Convergence properties of an adaptive lattice filter exploiting nonlinear dynamics of a biochemical reaction system

An adaptive lattice filter (ALF) which computes the PARCOR coefficients through a cyclic enzyme system has recently been developed by the author. Using nonlinear dynamics of the cyclic enzyme system, the ALF becomes robust against impulsive noise, and the stability of the estimated AR model can be ensured. The convergence properties of the ALF are studied. First, a theoretical expression for the asymptotic error variance of the PARCOR coefficient is derived. Simulation results are presented, and the theoretical and simulated values show a very good match. Next, the convergence speed of the proposed ALF is compared with that of the simplified ALF. The step sizes are then determined by using the above theoretical expression such that both ALF´s achieve the same error variance in steady states. The results show that the proposed ALF has excellent convergence properties than the simplified one