STABLE AND EFFICIENT LATTICE ALGORITHMS FOR ADAPTIVE IIR FILTERING

Conventional direct-form adaptive IIR filters suffer from potential instability problems, and as such there is a general interest in adaptive filters based on alternate parametrizations. The normalized lattice filter is one example of a filter structure whose stability can be ensured theoretically in a time-varying environment, and thus the structure is well suited for adaptive IIR filtering. Previous attempts at applying lattice structures to adaptive IIR filtering have met with gradient computations of O(N2) complexity. To overcome this computational burden, two new lattice-based algorithms are proposed for adaptive IIR filtering and system identification, with both algorithms of O(N) complexity. The first algorithm is a reinterpretation of the Steiglitz-McBride method, while the second is a variation on the output error method. State space models are employed to make the derivations transparent, and the methods can be extended to other parametrizations if desired. The set of possible stationary points of the algorithms are shown to be consistent with the convergent points obtained from the direct-form versions of the Steiglitz-McBride and output error methods, whose properties are well studied. The derived algorithms are as computationally efficient as existing direct-form based algorithms, while overcoming the stability problems associated with time-varying direct-form filters.