Fast adaptive identification of stable innovation filters

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 (TIB), the estimation problem is well conditioned, and a simple, low-rank initialization is available.