Recursive least squares filter

About: Recursive least squares filter is a research topic. Over the lifetime, 8907 publications have been published within this topic receiving 191933 citations.

New recursive-least-squares algorithms for nonlinear active control of sound and vibration using neural networks

Abstract: In recent years, a few articles describing the use of neural networks for nonlinear active control of sound and vibration were published. Using a control structure with two multilayer feedforward neural networks (one as a nonlinear controller and one as a nonlinear plant model), steepest descent algorithms based on two distinct gradient approaches were introduced for the training of the controller network. The two gradient approaches were sometimes called the filtered-x approach and the adjoint approach. Some recursive-least-squares algorithms were also introduced, using the adjoint approach. In this paper, an heuristic procedure is introduced for the development of recursive-least-squares algorithms based on the filtered-x and the adjoint gradient approaches. This leads to the development of new recursive-least-squares algorithms for the training of the controller neural network in the two networks structure. These new algorithms produce a better convergence performance than previously published algorithms. Differences in the performance of algorithms using the filtered-x and the adjoint gradient approaches are discussed in the paper. The computational load of the algorithms discussed in the paper is evaluated for multichannel systems of nonlinear active control. Simulation results are presented to compare the convergence performance of the algorithms, showing the convergence gain provided by the new algorithms.

Adaptive Energy Management of Electric and Hybrid Electric Vehicles

Abstract: An adaptive algorithm based on weighted recursive least squares is derived and implemented. The generality of the approach is underscored by the application of the algorithm to a 42 V lead acid and a high-voltage (375 V) nickel metal hydride battery system. The algorithm is fully recursive in that the only variables required for on-line regression are those of the previous time step and the current time step. A time-weighting technique often referred to as exponential forgetting is employed to damp exponentially the influence of older data on the regression analysis. The output from the adaptive algorithm is the battery state of charge (remaining energy), state of health (relative to the battery's nominal rating), and power capability. Such algorithms are likely to play a critical role in optimal operation of hybrid electric vehicles and on-board diagnostics. The behavior of the algorithm in terms of convergence, accuracy, and robustness is examined.

A Recursive Orthogonal Least Squares Algorithm for Training RBF Networks

Abstract: A recursive orthogonal least squares (ROLS) algorithm for multi-input, multi-output systems is developed in this paper and is applied to updating the weighting matrix of a radial basis function network. An illustrative example is given, to demonstrate the effectiveness of the algorithm for eliminating the effects of ill-conditioning in the training data, in an application of neural modelling of a multi-variable chemical process. Comparisons with results from using standard least squares algorithms, in batch and recursive form, show that the ROLS algorithm can significantly improve the neural modelling accuracy. The ROLS algorithm can also be applied to a large data set with much lower requirements on computer memory than the batch OLS algorithm.

An Adaptive Spatial Filter for User-Independent Single Trial Detection of Event-Related Potentials

Abstract: Goal: Current brain–computer interfaces (BCIs) are usually based on various, often supervised, signal processing methods. The disadvantage of supervised methods is the requirement to calibrate them with recently acquired subject-specific training data. Here, we present a novel algorithm for dimensionality reduction (spatial filter), that is ideally suited for single-trial detection of event-related potentials (ERPs) and can be adapted online to a new subject to minimize or avoid calibration time. Methods: The algorithm is based on the well-known xDAWN filter, but uses generalized eigendecomposition to allow an incremental training by recursive least squares (RLS) updates of the filter coefficients. We analyze the effectiveness of the spatial filter in different transfer scenarios and combinations with adaptive classifiers. Results: The results show that it can compensate changes due to switching between different users, and therefore allows to reuse training data that has been previously recorded from other subjects. Conclusions: The presented approach allows to reduce or completely avoid a calibration phase and to instantly use the BCI system with only a minor decrease of performance. Significance: The novel filter can adapt a precomputed spatial filter to a new subject and make a BCI system user independent.