Real-time Kalman filter implementation for active feedforward control of time-varying broadband noise and vibrations

Tracking behavior and the rate of convergence are critical properties in active noise control applications with time-varying disturbance spectra. As compared to the standard filtered-reference Least Mean Square (LMS) algorithm, improved convergence can be obtained with schemes based on preconditioning, affine projections, Recursive Least Squares (RLS), and other methods. The RLS method potentially leads to very fast convergence but straightforward implementations may suffer from round-off errors and suboptimal tracking behavior. In this paper a Kalman filter approach is used which, as compared to RLS, includes a covariance weighting for model output errors in order to improve tracking behavior and robustness. An orthogonal transformation scheme was used to reduce the influence for round-off errors of the Kalman recursions. In this paper an extension is given for multiple input multiple output systems, and results of a real-time implementation are presented. Conclusions are given regarding the suitability for real-time implementation of previous formulations. Different parameterizations of the secondary path model between the active control source and the error sensor are compared. Real-time results demonstrate the rapid convergence for reduction of noise in a duct, as well as numerical stability during extended operation intervals.