Maximum Likelihood Parameter Estimation in General State-Space Models using Particle Methods

A large number of time series can be described by nonlinear, non-Gaussian state-space models. While state estimation for these models is now routinely performed using particle filters, maximum likelihood estimation of the model parameters is much more challenging. In this paper, we present new numerical methods to approximate the derivative of the optimal filter. We use this to perform batch and recursive maximum likelihood parameter estimation and tracking by maximizing the likelihood through a gradient ascent method. We generalize the method to include the second derivative of the optimal filter. This provides estimates of the Hessian of the likelihood and can be used to accelerate the gradient ascent method.