Kernel Adaptive Filtering Subject to Equality Function Constraints

Kernel adaptive filters (KAFs) are powerful tools for online nonlinear system modeling, which are direct extensions of traditional linear adaptive filters in kernel space, with growing linear-in-the-parameters (LIP) structure. However, like most other nonlinear adaptive filters, the KAFs are "black box" models where no prior information about the unknown nonlinear system is utilized. If some prior information is available, the "grey box" models may achieve improved performance. In this work, we consider the kernel adaptive filtering with prior information in terms of equality function constraints. A novel Mercer kernel, called the constrained Mercer kernel (CMK), is proposed. With this new kernel, we develop the kernel least mean square subject to equality function constraints (KLMS-EFC), which can satisfy the constraints perfectly while achieving significant performance improvement.