Least-squares Estimation Algorithm Research Articles

A Robust and Regularized Algorithm for Recursive Total Least Squares Estimation

A Robust and Regularized Algorithm for Recursive Total Least Squares Estimation

Distributed Constrained Nonlinear Least-Squares Estimation Algorithm Over Unbalanced Directed Networks

Distributed Constrained Nonlinear Least-Squares Estimation Algorithm Over Unbalanced Directed Networks

Positioning Control Strategy of Hydraulic Support Pushing System in Fully Mechanized Coal Face

At present, the hydraulic support pushing system in coal mines usually uses an electrohydraulic directional valve as the control component. However, the existing control methods based on high-speed on–off valve, servo, and proportional control methods are not suitable for solving such problems because of the nonideal characteristics of the electrohydraulic directional valve, such as discrete input values, low switching frequency, and time delay. This paper proposes a positioning control scheme based on online predictive feedback for the control of hydraulic cylinders by electrohydraulic directional valves. In this scheme, the recursive least-squares estimation algorithm with genetic factors is used to identify the required prediction model in real time, and an improved radial basis function network based on generalized growth and shear is used to realize the online fitting of the target trajectory function. The online learning algorithm provides accurate prediction information for the switching control method, and finally, the hydraulic cylinder can be positioned near the target position using the optimal control method. By using the above methods, a well-designed model can be accurately identified, fundamentally solving the problem of control difficulties caused by the nonideal characteristics of the electrohydraulic directional valve. Finally, the effectiveness of the control scheme is verified through simulation analysis and physical experiment research, which proves that the control strategy can realize accurate and fast positioning control for the hydraulic support pushing system of a fully mechanized mining face.

High-dimensional multivariate autoregressive model estimation of human electrophysiological data using fMRI priors

Multivariate autoregressive (MVAR) model estimation enables assessment of causal interactions in brain networks. However, accurately estimating MVAR models for high-dimensional electrophysiological recordings is challenging due to the extensive data requirements. Hence, the applicability of MVAR models for study of brain behavior over hundreds of recording sites has been very limited. Prior work has focused on different strategies for selecting a subset of important MVAR coefficients in the model to reduce the data requirements of conventional least-squares estimation algorithms. Here we propose incorporating prior information, such as resting state functional connectivity derived from functional magnetic resonance imaging, into MVAR model estimation using a weighted group least absolute shrinkage and selection operator (LASSO) regularization strategy. The proposed approach is shown to reduce data requirements by a factor of two relative to the recently proposed group LASSO method of Endemann et al (Neuroimage 254:119057, 2022) while resulting in models that are both more parsimonious and more accurate. The effectiveness of the method is demonstrated using simulation studies of physiologically realistic MVAR models derived from intracranial electroencephalography (iEEG) data. The robustness of the approach to deviations between the conditions under which the prior information and iEEG data is obtained is illustrated using models from data collected in different sleep stages. This approach allows accurate effective connectivity analyses over short time scales, facilitating investigations of causal interactions in the brain underlying perception and cognition during rapid transitions in behavioral state.

Parameter estimation for a global tide and surge model with a memory-efficient order reduction approach

Accurate parameter estimation for the Global Tide and Surge Model (GTSM) benefits from observations with long time-series. However, increasing the number of measurements leads to a large computation demand and increased memory requirements, especially for the ensemble-based methods that assimilate the measurements at one batch. In this study, a memory-efficient parameter estimation scheme using model order reduction in time patterns is developed for a high-resolution global tide model. We propose using projection onto empirical time-patterns to reduce the model output time-series to a much smaller linear subspace. Then, to further improve the estimation accuracy, we introduce an outer-loop, similar to Incremental 4D-VAR, to evaluate model-increments at a lower resolution and subsequently reduce the computational cost. The inner-loop optimizes parameters using the lower-resolution model and an iterative least-squares estimation algorithm called DUD. The outer-loop updates the initial output from the high-resolution model with updated parameters from the converged inner-loop and then restarts the inner-loop. We performed experiments to adjust the bathymetry with observations from the FES2014 dataset. Results show that the time patterns of the tide series can be successfully projected to a lower dimensional subspace, and memory requirements are reduced by a factor of 22 for our experiments. The estimation is converged after three outer iterations in our experiment, and tide representation is significantly improved, achieving a 34.5% reduction of error. The model’s improvement is not only shown for the calibration dataset, but also for several validation datasets consisting of one year of time-series from FES2014 and UHSLC tide gauges.

