particle cardinality balanced multi-target multi-Bernoulli filter and its implementation was proposed in [13].…”

“…Reference [21] presents an implementation of box-particle filter on extended target. Various works have shown that the box-particle filter can reach a similar performance as the traditional particle filter with less computational complexity and runtime [11][12][13], [18].…”