A family of adaptive filter algorithms with decorrelating properties

Although the normalized least mean square (NLMS) algorithm is robust, it suffers from low convergence speed if driven by highly correlated input signals. One method presented to overcome this problem is the Ozeki/Umeda affine projection (AP) algorithm. The algorithm applies update directions that are orthogonal to the last P input vectors and thus allows decorrelation of an AR(P) input process, speeding up the convergence. This correspondence presents a simple approach to show this property, which furthermore leads to the construction of new algorithms that can handle other kinds of correlations such as MA and ARMA processes. A statistical analysis is presented for this family of algorithms. Similar to the AP algorithm, these algorithms also suffer a possible increase in the noise energy caused by their pre-whitening filters.