New Formulation and Solution to the Navigation State Vector Estimation Problem

Charles Shapiro

Abstract:	When the states vector estimation problem is formulated in terms of probability and statistics all modern single cycle recursive filters can be seen to have the same fundamental theoretical flaw, they continuously approximate the posterior probability density function of the state vector by the Gaussian distribution defined by the filters estimate and covariance matrix. For many estimation problems this Gaussian approximation is justified, however whenever there is a need to “tune the filter” these Gaussian approximations are probably not justified and these problems would be better solved by an estimation methodology that has no theoretical flaws. This paper describes such a state vector estimation methodology that does not require the propagation of the posterior probability density function and is based on three fundamental premises: (1) There exists a derivable deterministic expression for the posterior probability density function of the state vector at any instant of time which encompasses all the information contained in the estimation problem, (2) the implementation of the algorithm should be based on calculating a value for the state vector that is sufficiently close to maximizing this probability density function , (3) the implementation of the algorithm needs to satisfy the systems real-time computer requirements. Presented is a statistical theory that supports a general derivation of the expression for the probability density function which employs classical nonlinear least squares parameter optimization concepts, but with significant extensions, and the Kalman covariance matrix concept to represent that portion of the past data not being processed. This methodology is applicable to real-time nonlinear estimation problems that contain stochastic dynamic processes and sensor measurement errors that have colored and/or white noise statistics. Given today’s computer technology this methodology should be able to provide significantly superior solutions to many navigation estimation problems.
Published in:	Proceedings of the 2004 National Technical Meeting of The Institute of Navigation January 26 - 28, 2004 The Catamaran Resort Hotel San Diego, CA
Pages:	840 - 861
Cite this article:	Shapiro, Charles, "New Formulation and Solution to the Navigation State Vector Estimation Problem," Proceedings of the 2004 National Technical Meeting of The Institute of Navigation, San Diego, CA, January 2004, pp. 840-861.
Full Paper:	ION Members/Non-Members: 1 Download Credit Sign In