Reduced orderfilters are generaUy biased, and the equations necessary to evaluate the bias, variance, and meansquare estimates in tradeoff analyses indicate that separation between estimation and control is not possible.
Summary--It is shown that a reduced order filter is in general biased. The equations necessary to evaluate the bias, variance, and mean square estimation error for a reduced order filter are presented. From these equations it can be observed that separation between control and estimation does not occur. The equations can be used for hardware tradeoff analysis, reduced order filter sensitivity analysis, and reduced order filter synthesis.
I. INTRODUCTION
THE KALMAN filter has been utilized in many applications throughout the last decade. These applications range from chemical processing plants to aerospace navigation and guidance [l-3]. In many of these applications the implemented filter did not behave as the theoretical analysis showed as its predicted behavior. Rather than achieving a degree of optimality, the filter diverged[4] causing an erroneous state estimate to be generated. This problem is due to several causes: erroneous state models including neglected biases, incomplete or erroneous knowledge of statistical models for filter derivation, nonlinearities, and roundoff and truncation errors [5,6]. With respect to the erroneous state model problem, many filter designs have been developed without due regard to additional states that arise because of error sources such as biases, first or higher order Markov processes driving the dynamic system and/or the measurement system. As is well known [7,8], one may use state augmentation techniques in order to take these errors into account. However, this may lead to a significant and perhaps intolerable state dimensionality if a fully optimal Kalman