Functional Bayesian Filter

We present a general nonlinear Bayesian filter for high-dimensional state estimation using the theory of reproducing kernel Hilbert space (RKHS). By applying method and representer theorem to perform linear quadratic in functional space, we derive recursive estimator dynamical system original input space. Unlike existing extensions Kalman where dynamics are assumed known, state-space representation Functional Filter (FBF) is completely learned online from measurement data form an infinite impulse response (IIR) or recurrent network RKHS, with universal approximation property. Using positive definite function satisfying Mercer’s conditions compute evolve information quantities, FBF exploits both statistical time-domain about signal, extracts higher-order moments, preserves properties covariances without ill effects due conventional arithmetic operations. apply this novel adaptive filtering (KAF) training, chaotic time-series cooperative Gaussian non-Gaussian noises, inverse kinematics modeling. Simulation results show outperforms Kalman-based algorithms.