Rao-Blackwellization

Resources:

• page=99
• page=381

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A way of handling unlinearities in a system where only some states are unlinear by using a Particle Filter to estimate the nonlinear states, and a Kalman Filter on the linear states. This is more accurately known as a Rao-Blackwellized Particle Filter (RBPF), and is given by the general form

$$\begin{array}{rl}{x}_k^n& =f_k(x_{k-1}^n)+v_k^n\\ x_k^l& =A_k(x_{k-1}^n)x_{k-1}^l+v_k^l\\ z_k& =h(x_k^n)+C_k(x_k^n)x_k^l+w_k\end{array}$$

Where the noises are zero-mean Gaussian with covariances $Q^n$, $Q^l$ and $R$ respectively.