The notched probabilistic data association filter

A new approximation of the Bayes posterior target process for the tracking of a known number of targets is presented. The new method approximates the multi-target probability density function (pdf) of the Bayes posterior process as the product of single target pdfs where, each individual single target pdf is calculated conditioned on the best estimate of the states of other existing targets. The exact pdf of an individual target conditioned on the states of other existing targets is derived for the two and three interacting target cases. For problems that involve more than three interacting targets, an approximation for the conditional target pdf is derived. In a numerical study, the new approximation is compared to the joint probabilistic data association filter (JPDAF). In comparison to the standard JPDAF, the proposed method exhibits lesser bias, lesser tracking error and is especially better in handling the separation of targets.