Recursive Least-squares Adaptive Filter Research Articles

Research on cascade control method for turboshaft engine with variable rotor speed

Abstract In order to realize high-quality control for turboshaft engine with variable rotor speed, a cascade control method based on the acceleration estimator of gas turbine speed (N gdot ) through Complementary filtering – incremental nonlinear dynamic inversion (CF-INDI)with Newton’s prediction is proposed. Firstly, an adaptive torsional suppression method based on the Recursive Least Square (RLS) algorithm and combined with the control index of power turbine speed is proposed and designed to solve the torsional instability of control system in turboshaft engine with variable rotor speed. Then, an online N gdot estimated method based on CF-INDI with Newton’s prediction is developed, and the complementary filtering method is applied to compensate for the inaccuracy of the state variable model available at a single working point, and Newton prediction is used to alleviate the problem of lagging acceleration estimate, which is accessible to realize the cascade control for turboshaft engine based on N gdot . The simulation results show that the RLS adaptive torsional filter can effectively suppress the low-order torsional components with frequencies of 1.2 Hz and 2.0 Hz mixing in power turbine speed, and the torsional suppression effect is remarkable. In addition, under different flight conditions, CF-INDI with Newton prediction is faster and more accurate than INDI N gdot estimate, and smoother than central difference method, which proves the feasibility of INDI N gdot estimator. Meanwhile, after the application of CF-INDI with Newton prediction N gdot estimator in cascade control, the anti-interference capacity of power turbine speed is stronger, and the dynamic control effect is superior, which has satisfactory robustness performance.

Application of Diversity Combining with RLS Adaptive Filtering in Data Transmission in a Hydroacoustic Channel.

When transmitting data in a hydroacoustic channel under difficult propagation conditions, one of the problems is intersymbol interference (ISI) caused mainly by the effect of multipath propagation. This phenomenon leads to a decrease in transmission parameters, and sometimes completely prevents it. Therefore, we have made an attempt to use diversity combining with Recursive Least Squares (RLS) adaptive filtering to improve the quality of data transmission in a hydroacoustic channel with strong reflections. The method was tested in simulation and during measurements in a real environment. The influence of the method on data transmission in the hydroacoustic channel was examined in detail. The obtained results allow us to draw conclusions regarding the purposefulness of use of diversity combining and RLS adaptive filtering in order to improve the quality of data transmission by reducing the effect of ISI.

Robust De-Noising Technique for Accurate Heart Rate Estimation Using Wrist-Type PPG Signals

Heart rate (HR) estimated using the photoplethysmography (PPG) signals during intense physical exercise is highly onerous owing to the existence of noise components like motion artifacts (MA’s) in the PPG signal. In this work, a robust de-noising technique for accurate HR estimation from the corrupted PPG signal is reported. The de-noising technique reported employs three pairs of Recursive Least Squares (RLS) as well as Normalized Least Mean Squares (NLMS) adaptive filters. The de-noised PPG signal obtained at the output of RLS and NLMS adaptive filters are combined using the sigmoid function. The three MA reduced PPG signals obtained from each adaptive filter pair are again combined using softmax activation function to form a MA reduced PPG signal from which the HR is estimated. Fast Fourier Transform (FFT) is used to estimate the HR and phase vocoder is used to refine the estimated HR. The proposed method is tested on the publically available 23 PPG datasets and it resulted in an HR estimation error of 1.89 beat per minute (BPM). The HR estimated using the proposed technique is found to be accurate and the HR estimation error is 1.89 BPM which is less when compared to other existing HR estimation mechanisms that reported an error of 1.97 BPM and 2.09 BPM.

Transmission Line Protective Relay Based on Recursive Least-Square Filters and Weights Analysis

The purpose of this study takes advantage of real-time hardware and software co-simulation to integrate a recursive least-square adaptive filter into a relay design for transmission line protection. The relay trip logic is controlled with a recursive least-square filter that analyzes the weights and cumulative error auto-correlation for magnitude and angles per phase. This analysis allows to detect and identify the fault type. The study focuses on the modelling of a consistent testing case study designed for transmission lines protections based on the EMTP reference model. The proposed solution could be scalable to protect other elements in power systems. It is consistent with current technological tools, and the RLS algorithm optimizes the computational performance of the relay.

Evoked Hemodynamic Response Estimation to Auditory Stimulus Using Recursive Least Squares Adaptive Filtering with Multidistance Measurement of Near-Infrared Spectroscopy.

