Linear Error Research Articles

Offshore wind power generation system control using robust economic MPC scheme

With the increasing penetration of wind power in the modern power system, the economic model predictive control (EMPC) has been widely employed in the control of the offshore wind power generation system for promoting the dynamic economy. A robust EMPC strategy, aiming to minimizing damage to the turbine while maximizing the electric power output, is developed in this paper to enhance the dynamic economic performance under uncertain wind speed variation. A linear model is utilized to approximate the original nonlinear behavior of the wind power generation system, while the consequent linearization error is taken as the external disturbance of the control system. A linear feedback controller with a robust control invariant set is designed to restrict the deviation between the nominal linear system and the actual nonlinear wind power generation system. Plant simulations, as well as NREL FAST code testing, are given to demonstrate the proposed controller's effectiveness throughout the overall operating region.

Drift Resilient Frequency-Based Sensor Interface Architectures with Adaptive Clock Frequency

Maintaining the accuracy of a sensor system across various operating conditions has always been a challenge, especially for those operating in harsh surroundings such as a radiation environment. Concerning frequency-based sensor interfaces, supply voltage drifts and gain shift of the voltage-to-frequency converter (VFC) are critical design issues. These manifest as gain, offset, and linearity errors at the system level and therefore require continuous correction mechanisms. In this paper, dynamic gain and offset error-compensated open-loop frequency-based sensor interface architectures with adaptive clock frequency are proposed, which result in a ratiometric digital output. To address the mismatch issue, two architectures, one with periodic swapping of the VFCs’ inputs and outputs, and the other with the use of a single analog-to-digital converter (ADC) as an analog front end, are developed. The concepts were demonstrated with implementations on a Zynq board (ZYBO). The results of the first architecture showed that for a 25% gain mismatch between the VFCs, the output gain error was reduced from around 7.4% to 0.79% and the offset error was reduced from around 11.8% to 0.01%. Additionally, for the second architecture, a maximum of 0.11% gain error and 0.1% offset error were recorded for an emulated ±25% supply drift.

Outlier‐robust zonotope set‐membership filter for discrete‐time nonlinear system

AbstractTransient sensor malfunction, improper replacement measures, and large non‐Gaussian noise can cause data outliers in real‐world scenarios. In this article, an outlier‐robust zonotope set‐membership filter is proposed for uncertain nonlinear systems susceptible to outliers. In order to linearize nonlinear systems, a linearization method based on Stirling's interpolation formula is proposed. Then, an outlier detector utilizing the linearization error bounds, the prediction domain, and the output feasible domain is constructed. Based on the linearized system, a tight strip construction method is given to reduce the conservatism of the estimated enclosure. Moreover, a prediction‐correction‐backward reconstruction filter structure is designed to improve estimation accuracy and reduce conservatism. The proposed structure fuses historical data to attenuate the impact of uncertainty on the system. The robustness, guarantee, and convergence of the proposed filter are investigated. Finally, the effectiveness of the proposed approach is evaluated by two simulation examples.

Channel Estimation for RIS-Assisted MIMO Systems in Millimeter Wave Communications

The large number of estimated parameters in a reconfigurable intelligent surface (RIS) makes it difficult to achieve accurate channel estimation accuracy in 6G. Therefore, we suggest a novel two-phase channel estimation framework for uplink multiuser communication. In this context, we propose an orthogonal matching pursuit (OMP)-based linear minimum mean square error (LMMSE) channel estimation approach. The OMP algorithm is used in the proposed algorithm to update the support set and pick the columns of the sensing matrix that are most correlated with the residual signal, which successfully reduces pilot overhead by removing redundancy. Here, we use LMMSE’s advantages for handling noise to address the problem of inadequate channel estimation accuracy when the signal-to-noise ratio (SNR) is low. Simulation findings demonstrate that the proposed approach outperforms least-squares (LS), traditional OMP, and other OMP-based algorithms in terms of estimate accuracy.

Ellipsotopes: Uniting Ellipsoids and Zonotopes for Reachability Analysis and Fault Detection

Ellipsoids are a common representation for reachability analysis, because they can be transformed efficiently under affine maps, and they allow conservative approximation of Minkowski sums, which let one incorporate uncertainty and linearization error in a dynamical system by expanding the size of the reachable set. Zonotopes, a type of symmetric, convex polytope, are similarly frequently used, because they allow efficient numerical implementations of affine maps and exact Minkowski sums. Both of these representations also enable efficient, convex collision detection for fault detection or formal verification tasks, wherein one checks if the reachable set of a system collides (i.e., intersects) with an unsafe set. However, both representations often result in conservative representations for reachable sets of arbitrary systems, and neither is closed under intersection. Recently, representations such as constrained zonotopes and constrained polynomial zonotopes have been shown to overcome some of these conservativeness challenges, and are closed under intersection. However, constrained zonotopes can not represent shapes with smooth boundaries such as ellipsoids, and constrained polynomial zonotopes can require solving a non-convex program for collision checking or fault detection. This paper introduces <i>ellipsotopes</i>, a set representation that is closed under affine maps, Minkowski sums, and intersections. Ellipsotopes combine the advantages of ellipsoids and zonotopes while ensuring convex collision checking. The utility of this representation is demonstrated on several examples.

