Recursive Least-squares Filter Research Articles

A Dual-Recursive-Least-Squares Algorithm for Automotive Radar Interference Suppression

Automotive radar sensors are widely used in vehicles so as to allow the “advanced driver assistance systems (ADAS)” to work. As far as we are concerned, no mandatory regulations were established so far for interference control in the cases where multiple vehicles equipped with automotive radars exist in close proximity. Consequently, those inter-vehicle cross-interference easily result in the radar performance degradation, e.g. incapability of target detection and identification. In this paper, an interference suppression algorithm is proposed which utilizes two Recursive-Least-Square (RLS) adaptive filters to estimate, the interference signals caused by the “aggressor” radar and the echo signals from the “ego” radar. The algorithm operates in the iterative mode with its initial input being the originally received beat signals involving interference. In each iteration, the estimates of the interference signals and of the clean signals are calculated sequentially by the two RLS filters, and the beat signal is updated with parts of the fragments substituted with their interference-mitigated counterparts. Such iterative operations stop when the convergence criterion, e.g. none of the fragments in the beat signals are considered being interfered, is achieved or the iteration number reaches the limit predefined due to the practical constraints. Simulation and measurement results demonstrate that the proposed dual-RLS-based algorithm outperforms the existing methods in terms of lower interference-to-signal ratio resultant and superior capability of retrieving the original range-Doppler profile.

Synchronized Human-Humanoid Motion Imitation

We present a tele-operation control framework that (i) enhances the upper motion synchrony between a user and a robot using the minimum-jerk model coupled with a recursive least-square filter, and (ii) synchronizes the walking pace by predicting user's stepping frequency using motion capture data and a deep learning model. By integrating (i) and (ii) in a task-space whole-body controller, we achieve full-body synchronization. We assess our humanoid-to-human whole-body synchronized motion model on the HRP-4 humanoid robot in forward, lateral and backward walks with concurrent upper limbs motions experiments.

A Methodology for Enhancing SSVEP Features Using Adaptive Filtering Based on the Spatial Distribution of EEG Signals.

In this paper, we propose a classification algorithm of EEG signal based on canonical correlation analysis (CCA) and integrated with adaptive filtering. It can enhance the detection of steady-state visual evoked potentials (SSVEPs) in a brain-computer interface (BCI) speller. An adaptive filter is employed in front of the CCA algorithm to improve the signal-to-noise ratio (SNR) of SSVEP signals by removing background electroencephalographic (EEG) activities. The ensemble method is developed to integrate recursive least squares (RLS) adaptive filter corresponding to multiple stimulation frequencies. The method is tested by the SSVEP signal recorded from six targets by actual experiment and the EEG in a public SSVEP dataset of 40 targets from Tsinghua University. The accuracy rates of the CCA method and the CCA-based integrated RLS filter algorithm (RLS-CCA method) are compared. Experiment results show that the proposed RLS-CCA-based method significantly improves the classification accuracy compared with the pure CCA method. Especially when the number of EEG leads is low (three occipital electrodes and five non occipital electrodes), its advantage is more significant, and accuracy reaches 91.23%, which is more suitable for wearable environments where high-density EEG is not easy to collect.

Alignment scheme optimization when gyro accuracy inconsistency for inertial navigation system

Rotation modulation technology can average out constant errors in fiber optic gyro (FOG) rotational inertial navigation system (RINS). As a result, angle random walk (ARW) of FOGs plays a significant role in the precision of initial alignment. Using different gyros as horizontal gyros gradually transitioned from theory to practical application with the advancement of design philosophy. The theoretical formula between azimuth alignment accuracy and random walk coefficients (RWCs) of two horizontal gyros is deduced in this paper. A completely new multiple rotations and stationary alignment scheme is suggested. A recursive least-squares filter with azimuth variation in body reference frame and accelerometer outputs in navigation frame as measurements is constructed. The efficiency of this method is demonstrated through simulation and experimentation. The findings demonstrate that using this formula and alignment scheme, azimuth alignment accuracy could be greatly increased, which can be improved by 10.85% compared to common continuous rotation alignment scheme.

