Joint detection/estimation for modal order selection in Gaussian and nonGaussian noise

The authors present a general approach to determining the number of sinusoids present in measurements corrupted by additive white Gaussian and nonGaussian noise. The approach involves the simultaneous application of maximum a posteriori detection and nonlinear estimation using either the extended Kalman filter when the noise is Gaussian, or the extended high order filter when the noise is nonGaussian. The problem is formulated as a multiple hypothesis testing problem with assumed known a priori probabilities for each hypothesis. The advantage of the approach lies in the potential to accommodate time-varying as well as time-invariant parameters in the measurement model. Experimental evaluation of the approach demonstrates excellent performance in selecting the correct model order and estimating the system parameters even for signal-to-noise ratios as low as -5 dB