An analysis of a new nonlinear estimation technique: The state-dependent Ricatti equation method

Research into nonlinear estimation techniques for terminal homing missiles has been conducted for many decades. The terminal state estimator, also called the guidance filter, is responsible for providing accurate estimates of target motion for use in guiding the missile to a collision course with the target. Some form of the extended-Kalman filter (EKF) has become the standard estimation technique employed in most modern weapon guidance systems. EKF linearization of nonlinear dynamics and/or measurements can cause problems of divergence when confronted by highly nonlinear conditions. The objective of this dissertation is to analyze a new nonlinear estimation technique that is based on the parameterization of the nonlinearities. This parameterization converts the nonlinear estimation problem into the form of a steady-state continuous Kalman filtering problem with state-dependent coefficients.; This new technique, called the state-dependent Ricatti equation filter (SDREF), allows the nonlinearities of the system to be fully incorporated into the filter design, before stochastic uncertainties are imposed, without the need for linearization.; The SDREF was investigated in three problems: an exoatmospheric, terminal homing, ballistic-missile intercept problem; a highly nonlinear pendulum example; and an algorithmic loss of observability problem.; The exoatmospheric guidance problem examined nonlinear measurements with linear dynamics. To investigate the SDREF when used with a combination of nonlinear dynamics and nonlinear measurements, a highly nonlinear, two-state pendulum problem was also examined.; While these problems were useful in gaining insight into the performance characteristics of the SDREF, no formal proof of stability could be determined for the original formulation of the estimator. The original SDREF solved an algebraic SDRE that arose from an infinite-time horizon formulation of the nonlinear filtering problem. A modification to the SDREF formulation was developed that led to a differential SDREF, and a proof for local asymptotic stability was achieved. The modification removed the infinite-time horizon assumption and integrated the coupled state-dependent state and covariance equations. This new form of the estimator is called the modified SDREF (MSDREF). A problem involving algorithmic loss of observability was then examined. This problem shows a performance advantage when using parameterization versus linearization as in the EKF technique.