Recursive parametric tests for multichannel adaptive signal detection

The parametric Rao and generalized likelihood ratio test (GLRT) detectors, recently developed by exploiting a multichannel autoregressive (AR) model for the disturbance, has been shown to perform well with very limited or no training data. The AR model order, however, should be estimated by some model order selection technique. Standard non-recursive implementation of the parametric detectors is computationally intensive, since the parameters have to be estimated for each possible model order. This paper presents recursive versions of the parametric detectors using the multichannel Levinson algorithm, which is used to recursively solve the multichannel Yule-Walker equations and find parameter estimates used by these detectors. Estimation of the AR model order can also be naturally integrated since the multichannel Levinson algorithm yields parameter estimates at every recursion (i.e., for every AR model order). Numerical results show that the proposed recursive parametric tests that assume no knowledge about the model order perform quite close to the corresponding non-recursive parametric detectors at reduced computational complexity, even though the latter requires exact knowledge of the model order.