Student’s t-Based Robust Poisson Multi-Bernoulli Mixture Filter under Heavy-Tailed Process and Measurement Noises

Abstract

A novel Student’s t-based robust Poisson multi-Bernoulli mixture (PMBM) filter is proposed to effectively perform multi-target tracking under heavy-tailed process and measurement noises. To cope with the common scenario where the process and measurement noises possess different heavy-tailed degrees, the proposed filter models this noise as two Student’s t-distributions with different degrees of freedom. Furthermore, this method considers that the scale matrix of the one-step predictive probability density function is unknown and models it as an inverse-Wishart distribution to mitigate the influence of heavy-tailed process noise. A closed-form recursion of the PMBM filter for propagating the approximated Gaussian-based PMBM posterior density is derived by introducing the variational Bayesian approach and a hierarchical Gaussian state-space model. The overall performance improvement is demonstrated through three simulations.

Adaptive Multi-Hypothesis Marginal Bayes Filter for Tracking Multiple Targets

“…In the experiment, parameters v min and v max in (7) are set to v min = 5ms −1 and v max = 50 ms −1 ; the number of hypotheses in the AMHMB filter is set to K = 30, and its other parameters are ρ τ = 0.5, τ 1 = τ 2 = 10 −5 , and τ 3 = 4; and the other parameters of the AAMMTB filter, AGLMB filter, and AGLMB1 filter are identical to those in Ref. [35], Ref.…”

“…Multi-target tracking (MTT) is a process that uses the sensor observations with clutter, missed detection, and noise to acquire the state vectors of targets at different time steps [1][2][3]. It finds numerous applications in maritime surveillance, air traffic monitoring, self-driving vehicles, and advanced driver-assistance systems [4], thereby attracting the extensive attention of scholars [5][6][7][8][9]. Many approaches such as random finite set (RFS) [1,2], multiple hypothesis tracking [10], and joint probabilistic data association [11] have been proposed to perform multi-target tracking.…”

Filtering in Triplet Markov Chain Model in the Presence of Non-Gaussian Noise with Application to Target Tracking

“…In general, these strategies can be divided into three categories [23]. The first uses heavy-tailed distributions to model non-Gaussian noise, such as the most commonly used t-distribution [5,11,12,24]. However, unlike the Gaussian distribution, the t-distribution is difficult to analytically handle, resulting in the corresponding filtering algorithms not having a closed form solution.…”

Multi-Hypothesis Marginal Multi-Target Bayes Filter for a Heavy-Tailed Observation Noise

“…Multi-target tracking (MTT) is the process of estimating the states of multiple moving targets at different time steps according to a set of sensor observations. It has received extensive attention from scholars [1][2][3][4][5][6][7][8] due to its wide application in many real systems, such as intelligent transportation systems, video surveillance systems, radar tracking systems, etc. Two major groups of MTT algorithms have been reported in a lot of articles [9][10][11][12][13][14][15][16][17][18].…”