A Window-based Tensor Decomposition Approach to Data-Association for Multi Target Tracking

Traditional observation-to-track data association algorithms, such as Bayesian methods, suffer from exponential growth in computational complexity with increase in a number of targets, especially in dense environments with low signal-to-noise ratio. This paper utilizes tensor decomposition, a commonly used technique to tackle “curse of dimensionality” in high dimensional applications, to reduce the aforementioned complexity in data association problems. The Joint Probabilistic Data Association (JPDA) is a pseudo-Bayesian sub-optimal filter that lends itself to be modified within the framework of incremental tensor decomposition to reduce its computational burden resulting from computing the probabilities of noncompeting join association events or “feasible events”. The number of feasible events is reduced by a using a “core” tensor instead of the complete set of measurements received at a specified instance in time. Furthermore, to reduce computational overhead while performing decomposition, many such measurements are combined into “batches”. The “core” tensor is obtained from Dynamic Tensor Analysis (DTA). This reduction in computational burden from the new tensor based JPDA method when compared to the traditional JPDA method is demonstrated via a numerical example of a Space Situational Awareness Problem (SSA).