We present a probabilistic approach for estimating chirp signal and its instantaneous frequency function when the true forms of the chirp and instantaneous frequency are unknown. To do so, we represent them by joint cascading Gaussian processes governed by a non-linear stochastic differential equation, and estimate their posterior distribution by using stochastic filters and smoothers. The model parameters are determined via maximum likelihood estimation. Theoretical results show that the estimation method has a bounded mean squared error. Experiments show that the method outperforms a number of baseline methods on a synthetic model, and we also apply the method to analyse a gravitational wave data.

翻译：我们提出一种概率方法来估计正正弦信号及其当量和瞬时频度的真实形式未知时的瞬时频率功能。 为此,我们通过非线性蒸汽微分方程式管理的联合累加高西亚进程来代表它们,并通过使用随机过滤器和滑动器来估计其后部分布。模型参数是通过最大可能性估计确定的。理论结果显示,估计方法有一个界限平均正方形错误。实验显示,该方法在合成模型上优于若干基线方法,我们还运用该方法分析引力波数据。