Adaptive estimation of sparse channel based on modified RLS for coherent underwater acoustics communications

A new channel estimation approach used in coherent underwater acoustic communication system is presented in this paper. The proposed method consists of two steps: (1) obtain the initial channel estimation based on least square (LS) and the sparse characteristics of underwater acoustic channels; (2) track the channels using the modified recursive least squares (RLS). In the first step, the threshold value to set all coefficients below it to zero is deduced. In the second step, a modified RLS based on the idea of RLS and Kalman filter terminology is proposed. Experimental results show that the proposed method can track underwater acoustic channels well. The lower symbol error rate (SER) and higher output SNR can be achieved.

Beam and Channel Tracking for 5G Communication Systems Using Adaptive Filtering Techniques: A Comparison Study

In this paper, we study the problem of beam tracking of a multipath channel in millimeter-wave massive MIMO communication system using adaptive filters. We focus on the performance of least-mean-square filter (LMS) and recursive least-squares filter (RLS) algorithms, compared to a reference extended Kalman filter (EKF), in scenarios where the wireless channel is dominated by a single line of sight (LOS) path or a small number of strong paths. The signal direction and channel coefficients are tracked and updated using these filters. Our results recommend that beamforming systems at millimeter-wave bands should consider variable number of paths rather than a single dominant LOS path. Furthermore, we show that the mean squared-error (MSE) of the innovation process gives a better overall view of the tracking performance than the MSE of the state parameters.

Estimation of state-of-power capability for lithium-ion battery considering limiting conditions recalibration

ABSTRACT As one of the most significant deciding factors for energy management systems (EMSs) and battery management systems (BMSs) in electrified vehicles, battery state-of-power (SOP) estimation is an area of interest in battery research. Battery model parameters change obviously under the limiting working condition of SOP, and the available maximum current and state-of-charge (SOC) have to be updated for accurate SOP estimation. This paper tries to contribute to the existing literature as follows: Based on Thevenin model, recursive least-square (RLS) and H-infinity filter algorithm are adopted for parameter identification and SOC estimation for a recalibration purpose to improve the prediction of battery SOP under variable degradation. Multi-constraints are firstly adopted to calculate the limiting current, and the response function of capacity loss-temperature-discharge rate is brought back to correct the actual capacity at this current for the revised limiting current with consideration of weight distribution ratio. Finally, the experiment verifies that the final maximum charging-discharging current modifies the initial calculation value by 5% and 4%, and realizes the more accurate online SOP estimation. This method provides a more accurate and reliable SOP estimation method for electric vehicles.

Muscle Artifact Removal Toward Mobile SSVEP-Based BCI: A Comparative Study

Steady-state visual evoked potential (SSVEP) serves as one of the extensively utilized paradigms for brain–computer interface (BCI). SSVEP-based BCI has advantages of good classification accuracy, high information transfer rate (ITR), and little user training. However, there exist few studies investigating SSVEP-based BCI in the mobile situation, where electroencephalography (EEG) data are inevitably contaminated by muscle activities, and meanwhile, a limited number of channels are preferred. In this study, two major muscle artifact removal schemes are investigated in the dynamic scenario. One scheme adopts state-of-the-art blind source separation (BSS) methods without electromyogram (EMG) reference, while the other utilizes auxiliary EMG channels as a reference in the denoising process. To evaluate the performance of two schemes, we have tested them on real EEG data collected from ten subjects. The results demonstrate that, in the few-channel condition of SSVEP data, there are classification accuracy improvements of 9.93% for the canonical correlation analysis (CCA) indicator and 15.72% for the task-related component analysis (TRCA) indicator after processed by recursive least-squares (RLS) filtering with auxiliary EMG, and in the single-channel condition, there are classification accuracy improvements of 22.00% for the CCA indicator and 24.42% for the TRCA indicator after RLS filtering, averaged across all the subjects and data lengths. However, the BSS-based methods fail to improve the classification accuracies of SSVEP. Thus, it is of necessity to mount additional EMG channels for effective muscle activity suppression. This study provides an insightful suggestion for future real-life BCI applications.

