Adaptive Second-order Volterra Filter Research Articles

Control of VSC for enhancement of power quality in off‐grid distributed power generation

In this study, a control algorithm based on non-linear adaptive second-order Volterra filter (NLVF) is utilised to operate the voltage-source converter (VSC). The main role of VSC is to supply compensating current to improve the power quality in wind-based off-grid distributed power generation system. This off-grid system consists of three-phase induction generator, VSC and non-linear loads. The proposed control algorithm is adaptive as well as non-linear in nature. The characteristic of Volterra series is exploited to generate the reference source current for VSC operation. The NLVF estimates the active and reactive weights of fundamental load current for reference current generation. It mitigates the power quality problems created by disturbances in non-linear load or wind oscillations on off-grid system. The solution of power quality problems such as the presence of harmonics in supply current, load unbalance and reactive power compensation is obtained. Nevertheless, voltage and frequency control are also achieved. The VSC is used as a shunt compensator in the system. The entire off-grid system is designed and validated through the laboratory prototype development. The objective of the system is achieved and the steady state and dynamic performance is found satisfactory.

Pipelined set-membership approach to adaptive Volterra filtering

Due to the high computational complexity required by Volterra filter, some of its practical implementations consider pipelined adaptive Volterra filter architecture with two layers structure. However, its main challenges are the poor robustness against impulsive noise, slow convergence and high computational complexity for long memory high order expansion on each module. In this paper, we firstly extend the pipelined second-order adaptive Volterra filter to its high order version. Then, to reduce the computational complexity and improve the robust performance of pipelined adaptive Volterra filter architecture, the pipelined adaptive Volterra set-membership (PAVF-SM) algorithm and its robust version (PAVF-RSM) are proposed, which are derived from the least-perturbation property and adaptive approximation principle. Due to the inherent variable step size and nonlinear selective update mechanisms, the proposed PAVF-SM and PAVF-RSM algorithms achieve lower complexity and improved convergence performance. Simulations also verify the improved performance of the PAVF-SM and PAVF-RSM algorithms under Gaussian noise and impulsive noise environments.

Pipelined robust M-estimate adaptive second-order Volterra filter against impulsive noise

The main limits on adaptive Volterra filters are their computational complexity in practical implementation and significant performance degradation under the impulsive noise environment. In this paper, a low-complexity pipelined robust M-estimate second-order Volterra (PRMSOV) filter is proposed to reduce the computational burdens of the Volterra filter and enhance the robustness against impulsive noise. The PRMSOV filter consists of a number of extended second-order Volterra (SOV) modules without feedback input cascaded in a chained form. To apply to the modular architecture, the modified normalized least mean M-estimate (NLMM) algorithms are derived to suppress the effect of impulsive noise on the nonlinear and linear combiner subsections, respectively. Since the SOV-NLMM modules in the PRMSOV can operate simultaneously in a pipelined parallelism fashion, they can give a significant improvement of computational efficiency and robustness against impulsive noise. The stability and convergence on nonlinear and linear combiner subsections are also analyzed with the contaminated Gaussian (CG) noise model. Simulations on nonlinear system identification and speech prediction show the proposed PRMSOV filter has better performance than the conventional SOV filter and joint process pipelined SOV (JPPSOV) filter under impulsive noise environment. The initial convergence, steady-state error, robustness and computational complexity are also better than the SOV and JPPSOV filters.

Nonlinear System Identification Using a Subband Adaptive Volterra Filter

This paper presents a flexible and efficient subband adaptive second-order Volterra filter (SBVF) structure for nonlinear system identification. The structure is first described in detail, where the underlying filter-bank scheme and adaptive filtering algorithms are explained, followed by a computational complexity analysis. Simulation results are then presented, showing that the proposed structure can achieve equal system-identification performance compared with that of a fullband second-order Volterra structure at a much-reduced complexity. In addition, the structure provides a more precise system model compared with that of a linear-only structure at a potentially similar computational expense. The results also demonstrate the suggested structure's ability to exploit a priori knowledge of the nature of the system nonlinearity through selectable nonlinear subband filtering, resulting in further complexity savings. The simulation results are experimentally verified under a practical acoustic-echo-cancellation scenario. It is shown that the SBVF structure can achieve up to a 10-dB lower mean-square error than that of a linear-only model at a comparable complexity.

A Design Method of Parallel Fast RLS Second-Order Adaptive Volterra Filter

The adaptive Volterra filter (AVF) is attractive in adaptive filtering applications because its expansion is a linear combination of the input and output signals. However, the formidable computational work of AVF is prohibitive for practical applications. In this letter, we present a parallel fast recursive least squares (RLS) second-order adaptive Volterra filter (PAVF) to reduce computational load. Our discussion is based on the approach of the fast RLS AVF [3], by which the computational complexity has been reduced to O(N3) multiplications per time instant, where O(·) denotes order of, and N is the filter length. Proposed PAVF consists of several subfilters partitioned from the conventional AVF, with parallel implementation, the computational work can be reduced effectively. Several simulation results are presented to validate the proposed method.

Asymmetry Compensation by Nonlinear Adaptive Partial Response Equalizer for 31.3 GB Blu-ray Disk ROM

We investigated a nonlinear adaptive partial response equalizer for the asymmetry compensation of a 31.3 GB higher linear density Blu-ray disc read only memory (ROM) with a 16% asymmetry. A second-order adaptive Volterra filter approximately equalizes a nonlinear signal into a linear one. We reduced its calculation complexity to design a digital circuit in optimum hardware resources by the result of computer simulations. Then we designed an adaptive Volterra filter on an FPGA evaluation board for bit error rate measurements. Finally, we determined that an adaptive Volterra filter has a capability to obtain improved bit error rates by signal linearization in a conventional Viterbi detector for PR(1221).

