Topic
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.
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TL;DR: A generalized normalized gradient descent algorithm for linear finite-impulse response (FIR) adaptive filters is introduced that adapts its learning rate according to the dynamics of the input signal, with the additional adaptive term compensating for the simplifications in the derivation of NLMS.
Abstract: A generalized normalized gradient descent (GNGD) algorithm for linear finite-impulse response (FIR) adaptive filters is introduced. The GNGD represents an extension of the normalized least mean square (NLMS) algorithm by means of an additional gradient adaptive term in the denominator of the learning rate of NLMS. This way, GNGD adapts its learning rate according to the dynamics of the input signal, with the additional adaptive term compensating for the simplifications in the derivation of NLMS. The performance of GNGD is bounded from below by the performance of the NLMS, whereas it converges in environments where NLMS diverges. The GNGD is shown to be robust to significant variations of initial values of its parameters. Simulations in the prediction setting support the analysis.
238 citations
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TL;DR: In this article, a multi-timescale method for dual estimation of state of charge (SOC) and capacity with an online identified battery model is presented, where the model parameters are online adapted with the vector-type recursive least squares (VRLS) to address the different variation rates of them.
235 citations
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TL;DR: A new kind of adaptive equalizer that operates in the spatial-frequency domain and uses either least mean square (LMS) or recursive least squares (RLS) adaptive processing and requires only /spl sim/50 complex operations per detected bit, which is close to achievable with state-of-the-art digital signal processing technology.
Abstract: We introduce a new kind of adaptive equalizer that operates in the spatial-frequency domain and uses either least mean square (LMS) or recursive least squares (RLS) adaptive processing. We simulate the equalizer's performance in an 8-Mb/s quaternary phase-shift keying (QPSK) link over a frequency-selective Rayleigh fading multipath channel with /spl sim/3 /spl mu/s RMS delay spread, corresponding to 60 symbols of dispersion. With the RLS algorithm and two diversity branches, our results show rapid convergence and channel tracking for a range of mobile speeds (up to /spl sim/100 mi/h). With a mobile speed of 40 mi/h, for example, the equalizer achieves an average bit error rate (BER) of 10/sup -4/ at a signal-to-noise ratio (SNR) of 15 dB, falling short of optimum linear receiver performance by about 4 dB. Moreover, it requires only /spl sim/50 complex operations per detected bit, i.e., /spl sim/400 M operations per second, which is close to achievable with state-of-the-art digital signal processing technology. An equivalent time-domain equalizer, if it converged at all, would require orders-of-magnitude more processing.
231 citations
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TL;DR: In this article, a regularized robust recursive least squares (R3LS) method was proposed for online estimation of power-system electromechanical modes based on synchronized phasor measurement unit (PMU) data.
Abstract: This paper proposes a regularized robust recursive least squares (R3LS) method for online estimation of power-system electromechanical modes based on synchronized phasor measurement unit (PMU) data. The proposed method utilizes an autoregressive moving average exogenous (ARMAX) model to account for typical measurement data, which includes low-level pseudo-random probing, ambient, and ringdown data. A robust objective function is utilized to reduce the negative influence from nontypical data, which include outliers and missing data. A dynamic regularization method is introduced to help include a priori knowledge about the system and reduce the influence of under-determined problems. Based on a 17-machine simulation model, it is shown through the Monte Carlo method that the proposed R3LS method can estimate and track electromechanical modes by effectively using combined typical and nontypical measurement data.
230 citations
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TL;DR: This article showed that least square cross-validation is asymptotically optimal for density estimation, rather then simply consistent, in the sense that the tail conditions are only slightly more severe than the hypothesis of finite variance.
Abstract: We prove that the method of cross-validation suggested by A. W. Bowman and M. Rudemo achieves its goal of minimising integrated square error, in an asymptotic sense. The tail conditions we impose are only slightly more severe than the hypothesis of finite variance, and so least squares cross-validation does not exhibit the pathological behaviour which has been observed for Kullback-Leibler cross-validation. This is apparently the first time that a cross-validatory procedure for density estimation has been shown to be asymptotically optimal, rather then simply consistent.
229 citations