Probabilistic Estimation of Instantaneous Frequencies of Chirp Signals

TL;DR

This paper introduces a probabilistic method using Gaussian processes and stochastic filtering to estimate the instantaneous frequency of chirp signals, outperforming existing techniques on synthetic and real data.

Contribution

It develops a novel continuous-time probabilistic framework with theoretical bounds for accurate chirp signal frequency estimation.

Findings

Outperforms state-of-the-art methods on synthetic data

Works effectively on real-world datasets without tuning

Provides theoretical bounds for estimation error

Abstract

We present a continuous-time probabilistic approach for estimating the chirp signal and its instantaneous frequency function when the true forms of these functions are not accessible. Our model represents these functions by non-linearly cascaded Gaussian processes represented as non-linear stochastic differential equations. The posterior distribution of the functions is then estimated with stochastic filters and smoothers. We compute a (posterior) Cram\'er--Rao lower bound for the Gaussian process model, and derive a theoretical upper bound for the estimation error in the mean squared sense. The experiments show that the proposed method outperforms a number of state-of-the-art methods on a synthetic data. We also show that the method works out-of-the-box for two real-world datasets.