  The adaptive identification of the impulse response of an innovation filter
is considered. The impulse response is a finite sum of known basis functions
with unknown coefficients. These unknown coefficients are estimated using a
pseudolinear regression. This estimate is implemented using a square root
algorithm based on a displacement rank structure. When the initial conditions
have low displacement rank, the filter update is $O(n)$. If the filter
architecture is chosen to be triangular input balanced, the estimation problem
is well-conditioned and a simple, low rank initialization is available.
