Ellipsoidal Constraint Research Articles

Set-Membership State Estimation for Multirate Nonlinear Complex Networks Under FlexRay Protocols: A Neural-Network-Based Approach.

In this article, the set-membership state estimation problem is investigated for a class of nonlinear complex networks under the FlexRay protocols (FRPs). In order to address practical engineering requirements, the multirate sampling is taken into account which allows for different sampling periods of the system state and the measurement. On the other hand, the FRP is deployed in the communication network from sensors to estimators in order to alleviate the communication burden. The underlying nonlinearity studied in this article is of a general nature, and an approach based on neural networks is employed to handle the nonlinearity. By utilizing the convex optimization technique, sufficient conditions are established in order to restrain the estimation errors within certain ellipsoidal constraints. Then, the estimator gains and the tuning scalars of the neural network are derived by solving several optimization problems. Finally, a practical simulation is conducted to verify the validity of the developed set-membership estimation scheme.

Joint State and Unknown Input Estimation for a Class of Artificial Neural Networks With Sensor Resolution: An Encoding-Decoding Mechanism.

This article is concerned with the joint state and unknown input (SUI) estimation for a class of artificial neural networks (ANNs) with sensor resolution (SR) under the encoding-decoding mechanisms. The consideration of SR, which is an important specification of sensors in the real world, caters to engineering practice. Furthermore, the implementation of the encoding-decoding mechanism in the communication network aims to accommodate the limited bandwidth. The objective of this study is to propose a set-membership estimation algorithm that accurately estimates the state of the ANN without being influenced by the unknown input while accounting for the SR and the encoding-decoding mechanism. First, a sufficient condition is derived to ensure an ellipsoidal constraint on the estimation error. Then, by addressing an optimization problem, the design of the estimator gains is accomplished, and the minimal ellipsoidal constraint on the state estimation error is obtained. Finally, an example is provided to confirm the validity of the proposed joint SUI estimation scheme.

Hybrid pedestrian positioning system using wearable inertial sensors and ultrasonic ranging

Pedestrian positioning system (PPS) using wearable inertial sensors has wide applications towards various emerging fields such as smart healthcare, emergency rescue, soldier positioning, etc. The performance of traditional PPS is limited by the cumulative error of inertial sensors, complex motion modes of pedestrians, and the low robustness of the multi-sensor collaboration structure. This paper presents a hybrid pedestrian positioning system using the combination of wearable inertial sensors and ultrasonic ranging (H-PPS). A robust two nodes integration structure is developed to adaptively combine the motion data acquired from the single waist-mounted and foot-mounted node, and enhanced by a novel ellipsoid constraint model. In addition, a deep-learning-based walking speed estimator is proposed by considering all the motion features provided by different nodes, which effectively reduces the cumulative error originating from inertial sensors. Finally, a comprehensive data and model dual-driven model is presented to effectively combine the motion data provided by different sensor nodes and walking speed estimator, and multi-level constraints are extracted to further improve the performance of the overall system. Experimental results indicate that the proposed H-PPS significantly improves the performance of the single PPS and outperforms existing algorithms in accuracy index under complex indoor scenarios.

Operation mechanism of rural sports governance and implementation path of participatory governance based on mathematical statistics model of Guizhou “The Annual Basketball Event” phenomenon

Abstract Rural public services can be improved by optimizing rural sports governance. In this paper, mathematical-statistical methods for data mining are studied based on the phenomenon of village BA in Guizhou. According to the basic statistical inference method, the data deletion model and the mean drift model under ellipsoidal constraint are discussed to obtain the equivalence between the diagnostic statistics of the two models. The relationships between the estimated quantities before and after deletion and the hat matrix are given for the data deletion model, and the influence functions under such constraints are established while the corresponding mining algorithms for the influence points are designed. The behaviors of participation in the physical exercise had an OR of 4.716 in the model and an OR of 1.375 for walking cumulatively for more than 10 minutes per day, with highly significant differences.