81 Gb/s Dual-Polarization Discrete Eigenvalue Transmission Based on Nonlinear Fourier Transform

We investigated dual-polarization (DP) discrete eigenvalue transmissions and propose to shift the solitons in one polarization by half a symbol period with respect to the soliton train in the other polarization. Simulation results are conducted to illustrate its advantages over conventional schemes. Experiments of a net 81 Gb/s dual-polarization discrete eigenvalue transmissions over 650 km are also demonstrated with the help of DP multi-symbol linear minimum mean-squared error (DP-MS-LMMSE) filters for eigenvalues and b-coefficients.

Performance Analysis of Active RIS-Aided Systems in the Face of Imperfect CSI and Phase Shift Noise

The linear minimal mean square error (LMMSE) estimator for active reconfigurable intelligent surface (RIS)-aided wireless systems is formulated. Furthermore, based on the moment-matching method, we employ the Gamma distribution to approximate the distribution of the instantaneous received signal-to-interference-plus-noise ratio (SINR), and then derive the closed-form outage probability and ergodic channel capacity in the presence of realistic channel estimation errors, the thermal noise of RIS amplifiers and the RIS phase shift noise. Our theoretical analysis and simulation results show that the introduction of RIS amplifiers is equivalent to increasing of the transmit power, and also present the performance degradation resulting from the channel estimation error and the RIS phase noise.

Array Calibration and Digital Predistortion Training Using Embedded Near-Field Feedback Probes and Orthogonal Coding for Enhancing the Performance of Millimeter-Wave Beamforming Arrays

This letter proposes an active array calibration and digital predistortion (DPD) training method that relies on a series of measurement data captured using near-field (NF) probes embedded within the array to enhance the performance of millimeter-wave (mm-wave) radio frequency (RF) beamforming arrays. These measurements are obtained using phase settings that are based on orthogonal coding to enable the characterization of the linear and nonlinear errors in the array’s RF chains. The use of embedded NF probes in the proposed method makes it suitable for infield testing. Specifically, the proposed theory is formulated to allow for beamforming-phase-dependent error calibration as well as array linearization without resorting to element-wise measurement or far-field (FF)-based feedback. Furthermore, the proposed theory does not impose a flat coupling requirement between the NF probes and the array antenna elements. Experimental results are conducted on a custom-built 16-element RF beamforming array with four embedded NF probes and operated at 37.5 GHz. The measurements revealed that applying the proposed calibration method reduced the imbalance in the radiation pattern side lobes by up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2$</tex-math> </inline-formula> dB and achieved comparable performance to element-wise FF-based calibration. Furthermore, the proposed DPD training method enabled increasing the effective isotropic radiated power (EIRP) from 32 to 34.2 dBm while maintaining an error vector magnitude (EVM) below 3.5%.

IRS-Assisted MISO System With Phase Noise: Channel Estimation and Power Scaling Laws

Recent studies have shown that intelligent reflecting surfaces (IRS) can significantly improve the spectral and energy efficiency of wireless communication links. However, most works assume perfect transceivers and IRS, which is impractical in real communication systems. In this work, we study the effect of the hardware impairments in IRS-assisted MISO systems with single user, where we consider both phase noise caused by the imperfect transceivers and IRS. To this end, we propose a linear minimum mean square error (LMMSE) channel estimation algorithm that takes the phase noise into account. Furthermore, we study the impact of phase noise on the downlink performance of an IRS-assisted system. Both analytical and numerical results are presented, where we prove that the transceiver phase noise can be compensated with the optimized IRS, while the IRS phase noise remains but is not exacerbated. As the number of reflective elements <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> approaches infinity, the IRS phase noise results in a constant loss in terms of the ergodic rate. Moreover, we find that the phase noise has no impact on the scaling laws. If the direct channel is blocked and as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> → ∞, the transmit power can be scaled down by 1/ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> and 1/ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , respectively, for random and optimized IRS, without compromising the received signal to noise ratio (SNR).

