Algorithm

Philosophy

Bayesian probability

Statistics

Telecommunications

Computer science

Adaptive beamformer

A priori and a posteriori

Beamforming

Signal processing

Pattern recognition (psychology)

Mathematics

Maximum a posteriori estimation

Epistemology

Artificial intelligence

Minimum-variance unbiased estimator

Probability density function

Maximum likelihood

Radar

Mean squared error

IEEE Transactions on Signal Processing

An adaptive beamformer that is robust to uncertainty in source direction-of-arrival (DOA) is derived using a Bayesian approach. The DOA is assumed to be a discrete random variable with a known a priori probability density function (PDF) that reflects the level of uncertainty in the source DOA. The resulting beamformer is a weighted sum of minimum variance distortionless response (MVDR) beamformers pointed at a set of candidate DOAs, where the relative contribution of each MVDR beamformer is determined from the a posteriori PDF of the DOA conditioned on previously observed data. A simple approximation to the a posteriori PDF results in a straightforward implementation. Performance of the approximate Bayesian beamformer is compared with linearly constrained minimum variance (LCMV) beamformers and data-driven approaches that attempt to estimate signal characteristics or the steering vector from the data.

A Bayesian approach to robust adaptive beamforming