A Derivative-free Trust-region Method for Optimization on the Ellipsoid

Optimization methods play a crucial role in various fields and applications. In some optimization problems, the derivative information of the objective function is unavailable. Such black-box optimization problems need to be solved by derivative-free optimization methods. At the same time, optimization problems with ellipsoidal constraints are important and have widespread applications in various fields as well. Following the development of the late professor M. J. D. Powell’s efficient derivative-free trust-region optimization methods, this paper considers solving derivative-free optimization problems on the ellipsoid. Our new optimization solver EC-NEWUOA for problems on the ellipsoid in ℜ n is designed based on Powell’s derivative-free software NEWUOA for unconstrained optimization problems. The proposed techniques for our new method mainly include using the Courant penalty function, the augmented Lagrangian method, and the projection technique. Details about the method and theoretical analysis are included in this paper. We also compare our new method with other algorithms by solving test problems and then show the numerical advantages of our new method.

Set-membership filtering for two-dimensional shift-varying systems with stochastic communication protocol and uniform quantization

This paper is concerned with the set-membership filtering problem for the two-dimensional shift-varying systems subject to the stochastic communication protocol and uniform quantization effects. To prevent the data transmission from collisions, only one sensor can transmit the measured information to the filter at each sampling shift instant, and the selected sensor is determined by the scheduling strategy of the stochastic communication protocol. On the contrary, the uniform quantization mechanism has been employed to mitigate the influence of quantization error on filtering performance. Incorporating the stochastic communication protocol and uniform quantization mechanism, this paper proposes a set-membership filter design framework for the two-dimensional shift-varying systems with unknown-but-bounded noises. Sufficient conditions are derived for the existence of desired set-membership filter by utilizing double mathematical induction, such that the estimation error resides within the ellipsoidal set. Moreover, the optimal filtering algorithm is given by minimizing the ellipsoidal constraints. Finally, several examples are provided to illustrate the effectiveness of the proposed filter design algorithm.

Application-Oriented Input Spectrum Design in Closed-Loop Identification

In the paper, a problem of real-time input design, where the spectral characteristic of the external excitation signal is optimized considering the fixed bound on the ellipsoidal constraint applied to the quality measure of the estimated model, has been presented. We designed a compensator close to the complementary sensitivity function such that the resulting closed-loop system is stable and guarantees robust performance. The contribution of this work comprises a comparison of the KYP and frequency grid methods for the worst-case minimization between the identified plant and all models in the uncertainty region. It has been noted that the input design problem considering the frequency grid is far more numerically robust than the KYP method and guarantees that more than 90% of the estimated model parameters are clustered inside the assumed confidence region. The proposed approach is verified by numerical examples, and the sensitivity of the input spectrum design to the estimates of model parameters is discussed.

Performance Error Estimation and Elastic Integral Event Triggering Mechanism Design for T–S Fuzzy Networked Control System Under DoS Attacks

This article analyzes the mechanism of denial-of-service (DoS) attacks initiated by hackers from the perspective of computer networks. In order to effectively estimate the performance error generated by the T–S fuzzy networked control systems under DoS attacks, we transform the performance error estimation problem into the one of finding ellipsoid constraints <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathfrak {J}(P_{i})$</tex-math></inline-formula> . First, improved Lyapunov–Krasovskii functions (LKFs) based on fuzzy membership functions are constructed, which combine the characteristics of nonlinear problems in the system to reduce the initial constraints. Then, a second-order weight method (SOWM) is introduced to divide the time interval of sampling meticulously. Besides, the information stored in the LKFs is enhanced. Furthermore, we construct the novel looped functions by relying on the SOWM. Next, a suitable integral elastic event trigger mechanism is established to ensure that the performance errors caused by the attacks are estimated. Finally, the feasibility of the proposed method is verified by a two-degree-of-freedom helicopter system.

