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A Combined Order Selection and Parameter Estimation Algorithm for Coupled Harmonics

The problem of estimating the fundamental frequency and the amplitudes and phases of corresponding harmonics is considered. Many battlefield vehicles generate coupled harmonic acoustics. These features are useful in tracking and classifying battlefield targets. As discussed in [1], harmonic line association (HLA) is a feasible approach to target identification in single or multiple target scenarios. In addition, the harmonic line estimates may be useful in improving target tracking and counting. For distributed sensor networks, the harmonic line estimates can also be used in conjunction with direction-of-arrival (DOA) estimates to separate targets temporally and spatially. Once the coupled harmonic parameters are estimated, the residual allows any broadband energy to be exploited. This work investigates the case with a single source generating frequency coupled harmonics in the presence of Gaussian noise. The parameters of coupled harmonics are estimated using nonlinear least-squares (NLS). Previous works have assumed the number of harmonics is known [2, 3, 4, 5]. In this work, as with [6, 7], the number of harmonics is assumed unknown. The NLS method is combined with order selection methods (such as Rissanen’s minimum description length (MDL) [8]), to generate statistically efficient estimates in white and colored noise.