Equivariant Filter (EqF)

The kinematics of many systems encountered in robotics, mechatronics, and avionics are naturally posed on homogeneous spaces; that is, their state lies in a smooth manifold equipped with a transitive Lie group symmetry. This paper proposes a novel filter, the <i>Equivariant Filter (EqF)</i>, by posing the observer state on the symmetry group, linearising global error dynamics derived from the equivariance of the system, and applying extended Kalman filter design principles. We show that equivariance of the system output can be exploited to reduce linearisation error and improve filter performance. Simulation experiments of an example application show that the EqF&#x00A0;significantly outperforms the extended Kalman filter and that the reduced linearisation error leads to a clear improvement in performance.

Virtual angle‐based adaptive control for trajectory tracking and balancing of ball‐balancing robots without velocity measurements

SummaryThis article proposes a virtual angle‐based adaptive control method for trajectory tracking and balancing of ball‐balancing robots without velocity measurements. The trajectory tracking and balancing control of ball‐balancing robots is challenging due to underactuation and uncertain nonlinearities. The hierarchical control strategy, which designs the control system using a linear combination of trajectory tracking and balancing errors, can be a solution. However, it has a local minimum problem where the convergence of tracking and balancing errors is not guaranteed even though the linear combination error is zero. Therefore, a virtual angle‐based control method is presented, which can solve the underactuation problem without the local minimum issue. In addition, a neural network‐based observer is developed to estimate the velocity information of ball‐balancing robots with uncertainties, and the input saturation problem is considered. It is proven that all tracking and balancing errors are bounded and can be made arbitrarily small in the Lyapunov sense. Finally, simulation results are provided to verify the effectiveness of the proposed control system.

Geometric Error Parameterization of a CMM via Calibrated Hole Plate Archived Utilizing DCC Formatting

This study implemented the measurement results and administrative information obtained from the hole plate into the Digital Calibration Certificate (DCC). The DCC comprises three parts: Norms and Standards, Hierarchical Structure, and XML as Exchange Format. DCCs play a significant role in the field of metrology and statistics by ensuring data interoperability, correctness, and traceability during the conversion and transmission process. The hole plate is a length standard used for two-dimensional geometric error measurements. We evaluated the accuracy of the high-precision coordinate measuring machine (CMM) in measuring a hole plate and compared the measurement error results obtained from the hole plate with those of the laser interferometer, autocollimator, and angle square. The results show that the maximum difference in linear error is −0.30 μm, the maximum difference in angle error is −0.78″, and the maximum difference in squareness error is 4.54″. The XML is designed for machine-readability and is modeled and edited using the XMLSpy 2022 software, which is based on information published by PTB. The administrative management and measurement results tasks are presented in PDF format, which is designed for human-readability and ease of use. Overall, we implemented the measurement results and information obtained from the hole plate into the DCC.

Wind-storage combined system based on just-in-time-learning prediction model with dynamic error compensation

High-performance wind power prediction (WPP) models can decrease the uncertainty of the whole energy system to balance energy supply and demand more effectively. However wind power process is characterized by the complicated mechanism and strong nonlinearity, which makes it difficult to establish a high-performance WPP model. In this paper, wind-storage combined system (WSCS) based on just-in-time-learning (JITL) prediction model with dynamic error compensation is proposed for high-performance WPP. This method can describe the characteristics of local wind power process efficiently and accurately by approximating the nonlinear process into a composite process with dynamic linear autoregression and static nonlinear error compensation. What's more, a WSCS model is proposed to indirectly improve the prediction accuracy. The model employs energy storage systems (ESS) to complement wind farm output to improve the wind power fluctuation and the performance of WPP. Simulation results verify that the proposed model has high prediction performance and generalization ability. Specifically, the RMSE, MAE and MAPE are 58.8728KW, 33.1277KW, 4.5877 % for gale season in a month. The RMSE, MAE and MAPE are 52.2014KW 33.2680KW, 2.3628 % for breeze season in a month. And WSCS indirectly improved the accuracy of the day-ahead prediction that reduced the RMSE from 414.4409KW to 182.2397KW. Accordingly, the research results can improve the WPP technology and reduce the redundant energy of wind power through ESS to facilitate the storage of ESS and improve the wind power fluctuation.

