Information-based performance measures for model-based estimation

Abstract

Classical estimation is conventionally evaluated via the Cramer-Rao Lower Bound on the estimate. When prior information is available, Bayesian estimation can be used if this information is available in statistical form. However, when the prior information is in the form of a physical model, such as in a tracking scheme, it is not clear how much improvement will be provided, since it is not in statistical form. Here it is shown how this problem can be dealt with using the Fisher information matrix by introducing the model into a Kalman estimator. Since the state error covariance provided by a steady-state Kalman estimator is the inverse of the Fisher matrix, it directly provides a statistical measure of the information provided by the model. Then by relating the Fisher information matrix to the Kullback-Liebler distance, it is shown how the Fisher matrix is scaled to provide its information in bits. The model can then be evaluated as to how much information it provides to the estimator. An example using a moving towed array as a bearing estimator will be presented. It will be quantitatively shown that inclusion of the array motion in the estimator will improve the estimation performance