The utilization of data measurement residuals for adaptive kalman filtering

In recent years the Kalman filter has been utilized extensively for passive target motion analysis (TMA). Unfortunately, in these applications divergence is a common problem. Available methods for eliminating divergence ultimately involve increasing filter sensitivity by discounting the influence of past data. However, this procedure makes the filter more susceptible to random errors; therefore to avoid unnecessarily sacrificing noise performance, adaptive control is required. In this paper the Kalman filter equations are derived and the associated data measurement residuals are examined to determine their suitability for providing adaptive control. An important relationship between the system performance index and the data residuals is established. By exploiting this relationship, pertinent statistical properties of the performance index are deduced and are subsequently utilized as a basis for formulating practical adaptive control criteria. A simulated example is presented to demonstrate divergence (e. g., tracking of a maneuvering target) and significant improvement in performance is noted when adaptive control is appended.