A framework for subspace identification methods

Similarities and differences among various subspace identification methods (MOESP, N4SID and CVA) are examined by putting them in a general regression framework. Subspace identification methods consist of three steps: estimating the predictable subspace for multiple future steps, then extracting state variables from this subspace and finally fitting the estimated states to a state space model. The major differences among these subspace identification methods lie in the regression or projection methods used in the first step to remove the effect of the future inputs on the future outputs and thereby estimate the predictable subspace, and in the latent variable methods used in the second step to extract estimates of the states. The paper compares the existing methods and proposes some new variations by examining them in a common framework involving linear regression and latent variable estimation. Limitations of the various methods become apparent when examined in this manner. Simulations are included to illustrate the ideas discussed.