Free-walking: Pedestrian inertial navigation based on dual foot-mounted IMU

The inertial navigation system (INS), which is frequently used in emergency rescue operations and other situations, has the benefits of not relying on infrastructure, high positioning frequency, and strong real-time performance. However, the intricate and unpredictable pedestrian motion patterns lead the INS localization error to significantly diverge with time. This paper aims to enhance the accuracy of zero-velocity interval (ZVI) detection and reduce the heading and altitude drift of foot-mounted INS via deep learning and equation constraint of dual feet. Aiming at the observational noise problem of low-cost inertial sensors, we utilize a denoising autoencoder to automatically eliminate the inherent noise. Aiming at the problem that inaccurate detection of the ZVI detection results in obvious displacement error, we propose a sample-level ZVI detection algorithm based on the U-Net neural network, which effectively solves the problem of mislabeling caused by sliding windows. Aiming at the problem that Zero-Velocity Update (ZUPT) cannot suppress heading and altitude error, we propose a bipedal INS method based on the equation constraint and ellipsoid constraint, which uses foot-to-foot distance as a new observation to correct heading and altitude error. We conduct extensive and well-designed experiments to evaluate the performance of the proposed method. The experimental results indicate that the position error of our proposed method did not exceed 0.83% of the total traveled distance.

Neural-Network-Based Set-Membership Fault Estimation for 2-D Systems Under Encoding-Decoding Mechanism.

In this article, the simultaneous state and fault estimation problem is investigated for a class of nonlinear 2-D shift-varying systems, where the sensors and the estimator are connected via a communication network of limited bandwidth. With the purpose of relieving the communication burden and enhancing the transmission security, a new encoding-decoding mechanism is put forward so as to encode the transmitted data with a finite number of bits. The aim of the addressed problem is to develop a neural-network (NN)-based set-membership estimator for jointly estimating the system states and the faults, where the estimation errors are guaranteed to reside within an optimized ellipsoidal set. With the aid of the mathematical induction technique and certain convex optimization approaches, sufficient conditions are derived for the existence of the desired set-membership estimator, and the estimator gains and the NN tuning scalars are then presented in terms of the solutions to a set of optimization problems subject to ellipsoidal constraints. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed estimator design method.

Probabilistic-Constrained Distributed Set-Membership Estimation Over Sensor Networks: A Dynamic Periodic Event-Triggered Approach

This article is concerned with the event-triggered probabilistic-constrained distributed set-membership estimation problem for a discrete-time nonlinear system over sensor networks. For saving communication resource, a novel discrete-time dynamic periodic event-triggered mechanism (ETM) is first developed for the sensor network. Under the proposed method, the sensor node calculates the ETM in a periodic manner and the threshold is adjusted dynamically. Thereafter, a distributed set-membership estimator is constructed, and a probability-based estimated ellipsoidal constraint is put forward to acquire a more flexible set-membership estimation algorithm. Simultaneously, an auxiliary-function-dependent approach is proposed to derive the criterion for the co-design of the probabilistic-constrained set-membership estimator and the event-triggered parameter such that the system states reside in the estimated ellipsoid with a pre-specified probability. The auxiliary function is constructed in a piecewise style aiming to deal with the sawtooth constraint of sampling signals. Furthermore, a recursive convex optimization algorithm with regard to the estimated ellipsoid is presented. Finally, a simulation example is employed to verify the validity of the developed method.

Set-membership filtering for two-dimensional systems with dynamic event-triggered mechanism

In this paper, the set-membership filtering problem is investigated for a class of two-dimensional (2-D) shift-varying systems described by the general Fornasini-Marchesini second model with a dynamic event-triggered mechanism. The sensors are communicated with the remote filter through a communication network of limited bandwidth. In order to improve the efficiency of utilizing the network resources, a dynamic event-triggered mechanism is exploited for the 2-D shift-varying system, and a set-membership filter is then designed for 2-D systems subject to unknown-but-bounded noises so that the actual system state is guaranteed to reside within an optimized ellipsoidal set. By means of the mathematical induction technique and the set theory, sufficient conditions are derived to ensure the existence of the desired set-membership filter. Furthermore, the filter gains are obtained by solving a set of optimization problems subject to ellipsoidal constraints. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed filter design method.

