Performance bounds for tracking algorithms based on a time-varying third-order nonlinear model

The problem of deriving accurate algorithms for tracking of maneuvering targets is central in many applications, such as radar and sonar. Assuming that a certain model is indeed capable of describing the unknown system, it is still important to have a measure of the achievable accuracy. Clearly, the Cramer-Rao inequality has been applied to a large number of different parameterized models to obtain a lower bound of the variance of any unbiased estimate of the true system parameters. Also, in a tracking scenario it is of great interest to be able to quantify the best possible performance that can be achieved. For this purpose certain time-varying Cramer-Rao lower bounds, CRB´s are derived in the following. These bounds are based on the assumption of a third-order model which incorporates both time-varying and time-invariant parameters. In addition, possible measurement nonlinearities are taken into account. The so obtained CRB´s depend on not only the unknown filter parameters but also certain second-order statistics, namely the variance of the (presumedly random) target acceleration and the measurement noise. In general, it is of great importance to be able to quantify the impact of different values of these quantities, which typically are unknown in practice. The tracking behavior of the computationally efficient Recursive Prediction Error Method, RPEM based on the considered nonlinear three - state filter model, is examplified and compared to the CRB´s that have been derived here.