Application of optimized Kalman filtering in target tracking based on improved Gray Wolf algorithm

This paper presents an extended Kalman filter for pose estimation using noise covariance matrices based on sensor output. Compact and lightweight nine-axis motion sensors are used for motion analysis in widely various fields such as medical welfare and sports. A nine-axis motion sensor includes a three-axis gyroscope, a three-axis accelerometer, and a three-axis magnetometer. Information obtained from the three sensors is useful for estimating joint angles using the Kalman filter. The extended Kalman filter is used widely for state estimation because it can estimate the status with a small computational load. However, determining the process and observation noise covariance matrices in the extended Kalman filter is complicated. The noise covariance matrices in the extended Kalman filter were found for this study based on the sensor output. Postural change appears in the gyroscope output because the rotational motion of the joints produces human movement. Therefore, the process noise covariance matrix was determined based on the gyroscope output. An observation noise covariance matrix was determined based on the accelerometer and magnetometer output because the two sensors’ outputs were used as observation values. During a laboratory experiment, the lower limb joint angles of three participants were measured using an optical 3D motion analysis system and nine-axis motion sensors while participants were walking. The lower limb joint angles estimated using the extended Kalman filter with noise covariance matrices based on sensor output were generally consistent with results obtained from the optical 3D motion analysis system. Furthermore, the lower limb joint angles were measured using nine-axis motion sensors while participants were running in place for about 100 s. The experiment results demonstrated the effectiveness of the proposed method for human pose estimation.

A weighing error compensation method using IGWO–LMBPNN, which combines an improved gray wolf optimization algorithm (IGWO) with the Levenberg–Marquardt backpropagation neural network (LMBPNN), is proposed to enhance truck scale accuracy. It uses output signals from multiple load cells as inputs to the neural network for establishing the error compensation model. The IGWO algorithm is used to initialize the weights and biases of the model, while the LMBPNN algorithm further optimizes these parameters. To evaluate the effectiveness of the IGWO–LMBPNN method, it was compared with the existing compensation methods, including BPNN, LMBPNN, gray wolf optimization with LMBPNN (GWO–LMBPNN), particle swarm optimization with LMBPNN (PSO–LMBPNN), and Fine Gaussian SVM. The experimental results demonstrate a significant improvement in error reduction for truck scale weighing. The mean absolute error (MAE) of IGWO–LMBPNN is 8.5 kg, which was reduced by 38.8%, 29.2%, 19%, 21.3%, and 33.1% compared with BPNN, LMBPNN, GWO–LMBPNN, PSO–LMBPNN, and Fine Gaussian SVM, respectively. These findings not only verify the efficacy of the IGWO–LMBPNN in enhancing weighing accuracy but also highlight its potential for other practical applications.

The satellite clock plays a key role in the global navigation satellite system (GNSS). The accuracy of GNSS and its applications depend on the quality of the satellite clock. Therefore, precisely estimating and predicting the satellite clock is an important issue in the fields of GNSS and its application. As an optimal estimation algorithm, Kalman filter has been used to estimate and predict the satellite clock. However, in a conventional Kalman filter algorithm, the noise covariance matrices of satellite clock need to be predetermined, which restricts its further applications since the noise covariance matrices, especially the process noise covariance matrix, are usually unknown in the real cases. With inappropriate noise covariance matrices, the state estimation of conventional Kalman filter is suboptimal. To cope with this problem, a new noise covariance matrix estimation method of Kalman filter is proposed, and then we apply it to the problem of satellite clock estimation and prediction. Considering the fact that the process noise covariance matrix depends on the unknown noise parameters, the problem of estimating process noise covariance matrix can be solved by estimating the unknown noise parameters. First, the correlation between the Kalman innovations is used to establish a linear relationship with the unknown noise parameters. Then the unknown parameters can be estimated by least-squares estimation. Finally, the satellite clock can be estimated and predicted with the estimated noise parameters. In the new method, no prior information about the noise parameters is needed. Even with some extreme prior noise parameters, the new method can also work very well and has good convergence properties. For comparison, we conduct two experiments using the new method and the adaptively robust Kalman filter with classified adaptive factors based on opening windows separately, both results are consistent with each other very well, which verifies the correctness and effectiveness of this new method.

One of the objectives of electrical distribution networks is to provide customers with access to high‐quality electricity. Because any disruptions in these systems result in voltage disorders, different devices are employed to offset these disruptions on consumers who are more susceptible. One of the most important and contemporary pieces of equipment that is connected in series with the network is dynamic voltage restoration (DVR), which shields delicate loads from network voltage issues by injecting the proper voltage. This article presents a DVR control scheme optimized with improved grey wolf optimization (IGWO) that uses a proportional derivative (PD) controller and adaptive notch filter (ANF). The output LC filter’s resistance has been removed, and the control system has actively engaged in oscillation damping in order to accelerate dynamic responsiveness and lower system losses. The major component of the voltage, which comprises its frequency, amplitude, and phase, is extracted using ANF. The capacitor current of the output filter in this structure is fed back to the control system and from the current mode control in the inner loop to boost stability. Owing to the occasionally complex dynamic behavior in distribution networks, particularly during a fault, the system’s frequency response has been altered and response speed has been accelerated using the PD controller. This kind of controller is distinguished by its accurate functioning in the presence of frequency deviations and its swifter dynamic reaction in the face of voltage swell and sag. In order to improve the THD and voltage sag indicators of the sensitive load, the PD coefficients were adjusted using the IGWO algorithm. As a consequence, the simulation results demonstrated that the suggested controller performed better than traditional controllers.

