An approximate maximum likelihood algorithm for direction finding with diversely polarized arrays

Improved direction-finding (DF) performance may be realized by employing a diversely polarized antenna array. However, maximum likelihood (ML) DF algorithms for such an array have greater computational complexity than those for a uniformly polarized array with the same number of antenna elements. In particular, the dimension of the nonlinear search embedded in ML estimation of azimuth and elevation is twice as large with a diversely polarized array as with a uniformly polarized array. While ML is a practical and powerful technique for small search dimensions, it rapidly becomes intractable as the dimension increases. The authors propose a new approximate maximul likelihood (AML) algorithm for reduced-complexity direction finding with diversely polarized arrays. The AML algorithm eliminates the polarization dimensions by incorporating a suboptimal but effective polarization estimate into the exact likelihood function. Optimization of the resulting approximate likelihood function requires half the search dimension of the exact likelihood function. To assess the performance of the AML algorithm, the authors develop an approach for measuring the sensitivity of the estimator to errors in the sensor covariance matrix; these errors may result from model mismatch, finite integration time, or other factors. The approach is applicable to a large class of parameter estimators that maximize a differentiable objective function of the parameters and the data. The authors derive numerically a sensitivity matrix that maps perturbations of the covariance matrix onto perturbations of the estimated directions. They analyze the sensitivity matrix to compare the performance of Schmidt´s MUSIC method, the exact ML method, and the AML method for a simulated scenario with two sources of arbitrary correlation and polarization. The results show that the proposed AML algorithm typically performs as well as ML and, that both ML and AML often perform much better than MUSIC. The AML algorithm is an attractive alternative to ML, obtaining comparable DF performance from a diversely polarized array with reduced computational complexity