Kernel Smoothing Conditional Particle Filter With Ancestor Sampling

We introduce a new method for simultaneous estimation of parameters and latent process dynamics in nonlinear and non-Gaussian state space models. Combining kernel smoothing, conditional particle filters, and ancestor sampling, our approach builds upon foundational insights from prior research. We dynamically adjust the kernel bandwidth using the Kullback-Leibler divergence criterion between the filtering and prediction distributions, ensuring robust exploration of the parameter space. This technique effectively addresses variance inflation issue and mitigates filter divergence and degeneracy. Furthermore, our method is versatile, compatible with a diverse range of kernels, broadening its applicability. It achieves competitive or superior performance while requiring significantly fewer particles than comparable methods, substantially reducing the computational load. Moreover, our approach can be extended to models with complex dependencies. Through comprehensive numerical simulations, we compare our method with current state-of-the-art algorithms, demonstrating that our approach achieves comparable, if not superior, performance while reducing the computational burden, particularly in high-dimensional settings.