Abstract
A novel version of the constrained affine projection (CAP) algorithm, referred to as the equally constrained affine projection (ECAP) algorithm is derived simultaneously to satisfy both the linear constraints and the residual conditions by means of the Lagrange method. In a geometrical view, the ECAP algorithm is interpreted to show a one-step optimization even with the parameter perturbation that is orthogonal to the constraint hyperplane, while the CAP algorithm yields two steps to reach at the optimal point. An adaptive filtering simulation with linear constraints depicts its behavior.
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