Estimation Using Stochastic Feedback with Applications to Integrated Navigation Systems

This paper discusses an approach to linear estimation through use of a "control" fed back into the system to cancel out the effect of disturbances or error signals. Although this approach has very restricted application, it has found important usage in integrated navigation systems where one subsystem is an inertial measurement system. This approach is shown to be suboptimal and is compared with the optimal with respect to estimation accuracy and sensitivity to modeling errors. The feedback approach to estimation is shown to be similar to error estimation and correction in which the error states of the system are estimated and external correction applied. For discrete estimation using the feedback approach it is shown that error variance and Kalman gains for one-stage prediction should be used. Two examples are considered which compare the feedback approach to the optimum estimation approach. The system of the first example is quite simple, but provides simple analytical comparisons of the two estimation approaches. The second example system consists of a single-axis inertial guidance system and an independent position measuring system. Accuracy and sensitivity to modeling errors are compared. Other advantages and disadvantages of the two estimation approaches are discussed.