Tensor Recursive Least Squares Filters for Multichannel Interrelational Signals

It is well known that recursive least squares (RLS) filter is a prevalent adaptive filter that recursively updates the filter-coefficients to minimize a weighted cost function related to an input signal. Conventionally, such an input signal is a sequence of scaler numbers. Multichannel signals generated from one or more sources are often encountered nowadays. Therefore, there emerges a urgent demand to generalize the conventional RLS filter to accommodate multichannel signals with implicit interrelations. The key issue of this new generalization is to convert the correlation matrix involved in the conventional RLS filter for one-dimensional input to the correlation tensor required by the new RLS filter for multi-dimensional input. Due to lack of the sufficient mathematical framework of the required tensor operations, here we make the first attempt to established the new tensor recursive least squares filter (TRLS) theory based on our newly derived Woodbury tensor identity. We apply the Woodbury tensor identity to design a recursive algorithm for updating the weight-tensor. Furthermore, the performance analysis of the proposed new TRLS algorithm, including mean-squared deviation and misadjustment, are facilitated using the established tensor calculus theory. Numerical experiments are also presented to investigate the convergence speed, mean-squared deviation, and misadjustment for input signals with various statistical characteristics and different dimensions.

Restoration of the electrocardiogram during mechanical cardiopulmonary resuscitation

Objective: An artefact-free electrocardiogram (ECG) is essential during cardiac arrest to decide therapy such as defibrillation. Mechanical cardiopulmonary resuscitation (CPR) devices cause movement artefacts that alter the ECG. This study analyzes the effectiveness of mechanical CPR artefact suppression filters to restore clinically relevant ECG information. Approach: In total, 495 10 s ECGs were used, of which 165 were in ventricular fibrillation (VF), 165 in organized rhythms (OR) and 165 contained mechanical CPR artefacts recorded during asystole. CPR artefacts and rhythms were mixed at controlled signal-to-noise ratios (SNRs), ranging from –20 dB to 10 dB. Mechanical artefacts were removed using least mean squares (LMS), recursive least squares (RLS) and Kalman filters. Performance was evaluated by comparing the clean and the restored ECGs in terms of restored SNR, correlation-based similarity measures, and clinically relevant features: QRS detection performance for OR, and dominant frequency, mean amplitude and waveform irregularity for VF. For each filter, a shock/no-shock support vector machine algorithm based on multiresolution analysis of the restored ECG was designed, and evaluated in terms of sensitivity (Se) and specificity (Sp). Main results: The RLS filter produced the largest correlation coefficient (0.80), the largest average increase in SNR (9.5 dB), and the best QRS detection performance. The LMS filter best restored VF with errors of 10.3% in dominant frequency, 18.1% in amplitude and 11.8% in waveform irregularity. The Se/Sp of the diagnosis of the restored ECG were 95.1/94.5% using the RLS filter and 97.0/91.4% using the LMS filter. Significance: Suitable filter configurations to restore ECG waveforms during mechanical CPR have been determined, allowing reliable clinical decisions without interrupting mechanical CPR therapy.

CASINOR: Combination of adaptive filters using single noise reference signal for heart rate estimation from PPG signals

The accuracy of the heart rate (HR) estimated from the photoplethysmography (PPG) signal is always skeptical due to the ubiquity of the motion artifact (MA) in the signal. To ensure the HR estimated from the PPG signal is accurate, a new algorithm is proposed for the removal of MA component from the PPG signal using accelerometer signals. In this paper, the combination of adaptive filters using single noise reference signal referred to as CASINOR is proposed. The recursive least square (RLS) and normalized least mean square (NLMS) adaptive filters are used for denoising the PPG signals. The selection of single noise reference signal is based on the power value of the accelerometer signals. The MA-reduced PPG signals obtained from these RLS and NLMS filters are combined to a single PPG signal using sigmoid function, and the HR is estimated. The estimated HR is refined by using phase vocoder. The proposed method resulted in less HR estimation error of 1.92 beat per minute (BPM) on 23 PPG datasets (IEEE SP CUP 2015). Reduced error value, less computational time and improved accuracy augment this technique to be implemented in wearable devices.