Comprehensive Evaluations of NLOS and Linearization Errors on UWB Positioning

Currently, ultra-wide band (UWB) is adopted as a useful high-accuracy positioning technique in satellite-blocked areas. However, UWB’s positioning performance would be limited significantly because of non-line of sight (NLOS) errors. Additionally, the truncation errors in these linearization-based adjustments such as least squares (LS) and extended Kalman filter (EKF) would also visibly degrade UWB positioning accuracy. To overcome the impacts of NLOS errors and truncation errors, this paper introduced a robust-theory-based particle filter (RPF) into UWB positioning. In such a method, the IGG-III model and PF were adopted to limit the impacts of NLOS errors and truncation errors, respectively, by introducing a weight inflation factor and particle group. For comparison, the Bancroft, LS, EKF, unscented Kalman filter (UKF), cubature Kalman filter (CKF), PF, and RPF were also presented. Here, the influences of truncation errors were analyzed by comparing the results based on LS and EKF with those calculated by UKF, CKF, and PF. The impacts of NLOS errors were evaluated by making a comparison between the results of PF and RPF. Results based on a set of simulated UWB data and a group of experiment UWB data demonstrated that the RPF can significantly avoid the positioning errors caused by both truncation errors and NLOS errors. In general, position improvements percentages of 57.2%, 52.7%, 39.6%, 38.2%, 26.6%, and 20.4% can be obtained by RPF compared to those calculated by Bancroft, LS, EKF, UKF, CKF, and PF, respectively. As a comparison, the truncation error would lead to about 8.1%, 10.1%, and 33.2% accuracy decrease in the north, east, and vertical directions on average. Such accuracy-decrease rates caused by NLOS were 6.1%, 5.2%, and 25%.

Research on Path Tracking for an Orchard Mowing Robot Based on Cascaded Model Predictive Control and Anti-Slip Drive Control

In complex orchard environments, orchard mowing robots are prone to longitudinal slippage because of the characteristics of tires and the adhesion conditions of the road surface, which makes it difficult for the robots to maintain high-precision path tracking and autonomous navigation positioning. This not only affects the accuracy of path tracking but also leads to unstable motion for the mowing robots. To solve the above problems, we take an orchard mowing robot as the control object and establish a cascaded path-tracking controller and an adaptive time domain model based on a kinematics model. By designing a linear error model, an objective function, and constraint conditions for the mowing robot, the optimal linear velocity and angular velocity of the mower are obtained and converted into the speed of the driving wheel. Then, an anti-slip driving controller is designed based on fuzzy control of the slip rate. The slip-rate-based fuzzy controller is constructed according to the real-time speed of the mower and the reference speed of the driving wheel solved by the model predictive controller, and anti-slip driving control is implemented through a combination of a PID controller and a tire dynamics model. To verify the effectiveness of the proposed method, simulation and field experiments are conducted. The experimental results show that the slip rate of the driving wheel of the mower remains within the target slip rate range in the orchard working environment, avoiding excessive driving wheel sliding. Furthermore, the average lateral error of the path-tracking controller is controlled within 0.05 m, and the average value of the longitudinal error is kept within 0.04 m, which satisfies the control accuracy requirements of lawn mower operations. The proposed method provides a reference optimization scheme for improving the path-tracking and motion stability of a mowing robot.

A Novel Multistage Back Projection Fast Imaging Algorithm for Terahertz Video Synthetic Aperture Radar

Terahertz video synthetic aperture radar (THz-ViSAR) has tremendous research and application value due to its high resolution and high frame rate imaging benefits. However, it requires more efficient imaging algorithms. Thus, a novel multistage back projection fast imaging algorithm for the THz-ViSAR system is proposed in this paper to enable continuous playback of images like video. The radar echo data of the entire aperture is first divided into multiple sub-apertures, as with the fast-factorized back projection algorithm (FFBP). However, there are two improvements in sub-aperture imaging. On the one hand, the back projection algorithm (BPA) is replaced by the polar format algorithm (PFA) to improve the sub-aperture imaging efficiency. The imaging process, on the other hand, uses the global Cartesian coordinate system rather than the local polar coordinate system, and the wavenumber domain data of the full aperture are obtained step by step through simple splicing and fusion, avoiding the amount of two-dimensional (2D) interpolation operations required for local polar coordinate system transformation in FFBP. Finally, 2D interpolation for full-resolution images is carried out to image the ground object targets in the same coordinate system due to the geometric distortion caused by linear phase error (LPE) and the mismatch of coordinate systems in different imaging frames. The simulation experiments of point targets and surface targets both verify the effectiveness and superiority of the proposed algorithm. Under the same conditions, the running time of the proposed algorithm is only about 6% of FFBP, while the imaging quality is guaranteed.

A robust cooperative localization algorithm based on covariance intersection method for multi-robot systems.

