An optimal window length for the PWVD with application to passive acoustic parameter estimation

This paper considers the derivation of an optimal window length for the fourth-order polynomial Wigner-Ville distribution (PWVD₄ ), for the purpose of instantaneous frequency (IF) estimation. The optimal window length represents a compromise between the estimator IF error and statistical consistency. The criterion of optimality that we employ is the minimum mean square IF estimation error. The PWVD₄ optimal window length theory is then applied to the problem of estimating the time-varying acoustic IF of an over-flying aircraft. In the high SNR case, the windowed PWVD₄ is seen to provide a more accurate IF estimate than those given by the Wigner-Ville Distribution (WVD) and the short-time Fourier transform (STFT)