Low-complexity and model-free parameter tracking algorithms

Under conditions of linearity and Gaussianity, the Kalman filter is the optimum algorithm for tracking a vector of unknown parameters. However, the Kalman filter has two draw-backs: it requires (a) a high (cubic) computational complexity in the number of parameters; (b) knowledge of an accurate model for the parameter variation. The performance of the Kalman filter can be greatly degraded if the model for parameter variation is not close to the truth. This problem led to the proposal of a large number of robust alternatives to the Kalman filter. This paper describes a linear-complexity alternative to the Kalman filter that does not require accurate models, leveraging the diverse strengths of multiple adaptive filters. We demonstrate the potential of a combination of four adaptive filters with variable step-sizes to provide near-to-optimal tracking performance in the presence of rapidly changing parameters.