A new integrated analytics approach for wind turbine fault detection using wavelet, RLS filter and random forest

ABSTRACT Nowadays wind energy production is growing fast, and the cost of operation and maintenance is growing fast also. Most wind turbines (WTs) are equipped with supervisory control and data acquisition (SCADA) system for system control and logging data. Huge amounts of data acquired for SCADA systems can be used for condition monitoring and fault detection (CMDF) by applying data mining methods. However, the collected data are not used effectively. Few researches are about input and output data optimization and proper feature selection. In this paper, the proposed method regards SCADA data as data points. Wavelet analysis is applied to the input signal to make noise reduction and uses recursive least square (RLS) filter to reduce false alarm rate. On the basis of the general model-based CMDF approach, the random forest algorithm is used to find the best input features. With these methods applied, a more precise output is obtained as well and greatly reduces the false alarm rate as well. Experiments are given with real SCADA data to show the effectiveness of the proposed method.

Adaptive Control of a Piezo-Actuated Steering Mirror to Restrain Laser-Beam Jitter

Tracking, pointing, and imaging performances of precision laser systems are restricted by laser-beam jitter, which is time varying or uncertain. This paper proposes an adaptive control that uses a piezo-actuated steering mirror to actively resist the jitter and achieve precise pointing. First, in order to realize the single-valued linear input–output relationship, which can simplify the adaptive-control design and improve the stability and convergence rate of the adaptive filter algorithm, the hysteresis non-linearity of the piezo-actuators is feedforward compensated. Then, an adaptive controller is built based on an adaptive lattice recursive least-square filter that identifies the disturbance statistics in real-time by utilizing sensor data from a position sensing detector. The developed controllers are verified on a jitter-control system. Experimental results demonstrate that the adaptive-control method significantly extends the disturbance-rejection bandwidth, and that the control performance surpasses the conventional proportion-integral-differential (PID) control method.

Particle Swarm Intelligence Based Univariate Parameter Tuning of Recursive Least Square Algorithm for Optimal Heart Sound Signal Filtering

Heart Sound Signal (HSS) is considered as one of the important bio-signals. It carries vital information about the heart functions. For bio-acoustic observations, the HSS is diagnosed and recorded with auscultatory procedures. During auscultation, the noisy components gets added along with the reading. The physician’s individual diagnostic experience, ecological noise and the intersection of heart and lung sound signal (LSS) are considered as the major noisy components in HSS diagnosis. Suppression of LSS from the HSS is a challenging task. Due to its quasi stationary nature, adaptive filtering techniques are used for the noise removal. In this paper, Recursive Least Square (RLS) adaptive algorithm is proposed to obtain the HSS from the noisy mixture. Faster convergence is a benefit in selecting RLS algorithm over other adaptive algorithms. The forgetting factor is one of the important parameters of RLS which defines the convergence. The RLS performance is improved by choosing an optimal forgetting factor. A Particle Swarm Optimization (PSO) based search algorithms are deployed for optimization. To enhance the implementation time, a Dynamic Neighbourhood Learning Particle Swarm Optimizer (DNL-PSO) is analysed. In DNL-PSO, each particle studies from its knowledge in dynamically varying neighbourhood that prevents early convergence. The normal HSS with different LSS interference is taken to assess the RLS filter performance. In this paper, the RLS algorithm performance is compared with Least Mean Square (LMS) adaptive algorithms. Various metrics are used to compare the performance of both RLS and optimization algorithms.

Classification of Tectonic and Nontectonic Earthquakes by an Integrated Learning Algorithm

A machine learning model for accurate and quick classification of tectonic and nontectonic earthquakes is proposed. Firstly, an improved method is proposed for detection of first arrivals. An iterative approach is applied for the multiwindow algorithm to decrease its computational cost, then a new method for detection of first arrivals is proposed by combining the improved multiwindow algorithm with a recursive least-squares filter and the Akaike information criterion. Secondly, it is shown that the integrated learning algorithm is a suitable method for classification, then four suitable features are manually selected to train it. Thirdly, the three parameter values of the integrated learning model are determined to improve its accuracy. Finally, based on seismic data from the China Earthquake Networks Center, simulations are conducted to test the validity of the proposed method for detection of first arrivals, then the classification accuracy is tested. The results show an accuracy of the model of 88.88%, indicating effective classification performance.

Design of an online-tuned model based compound controller for a fully automated artificial pancreas.