A Cooperative Positioning Method of Connected and Automated Vehicles with Direction-of-Arrival and Relative Distance Fusion

The rapid development of science and technology has created favorable conditions for Connected and Automated Vehicles (CAVs). Accurate localization is one of the fundamental functions of CAV to realize some advanced operations such as vehicle platooning. However, complicated urban traffic environments, such as the flyover, significantly influence vehicular positioning accuracy. The inability of CAV to accurately perceive self-localization information has become an urgent issue to be addressed. This paper proposed a novel cooperative localization method by introducing the relative Direction-of-Arrival (DOA) and Relative Distance (RD) into CAV to improve the localization accuracy of CAV in the multivehicle environment. First, the three-dimensional positioning error model of the host vehicle concerning adjacent vehicles in azimuth angle and pitch angle and intervehicle distances under the vehicle-to-vehicle communication was established. Second, two least-squares estimation algorithms, linear and nonlinear, are established to decrease the position errors by combining relative DOA and RD measurement information. To verify the proposed algorithm's effect, the PreScan-Simulink joint simulation is carried out. The results show that the host vehicle's localization accuracy by the proposed method can be improved by 25% compared with direct linearization. Besides, by combining relative DOA and relative RD measurement, the locating capability of the least-square-based nonlinear optimization method can be enhanced by 22%.

Privacy-preserving indoor localization based on inner product encryption in a cloud environment

How to utilize the resource-rich cloud to provide scalable indoor localization service to solve the problem of limited user equipment resources while preventing privacy leakage has become a hot topic. A novel privacy-preserving indoor localization scheme based on Inner Product Encryption in a cloud environment is proposed to address this issue. By using the computability of Inner Product Encryption on ciphertext without exposing plaintext information, an honest-but-curious cloud server estimates the users location without obtaining any private information. The least-squares estimation algorithm of the Time Difference location system is decomposed into the basic form of the inner product of two sets of vectors. One is the anchor information encrypted with Inner Product Encryption during the offline phase, the other is the users distance difference information encrypted and sent to the cloud server during the online phase. To hide the users real location, the users real distance difference information and several decoy information are encrypted and included in a request to achieve k-Anonymity. The location estimation algorithm operates on the cloud to locate the user from the ciphertext. In addition, three optimization methods applied to cloud server location estimation algorithm were designed to further improve the performance. The experimental results and theoretical analysis show that the proposed scheme consumes less time, and has a lower communication overhead, while maintaining positioning accuracy. At the same time, the scheme protects the users locational and data privacy of the indoor positioning service provider when migrating the indoor positioning services to the cloud environment.

An exponential smoothing channel estimation method for MIMO-OFDM system

In order to solve the problem of inaccurate channel estimation of least square (LS) algorithm for multiple input multiple output orthogonal frequency division multiplexing (MIMO-OFDM) system under time-varying channel, a novel channel estimation method using exponential smoothing algorithm (ESA) is proposed in this paper. Based on LS estimation algorithm and ESA theory, the proposed method fully exploits the variation law of time-varying channel, adopts the predicted results of the previous time to predict the estimation value of the current time by iterative computations, and utilizes the low-pass character of the ESA equivalent filter to reduce the random disturbance. Therefore, the additive white Gaussian noise (AWGN) existing in LS algorithm is effectively suppressed and the estimation accuracy is further improved. Simulation results show that, compared with the traditional channel estimation approaches, the proposed method can provide high estimation accuracy with low computational complexity, especially under time-varying channel and low SNR conditions..

A two-stage observer for the compensation of actuator-induced disturbances in tool-force sensors

In this paper, a novel two-stage observer strategy for improving the measurement of tool forces is presented. The mass-spring-damper system which inevitably occurs when a tool and a (compliant) force sensor are combined is studied and its adverse influence on the measurement signal is analyzed. The proposed observer consists of two stages. The first stage captures the input-output characteristics from the control input to the tool force by a recursive least-squares estimation algorithm. The estimated tool characteristics are used in a second stage to suppress the oscillations in the measurement signal, which mainly occur due to the mass-spring-damper nature of the tool-sensor combination. In a tailored experimental test rig, which mimics the conditions in magnetic levitation, magnetic bearings, or magnetic strip positioning devices in hot-dip galvanizing lines, the efficacy and the high estimation accuracy of the developed observer strategy are demonstrated.