The wind tunnel balance signal detection system is widely employed in aerospace applications for the accurate and automated measurement of aerodynamic forces and moments. However, measurement errors arise under different environmental temperature. This paper addresses the issue of measurement accuracy under different temperature conditions by proposing a temperature compensation method based on an improved gray wolf optimization (IGWO) algorithm and optimized extreme learning machine (ELM). The IGWO algorithm is enhanced by improving the initial population position, convergence factor, and iteration weights of the gray wolf optimization algorithm. Subsequently, the IGWO algorithm is employed to determine the optimal network parameters for the ELM. The calibration decoupling experiment and high-low temperature experiment are designed and carried out. On this basis, ELM, GWO-ELM, PSO-ELM, GWO-RBFNN and IGWO-ELM are used for temperature compensation experiments. The experimental results show that IGWO-ELM has a good temperature compensation effect, reducing the measurement error from 20%FS to within 0.04%FS. Consequently, the accuracy and stability of the wind tunnel balance signal detection system under different temperature environments are enhanced.

The grey wolf optimization (GWO) algorithm, one of the recently proposed bio-inspired algorithms, simulates the leadership hierarchy and hunting mechanism of grey wolves in nature. The GWO has a good performance in some optimization tasks, but its search capacity decreases with the increasing search scope and dimension. This paper proposes an improved GWO (IGWO) algorithm, in which Levy flight strategy and a sine cosine operator with adaptive step are incorporated to significantly improve the performance of the algorithm. The Levy flight strategy is used to strengthen the efficiency of global search. The adaptive sine cosine operator is introduced to improve the local search ability. Experimental results based on twenty unconstrained benchmark problems show the superiority of the proposed IGWO. Furthermore, the IGWO is utilized in PID controller design. The comparison results show that the IGWO algorithm is better than, or at least comparable to, other well-established swarm intelligence algorithms.

The paper proposes a new Kalman filtering (KF) algorithm called VBI-MCKF that combines the variational Bayesian inference (VBI)-based KF algorithm and the maximum correntropy KF (MCKF) for visual tracking problem. The VBI-based KF algorithm works to estimate the unknown measurement noise covariance matrix (MNCM) and process noise covariance matrix (PNCM), and the MCKF works to deal with non-Gaussian process noise and measurement noise. In order to cater for the visual tracking target scenario, where the MNCM and PNCM are unknown and non-Gaussian, we modify the VBI-based KF algorithm to work for suddenly occurring outliers and modify the MCKF work for small bandwidth. Simulations show that the proposed VBI-MCKF algorithm performs well when both covariance matrices of Gaussian process noise and non-Gaussian measurement noise are unknown or inaccurate.

The Grey Wolf Optimization (GWO) Algorithm is a heuristic evolutionary algorithm inspired by the hunting and leadership mechanisms of the natural grey wolf. However, its location update equation has the disadvantages of strong development ability and weak exploration ability. To improve these shortcomings, we propose the RWCA-GWO algorithm. It occurs inspired by the random walk strategy and enhances the exploration ability of the leading wolves. Inspired by the analytic hierarchy process, a procedure for setting the weights of α, β, and δ are proposed. Besides, to promote the global convergence speed of the GWO algorithm, the initial population is generated by the chaotic initialization method. The simulation experiments are carried out with 11 test functions. The results show that for most cases, the performance of RWCA-GWO algorithm is significantly better than the standard grey wolf algorithm and other improved grey wolf algorithms under the same maximum fitness function evaluation times.

<p>Cloud manufacturing is a grand manufacturing concept aimed at reducing the waste of manufacturing resources. By borrowing the ideas of cloud computing and utilizing information technology to achieve high sharing of manufacturing resources, the core issues that both the supply and demand sides are concerned about in the cloud manufacturing process are price, product quality, and product production cycle. Therefore, this paper constructs a manufacturing process resource scheduling model that includes three elements. In order to solve the optimal solution of the model, an improved intelligent algorithm is used to solve it. The intelligent algorithm is based on the advantages of the gray wolf algorithm in solving accuracy and convergence speed. The integration of the Bat algorithm in the gray wolf algorithm improves the search ability and performance of the original gray wolf algorithm. At the same time, the gray wolf algorithm can avoid the convergence speed of the Bat algorithm from changing with the increase of iteration times. The phenomenon of slow or almost stopping. To avoid generating local optimal solutions, the accuracy of the cloud resource scheduling model and algorithm solution constructed in this paper were verified through the construction of a simulation environment. </p> <p> </p>

