Deterministic stabilty analyses of unit-norm constrained algorithms for unbiased adaptive IIR filtering

Recently, two simple gradient-based algorithms for unbiased IIR system identification in the presence of zero-mean correlated output noise were derived and shown to perform well in simulation. In this paper, we study the stability and robustness of these two adaptive filters, deriving strictly positive real (SPR) conditions on the overall unknown-plus-adaptive systems to guarantee convergence of the coefficients to their optimum values. Unlike other algorithms for unbiased IIR adaptive filtering, the stability of each of these algorithms depends on the initial values of the filter coefficients. However, near the optimum coefficient solutions, both algorithms are locally-stable, irrespective of the unknown system. Simulations verify the results of our analyses