Cramer-Rao bound for nonlinear filtering with Pd<1 and its application to target tracking

The paper investigates the Cramer-Rao bound for discrete-time nonlinear filtering in the case where the probability of detection of a sensor is less than unity. The theoretical formula involves the evaluation of exponentially growing number of possible miss/detection sequences. An approximation of the theoretical bound for practical applications, such as target tracking, where the number of sensor scans is large, is proposed. An application of the developed techniques to the well-known filtering problem of tracking a re-entry ballistic object is also presented