Stochastic approximation based PCA and its application to identification of EIV systems

The stochastic approximation based principal component analysis (SAPCA) algorithm is introduced to recursively estimate the eigenvectors and the corresponding eigenvalues of a symmetric matrix A based on observations A
_k
= A + ε
_k
with ε
_k
→ 0 as k → ∞. The estimates are strongly consistent. The SAPCA algorithm is then applied to identifying the matrix coefficients of the multivariate errors-in-variables (EIV) systems, and the estimates are also strongly consistent. The performance of SAPCA algorithm is testified by a simulation example.