In this paper, after reviewing the traditional Kalman filter formulation, a development of a fuzzy logic-based adaptive Kalman filter is outlined. The adaptation is in the sense of adaptively tuning, on-line, the measurement noise covariance matrix R or the process noise covariance matrix Q. This improves the Kalman filter performance and prevents filter divergence when R or Q are uncertain. Based on the whiteness of the filter innovation sequence and employing the covariance-matching technique the tuning process is carried out by a fuzzy inference system. If a statistical analysis of the innovation sequence shows discrepancies with its expected statistics then a fuzzy inference system adjusts a factor through which the matrices R or Q are tuned on line. This fuzzy logic-based adaptive Kalman filter is tested on a numerical example. The results are compared with these obtained using a conventional Kalman filter and a traditionally adapted Kalman filter. The fuzzy logic-based adaptive Kalman filter showed better results than its traditional counterparts.

The electrification of the transport sector increases the demand for a battery management system that allows the Li-ion battery to work in a sophisticated way to reach its maximum. The main focus of the battery management system is the estimation of the battery’s state of charge (SOC) which is an indicator to determine the driving range of an electric vehicle. However, battery modeling has a direct influence on SOC estimation. In this article, the equivalent circuit model (ECM) and extended Kalman filter (EKF) algorithm are combined for SOC estimation of the Li-ion battery. Since the performance of Kalman filter algorithms strictly depends on noise covariance matrices, incorrect values reduce the accuracy and make divergence in state estimation. Therefore, it is motivated to analyze the impact of process noise and measurement noise covariance matrix values on SOC estimation using Kalman filter algorithms. Ten different combinations of noise covariance matrices are employed to analyze the effect of these matrices on SOC estimation. As a result, the tuning of the filter is critical for improvement in state estimation regardless of the type of the battery model and filtering technique. The matrix values are chosen to take into account the convergence rate and estimation error. To validate the effectiveness of the chosen noise covariance matrices, the simulation results of the ECM based EKF estimation method is superimposed with the discharge curves available in the data sheet. The simulation results show minimal estimation error and a good convergence rate for tuned EKF.

Evaluate asphalt pavement frictional characteristics based on IGWO-NGBoost using 3D macro-texture data

The present article proposes a novel hybrid approach for addressing the synthesis problem of rectangular planar arrays under multiple constraints, through joint optimization of the weight function and the improved grey wolf optimization (IGWO) algorithm. Firstly, the grey wolf optimization (GWO) algorithm is improved by using tent chaotic mapping, nonlinear convergence factor, dominant wolf dynamic belief strategy, and opposition‐based learning strategy to increase the population diversity and the ability to jump out of the local optimum. Secondly, the array elements are weighted using the weight function to generate the position distribution matrix, which reduces the thinned matrix optimization time and improves the optimization efficiency. Finally, the position distribution matrix is used to generate the thinned array, and the IGWO algorithm is applied to perform the sparse optimization with multiple constraints. The effectiveness of the method is verified through numerical simulation and full‐wave simulation experiments, demonstrating its capability to enhance array antenna performance and reduce peak sidelobe level (PSLL). These experimental results hold significant engineering implications and provide valuable references for addressing the array distribution problem under multiple constraints.

Due to insufficient absolute positioning accuracy, industrial robots frequently face challenges in efficiently performing drilling and riveting operations during the assembly of aircraft and other large-scale workpieces. To enhance the absolute positioning accuracy of industrial robots, this paper proposes a novel kinematic calibration method for industrial robots based on the Improved Grey Wolf Optimization (IGWO) algorithm. Specifically, the method employs an enhanced selection and update strategy to avoid convergence stagnation and local optimum traps. The proposed method features a novel boundary search strategy, which leverages the Dimension-oriented Learning (DL) search strategy to enhance search speed and stability. Through parameter identification and calibration experiments, the effectiveness of the method was validated using an ABB IRB4600 industrial robot and a Leica laser tracker. Additionally, compared with the Levenberg–Marquardt (LM) algorithm, Particle Swarm Optimization (PSO), and Genetic Algorithm (GA), the IGWO algorithm demonstrates faster convergence and superior optimization performance. According to the calibration experimental results, by applying the IGWO algorithm, the absolute positioning accuracy of the industrial robot is ultimately improved from 1.918 mm to 0.475 mm and the absolute positioning accuracy is improved by 75.2%.

A grey wolf optimization algorithm based on an adaptive adjustment strategy (Improvements-Grey Wolf Optimization, IGWO) is proposed in this paper to address the issues with the Grey Wolf Optimization (GWO) algorithm, which has a slow convergence speed in the later stages and where the local search and global search cannot be taken into effective balance. First, a chaotic logistic map is used to initialize the population. Next, an inverse trigonometric function-based mathematical model is developed to achieve convergence purposes. Finally, a new location update method is used to update the next-generation location to improve search traversability. Additionally, the CEC2013-Benchmark standard test function was used to evaluate the benefits of performance compared to the standard GWO, PSO, and DEGWO (DE-Grey wolf optimization) algorithms. The improved GWO algorithm has greatly increased the convergence speed, search capability, and stability. It performs better than the other three algorithms as well.