Optimal source localization and tracking using arrays with uncertainties in sensor locations
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We develop a computationally efficient iterative algorithm for source localization and tracking using active/passive arrays with uncertainties in sensor locations. We suppose that the available data consist of time delay, or differential time delay, measurements of the signal wavefront across the array. We consider a general senario in which the array uncertainties may be correlated in time and in space. The proposed algorithm is optimal in the sense that it converges montonically to the Maximum Likelihood (ML) estimate of the source trajectory parameters. In the case of multiple sources, the algorithm makes an essential use of the information available from all sources to reduce the array uncertainties (the so-called array callibration) and thus to improve the localization accuracy of each signal source. We also derive new expressions for the log-likelihood gradient, the Hessian, and the Fisher's information matrix, that may be used for efficient implementation of gradient based algorithms, and for assessing the mean square error of the resulting ML parameter estimates.
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