The application of sum-product algorithm for data association

Data association uncertainty occurs when remote sensing devices yield measurements whose origin is uncertain, which is a fundamental problem in target tracking. Based on the number of modes involved, data association can be divided into single-mode data association and multiple-mode data association, the latter of which needs to address the additional uncertainty of measurement-to-mode association (mode association), apart from the uncertainty of target-to-measurement association. This paper formulates the data association problem as a graphical model with three different cases including single target single mode (STSM), multiple targets single mode (MTSM) and multiple targets multiple modes (MTMM), and utilizes the sum-product algorithm to approximate the marginal probability of the association matrix. Some toy examples are used to demonstrate the effectiveness of the sum-product algorithm.