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In this paper we address the problem of estimating the posterior distributionof the static parameters of a continuous time state space model with discretetime observations by an algorithm that combines the Kalman filter and aparticle filter. The proposed algorithm is semi-recursive and has a two layerstructure, in which the outer layer provides the estimation of the posteriordistribution of the unknown parameters and the inner layer provides theestimation of the posterior distribution of the state variables. This algorithmhas a similar structure as the so-called recursive nested particle filter, butunlike the latter filter, in which both layers use a particle filter, thisproposed algorithm introduces a dynamic kernel to sample the parameterparticles in the outer layer to obtain a higher convergence speed. Moreover,this algorithm also implements the Kalman filter in the inner layer to reducethe computational time. This algorithm can also be used to estimate theparameters that suddenly change value. We prove that, for a state space modelwith a certain structure, the estimated posterior distribution of the unknownparameters and the state variables converge to the actual distribution in $L_p$with rate of order $\mathcal{O}(N^{-\frac{1}{2}}+\delta^{\frac{1}{2}})$, where$N$ is the number of particles for the parameters in the outer layer and$\delta$ is the maximum time step between two consecutive observations. Wepresent numerical results of the implementation of this algorithm, inparticularly we implement this algorithm for affine interest models, possiblywith stochastic volatility, although the algorithm can be applied to a muchbroader class of models.

A Kalman particle filter for online parameter estimation with applications to affine models