Adaptive tracking of linear time-variant systems by extended RLS algorithms

Haykin, S.; Sayed, Ali H.; Zeidler, J.R.; Yee, P.; Wei, Paul

doi:10.1109/78.575687

Cited by 200 publications

(71 citation statements)

References 17 publications

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“…The RLS algorithm, which can be viewed as the deterministic counterpart of the Kalman filter theory, uses all of the information contained in the input data by introducing the forgetting factor λ into the design of the recursive algorithm [Haykin (2002)]. Compared to the LMS filter, the RLS filter exhibits an order of magnitude faster rate of convergence, but the LMS filter might display better tracking behavior than the RLS filter, which is model dependent, while the LMS algorithm is model independent [Haykin et al (1997);Haykin (2002)]. The Kalman filter theory [Kalman (1960)] uses the state-space approach for the describing of dynamical systems, and offers a solution to a class of recursive minimum mean-square estimation problems [Brown and Hwang (1997); Haykin (2002)].…”

Section: Theoretical Basismentioning

confidence: 99%

“…From the studies reported in the literature, it is known that the very simple least mean-square (LMS) recursive filtering method can exhibit a better tracking behavior than the RLS method [Haykin et al (1997)] because the LMS algorithm is model independent, while the RLS algorithm is model dependent [Sayed and Kailath (1994); Haykin (2002)]. According to this fact, an adaptive OT algorithm, based on the recursive LMS method, which, so far, is not being used as OT tools, is implemented here, together with the RLS OT filter [Bai et al (2002); Wu et al (2009)].…”

Section: Introductionmentioning

confidence: 99%

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A Comparative Study of Adaptive Order Tracking Techniques for Rotating Machinery Analysis: Computer Experiments and Practical Implementations

Veljkovic

Todorovič

2016

Adv. Data Sci. Adapt. Data Anal.

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This paper presents and investigates recursive order tracking (OT) techniques based on the least mean-square (LMS) method and the Vold-Kalman (VK) algorithm with a one pole structural equation, both of which could be realized as real-time applications. Additionally, for comparisons, two common adaptive OT filters are considered: the recursive least-squares (RLS) method and the VK algorithm with a two pole structural equation. The numerical implementations of the considered methods, through simulations on a representative noisy synthetic signal, including both close and crossing orders spectral components, are performed. The results indicate a possible degradation in the tracking performance of the RLS algorithm and the effectiveness of the simple LMS method, as well as both considered VK algorithms, for OT and distinguishing. The influence of the sampling frequency on the choosing of a weighting factor for the VK recursive OT filters is further investigated to extend the guidelines from the literature for using these methods. Two examples of practical implementations of the considered recursive OT methods are given: (i) the separation of the crossing orders arising in the laboratory test bench of the two unbalanced rotors rotating at independent frequencies and (ii) the one engineering application of fault diagnosis in the massive reduction gear on an excavator with a cable crowd, based on the distinguishing and separation of close orders. The experimental results justify the implementation of the proposed techniques as OT tools in industrial applications.

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Section: Theoretical Basismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Comparative Study of Adaptive Order Tracking Techniques for Rotating Machinery Analysis: Computer Experiments and Practical Implementations

Veljkovic

Todorovič

2016

Adv. Data Sci. Adapt. Data Anal.

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“…However, in fast fading channels, an averaging period equal to the coherence time of the channel is insufficient to overcome the effects of additive noise and characterize the multiuser interference (MUI) [1]. Furthermore, the use of optimized convergence parameters such as step sizes and forgetting factors into conventional adaptive algorithms extend their fading range and lead to improved convergence and tracking performance [8,[12][13][14][15][16][17][18]. However, the stability of adaptive step-sizes and forgetting factors can be a concern unless they are constrained to lie within a predefined region [19].…”

Section: Introductionmentioning

confidence: 99%

Bidirectional algorithms for interference suppression in multiuser systems

Clarke

Lamare

2015

J Wireless Com Network

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This paper presents adaptive bidirectional minimum mean-square error parameter estimation algorithms for fast-fading channels. The time correlation between successive channel gains is exploited to improve the estimation and tracking capabilities of adaptive algorithms and provide robustness against time-varying channels. Bidirectional normalized least mean-square and conjugate gradient algorithms are devised along with adaptive mixing parameters that adjust to the time-varying channel correlation properties. An analysis of the proposed algorithms is provided along with a discussion of their performance advantages. Simulations for an application to interference suppression in multiuser DS-CDMA systems show the advantages of the proposed algorithms.