The performance of functional near-infrared spectroscopy (fNIRS) is sometimes degraded by the interference caused by the physical or the systemic physiological activities. Several interferences presented during fNIRS recordings are mainly induced by cardiac pulse, breathing, and spontaneous physiological low-frequency oscillations. In previous work, we introduced a multidistance measurement to reduce physiological interference based on recursive least squares (RLS) adaptive filtering. Monte Carlo simulations have been implemented to evaluate the performance of RLS adaptive filtering. However, its suitability and performance on human data still remain to be evaluated. Here, we address the issue of how to detect evoked hemodynamic response to auditory stimulus using RLS adaptive filtering method. A multidistance probe based on continuous wave fNIRS is devised to achieve the fNIRS measurement and further study the brain functional activation. This study verifies our previous findings that RLS adaptive filtering is an effective method to suppress global interference and also provides a practical way for real-time detecting brain activity based on multidistance measurement.

Improved ‐RLS adaptive filter

In this Letter, the authors present an improved sparse recursive least squares (RLS) algorithm, which employs a novel approximation of the l 0 norm of the filter coefficient vector for regularising the RLS cost function. The proposed algorithm achieves improved performance over existing algorithms as demonstrated via numerical simulations.

Investigation of Sphere Decoder and Channel Tracking Algorithms for Media-Based Modulation over Time-Selective Channels

The performance of media-based modulation (MBM) systems, where additional information can be conveyed by the indices of the channel states created by RF mirrors, over time-selective channels is investigated. By transforming the MBM system model into a traditional MIMO system model, we first propose a reduced complexity sphere decoder algorithm. Then two channel tracking algorithms, which are based on least mean square adaptive filter and recursive least-squares adaptive filter, are employed in order to combat the performance loss caused by the time-varying channels. Numerical results show that the proposed sphere decoder and these two channel tracking algorithms perform well in MBM systems.

Removal of EOG artifacts from EEG using a cascade of sparse autoencoder and recursive least squares adaptive filter

Electrooculogram (EOG) artifacts are the most important form of interferences in electroencephalogram (EEG) based brain computer interfaces (BCIs). In traditional methods for EOG artifacts removal, either an additional EOG recording in real time or multi-channel (more than three channels) EEG recording is required. To address these limitations of existing methods, a method using a cascade of sparse autoencoder (SAE) and recursive least squares (RLS) adaptive filter is proposed to remove the EOG artifacts from EEG. The proposed approach consists of offline stage and online stage. The high-order statistical moments information in the EOG artifacts can be learned automatically by using only EOG signals during offline stage and so an SAE model is obtained. In the online stage, the learned SAE model is firstly used to identify and extract preliminary EOG artifacts from a given raw EEG signal. Then an RLS adaptive filter uses the identified EOG artifacts as reference signal to remove interference without parallel EOG recordings. Compared with the exiting methods, the proposed method has the following advantages: (i) nonuse of an additional EOG recording in removal process, (ii) few number of EEG channels being used in removal process, and (iii) time-saving. The performance of the proposed method is evaluated by EEG classification accuracy and time consumption. Compared with traditional methods, the proposed method is proven to be more effective and faster. Moreover, experiment results also show good generalization ability in cross-subject testing scenarios.

RLS Adaptive Filter With Inequality Constraints

In practical implementations of estimation algorithms, designers usually have information about the range in which the unknown variables must lie either due to physical constraints (such as power always being non-negative) or due to hardware constraints (such as in implementations using fixed-point arithmetic). In this letter, we propose a fast (i.e., whose complexity grows linearly with the filter length) version of the dichotomous coordinate descent recursive least-squares (RLS) adaptive filter which can incorporate constraints on the variables. The constraints can be in the form of lower and upper bounds on each entry of the filter, or norm bounds. We compare the proposed algorithm with the recently proposed normalized non-negative least-mean-squares (N-NLMS) and projected-gradient normalized LMS (PG-NLMS) filters, which also include inequality constraints in the variables.

Unsupervised robust recursive least-squares algorithm for impulsive noise filtering

A robust recursive least-squares (RLS) adaptive filter against impulsive noise is proposed for the situation of an unknown desired signal. By minimizing a saturable nonlinear constrained unsupervised cost function instead of the conventional least-squares function, a possible impulse-corrupted signal is prevented from entering the filter’s weight updating scheme. Moreover, a multi-step adaptive filter is devised to reconstruct the observed “impulse-free” noisy sequence, and whenever impulsive noise is detected, the impulse contaminated samples are replaced by predictive values. Based on simulation and experimental results, the proposed unsupervised robust recursive least-square adaptive filter performs as well as conventional RLS filters in “impulse-free” circumstances, and is effective in restricting large disturbances such as impulsive noise when the RLS and the more recent unsupervised adaptive filter fails.