The application of nonlinear least-squares estimation algorithms in atmospheric density model calibration

PurposeThe purpose of this paper is to focus on the performance of three typical nonlinear least-squares estimation algorithms in atmospheric density model calibration.Design/methodology/approachThe error of Jacchia-Roberts atmospheric density model is expressed as an objective function about temperature parameters. The estimation of parameter corrections is a typical nonlinear least-squares problem. Three algorithms for nonlinear least-squares problems, Gauss–Newton (G-N), damped Gauss–Newton (damped G-N) and Levenberg–Marquardt (L-M) algorithms, are adopted to estimate temperature parameter corrections of Jacchia-Roberts for model calibration.FindingsThe results show that G-N algorithm is not convergent at some sampling points. The main reason is the nonlinear relationship between Jacchia-Roberts and its temperature parameters. Damped G-N and L-M algorithms are both convergent at all sampling points. G-N, damped G-N and L-M algorithms reduce the root mean square error of Jacchia-Roberts from 20.4% to 9.3%, 9.4% and 9.4%, respectively. The average iterations of G-N, damped G-N and L-M algorithms are 3.0, 2.8 and 2.9, respectively.Practical implicationsThis study is expected to provide a guidance for the selection of nonlinear least-squares estimation methods in atmospheric density model calibration.Originality/valueThe study analyses the performance of three typical nonlinear least-squares estimation methods in the calibration of atmospheric density model. The non-convergent phenomenon of G-N algorithm is discovered and explained. Damped G-N and L-M algorithms are more suitable for the nonlinear least-squares problems in model calibration than G-N algorithm and the first two algorithms have slightly fewer iterations.

Improved least‐squares identification for multiple‐output non‐linear stochastic systems

This study considers the identification problems of multiple-output non-linear equation-error moving average systems. There exist the product items of the parameters between the non-linear and linear parts. To solve this difficulty, the key term separation technique is adopted. By using the model decomposition technique and the hierarchical identification principle, a maximum likelihood-based recursive extended least-squares estimation algorithm with reduced computational complexity is presented to estimate the parameters of the non-linear part and the linear part interactively. The simulation results demonstrate the effectiveness of the proposed method.

Modified Model-Free Adaptive Control using Compact-Form Dynamic Linearization Technique

Abstract Model-free adaptive control has been used to design feedback in cases when accurate mathematical modeling of the system can not be realized. By using only input-output information, the control approach is attractive with respect to minimal design efforts. In this contribution an improved model-free control program is proposed and applied to flexible systems. The main control idea is based on the compact-form dynamic linearization technique. A linearized controller structure which contains a matrix of unknown time-varying parameters namely pseudo-partial derivative can be designed. First, an equivalent linearized data-based model of the original system is established and corrected locally by using the recursive least-squares estimation algorithm. Then a modified objective function with respect to the controller parameter matrix considering minimization of the current tracking errors and its variations is proposed for control performance improvement. Finally, the required control inputs are calculated to fulfill control requirements. For illustration and as example, the newly introduced method is applied to reduce vibrations of an elastic crane representing a multivariable system. The control effectiveness is verified nummerically and compared with conventional model-free and PI controllers.

Self‐adapting multi‐peak water‐fat reconstruction for the removal of lipid artifacts in chemical exchange saturation transfer (CEST) imaging

Artifacts caused by strong lipid signals pose challenges in body chemical exchange saturation transfer (CEST) imaging. This study aimed to develop an accurate water-fat reconstruction method based on the multi-echo Dixon technique to remove lipid artifacts in CEST imaging. It is well known that fat has multiple spectral peaks. Furthermore, RF pulses in CEST preparation saturate each fat peak at different levels, complicating fat modeling. Therefore, a self-adapting multi-peak model (SMPM) is proposed to update relative amplitudes of fat peaks using numerical calculation. With the SMPM-based updating, nonlinear least-squares fitting combined with IDEAL (Iterative Decomposition of water and fat with Echo Asymmetry and Least-squares estimation) algorithms was used for water-fat reconstruction and B0 mapping. The proposed method was compared with the reported 3-point Dixon method and the fixed multi-peak model in a phantom study using a fat-free Z-spectrum obtained from MR spectroscopy acquisition as the ground truth. This method was also validated by in vivo experiments on human breast. In the phantom experiments, the Z-spectrum from the SMPM-based method agreed well with the fat-free Z-spectrum from CEST-PRESS (point-resolved spectroscopy), validating the effective removal of lipid artifacts, while a decrease or a rise that appeared at -3.5 ppm was observed in the Z-spectrum from the 3-point method and the FMPM-based method, respectively. In the in vivo experiments, no lipid artifacts were observed in the Z-spectrum or the amide CEST map from the SMPM-based method in the fibro-glandular region of the breast with high fat fractions. The SMPM-based method successfully removes lipid artifacts and significantly improves the accuracy of CEST contrast.