Low-Cost Single-Frequency DGNSS/DBA Combined Positioning Research and Performance Evaluation

In recent years, low-cost single-frequency GNSS receivers have been widely used in many fields such as mass navigation and deformation monitoring; however, due to the poor signal quality of low-cost patch antennae, it is difficult for carrier phase real-time kinematic (RTK) technology to fix the integer ambiguity. Differential GNSS (DGNSS) positioning with pseudorange can effectively meet the high robustness and reliability requirements for the submeter to the meter level positioning accuracy of UVA/vehicle/aerospace users. To improve the DGNSS positioning accuracy and reliability of low-cost single-frequency GNSS receivers in complex environments, we propose a differential barometric altimetry (DBA)-assisted DGNSS positioning algorithm, which solves the DGNSS observation equations jointly and rigorously with the Earth ellipsoidal constraint equations constructed by the DBA altitude. The DBA altitude accuracy at different baseline lengths was evaluated in detail, and the DGNSS positioning performance of the single-frequency low-cost u-blox receiver NEO-M8T with a patch antenna and DGNSS/DBA combined positioning performance with the BMP280 barometer was analyzed by several sets of static and dynamic experiments under different environments. The results show that the single-frequency NEO-M8T receiver with patch antenna DGNSS positioning accuracy is submeter level in the static environment and drops to meter level in the dynamic environment. GPS+BDS dual system has higher positioning accuracy than single GPS or single BDS. DGNSS/DBA combination has higher positioning accuracy than DGNSS, especially the root mean square error (RMSE) can be improved by 30% to 80% in the U direction and slightly improved in the N and E directions. This study can provide an effective solution reference for various applications of low-cost sensor fusion positioning in the mass consumer market.

F²IMU-R: Pedestrian Navigation by Low-Cost Foot-Mounted Dual IMUs and Interfoot Ranging

Foot-mounted inertial sensors become popular in many indoor or GPS-denied applications, including but not limited to medical monitoring, gait analysis, soldier, and first responder positioning. However, the foot-mounted inertial navigation relies largely on the aid of zero velocity update (ZUPT) and has encountered inherent problems, such as heading drift. This article implements a pedestrian navigation system based on dual foot-mounted low-cost inertial measurement units (IMUs) and interfoot ultrasonic ranging. The observability analysis of the system is performed to investigate the roles of the ZUPT measurement and the foot-to-foot ranging measurement in improving the state estimability. A Kalman-based estimation algorithm is mechanized in the Earth frame, rather than in the common navigation frame, which is found to be effective in depressing the linearization error in Kalman filtering. An ellipsoid constraint in the Earth frame is also proposed to further restrict the height drift. Simulation and real field experiments show that the proposed method has better robustness and positioning accuracy (about 0.1%–0.2% traveled distance) than the traditional pedestrian navigation schemes do.

Online collision avoidance trajectory planning for spacecraft proximity operations with uncertain obstacle

The spacecraft relative motion trajectory planning is one of the enabling techniques for autonomous proximity operations, especially in the increasingly complicated mission environments. Most traditional trajectory planning methods focus on improving the performance criteria in the deterministic conditions, whereas various uncertain elements in practice would significantly degrade the trajectory performance. Considering the uncertainties underlying the collision avoidance constraints, this paper suggests a model predictive control based online trajectory planning framework in which the obstacle information in higher-precision would be consistently updated by the onboard sensor. To improve the computational efficiency of the online planning framework, the rotating hyperplane (RH) technique is utilized to transform the nonlinear ellipsoidal keep-out zone constraints into convex formulations. And the concept of rotation window is introduced to eliminate the unexpected mismatch between the spacecraft motion and hyperplane rotation in the conventional RH method, which in sequence improves the RH method’s capability for multiple obstacle avoidance problem. Moreover, a three-dimensional (3-D) extension strategy is proposed to simplify the computation procedure when applying the RH method for a 3-D collision avoidance problem. Numerical simulations are carried out to validate the performance of the proposed online trajectory planning framework in addressing the uncertain collision avoidance constraints.

