A new sub-optimum estimation scheme is presented for multidimensional dynamic systems, the models of which can be any functions of states and arbitrary independent noises. This scheme depends upon the quantization of components of the state vector, blocks of state component sequences, hypothesis testing, and the Viterbi decoding algorithm. The state vector is sequentially estimated, component by component, in parallel and in blocks. The implementation of the scheme is achieved with a considerable memory reduction and is independent of time. Simulations, some of which are presented, have shown that the performance of the sub-optimum scheme is better than the performance of the extended Kalman filter for some non-linear models, whereas the performance of the scheme is almost as good as the performance of the Kalman filter for linear models with white gaussian disturbance and observation noises.