Pseudorandom Maximum Length Signal Design with Bias Compensation Least Squares Estimation for System Identification

The effect of input and output noise towards the identification of the best linear approximation of a system is investigated. This leads to the problem of errors-in-variables (EIV). The effectiveness of one particular EIV method, namely the bias compensation least squares estimation method, is analyzed, with simulations carried out on a first order bilinear system. It is shown that the use of perturbation signals with carefully selected harmonic properties can lead to significant improvements in the estimation of the best linear approximation of the system. In particular, a spectrum that is sparser but having a larger magnitude at the nonzero harmonics is found to be more robust towards the effect of noise.