Maximum likelihood processing for arrays with partially unknown sensor gains and phases

This paper addresses the problem of source direction-of-arrival (DOA) estimation using a sensor array, where some of the sensors are perfectly calibrated, while others are uncalibrated. An algorithm is proposed for estimating the source directions in addition to the estimation of unknown array parameters such as sensor gains and phases, as a way of performing array self-calibration. The cost function is an extension of the maximum likelihood (ML) criteria that were originally developed for DOA estimation with a perfectly calibrated array. A particle swarm optimization (PSO) algorithm is used to explore the high-dimensional problem space and find the global minimum of the cost function. The design of the PSO is a combination of the problem-independent kernel and some newly introduced problem-specific features such as search space mapping, particle velocity control, and particle position clipping. This architecture plus properly selected parameters make the PSO highly flexible and reusable, while being sufficiently specific and effective in the current application. Simulation results demonstrate that the proposed technique may produce more accurate estimates of the source bearings and unknown array parameters in a cheaper way as compared with other popular methods, with the root-mean-squared error (RMSE) approaching and asymptotically attaining the Cramer Rao bound (CRB) even in unfavorable conditions.