Tracking the direction-of-arrival of multiple moving targets by passive arrays: asymptotic performance analysis Academic Article uri icon

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abstract

  • This thesis is focused on the topic of tracking multiple moving targets by combining the spatial and temporal information obtained by a passive array. For stationary sources a unified constrained subspace fitting approach for estimating the DOA's of spatially close source signals is presented. The algorithm is based on the Karhunen-Loève expansion of the covariance matrix of the array manifold in a sector of interest and searches for an optimal signal subspace over the array manifold space, which has minimum principal angles with the data signal subspace generated from the array data. This method is shown to be asymptotically consistent. Although this algorithm involves only one-dimensional researches, its performance is comparable to those in which multi-dimensional optimization is used.

    We propose a maximum likelihood approach for tracking moving targets by passive arrays. A locally linear model is used for the source target motion dynamics, and the target state is shown to be strongly observable. An MTS (multiple target state) vector is defined to describe the source target state. The maximum likelihood estimator is based on a batch of array data. The initial MTS is estimated as the maximizing point of the likelihood function of a batch of array data, and the subsequent MTS vectors are predicted by the target dynamics. Since the association problem is embedded in the estimation problem, the natural ordering of the target state is kept as long as the initial target DOA.'s can be successfully resolved by the array. To cope with difficulties involved in the nonlinear optimization process a modified Gauss-Newton algorithm is proposed in which the Hessian is approximated by a positive semi-definite matrix to guarantee that the algorithm is descent. The asymptotic performance analysis has also been fully investigated, We show that the ML estimates of the MTS variables are asymptotically consistent. We also derive explicit formulas for the asYIitptotic covariance and the Cramér-Rao bounds for the MTS estimates, and it is found that the ML estimator is relatively efficient. To show the effectiveness of the ML tracking technique we compare the asymptotic performance of the ML estimator with that of the extended Kalman filter (EKF). Its performance is superior to that of the EKF. Numerical results are provided to demonstrate the performance of the ML tracking technique via computer simulations.

publication date

  • 1999