Adaptive stochastic filters with no strict positive real condition

A new adaptive stochastic filter structure is introduced which avoids the strict passivity test used as a sufficient condition for convergence required by existing adaptive schemes. The proposed algorithm consists of three stages. In the first stage, an autoregressive model is fitted and the residue obtained is used as an estimate of the noise. In the second stage, an autoregressive recursive moving average model is fitted using the residual of the first stage. A modified residual is then filtered using a parameter δ and the model obtained from the second stage to generate an improved estimate of the noise. In the third stage, this improved estimate of the noise is used to obtain a better autoregressive moving average model. It is shown that the proposed algorithm will also reduce the bias in the estimated parameters. The simulation results given show that the proposed filter compares favorably to the algorithm introduced by Mayne and Clark and also Landau. This filter is then applied to the adaptive line enhancement, sinusoidal detection, and adaptive spectral estimation problems to illustrate its usefulness.