Accurate human limb angle measurement: sensor fusion through Kalman, least mean squares and recursive least-squares adaptive filtering

Inertial sensors are widely used in human body motion monitoring systems since they permit us to determine the position of the subject's limbs. Limb angle measurement is carried out through the integration of the angular velocity measured by a rate sensor and the decomposition of the components of static gravity acceleration measured by an accelerometer. Different factors derived from the sensors’ nature, such as the angle random walk and dynamic bias, lead to erroneous measurements. Dynamic bias effects can be reduced through the use of adaptive filtering based on sensor fusion concepts. Most existing published works use a Kalman filtering sensor fusion approach. Our aim is to perform a comparative study among different adaptive filters. Several least mean squares (LMS), recursive least squares (RLS) and Kalman filtering variations are tested for the purpose of finding the best method leading to a more accurate and robust limb angle measurement. A new angle wander compensation sensor fusion approach based on LMS and RLS filters has been developed.

Flexible Riser Monitoring Using Hybrid Magnetic/Optical Strain Gage Techniques through RLS Adaptive Filtering

Flexible riser is a class of flexible pipes which is used to connect subsea pipelines to floating offshore installations, such as FPSOs (floating production/storage/off-loading unit) and SS (semisubmersible) platforms, in oil and gas production. Flexible risers are multilayered pipes typically comprising an inner flexible metal carcass surrounded by polymer layers and spiral wound steel ligaments, also referred to as armor wires. Since these armor wires are made of steel, their magnetic properties are sensitive to the stress they are subjected to. By measuring their magnetic properties in a nonintrusive manner, it is possible to compare the stress in the armor wires, thus allowing the identification of damaged ones. However, one encounters several sources of noise when measuring electromagnetic properties contactlessly, such as movement between specimen and probe, and magnetic noise. This paper describes the development of a new technique for automatic monitoring of armor layers of flexible risers. The proposed approach aims to minimize these current uncertainties by combining electromagnetic measurements with optical strain gage data through a recursive least squares (RLSs) adaptive filter.

Dynamic strain measurement system with fiber Bragg gratings and noise mitigation techniques

A low-cost fiber Bragg grating (FBG) vibrometer specifically suited for structural monitoring and aimed at the detection of low-amplitude vibrations is presented. The optical system exploits an intensity modulation principle of operation, while signal processing techniques are used to complement the transducer to improve the performances: a recursive least-squares adaptive filter improves the noise power mitigation by 14 dB, and an efficient spectral estimator permits operating spectral analysis even under high noise conditions. With these methods, a strain sensitivity of 5.6 nε has been achieved in the ±60 µε range. Experimental assessment tests carried out in typical structural monitoring contexts have demonstrated that the developed sensor is well suited to measure mechanical perturbations of different structures.

Low-Complexity RLS Algorithms Using Dichotomous Coordinate Descent Iterations

In this paper, we derive low-complexity recursive least squares (RLS) adaptive filtering algorithms. We express the RLS problem in terms of auxiliary normal equations with respect to increments of the filter weights and apply this approach to the exponentially weighted and sliding window cases to derive new RLS techniques. For solving the auxiliary equations, line search methods are used. We first consider conjugate gradient iterations with a complexity of operations per sample; being the number of the filter weights. To reduce the complexity and make the algorithms more suitable for finite precision implementation, we propose a new dichotomous coordinate descent (DCD) algorithm and apply it to the auxiliary equations. This results in a transversal RLS adaptive filter with complexity as low as multiplications per sample, which is only slightly higher than the complexity of the least mean squares (LMS) algorithm ( multiplications). Simulations are used to compare the performance of the proposed algorithms against the classical RLS and known advanced adaptive algorithms. Fixed-point FPGA implementation of the proposed DCD-based RLS algorithm is also discussed and results of such implementation are presented.

A research of UWB rake receiver based on novel RLS adaptive algorithm

A modified RAKE receiver based on novel Recursive Least Squares (RLS) adaptive algorithm is proposed. The receiver uses L-fingered correlators, which are composed of RLS adaptive filters, to enhance the performance of multipath receiving. It can also track the amplitude of the received signal to form a real-time amplitude estimation which is correlated with the power of excess delay bin. The simulation results based on the IEEE UltraWide Band (UWB) channel models (CM1 to CM4) show that the novel RLS algorithm can alter the attenuation estimation with the finger’s power delay profile, and RAKE receiver with few fingers can be employed to get high performance.

