Dimensionality Reduction of State-Space Model Based on Projection Theory and Orthogonalization

A new setting method was proposed for state space system, being able to estimate state space directly without increasing the dimension of state variables when a lagged state variable existed in measurement equation. The improved state-space system can be estimated still by the regular Kalman filter and have a strongly improvement in point estimate. Moreover, the Durbin and Koopman(D-K) sampling methodology can be utilized to smooth the state variable for Kalman smoother. A simulation experiment of the improved state-space system and comparison with the traditional method were conducted. The results show that, when in point estimation, the value of two systems is almost the same, but the improved model can reduce the computational time. Furthermore, D-K method seems more efficient comparing with the Kalman smoother, validating the efficiency of the posed method.