State smoothing and filtering with stack sequential schemes for non-linear dynamic systems with an Nth-order memory

A stack sequential decoding algorithm is used estimate states of dynamic models with an Nth-order memory.The state at the future and observation at the present are linear or non-linear functions of the disturbance noise, the observation noise, and either the present or N - 1 past discrete values of the state. States are estimated by approximating the state model by a finite state machine and then using a stack sequential decoding algorithm of Information Theory. The proposed suboptimum scheme is faster and more practical than the estimation schemes using the Viterbi decoding algorithm.