  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.
