Maximum entropy source bearing estimation

Abstract

Results of a simulation study of the application of the complex one-dimensional maximum entropy spectral analysis algorithm to the problem of source bearing estimation using a linear array are reported. The rms error in the source bearing estimates was observed to increase with decreasing signal-to-noise ratio (SNR), when the model order (p) approached the number of array elements (N), and when the source of interest was not well resolved from adjacent sources. Typical rms errors observed (for p = N/2) were 0.1 λ/D at an SNR of 10 dB, 0.2 λ/D at 0 dB, and 0.5 λ/D at −6 dB. The statistical variability and number of spurious peaks in the array response were observed to increase rapidly as p approached N. At SNR less than 0 dB the array response, even when averaged over 50 independent data sets, indicated numerous spurious sources when the model order was large. The equivalent number of degrees of freedom (df) of the array response, estimated as twice the square of the average divided by the variance of the response, were calculated and compared with df = N/p as conjectured by Parzen. Parzen's conjecture was consistent with the observed results for p ≪ N, but was found to be very optimistic at high model orders.