Use of interpolating functions in fast state estimation for dynamic systems with missing observations (Q920916)

This paper deals with the state estimation of discrete-time systems defined by \[ \{x(k+1)=f(k,x(k),w(k)),\quad z(k)=g(k,x(k),v(k)), \] where the state \(x(k)\in R^ m\), the observation \(z(k)\in R^ s\), both \(w(k)\in R^ n\) and \(v(k)\in R^ r\) are zero-mean noises with known statistics, f(\(\cdot)\) and g(\(\cdot)\) are given nonlinear functions. The estimation of x(k) is based on the missing observations z(\(\ell)\), where \(\ell\) takes only a part of the integers within (0,L]. Using a stack sequential decoding algorithm, the state model is approximated by a time-varying finite state machine: \(x_ q(k+1)=Q(f(k,x_ q(k),w_ d(k))\), \(k=0,1,...,L-1\). The proposed scheme is more practical and faster than the estimation scheme using the Viterbi decoding algorithm. Numerical simulations show the effectiveness of the scheme.