The posterior or Bayesian Cramer-Rao bound (BCRB) on the mean square error in tracking a moving target is developed based on the nonlinear filtering bound developed by Tichavsky et al (1998) and analyzed by Ristic et al (2004). The formulation uses a linear process model with additive Gaussian noise and a general non-linear measurement model, where the measurements are sensor array data. The bound is first applied to the problem of tracking the position and velocity of a moving target in a multistatic radar system. The result is an error bound ellipse that evolves as the target moves along its trajectory. The bound is also applied to the problem of tracking the bearing, bearing rate, and power level of a narrowband source in a passive sonar system and compared against simulated performance of several tracking algorithms. The recursive BCRB provides an efficient technique to analyze various system design trade-offs and serves as a benchmark for comparing tracking algorithms.