Artificial Intelligence-Aided Receiver for a CP-Free OFDM System: Design, Simulation, and Experimental Test

Orthogonal frequency division multiplexing (OFDM), usually with sufficient cyclic prefix (CP), has been widely applied in various communication systems. The CP in OFDM consumes additional resource and reduces spectrum and energy efficiency. However, channel estimation and signal detection are very challenging for CP-free OFDM systems. In this paper, we propose a novel artificial intelligence (AI)-aided receiver (AI receiver) for a CP-free OFDM system. The AI receiver includes a channel estimation neural network (CE-NET) and a signal detection neural network based on orthogonal approximate message passing (OAMP), called OAMP-NET. The CE-NET is initialized by the least-square channel estimation algorithm and refined by a linear minimum mean-squared error neural network. The OAMP-NET is established by unfolding the iterative OAMP algorithm and adding several trainable parameters to improve the detection performance. We first investigate their performance under different channel models through extensive simulation and then establish a real transmission system using a 5G rapid prototyping system for an over-the-air (OTA) test. Based on our study, the AI receiver can estimate time-varying channels with a single training phase. It also has great robustness to various imperfections and has better performance than those competitive algorithms, especially for high-order modulation. The OTA test further verifies its feasibility to real environments and indicates its potential for future communications systems.

Real-Time Disturbances Estimating and Compensating of Nonlinear Dynamic Model for Underwater Vehicles

To reduce the deviation caused by the stochastic environmental disturbances, estimating these disturbances is required to compensate the navigation system. Based on the idea of Kalman filter using least-squares algorithm for optimal estimation, a nonlinear disturbances estimator which can be perfectly integrated with cubature Kalman filter (CKF) is proposed. For the nonlinear disturbances estimator, the disturbances are estimated by gain matrix, innovation sequences, and innovation covariance generated by CKF. The disturbances estimating and compensating algorithm consists of three parts. Firstly, the navigation system state space model is established based on nonlinear dynamic model of six degrees of freedom. Secondly, the external disturbances are estimated by using CKF and a nonlinear estimator. Finally, the disturbances compensation is carried out by improving the system state equation. In view of the uncertainty of the dynamic model and the randomness of external disturbances, numerical simulation experiments are conducted in the circumstances of sinusoidal disturbances, random disturbances, and uncertain model parameters. The results demonstrate that the proposed method can estimate disturbances effectively and improves navigation accuracy significantly.

Fast accurate multi-key weight measurement

We consider an industrial problem brought to the Mathematics in Industry New Zealand study group in 2016, where items pass briefly over load cells resulting in a noisy oscillatory signal, from which the mass of the item is to be computed. We compare results obtained using a single load cell for one piece of fruit, with results from passing over two load cells in tandem or in succession with fruit on multiple keys. We develop mathematical models to assist with the computation of total load mass, considering both deterministic and statistical approaches. The fitting of simple harmonic motion plus a step function exhibits the possibility of rapid estimates of load mass. We find that using multiple keys to measure the weight of a fruit provides more accurate results than using the single-key method. References minz-2004, Case Study Compac. http://www.minz.org.nz/assets/downloads/Case-Study-Compac.pdf Kesilmis, Z., and Baran, T. (2016). A Geometric Approach to Beam Type Load Cell Response for Fast Weighing. doi:10.1007/s12647-016-0168-2 K. Levenberg, A method for the solution of certain non-linear problems in least squares. Quarterly of applied mathematics , 2(1944), pp. 164–168. http://www.jstor.org/stable/43633451 D. W. Marquardt, An algorithm for least-squares estimation of nonlinear parameters. Journal of the society for Industrial and Applied Mathematics , 11(1963), pp. 431–441. doi:10.1137/0111030

Observer-based cyber attack detection and isolation in smart grids

In this paper, we investigate the cyber security problem for large scale smart grid systems under false data injection attack. An observer-based algorithm is proposed to detect and isolate the cyber attack by using real-time synchrophasor measurements. Combining the smart grid system with graph theory, the system is divided into several different coupled areas via sparsity of the connection topology. According to the partition, the system is decomposed equivalently into several areas. Then, the output of the smart grid system can be gotten through wide area measurement system based on PMUs, and the asymmetric weighted Laplacian can be obtained by running a nonlinear least-square estimation algorithm. By designing a modified observer, the residual is computed, and the adaptive residual threshold, used to detect and isolate the attack in the areas of the system, is also shown with considering the system model uncertainties. Then, an iterative algorithm detecting and isolating the cyber attack is proposed based on the calculated residual threshold. Finally, some simulations are provided to illustrate the effectiveness of the proposed algorithm.

