Multi-component IF estimation

An adaptive approach to the estimation of the instantaneous frequency (IF) of non-stationary mono- and multi-component FM signals with additive Gaussian noise is presented. It is shown that the bias and variance of the IF estimate are functions of the lag window length. If there is a bias-variance trade-off, then the optimal window length for this tradeoff depends on the unknown IF law. Hence an adaptive algorithm with a time-varying and data-driven window length is needed. The adaptive algorithm can utilize any quadratic time-frequency distribution that satisfies certain conditions. A quadratic distribution that is most suitable for this approach is proposed. The algorithm estimates multiple IF laws by using a tracking algorithm for the signal components and utilizing the property that the proposed distribution enables non-parametric component amplitudes estimation. An extension of the proposed TFD consisting in the use of time-only kernels for adaptive IF estimation is also proposed