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.

翻译：我们提出了一种连续时间概率方法，用于在无法获取啁啾信号及其瞬时频率函数真实形式时对其进行估计。该模型通过非线性级联的高斯过程（以非线性随机微分方程形式表示）来表征这些函数。随后，利用随机滤波和平滑器估计函数的后验分布。我们计算了该高斯过程模型的（后验）克拉美-罗下界，并推导了均方意义下估计误差的理论上界。实验表明，所提方法在合成数据上的性能优于多种现有先进方法。同时，该方法在两个真实世界数据集上可直接应用。