Partitioned block frequency-domain adaptive second-order Volterra filter

Finite-length Volterra filters are known to be able to model a wide range of real world nonlinear systems. In this paper, we present an algorithm that allows for different memory lengths of the linear and quadratic Volterra kernel while preserving the advantages of fast convolution techniques in the frequency domain for a second-order Volterra filter. This is achieved by extending partitioned block methods to second-order Volterra filters. To obtain corresponding adaptive realizations of the proposed approach, we present generalizations of known frequency-domain algorithms for Volterra filters and partitioned block frequency-domain adaptive filters for linear systems, respectively. To exploit the advantages of adaptive frequency-domain algorithms with respect to convergence speed, we provide a frequency bin-wise normalization of the step-size parameters. To evaluate the performance of the proposed approach, simulation results are given for the application to nonlinear acoustic echo cancellation. The results confirm the improved convergence of a second-order partitioned block frequency-domain adaptive Volterra filter (PBFDAVF) compared with time-domain adaptation of the kernel coefficients.

A formulation of the convergence property for the second‐order adaptive volterra filter using NLMS algorithm

AbstractIn this paper, a formulation of the convergence property of the NLMS method, an updating algorithm for an adaptive Volterra filter, is discussed. To date, much research has been carried out on the convergence property of the updating algorithm in a linear adaptive filter. However, there has been insufficient study of the updating algorithm for the second‐order adaptive Volterra filter. In this paper, the convergence property of the E‐NLMS method, an updating algorithm in the second‐order adaptive Volterra filter, is formulated and the convergence property of the second‐order adaptive Volterra filter is theoretically determined. In the formulation of the convergence property we use the first‐order recursive filter expression, which is effective for studying various characteristics of the NLMS method in linear adaptive filters. In addition, it is recognized that the nature of the input signal to the diagonal (D) elements of the second‐order Volterra system is different from that of the input to the other (ED) components. By means of computer simulation, it is confirmed that the convergence property given by the derived theoretical equation can sufficiently express the actual convergence property. © 2002 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 85(10): 40–50, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.1124

An LMS adaptive second-order Volterra filter with a zeroth-order term: steady-state performance analysis in a time-varying environment

This article studies the steady-state performance of the least mean square (LMS) adaptive second-order Volterra filter (SOVF) with a zeroth-order term for Gaussian inputs. The mean-square-error (MSE) criterion is evaluated first. Then, SOV LMS algorithm-based updating equations are derived. Next, the steady-state performance of the recursions is analyzed for a random walk model for the unknown system parameters, and the steady-state excess MSE is evaluated. Finally, the theoretical performance predictions are shown to be in good agreement with simulation results, especially for small step sizes.

An adaptive technique for modeling second-order Volterra systems with sparse kernels

This paper proposes a simple technique for modeling second-order Volterra systems using an adaptive second-order Volterra delay filter (ASOVDF). The developed filter structure essentially extends an adaptive FIR delay filter to include linear and quadratic filter coefficients with an input assumed to be a zero-mean i.i.d. sequence with a symmetric distribution. The implementation of the ASOVDF is based on a stage-by-stage modeling process. At each stage, a dominant delay element is determined, the corresponding adaptive filter coefficient is incorporated to the adaptive filter coefficients from previous stages, and then these filter coefficients are adapted via the recursive least-squares algorithm. The ASOVDF requires few filter coefficients and has better performance and less computational complexity over the conventional adaptive second-order Volterra filter (ASOVF) in modeling second-order Volterra systems with sparse kernels.

High-order system identification with an adaptive recursive second-order polynomial filter

In this letter, an adaptive recursive nonlinear filter based on the Volterra series and an infinite impulse response (IIR) structure is considered. For certain types of nonlinear systems where high-order nonlinearities are recursively generated, we show that the adaptive recursive second-order polynomial filter has improved performance over the well-known (nonrecursive) adaptive second-order Volterra filter and a third-order Volterra filter. This filter represents an alternative to using a traditional Volterra filter whose order has been increased to match that of the system being modeled.

Adaptive second-order Volterra filtering and its application to second-order drift phenomena

This paper presents an adaptive second-order Volterra filter and its application to model-test data of a prototype tension leg platform (TLP). The least-squares approach of a second-order Volterra model and its adaptive filtering algorithm based on recursive least-squares are introduced. The second-order Volterra filter is applied to identify the linear and quadratically nonlinear relationship between irregular sea wave excitation and the surge response of a tension leg platform. Next, a deconvolution technique, based on the impulse invariance standard Z-transform, is utilized to recover the linear and quadratic forces exerted on the TLP. >

On the performance of a second-order adaptive Volterra filter

The impact of the bias or DC term on the performance of a second-order Volterra least-mean-square (LMS) filter is discussed. Without the DC term the filter may itself produce a biased output. It is shown that including a DC term always degrades adaptive system performance, in terms of both convergence and steady state. Unlike the usual LMS approach, the second-order scheme converges nonuniformly, even with white inputs. For deterministic signals an approximate transfer function descriptor is obtained for the second-order LMS filter. Jury (1964) tables are used to obtain explicit stability conditions.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A second-order adaptive Volterra filter with rapid convergence

An algorithm for updating the linear and quadratic weights of a second-order Volterra filter (SVF) is proposed. This algorithm uses a fast Kalman filter algorithm to calculate the Kalman gain vector used in updating the linear and quadratic weights of the SVF. The convergence of the algorithm for the quadratic weights is established. A simulation is then performed in which a fast Kalman filter implementation of an SVF is compared to an LMS implementation in a system identification problem. The fast Kalman filter implementation is shown to converge to the unknown system parameters considerably faster than the LMS implementation.