ML estimation and CRB for narrowband AR signals on a sensor array

This paper considers the exploitation of temporal correlation in inci- dent sources in a narrowband array processing scenario. The MLE and CRB are derived for parameter estimation of spatially uncorre- lated first order Gaussian autoregressive source signals with additive Gaussian spatially and temporally uncorrelated sensor noise. These are compared to the MLE and CRB for the usual uncorrelated (WN) sources model. The paper deals with the case where the number of data snapshots is small. Numerical simulations show that (i) there is no significant performance gain in the correlated signal case, and sig- nificantly, (ii) the WN MLE performance does degrade in the pres- ence of source correlation, which appears to be in contrast to some recently published work. Other signals, which may possess smaller bandwidths, will thus gen- erally yield correlated samples at baseband. It is therefore natural to ask whether this correlation can be exploited in the design of an esti- mator for all incident signals' AoAs. Studies such as (7) have shown that the MLE designed for independent Gaussian data samples is ro- bust to the presence of temporal correlation in the signals' samples, however there are no detailed studies concerning the performance of the MLE designed specifically for correlated signals. Some results are available concerning the CRB for correlated signals, when the spatio-temporal source correlation matrix is known (5), and these re- sults show that the CRB for correlated sources is lower than that for uncorrelated sources. However for large number of data snapshots, the difference between these CRBs becomes smaller. The threshold- ing behaviour of the correlated sources MLE has not been studied. We are specifically interested in those processing scenarios where computational complexity is not a limiting factor and that compu- tationally intensive techniques such as the correlated sources MLE can be justified if better performance can be obtained. It should be pointed out at this stage, that a signal state-space based approach us- ing the Expectation-Maximisation (EM) algorithm for ML AoA esti- mation of general linear Gauss-Markov sources with known models, has been proposed in (8). This algorithm iteratively applies a fixed- interval Kalman smoother to perform estimation of the signals, and a likelihood based method using the resulting signal estimates to find the AoAs.