State estimation using the reduced sufficient statistics algorithm

Ronald A. Iltis

doi:10.1117/12.279525

29 October 1997 State estimation using the reduced sufficient statistics algorithm

Ronald A. Iltis

Proceedings Volume 3163, Signal and Data Processing of Small Targets 1997; (1997) https://doi.org/10.1117/12.279525
Event: Optical Science, Engineering and Instrumentation '97, 1997, San Diego, CA, United States

Abstract

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.

Citation Download Citation

Ronald A. Iltis "State estimation using the reduced sufficient statistics algorithm", Proc. SPIE 3163, Signal and Data Processing of Small Targets 1997, (29 October 1997); https://doi.org/10.1117/12.279525

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