Compressive sensing system and method for bearing estimation of sparse sources in the angle domain

Compressive Sensing (CS) is an emerging area which uses a relatively small number of non-traditional samples in the form of randomized projections to reconstruct sparse or compressible signals. Direction-of-arrival (DOA) estimation is performed with an array of sensors using CS. Using random projections of the sensor data, along with a full waveform recording on one reference sensor, a sparse angle space scenario can be reconstructed, giving the number of sources and their DOA's. Signal processing algorithms are also developed and described herein for randomly deployable wireless sensor arrays that are severely constrained in communication bandwidth. There is a focus on the acoustic bearing estimation problem and it is shown that when the target bearings are modeled as a sparse vector in the angle space, functions of the low dimensional random projections of the microphone signals can be used to determine multiple source bearings as a solution of an l]-norm minimization problem.