All ordinary polynomials have series expansion of orthogonal polynomials, while Legendre polynomials, Hermite polynomials and Laguerre polynomials are special orthogonal polynomials.

This paper proved that a frequency stochastic sequence obtained from a stationarily correlated time series by using discrete Fourier transform is orthogonal.

The idea of the filter is to make discrepancy orthogonal at each step and get useful information from the discrepancy series as current state estimation.