The unbiased least-squares lattice

A modification to both the unnormalized and normalized least-squares lattice algorithms is presented which produces unbiased estimates of the lattice parameters without a significant increase in algorithm complexity. Unbiased parameter estimation is very useful for improving the numerical precision of the least-squares lattice algorithm because the parameters representing statistical estimates remain essentially constant in magnitude for stationary input data. In the unnormalized algorithm the large magnitudes of the cross-correlation and covariance parameters are avoided while in the normalized algorithm the decreasing magnitudes of the error signals are kept at unity variance (not less than unity) through appropriate scaling of the lattice recursions. Both unbiased algorithms require an additional integer parameter representing the number of data observations used in the parameter estimates at each stage.