EFFICIENT L-D FACTORIZATION ALGORITHMS FOR PDA, IMM AND IMMPDA FILTERS

Over the past twenty years, square-root factorization methods for Kalm an filtering have gained popularity due to increased numerical robustn ess and accuracy provided by these methods. However, square-root formu lations have not been developed for state-of-the-art tracking algorith ms, such as the probabilistic data association (PDA) (for tracking in clutter), interacting multiple model (IMM) (for tracking maneuvering t argets), and IMMPDA (for tracking maneuvering targets in clutter on tr ack formation). The only exception is the recent square-root implement ation of the probabilistic data association filter (PDAF) by Kenefic. We show that there is a substantially better implementation of the squ are-root PDAF than Kenefic's algorithm in terms of both numerical robu stness and computational efficiency. The computational savings of our algorithm are obtained by using successive L-D rank-one corrections in stead of the modified weighted Gram-Schmidt (MWG-S) technique for the overall covariance update. For the covariance prediction step, we pres ent an alternate implementation of the square-root version when the pr ocess noise covariance is time invariant, that requires successive L-D rank-one corrections obviating the need to use the computationally ex pensive MWG-S technique. On the average, the proposed algorithm for sq uare-root PDAF requires half the number of computations required by Ke nefic's algorithm. We extend the same approach to develop computationa lly efficient square-root algorithms for the IMM and IMMPDA filters.