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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.


Papers
More filters
Journal ArticleDOI
TL;DR: Based on its least-squares properties, numerical robustness, theoretical basis and the fact that it simultaneously estimates multiple models, the proposed AUDI algorithm is recommended for use in place of RLS and Bierman's UD factorization algorithm.
Abstract: An augmented UD identification (AUDI) algorithm for system identification is developed by rearranging the data vectors and augmenting the covariance matrix of Bierman's UD factorization algorithm. The structure of the augmented information (covariance) matrix is particularly easy to interpret and it is shown that the AUDI algorithm is a direct extension of the familiar recursive least squares (RLS) algorithm. The proposed algorithm permits simultaneous identification of the model parameters plus loss functions for all orders from 1 to n at each time step with approximately the same calculation effort as «th order RLS. This provides a basis for simultaneous model order and parameter identification so that problems due to over- and under-estimation of model can be avoided. Based on its least-squares properties, numerical robustness, theoretical basis and the fact that it simultaneously estimates multiple models, the proposed AUDI algorithm is recommended for use in place of RLS and Bierman's UD factorizatio...

48 citations

ReportDOI
15 Oct 1959
TL;DR: In this article, the general problem of least square analysis is discussed, with a special emphasis on functions in which the parameters appear nonlinearly and which can be fitted by Gauss' well-known iterative method.
Abstract: The general problem of least squares analysis is discussed. Special emphasis is placed on functions in which the parameters appear nonlinearly and which can be fitted by Gauss' well-known iterative method. The procedure is useful with any type of computing facility. A family of Fortrun II subroutines which solves problems with this method is presented. Several examples of functions fitted by the method are shown. (auth)

48 citations

Journal ArticleDOI
H. Dai1, N.K. Sinha1
01 May 1989
TL;DR: In this article, a robust recursive least-squares method has been proposed for bilinear system identification, which differs from earlier approaches in that it uses modified weights in the criterion for robustness.
Abstract: The least-squares method is one of the most efficient and simple identification methods commonly used. Unfortunately, it is very sensitive to large errors (outliers)in the input/output data. In such cases, it may never converge or give erroneous results. In practice, most real systems are nonlinear. Many of these can be suitably represented by bilinear models. In the paper, a robust recursive least-squares method has been proposed for bilinear system identification. It differs from earlier approaches in that it uses modified weights in the criterion for robustness. A theorem proving the convergence of the proposed algorithms included. Results of the simulation demonstrating the robustness of the proposed algorithm are also included.

48 citations

Journal ArticleDOI
Wei Li1, Deren Gong1, Meihong Liu1, Jian Chen1, Dengping Duan1 
TL;DR: In this article, an adaptive robust Kalman filter algorithm is derived to account for both process noise and measurement noise uncertainty, which is successfully implemented in relative navigation using global position system for spacecraft formation flying in low earth orbit, with real-orbit perturbations and non-Gaussian random measurement errors.
Abstract: An adaptive robust Kalman filter algorithm is derived to account for both process noise and measurement noise uncertainty. The adaptive algorithm estimates process noise covariance based on the recursive minimisation of the difference between residual covariance matrix given by the filter and that calculated from time-averaging of the residual sequence generated by the filter at each time step. A recursive algorithm is proposed based on both Massachusetts Institute of Technology (MIT) rule and typical non-linear extended Kalman filter equations for minimising the difference. The measurement update using a robust technique to minimise a criterion function originated from Huber filter. The proposed adaptive robust Kalman filter has been successfully implemented in relative navigation using global position system for spacecraft formation flying in low earth orbit, with real-orbit perturbations and non-Gaussian random measurement errors. The numerical simulation results indicate that the proposed adaptive robust filter can provide better relative navigation performance in terms of accuracy and robustness as compared with previous filter algorithms.

48 citations

Journal ArticleDOI
TL;DR: A robust and computationally efficient algorithm for removing power line interference from neural recordings, which features a highly robust operation, fast adaptation to interference variations, significant SNR improvement, low computational complexity and memory requirement and straightforward parameter adjustment.
Abstract: Power line interference may severely corrupt neural recordings at 50/60 Hz and harmonic frequencies. In this paper, we present a robust and computationally efficient algorithm for removing power line interference from neural recordings. The algorithm includes four steps. First, an adaptive notch filter is used to estimate the fundamental frequency of the interference. Subsequently, based on the estimated frequency, harmonics are generated by using discrete-time oscillators, and then the amplitude and phase of each harmonic are estimated through using a modified recursive least squares algorithm. Finally, the estimated interference is subtracted from the recorded data. The algorithm does not require any reference signal, and can track the frequency, phase, and amplitude of each harmonic. When benchmarked with other popular approaches, our algorithm performs better in terms of noise immunity, convergence speed, and output signal-to-noise ratio (SNR). While minimally affecting the signal bands of interest, the algorithm consistently yields fast convergence and substantial interference rejection in different conditions of interference strengths (input SNR from -30 dB to 30 dB), power line frequencies (45-65 Hz), and phase and amplitude drifts. In addition, the algorithm features a straightforward parameter adjustment since the parameters are independent of the input SNR, input signal power, and the sampling rate. The proposed algorithm features a highly robust operation, fast adaptation to interference variations, significant SNR improvement, low computational complexity and memory requirement, and straightforward parameter adjustment. These features render the algorithm suitable for wearable and implantable sensor applications, where reliable and real-time cancellation of the interference is desired.

48 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202356
2022104
2021172
2020228
2019234
2018237