Detection and estimation of changes in a polynomial-phase signal using the DPPT

This paper is concerned with on-line detection and estimation of changes in the parameters of a noisy polynomial-phase signal. This problem arises in vibration monitoring where the measured signals reflect both the nonstationarities due to the surrounding excitation, modelled by a polynomial-phase and the nonstationarities due to changes in the eigen structure, modelled by a break in the polynomial parameters. Development of a likelihood ratio test to detect and estimate changes in a polynomial-phase signal requires accurate estimation of the parameters vector after change, θ1. Use of the Maximum Likelihood Estimate (MLE) of θ1 is not practically useful since it involves the optimization of a multi-variable cost function. We propose to estimate θ1 by using the Discrete Polynomial-Phase Transform (DPPT) in order to derive a detector having asymptotically the same properties than the GLR one for a much lower computational cost. Experimental performances, mean delay to the detection as a function of mean time between false alarms, will be studied.