Low-rank adaptive filters

We introduce a class of adaptive filters based on sequential adaptive eigendecomposition (subspace tracking) of the data covariance matrix. These new algorithms are completely rank revealing, and hence, they can perfectly handle the following two relevant data cases where conventional recursive least squares (RLS) methods fail to provide satisfactory results: (1) highly oversampled smooth data with rank deficient of almost rank deficient covariance matrix and (2) noise-corrupted data where a signal must be separated effectively from superimposed noise. This paper contradicts the widely held belief that rank revealing algorithms must be computationally more demanding than conventional recursive least squares. A spatial RLS adaptive filter has a complexity of O(N/sup 2/) operations per time step, where N is the filter order. The corresponding low-rank adaptive filter requires only O(Nr) operations per time step, where r/spl les/N denotes the rank of the data covariance matrix. Thus, low-rank adaptive filters can be computationally less (or even much less) demanding, depending on the order/rank ratio N/r or the compressibility of the signal. Simulation results substantiate our claims. This paper is devoted to the theory and application of fast orthogonal iteration and bi-iteration subspace tracking algorithms.

An adaptive filter for steady-state evoked responses

A 2-weight adaptive filter that determines the amplitude and phase of steady-state evoked potentials is presented. Reference signals are derived from the visual stimulator that are related to corresponding harmonics of the response and the filter weights are adjusted so as to minimize the squared estimation error between the reference and the recorded signal using the recursive least squares (RLS) method. The filter, which acts as an adaptive bandpass filter, is followed by a detector based on the T circ 2 statistic. The performance of the RLS adaptive filter was compared to that of the conventional Discrete Fourier Transform (DFT) and the filtered DFT of Tang and Norcia in a series of simulations with known sinusoids buried in Gaussian noise and in EEG noise. In the simulations, the RLS adaptive filter detected signals at about 3–4 times lower signal to noise ratios than did the DFT. The RLS filter also outperformed the filtered DFT. Qualitatively similar results were obtained with human visual evoked potential recordings. The adaptive RLS filter significantly outperforms both the DFT and filtered DFT and is much simpler to implement than the filtered DFT method of Tang and Norcia.

A stability result for RLS adaptive bilinear filters

The article considers recursive least squares (RLS) adaptive nonlinear filtering using bilinear system models. It is shown that the extended RLS adaptive bilinear filter, as well as the equation-error RLS adaptive bilinear filter, are guaranteed to be stable in the sense that the time average of the squared estimation error is bounded whenever the underlying process that generates the input signals is stable in the same sense.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A numerically stable relay structure for fast RLS adaptive filtering

Long-term numerical instability is a critical problem in fast recursive least squares (RLS) adaptive algorithms. The author presents a numerically stable fast RLS relay structure (FRLS-RS), in which a conventional fast transversal RLS algorithm and a mixed time-and-order updating procedure are combined in a relay form to provide, with O(M) operations, the instantaneous filter-coefficient solution for each time step, where M is the order of the filter. Since continuous propagation of the FRLS-RS is limited to 2M+1 time steps, accumulation of the numerical errors is isolated. Both fixed-point analysis and computer simulations show that in the case of moderate precision, and when the order is not very high, the present structure is long-term numerically stable. Efficient implementation and exact initialization of the FRLS-RS are also considered. >

Tracking properties and steady-state performance of RLS adaptive filter algorithms

Adaptive signal processing algorithms derived from LS (least squares) cost functions are known to converge extremely fast and have excellent capabilities to "track" an unknown parameter vector. This paper treats analytically and experimentally the steady-state operation of RLS (recursive least squares) adaptive filters with exponential windows for stationary and nonstationary inputs. A new formula for the "estimation-noise" has been derived involving second- and fourth-order statistics of the filter input as well as the exponential windowing factor and filter length. Furthermore, it is shown that the adaptation process associated with "lag effects" depends solely on the exponential weighting parameter λ. In addition, the calculation of the excess mean square error due to the lag for an assumed Markov channel provides the necessary information about tradeoffs between speed of adaptation and steady-state error. It is also the basis for comparison to the simple LMS algorithm, in a simple case of channel identification, it is shown that the LMS and RLS adaptive filters have the same tracking behavior. Finally, in the last part, we present new RLS restart procedures applied to transversal structures for mitigating the disastrous results of the third source of noise, namely, finite precision arithmetic.