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Analysis and Extension of Lumped Parameter Nonlinear Estimation Algorithms,
AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OHIO SCHOOL OF ENGINEERING
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The system considered in this investigation is assumed to be modeled by a continuous nonlinear stochastic differential equation observed at discrete intervals by a nonlinear observation equation with additive noise. Becuase of the restrictions placed upon the stochastic differential equation, the Ito and Stratonovich interpretations are equivalent and the rules of ordinary calculus are used. Two second order filters with second order truncation of Taylor series nonlinear function representation and second central moment truncation of probability density function representation are presented. Their truncation and roundoff errors are analyzed. A perturbation form of second order filter is derived in order to reduce algorithm sensitivity to roundoff errors. A power series perturbation analysis about an arbitrary unspecified nominal trajectory is used to derive a new second order perturbation filter which is capable of accepting various deterministic nominal trajectories between discrete observations. Author
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