Description of a Program for Kalman Filtering and Rauch Smoothing Techniques Applicable to Nonlinear Systems with Continuous Evolution and Discrete Observation Models

摘要

The theory of Kalman filtering and Rauch smoothing when applied to dynamic systems whose evolution is governed by a nonlinear, continuous, differential equation and which are observed by a nonlinear discrete time equation is outlined. The FIKALM and LIRAUC subroutines which estimate the state and the characteristics of a dynamic system modeled by these equations are described. Automatic elimination of aberrant measurements, by comparing the predicted observation with the real observation, avoid preprocessing untreated measurements. The restoration, on smoothing, of a pseudocontinuous evolution noise, an observation residue and the estimation of their covariance matrices allows verification of the validity of the a priori evaluation of the noise levels on the evolution and observation. The trajectory and longitudinal attitude of an aircraft are estimated from radar observations.