Target tracking formulation of the SVSF as a probabilistic data association algorithm

Abstract

Target tracking algorithms are important for a number of applications, including: physics, air traffic control, ground vehicle monitoring, and processing medical images. The probabilistic data association algorithm, in conjunction with the Kalman filter (KF), is one of the most popular and wellstudied strategies. The relatively new smooth variable structure filter (SVSF) offers a robust and stable estimation strategy under the presence of modeling errors, unlike the KF method. The purpose of this paper is to introduce and formulate the SVSF-PDA, which can be used for target tracking. A simple example is used to compare the estimation results of the popular KF-PDA with the new SVSF-PDA.

Automotive Tracking Technique Using a New IMM Based PDA-SVSF

“…To deal with the data association uncertainty, the formulation of the PDA-SVSF is presented [14]. The PDA-SVSF is basically formulated for tracking single target in clutter.…”

“…Therefore, one can define , + 1 distinct association hypotheses at the time for these candidate measurements as follows [1,14]:…”

“…where ̂| i is the updated state given that the th hypothesis is correct and i is the corresponding association probability and calculated as follows [3,2,14]. 15) where is the gate probability [2], is the target detection probability and ℒ is the likelihood ratio of the measurement , if it is originated from the target, which is calculated as follows.…”

“…Assuming that the PDA-SVSF track is formed and there are imbedded models, the IMM-PDA-SVSF algorithm includes the following steps [1,14] 4. Updating the model probabilities: …”

“…In particular, due to its inherent robustness to modeling uncertainties and disturbances, the SVSF is an appropriate candidate for target tracking in clutter problems. In [14] a formulation of SVSF based PDA, namely PDA-SVSF, is proposed for single target tracking in the presence of measurement origin uncertainty. An extension of the method for multiple-target tracking is proposed in [15].…”