Tracking a general, frequency modulated signal in noise

Abstract

A general, frequency modulated (GFM) signal characterizes the vibrations produced by compressors, turbines, propellers, gears and other rotating machines in a dynamic environment. A GFM signal is defined as the composition of a real or complex, periodic or almost periodic function (the carrier) with a real, differentiable function (the modulation). The paper develops a frequency domain tracking algorithm for a GFM signal in noise using the expectation-maximization (EM) algorithm. The primary advantage of this approach is the ratios (harmonic numbers) of the carrier function do not need to be known a priori. The tracking algorithm exploits knowledge of the noise spectrum so that a separate normalization procedure is not required. The noise spectrum is incorporated into the tracking algorithm in essentially the same way that a clutter or noise model is incorporated into the probabilistic multi-hypothesis tracking algorithm (PMHT). Consequently, the GFM signal tracking algorithm presented in this paper is a PMHT-style algorithm. The algorithm's performance is compared to two other algorithms from the literature using Monte Carlo trials and a simulated signal.