An adaptive tracking algorithm for direction finding and array shape estimation in a nonstationary environment

This paper presents an adaptive tracking algorithm for the subspace-based direction of arrival estimation of multiple sources in a nonstationary, environment. The nonstationarities are due to moving sources or to timevarying distortions of the sensor array shape. The proposed algorithm relies on the properties of a linear operator, referred to as the Propagator, which only exploits the linear independency of the source steering vectors. The Propagator allows not only the calibration of the array shape, but also the determination of the source and the noise subspaces without any eigendecomposition of the cross-spectral matrix of the received signals. A gradientbased adaptive algorithm is here proposed for the on-line estimation of the Propagator. A theoretical analysis of the behaviour of this algorithm in a nonstationary environment is given. Simulations are carried out in the case of moving sources and in the case of a time-varying array shape. They exhibit the good performances of the proposed algorithm.