Stochastic System Analysis and Bayesian Model Updating

Introduction: In the case that the state-space model class is nonlinear, Kalman filter and RTS smoother breaks down. Although it is always possible to linearize the nonlinear model so that Kalman filter and RTS smoother can still apply approximately, they can be not reliable. On the other hand, stochastic simulation approaches are not limited to linear model classes and can be adopted to draw samples of the state conditioning on the observation even if the model is nonlinear. One of such stochastic simulation approaches is called particle filter. Let’s now consider a more general version of state-space equations: ( ) ( ) 1 , , , , k k k k k k k k k k X X u W Y X u V φ φ − = =