State Estimation with Small Non-Linearities.
STANFORD UNIV CALIF DEPT OF AERONAUTICS AND ASTRONAUTICS
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A variety of techniques are available for estimating the states of non-linear dynamic systems from noisy data. These procedures are generally equivalent when applied to linear systems. This report investigates the difference between several of these procedures in the presence of small dynamic and observational non-linearities. Four discrete estimation algorithms are analyzed. The first is a strictly least square estimator, while the other three are recursive algorithms similar to the Kalman filter used for estimating the states of linear systems. The product of this research is a group of analytic expressions for the mean and covariance of the error in each of those estimators so that they may be compared without lengthy Monte-Carlo simulations. The covariance expressions show that, to first order, all the estimators have the same covariance. Expressions for the means, however, show that each estimator has a different bias. Several examples are carried out demonstrating that the relative magnitudes of the bias errors in the various estimators can be a strong function of such parameters as initial covariances and number of data points being considered. In fact, under some circumstances it appears that more complicated seemingly superior algorithms can have larger biases than smaller ones. Author
- Statistics and Probability