Adaptive probability hypothesis density filter for multi-target tracking with unknown measurement noise statistics

Abstract

Under the Gaussian noise assumption, the probability hypothesis density (PHD) filter represents a promising tool for tracking a group of moving targets with a time-varying number. However, inaccurate prior statistics of the random noise will degrade the performance of the PHD filter in many practical applications. This paper presents an adaptive Gaussian mixture PHD (AGM-PHD) filter for the multi-target tracking (MTT) problem in the scenario where both the mean and covariance of measurement noise sequences are unknown. The conventional PHD filters are extended to jointly estimate both the multi-target state and the aforementioned measurement noise statistics. In particular, the Normal-inverse-Wishart and Gaussian distributions are first integrated to represent the joint posterior intensity by transforming the measurement model into a new formulation. Then, the updating rule for the hyperparameters of the model is derived in closed form based on variational Bayesian (VB) approximation and Bayesian conjugate prior heuristics. Finally, the dynamic system state and the noise statistics are updated sequentially in an iterative manner. Simulations results with both constant velocity and constant turn model demonstrate that the AGM-PHD filter achieves comparable performance as the ideal PHD filter with true measurement noise statistics.

Robust Multi-Target Tracking with Integrated Knowledge Model, Graph Structures, and Statistical Analysis in Unobservable Environments

“…The PHD (Probability Hypothesis Density) filter is a type of multi-target Bayesian filter that is used to estimate the number and states of targets in a surveillance region [12]. It employs a moment approximation to make the filtering problem computationally feasible.…”

“…The equations (12) describe the prediction step of the Gaussian Mixture Probability Hypothesis Density (GMPHD) filter. Here, the predicted intensity function at time t, 𝑣 𝑡 (𝑥), is computed as the weighted sum of 𝐽 𝑡 Gaussian components, each with weight 𝑤 𝑡 (𝑖) and mean 𝑚 𝑡 (𝑖) and covariance matrix 𝑃 𝑡 (𝑖) :…”

An innovative method for scene recognition and target tracking for adaptive cruise control in complex traffic environment

“…17 The KF-based and its improved methods are the preferred and widely used techniques. 18–21 However, there are some disturbances of the sensor measurements and driving environment, 22 which will produce a bad robustness or tracking accuracy within some complex environment. To restrict the effect of exogenous disturbances, the H ∞ theory is the preferred tool.…”

Multiple‐model Gaussian mixture probability hypothesis density filter based on jump Markov system with state‐dependent probabilities

“…In principle, the GM-PHD filter does not provide the trajectory of a target, so several methods have been proposed to achieve data association and track management [10,11]. Since the performance of the GM-PHD filter could be degraded (possibly significantly) in a highly cluttered environment, some studies have focussed on tracking targets in a highly cluttered environment [12,13]. In addition, the occurrence of miss detection can also degrade the tracking performance.…”