Kernel adaptive filter

About: Kernel adaptive filter is a research topic. Over the lifetime, 8771 publications have been published within this topic receiving 142711 citations.

An effective filtering for GRACE time-variable gravity: Fan filter

Abstract: [1] Spatial low-pass filtering is necessary for processing the GRACE time-variable gravity (TVG) data which are otherwise plagued with short-wavelength noises. Here we devise a new non-isotropic filter, called the fan filter: In terms of the spherical harmonic spectrum, the fan filter is simply a 2-D double filter consisting of a low-pass along the degree n (the same as the conventional isotropic filter) simultaneously with a low-pass along the order m, whose contour projection onto the (n, m) plane is fan-shaped. It is deterministic and independent of a priori or external information, its implementation is straightforward, and the result is objective. Most importantly, we show that this simple filter performs well among its counterparts under similar conditions, in particular against the N-S striping noises prevalent in the GRACE TVG solutions. We demonstrate this with Gaussian weights at filter length and hence spatial resolution as fine as 300 km. We also deduce the fan filter's nominal amplitude-reduction factor as a function of the filter length for TVG signals that follow the Kaula rule.

Data assimilation with the weighted ensemble Kalman filter

Abstract: In this paper, two data assimilation methods based on sequential Monte Carlo sampling are studied and compared: the ensemble Kalman filter and the particle filter. Each of these techniques has its own advantages and drawbacks. In this work, we try to get the best of each method by combining them. The proposed algorithm, called the weighted ensemble Kalman filter, consists to rely on the Ensemble Kalman Filter updates of samples in order to define a proposal distribution for the particle filter that depends on the history of measurement. The corresponding particle filter reveals to be efficient with a small number of samples and does not rely anymore on the Gaussian approximations of the ensemble Kalman filter. The efficiency of the new algorithm is demonstrated both in terms of accuracy and computational load. This latter aspect is of the utmost importance in meteorology or in oceanography since in these domains, data assimilation processes involve a huge number of state variables driven by highly non-linear dynamical models. Numerical experiments have been performed on different dynamical scenarios. The performances of the proposed technique have been compared to the ensemble Kalman filter procedure, which has demonstrated to provide meaningful results in geophysical sciences.

A fast least-squares algorithm for linearly constrained adaptive filtering

Abstract: An extension of the field of fast least-squares techniques is presented. It is shown that the adaptation gain, which is updated with a number of operations proportional to the number of transversal filter coefficients, can be used to update the coefficients of a linearly constrained adaptive filter. An algorithm that is robust to round-off errors is derived. It is general and flexible. It can handle multiple constraints and multichannel signals. Its performance is illustrated by simulations and compared with the classical LMS-based Frost (1972) algorithm.

Square Root Cubature Information Filter

Abstract: Nonlinear state estimation plays a major role in many real-life applications. Recently, some sigma-point filters, such as the unscented Kalman filter, the particle filter, or the cubature Kalman filter have been proposed as promising substitutes for the conventional extended Kalman filter. For multisensor fusion, the information form of the Kalman filter is preferred over standard covariance filters due to its simpler measurement update stage. This paper presents a new state estimation algorithm called the square root cubature information filter (SRCIF) for nonlinear systems. The cubature information filter is first derived from an extended information filter and a recently developed cubature Kalman filter. For numerical accuracy, its square root version is then developed. Unlike the extended Kalman or extended information filters, the proposed filter does not require the evaluation of Jacobians during state estimation. The proposed approach is further extended for use in multisensor state estimation. The efficacy of the SRCIF is demonstrated by a simulation example of a permanent magnet synchronous motor.

Nonlinear adaptive bilinear filters for active noise control systems

Abstract: The reference and error channels of active noise control (ANC) systems may be saturated in real-world applications if the noise level exceeds the dynamic range of the electronic devices. This nonlinear saturation degrades the performance of ANC systems that use linear adaptive filters with the filtered-X least-mean-square (FXLMS) algorithm. This paper derives a bilinear FXLMS algorithm for nonlinear adaptive filters to solve the problems of signal saturation and other nonlinear distortions that occur in ANC systems used for practical applications. The performance of this bilinear adaptive filter is evaluated in terms of convergence speed, residual noise in steady state, and the computational complexity for different filter lengths. Computer simulations verify that the nonlinear adaptive filter with the associated bilinear FXLMS algorithm is more effective in reducing saturation effects in ANC systems than a linear filter and a nonlinear Volterra filter with the FXLMS algorithm.