Nonlinear filter problems arise in many applications such as communications and signal processing. Commonly used numerical simulation methods include Kalman filter method, particle filter method, etc. In this paper a novel numerical algorithm is constructed based on samples of the current state obtained by solving the state equation implicitly. Numerical experiments demonstrate that our algorit...

Using particle filter to figure visual object tracking, a key problem is to choose appropriate image features as the observation model. In this paper, we present a novel particle filter based object tracking framework via the combination of state and observation optimization. We apply the technique to articulated human movement tracking. Result demonstrates the effectiveness of our method in so...

We study the stability of the optimal filter w.r.t. its initial condition and w.r.t. the model for the hidden state and the observations in a general hidden Markov model, using the Hilbert projective metric. These stability results are then used to prove, under some mixing assumption, the uniform convergence to the optimal filter of several particle filters, such as the interacting particle fil...