Adaptive neuro-fuzzy inference system based under-frequency load shedding for Tamil Nadu

Under-frequency load shedding (UFLS) is a popular technique around the world, especially in India for maximizing the power system stability and to avoid blackout in case of contingency. Electricity demand–supply gap due to generation failure is the main cause for power shortage, which leads to frequency degradation and major collapse of the whole system. Load shedding helps utility to restore the system stability. But the traditional load shedding methods shed incorrect as well as excess load which increases economic loss to utility and discomfort to customers. In this paper, an adaptive neuro-fuzzy inference system (ANFIS) based UFLS controller using back-propagation and least-square estimation algorithm is simulated and tested for Tamil Nadu power system, a leading industrialized state of India with an objective to shed minimum possible load. The simulations are carried out using MATLAB toolbox. The performance of the proposed ANFIS based UFLS controller is compared with an artificial neural network (ANN) based controller. The comparison of ANN and ANFIS based UFLS shows that by using the proposed ANFIS controller, the amount of load shed could be reduced between 83 and 1264 MW for various generation–load scenarios, which significantly benefits both utility and customers to enhance energy security and revenue up to 7.5 million INR per hour.

Comparison of least squares and exponential sine sweep methods for Parallel Hammerstein Models estimation

Abstract Linearity is a common assumption for many real-life systems, but in many cases the nonlinear behavior of systems cannot be ignored and must be modeled and estimated. Among the various existing classes of nonlinear models, Parallel Hammerstein Models (PHM) are interesting as they are at the same time easy to interpret as well as to estimate. One way to estimate PHM relies on the fact that the estimation problem is linear in the parameters and thus that classical least squares (LS) estimation algorithms can be used. In that area, this article introduces a regularized LS estimation algorithm inspired on some of the recently developed regularized impulse response estimation techniques. Another mean to estimate PHM consists in using parametric or non-parametric exponential sine sweeps (ESS) based methods. These methods (LS and ESS) are founded on radically different mathematical backgrounds but are expected to tackle the same issue. A methodology is proposed here to compare them with respect to (i) their accuracy, (ii) their computational cost, and (iii) their robustness to noise. Tests are performed on simulated systems for several values of methods respective parameters and of signal to noise ratio. Results show that, for a given set of data points, the ESS method is less demanding in computational resources than the LS method but that it is also less accurate. Furthermore, the LS method needs parameters to be set in advance whereas the ESS method is not subject to conditioning issues and can be fully non-parametric. In summary, for a given set of data points, ESS method can provide a first, automatic, and quick overview of a nonlinear system than can guide more computationally demanding and precise methods, such as the regularized LS one proposed here.

Speed Effect to a Quarter Car ARX Model Based on System Identification

This paper presents the effect of car speeds on a quarter car passive suspension system model dynamics. The model is identified using system identification technique, in which the input-output data are collected by running a test car on an artificial road surface with two different speeds i.e., 10 km/h and 20 km/h. The quarter car passive suspension system dynamics is assumed to have an ARX model structure and identified using linear least-square estimation algorithm. The car vertical body acceleration, which is the output variable, is measured by installing an accelerometer sensor on the car body, above the suspension. On the other hand, the car shaft acceleration, which is the input variable, is measured by installing an accelerometer sensor at the lower arm of the car suspension. The best model for the 10 km/h car speed gives the output order () = 4, the input order () = 2, delay (<em>d)</em> = 1, the best fit = 90.65%, and the Akaike’s Final Prediction Error (FPE) = 5.315e-06. In contrast, the 20 km/h speed results in 4^th output order (), 1^stthe input order (), 1^st delay (<em>d)</em>, the best fit of 91.05%, and 7.503e-05Akaike’s FPE. These results show that the higher speed reduces the effect of the road surface to car dynamics, which is indicated by the order of the model