Fixed point error analysis of the normalized ladder algorithm

In this paper, an attempt is made to analyze the fixed point error performance of the normalized ladder algorithm for autoregressive system identification, assuming rounding arithmetic. The paper contains two main results; i) A simplified theoretical expression for predicting the average bias in the estimated reflection coefficients at any stage, and ii) a recursive relation for the average error, arising from finite precision arithmetic, in the squared residuals. The second result illustrates how the errors made in one stage affect the errors in the succeeding stages. Simulations are performed to check the theorical predictions.