Posterior Cramer-Rao lower bounds for bearing-only tracking

In the state estimation of passive tracking systems, the traditional approximate expression for the Cramer-Rao lower bound (CRLB) does not take two factors into consideration, that is, measurement origin uncertainty and state noise. Such treatment is only valid in ideal situation but it is not feasible in actual situation. In this article, considering the two factors, the posterior Cramer-Rao lower bound (PCRLB) recursion expression for the error of bearing-only tracking is derived. Then, further analysis is carried out on the PCRLB. According to the final result, there are four main parameters that play a role in the performance of the PCRLB, that is, measurement noise, detection probability, state noise and clutter density, amongst which the first two have greater impact on the performance of the PCRLB than the others.