State estimation using the reduced sufficient statistics algorithm
R.A. Iltis · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1997
The reduced sufficient statistics (RSS) algorithm was originally developed by Kulhavy for parameter estimation only. Here, we present a modified form of the RSS algorithm which recursively computes a model posterior probability density function for the state vector. The model density is chosen to be a multidimensional Haar basis representation with dyadic scale, such that the basis functions are disjoint hypercubes. It is then shown that the model density coefficients can be obtained in closed form for this choice of basis functions. A critical part of the modified RSS algorithm is the approximation of the one-step predicted density for the state vector. It is shown that when the transition density for the state vector also has dyadic scale, that a closed-form recursion is ultimately obtained for both predicted and filtered approximating densities. Finally, an application of the algorithm to target tracking using bearings-only measurements is given.