Perturbation analysis of regularized ESPRIT for noncircular signal direction finding with one solitary acoustic vector-sensor

In this contribution, the perturbation analyses of both the norm-penalized regularized ESPRIT and the subspace-constraint regularized ESPRIT devised for single-acoustic-vector-sensor direction finding of multiple noncircular signals are provided. It is shown that the norm-penalized regularized ESPRIT is biased (but bounded) and have a minimum mean-squared-error (MSE) for some finite regularization factor whereas the subspace-constraint regularized ESPRIT is unbiased and its MSE approaches minimum when the regularization factor becomes infinite. This observation is potentially useful for the determination of regularization parameters. Simulation results are also given to validate the analyses.