This paper deals with the development of a control algorithm that can predict optimal insulin doses without patients' intervention in fully automated artificial pancreas system. An online-tuned model based compound controller comprising an online-tuned internal model control (IMC) algorithm and an enhanced IMC (eIMC) algorithm along with a meal detection module is proposed. Volterra models, used to develop IMC and eIMC algorithms, are developed online using recursive least squares (RLS) filter. The time domain kernels, computed online using RLS filter, are converted into frequency domain to obtain Volterra transfer function (VTF). VTFs are used to develop both IMC and eIMC algorithms. The compound controller is designed in such a way that eIMC predicts insulin doses when the glucose rate increase detector of meal detection module is positive, otherwise conventional IMC takes the control action. Experimental results show that the compound controller performs robustly in the presence of higher and irregular amounts of meal disturbances at random times, very high actuator and sensor noises and also with the variation in insulin sensitivity. The combination of compound control strategy and meal detection module compensates the shortcomings of both slow subcutaneous insulin action that causes postprandial hyperglycemia, and delayed peak of action that causes hypoglycaemia. Graphical Abstract A fully-automated artificial pancreas system containing glucose sensor, insulin pump and control algorithm. Block diagram showing the control algorithm i.e., online-tuned compound IMC comprising enhanced IMC, conventional IMC and meal detection module, developed in the present work.

Removal of ECG Artifacts From EEG Using an Effective Recursive Least Square Notch Filter

Electroencephalogram (EEG) is a common tool for medical diagnosis, cognitive research, and managing neurological disorders. However, EEG is usually contaminated with various artifacts, making it difficult to interpret EEG data. In this study, a recursive least square (RLS) notch filter was developed to effectively suppress electrocardiogram (ECG) artifacts from EEG recordings. ECG artifacts were estimated and modeled using the instantaneous frequency of the cardiac cycle. Then it was adaptively estimated using a RLS filter and directly subtracted from contaminated EEG data. Based on the validation measures of improvement of normalized power spectrum (INPS), mean square error (MSE) and information quantity (IQ), the performance of ECG artifacts suppression was compared among the proposed RLS approach, independent component analysis (ICA) and blind deconvolution method under information maximization (Infomax) on simulated and animal experimental data. Simulation data demonstrated that INPS of RLS method (19.75(18.37,20.95) dB) was significantly higher than that of ICA (4.35(3.35,5.41) dB) and Infomax (5.76(4.60,6.88) dB). Meanwhile, MSE of RLS method (0.20(0.08,0.53) μV 2 ) was considerably lower than that of ICA (5.59(2.35,19.79) μV 2 ) and Infomax (3.21(1.01,10.69) μV 2 ). Animal experimental data showed that INPS was 1.76(0.42,9.40) dB for RLS method, which was dramatically higher than that of ICA (0.02(0.00,0.14) dB) and Infomax (0.57(0.08,2.45) dB). The calculated IQ for RLS method (0.331(0.021,0.584)) was relatively lower than that of raw EEG (0.350(0.070,0.586)), ICA (0.350(0.069,0.581)) and Infomax (0.341(0.050,0.585)). The RLS notch filter can effectively eliminate ECG artifacts from EEG and preserve the majority of EEG information with little loss.

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.

Ambient Data-Based Online Electromechanical Mode Estimation by Error–Feedback Lattice RLS Filter

This paper proposes a novel error-feedback lattice recursive least-squares (EF-LRLS) filter for online estimation of power system oscillatory modes. The EF-LRLS filter is applied to ambient data provided by phasor measurement units to identify the autoregressive (AR) model parameters. This filter has a modular structure; accordingly, if the length of the filter equals $N$ , it identifies AR(1) to ${\rm{AR(}}N)$ models concurrently. In the proposed method, removing very low and high frequencies and resampling steps are fulfilled in an online fashion. This adaptive filter has less computational complexity than standard RLS filter, making it an appropriate choice for online system identification. The proposed algorithm is tested using simulated ambient data of the 16-machine, 68-bus test system, as well as real measurement data of the WSCC system breakup on Aug. 10, 1996. Performance of the proposed algorithm is examined under different conditions with different amplitudes of variation and signal-to-noise ratio. The results prove accuracy, robustness, and effectiveness of the proposed method.

Signal conditioning for the recursive least-squares filter in ultrasonic testing of materials

Signal conditioning for the recursive least-squares filter in ultrasonic testing of materials