Performance bounds for GMTI tracking

The Posterior Crame'r-Rao Lower Bound (PCRLB} is defined to be the inverse of the Fisher information matrix, and provides a bound on the optimal achievable accuracy of target state estimation. In this paper we derive the PCRLB for tracking road-based vehicles using ground moving target indicator (GMTI} sensors. Calculating the PCRLB represents a challenging problem because we must take into account the structure of the road network and the concomitant constraints it applies to the target motion. In this case no analytical closed form solution for the PCRLB exists, but we are able to derive the bound via Monte Carlo simulation. However; we demonstrate that the PCRLB is over-optimistic, which could be a result of the potential multi-modality of the target distribution at each junction. In the second half of this paper we introduce an altemative performance measure (APM} for GMTI tracking that resembles the error covariance of an extended Kalman filter with measurements linearised around the true target state and known target manoeuvres. This performance measure is proven to be less optimistic than the PCRLB. Moreover; of greater importance, the APM is shown to accurately predict the peflormance of the state-of-the-art variable structure, multiple model particle jltel:

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