A time-recursive lattice algorithm for autoregressive estimation

A time-recursive least-squares lattice estimation algorithm is presented. The reflection coefficients, k
j
, are estimated from residual energy estimates,
\hat{RE}_{j}
, so that
|\hat{k}_{j}| < 1
for all j. Thus the stability of the inverse filter is guaranteed. Computation and storage may be reduced by normalizing the forward and backward prediction errors throughout the lattice by the square roots of estimates of their respective energies. Also, this ensures that all lattice quantities are bounded in magnitude by one, facilitating fixed-point implementation. The computational requirement of both normalized and unnormalized forms is proportional to the lattice order per time update.