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, θ
1
. Use of the Maximum Likelihood Estimate (MLE) of θ
1
is not practically useful since it involves the optimization of a multi-variable cost function. We propose to estimate θ
1
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.