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“…In matrix generalization of the momentum LMS (MLMS) algorithm case of a time-varying model, adaptive algorithms like LMS try to [14]. track the time variation of the system impulse response, as analyzed in [4,5,6]. However, this tracking is done on a sample-by-sample 2.…”

Section: Introductionmentioning

confidence: 99%

Basis Expansion Adaptive Filters for Time-Varying System Identification

Rugini

Leus

2007

2007 2nd IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing

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ABSTRACTblock adaptive (OBA) and the OBA shifting (OBAS) algorithms [9]. However, the tracking performance of all these block algorithms We show by simulations that our proposed BE-LMS is able to track ple stochastic gradient type of algorithms, lead by the least mean the system time variation better than the NLMS, while maintaining squares (LMS) family, to more elaborated algorithms like those begood convergence properties in case of overlapping blocks. To even longing to the recursive least squares (RLS) class [1,2,3].further improve the tracking capabilities, we also propose another A common feature of most of these algorithms is that they have BEM-based adaptive algorithm that has a nice connection with the been initially derived assuming a time-invariant system model. In matrix generalization of the momentum LMS (MLMS) algorithm case of a time-varying model, adaptive algorithms like LMS try to [14]. track the time variation of the system impulse response, as analyzed in [4,5,6]. However, this tracking is done on a sample-by-sample 2. SYSTEM MODEL basis, by using limited information about the past. This past information can be better taken into account by using a block of data ratherThe system under consideration is a linear time-varying system with than one single sample. As a consequence, to track time-varying additive noise, whose input-output relation is expressed by systems, a block-by-block algorithm could potentially be more ben-L-1 eficial than a sample-by-sample approach, especially if the blocks L-1 are overlapping. 31n = h0,1xn l + en,(1) Traditionally, block adaptive filtering techniques have been de-1-0 veloped to reduce complexity in the time-invariant case, by exploitwhere yn is the output, hn,1 is the linear time-varying system iming fast convolution methods. For example, the block LMS (BLMS) pulse response, assumed finite with L taps, Xn is the input, and en algorithm [3,7] uses an average gradient over a block of samples is the additive noise. Given Xn and yn, our goal is to find a linear to estimate the impulse response. In case of non-overlapping blocks, time-varying filter hn,1 such that BLMS has approximately the same steady-state performance of LMS [7,8], with computational savings due to the shared operations. How-L-1 ever, if the blocks are overlapping, as in the sliding-window LMS Yn =E hn,lXn-1 (SW-LMS), the convergence and the steady-state performance of l=0 block adaptive algorithms improve, at the expense of an increased complexity caused by the repeated processing of the same data [3].is as close as possible to yn. The filter h,l can then be consideredThe convergence of both BLMS and SW-LMS can further be imas an estimate of the system impulse response hn,1.provd byallwinga tme-vryig stp sze, eadng t th optmum To describe the proposed adaptive algorithms, we will first reprovd b alowig a imevaringstepsiz, ladig totheoptmum shape the system input-output relation, and then we will make use This research was supported in part by NWO-STW under the VIDI proof the limited time-varyin...

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Adaptive tracking of linear time-variant systems by extended RLS algorithms

Cited by 200 publications

References 17 publications

A Comparative Study of Adaptive Order Tracking Techniques for Rotating Machinery Analysis: Computer Experiments and Practical Implementations

A Comparative Study of Adaptive Order Tracking Techniques for Rotating Machinery Analysis: Computer Experiments and Practical Implementations

Bidirectional algorithms for interference suppression in multiuser systems

Basis Expansion Adaptive Filters for Time-Varying System Identification

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