Cooperative localization is an arising research problem for multi-robot system, especially for the scenarios that need to reduce the communication load of base stations. This article proposes a novel cooperative localization algorithm, which can achieve high accuracy localization by using the relative measurements among robots. To address uncertainty in the measuring robots' positions and avoid linearization errors in the extended Kalman filter during the measurement update phase, a particle-based approximation method is proposed. The covariance intersection method is then employed to fuse preliminary estimations from different robots, guaranteeing a minimum upper bound for the fused covariance. Moreover, in order to avoid the negative effect of abnormal measurements, this article adopts the Kullback-Leibler divergence to calculate the distances between different estimations and rejects to fuse the preliminary estimations far from the estimation obtained in the prediction stage. Two simulations are conducted to validate the proposed algorithm. Compared with the other three algorithms, the proposed algorithm can achieve higher localization accuracy and deal with the abnormal measurement.

HEX: a safe research framework for hybrid EMT X-ray navigation

PurposeNavigating with continuous X-ray provides visual guidance, but exposes both surgeon and patient to ionizing radiation, which is associated with serious health risks. Interleaving fluoro snapshots with electromagnetic tracking (EMT) potentially minimizes radiation.MethodsWe propose hybrid EMT + X-ray (HEX), a research framework for navigation with an emphasis on safe experimentation. HEX is based on several hardware and software components that are orchestrated to allow for safe and efficient data acquisition.ResultsIn our study, hybrid navigation reduces radiation by 71% with cubic, and by 40% with linear error compensation while achieving submillimeter accuracy. Training points for compensation can be reduced by half while keeping a similar accuracy–radiation trade-off.ConclusionThe HEX framework allows to safely and efficiently evaluate the hybrid navigation approach in simulated procedures. Complementing intraoperative X-ray with EMT significantly reduces radiation in the OR, increasing the safety of patients and surgeons.

Real‐time precise orbit determination for FY‐3C and FY‐3D based on BDS and GPS onboard observation

AbstractThe code multipath error associated with elevation in BDS‐2 is one of the main factors whose impact on the precision of real‐time reduced‐dynamic precise orbit determination (POD) using spaceborne multi‐global navigation satellite systems (GNSS) observation data for FengYun‐3C (FY‐3C) and FengYun‐3D (FY‐3D) satellites. The aim is to construct a code multipath piece‐wise linear error model and analyse the contribution of BDS‐2 to the performance of low earth orbit POD. Conclusions are drawn out from the experimental results: (1) the real‐time POD average precision of FY‐3C and FY‐3D is improved by about 11% and 12% after the correction of BDS‐2 code multipath error; (2) Due to the small number of available BDS‐2 satellites and the limited accuracy of geostationary earth orbit (GEO) satellite real‐time orbit products, the precision of the real‐time overlapping comparison for FY‐3C/FY‐3D by using the BDS‐2 onboard observation data can only reach the decimetre level. However, with the BDS‐2 signal capture capability of the FY‐3D onboard GNSS Occultation Sounder upgraded, the average precision of the BDS‐2‐based POD for FY‐3D is better than that of FY‐3C in each direction and with 10% improvement in the average 3 dimensional‐root mean square (3D‐RMS); (3) Cases of onboard global positioning system (GPS), GPS + BDS‐2 (with GEO), and GPS + BDS‐2 (without GEO) for real‐time POD can meet 5–8 cm precision requirement. The average 3D‐RMS of the real‐time POD for FY‐3C/FY‐3D, which utilises onboard GPS + BDS‐2 data is inferior only to GPS data, owing to the influence of the orbit accuracy of GEO satellites. However, after excluding the influence of GEO satellites, the average result (3D‐RMS) of the real‐time POD for FY‐3C (6.11 cm) and FY‐3D (5.95 cm) is better than those of other cases.

A linear formulation for misaligned helical gear contact analysis using analytical contact stiffnesses

A comparative assessment of analytical gear mesh stiffness modelling techniques is presented in this study, culminating into an optimized method for spur and helical gear stiffness modelling. First, by selectively combining different analytical methods presented in literature, the total stiffness of a spur gear pair is obtained as a series and parallel connection of springs. In doing so, an overall compliance matrix is obtained that relates the linear transmission error of the gear pair to the gear contact force distribution. Starting from the spur gear stiffness model, the model is extended to a novel method for analytically computing the contact stiffness of helical gears, with particular attention devoted to axial stiffness and slice coupling effects. The couplings between slices, which relate forces and deflections of different slices, are included in the compliance matrix analytically using a combination of exponential decay functions and the moment image method. The performance of the novel method is numerically validated by comparing the model predictions for spur and helical gears under both perfectly aligned and misaligned conditions, including microgeometry modifications, with finite element simulations.