A Non-Markovian Prediction for the GM-PHD Filter Based on Recurrent Neural Networks

Bayesian multi-target filtering has become an essential signal processing technique for a plethora of applications, most prominently for radar, sonar, and image processing. It provides an automated way to study the dynamics of objects based on a set of carefully chosen process and sensor models. However, the estimation performance strongly depends upon the suitability of those models and a poor match between the true object behaviour and its describing model can lead to grave misinterpretations of the situation, especially in the presence of ambiguities or missed detections. Traditionally, analytic solutions such as the Near-Constant Velocity (NCV) or the Constant Turn (CT) models are selected to describe the target dynamics, often under the Markov assumption that disregards information before the current time step. In this paper, a Gaussian Mixture Probability Hypothesis Density (GM-PHD) filter is presented whose transition function is a Recurrent Neural Network with Long Short-Term Memory that is especially designed to predict a full Gaussian density. It is shown in simulation that the proposed method prevents the filter from overestimating the number of objects in the presence of false alarms or missed detections and helps resolve ambiguities when targets are close to each other.