Adaptive noise canceler and its applications for systems with time-variant correlative noise

In order to gain a true signal from the signal polluted by time-variant correlative noises, an adaptive noise canceler (ANC) is proposed. We develop an observation model using the ARMA process. The time-variant parameter vector of the ARMA model is described by using a generalized random walk model. Under the conditions that input and output noises are jointly normal white noises, we deduce the adaptive Kalman filter (AKF) of the parameter vector and the maximum a posterior (MAP) estimator of the noise statistics. The ANC consists of the AKF and the MAP estimator. Simulation results are obtained by using a conventional smooth signal with sinusoidal components as well as the "non-smooth" signal of recorded oil well colour spectrum data with time-variant correlative noise.