Instantaneous Frequency Estimation When the Amplitude is a Stochastic Process Using Stochastic Calculus and Bootstrapping

Stochastic calculus methods are used to estimate the frequencies of a polynomial sinusoid when the amplitude is modeled as an Ornstein-Uhlenbeck process. Using stochastic calculus, one is able to develop a stochastic differential equation that relates the observations to the frequencies. The likelihood function is obtained through Girsanov theory and the Radon-Nikodym derivative. Maximum likelihood estimates are obtained numerically using stochastic annealing. Bootstrapping is used to improve the estimate of the frequencies.