Error assessment of the estimated coefficients obtained in system identification technique

System identification technique plays an important role in many electrical devices. In this technique, an adaptive filter models the unknown system with a Finite Impulse Response (FIR) or an Infinite Inverse Response (IIR) filter. This paper concentrates on the system identification technique based on the least squares criterion and evaluates the relationship between each estimated coefficient (obtained by the adaptive filter) and its corresponding coefficient in the unknown system. By logically classifying the variables, the amount of error between these two corresponding coefficients is evaluated and precisely expressed based on the auto-correlation lags of the input signal of the system and the coefficients of the unknown system. Also, the computed error is simplified for two particular cases in which the input signal of the system is an ideal zero-mean white Gaussian noise or a windowed (short-time) zero-mean white Gaussian noise. Experimental results provided in the simulation part verify the arithmetic expressions presented in the paper.