# Probabilistic Estimation of Instantaneous Frequencies of Chirp Signals

arXiv: https://arxiv.org/abs/2205.06306 · HTML: https://mlsanity.com/paper/2205.06306/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 31 references that are in the map.
- First posted on arXiv 12 May 2022.

## Builds on (most cited first, 5 of 5)

- [Deep State-Space Gaussian Processes](https://mlsanity.com/paper/2008.04733/) (2020)
- [Taylor Moment Expansion for Continuous-Discrete Gaussian Filtering and Smoothing](https://mlsanity.com/paper/2001.02466/) (2020)
- [State-space deep Gaussian processes with applications](https://mlsanity.com/paper/2111.12604/) (2021)
- [On stability of a class of filters for non-linear stochastic systems](https://mlsanity.com/paper/1809.05667/) (2018)
- [Bayesian Pitch Tracking Based on the Harmonic Model](https://mlsanity.com/paper/1905.08557/) (2019)

## Abstract (arXiv)

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.