Extended Kernel Recursive Least Squares Algorithm

Weifeng Liu, Il Park, Yiwen Wang, J.C. Principe
2009 IEEE Transactions on Signal Processing  
This paper presents a kernelized version of the extended recursive least squares (EX-KRLS) algorithm which implements for the first time a general linear state model in reproducing kernel Hilbert spaces (RKHS), or equivalently a general nonlinear state model in the input space. The center piece of this development is a reformulation of the well known extended recursive least squares (EX-RLS) algorithm in RKHS which only requires inner product operations between input vectors, thus enabling the
more » ... pplication of the kernel property (commonly known as the kernel trick). The first part of the paper presents a set of theorems that shows the generality of the approach. The EX-KRLS is preferable to: (1) a standard kernel recursive least squares (KRLS) in applications that require tracking the state-vector of general linear statespace models in the kernel space, or (2) an EX-RLS when the application requires a nonlinear observation and state models. The second part of the paper compares the EX-KRLS in nonlinear Rayleigh multipath channel tracking and in Lorenz system modeling problem. We show that the proposed algorithm is able to outperform the standard EX-RLS and KRLS in both simulations. Index Terms Extended recursive least squares, Kalman filter, kernel methods, reproducing kernel Hilbert spaces.
doi:10.1109/tsp.2009.2022007 fatcat:kupa7zogrzcnbn5jwx2dsg256y