  Using Kalman techniques, it is possible to perform optimal estimation in
linear Gaussian state-space models. We address here the case where the noise
probability density functions are of unknown functional form. A flexible
Bayesian nonparametric noise model based on Dirichlet process mixtures is
introduced. Efficient Markov chain Monte Carlo and Sequential Monte Carlo
methods are then developed to perform optimal batch and sequential estimation
in such contexts. The algorithms are applied to blind deconvolution and change
point detection. Experimental results on synthetic and real data demonstrate
the efficiency of this approach in various contexts.