Relaxed zero-forcing beamformer under temporally-correlated interference

The relaxed zero-forcing (RZF) beamformer is a quadratically-and-linearly constrained minimum variance beamformer. The central question addressed in this paper is whether RZF performs better than the widely-used minimum variance distortionless response and zero-forcing beamformers under temporally-correlated interference. First, RZF is rederived by imposing an ellipsoidal constraint that bounds the amount of interference leakage for mitigating the intrinsic gap between the output variance and the mean squared error (MSE) which stems from the temporal correlations. Second, an analysis of RZF is presented for the single-interference case, showing how the MSE is affected by the spatio-temporal correlations between the desired and interfering sources as well as by the signal and noise powers. Third, numerical studies are presented for the multiple-interference case, showing the remarkable advantages of RZF in its basic performance as well as in its application to brain activity reconstruction from EEG data. The analytical and experimental results clarify that the RZF beamformer gives near-optimal performance in some situations.

Two-stage robust optimization for practical reactive power in distribution network based on multiple constraint convex approximation

In multi-time-scale optimization frameworks of daily, hourly, and minute levels, centralized optimization has a demand for real-time communication and prediction technology. In the distribution network of an undeveloped area, the minute level optimization does not work because of the lack of accurate prediction and real-time communication. The practical reactive power originally obtained from the minute-level optimization does not exist, and the uncertainty should be considered in hourly level optimization. In this study, a two-stage robust optimization at the hourly level is proposed to minimize the network loss without the minute level optimization. A simple data-based method of modeling multiple uncertainty is proposed, which directly uses historical data with minimal mathematical knowledge. The multiple uncertainty set contains the interval constraint and convex hull of an ellipsoid constraint. The convex hull of the ellipsoid constraint is formed by ellipse tangents. In addition, the practical reactive power cannot be obtained through the common robust inverter dispatch strategy, which sets the maximum available active power as an uncertain variable. A pseudo-decoupling dispatch strategy is proposed to approximate the separation of reactive power and uncertainty and obtain the practical reactive power. The Benders decomposition framework is used to solve the two-stage robust optimization, and a feasible linear constraint generated from the subproblem is added to the master problem. The simulation results demonstrate the effectiveness of the proposed method.

Set-membership filtering for piecewise linear systems with censored measurements under Round-Robin protocol

In this paper, the set-membership filtering problem is investigated for a class of piecewise linear systems with state constraintsand censored measurements under the Round-Robin (RR) protocol. First of all, the mode of the piecewise linear system is determined by itsstate. The noises under consideration satisfy two ellipsoid constraints. According the schedule of the RR protocol, a set of piecewise linearfilters is constructed in terms of the censored measurements transmitted through the shared network. The objective of this paper is todesign a set of filter gains such that the augmented dynamics satisfies the desirable ellipsoid constraint in the simultaneous presence of stateconstraints, censored measurements and RR protocol. A sufficient condition for the existence of piecewise linear filters is obtained and aconvex optimisation method is presented to derive the minimized ellipsoid in the sense of matrix trace. Finally, a simulation example is givento verify the effectiveness of the proposed design method.

Admissibility in general Gauss–Markov model with respect to an ellipsoidal constraint under weighted balanced loss

Under weighted balanced loss function, we obtain the best linear unbiased estimator of regression coefficient in general Gauss–Markov model and discuss the admissibility of linear estimators of the regression coefficient with respect to an ellipsoidal constraint. We establish necessary and sufficient conditions for the admissibility of the linear estimators () among the class of homogeneous and inhomogeneous linear estimators, respectively.

Robust predictive control for anti-rolling path following of underactuated surface vessels using adaptive Kalman filter

With the strong time-varying disturbances in wave fields, the large sway motion of underactuated surface vessels can be caused leading to the control performance reduction and large range of roll angle, such that a novel path following control with roll constraints is proposed. Firstly, the affine switching system model is constructed with coupled surge, sway, roll, and yaw. Then, with augmented state adaptive Kalman filter, the estimations of system state and disturbance can be obtained for the feedforward compensation. Considering the existing estimation error between real and estimated states, the state estimation has been adopted directly in the controller design for the performance improvements. With the convex optimization of linear matrix inequalities, the invariant ellipsoid constraint ensures the close-loop system uniformly bounded and stable. Lastly, the simulation results have verified the effectiveness of the designed control approach.