Initial Estimation Error Research Articles

Inverse estimation of heat flux and temperature field for a nonlinear heat transfer system using step-renewed two-stage Kalman filter

Inverse estimation of the thermal input and states is a useful tool for the monitoring of a thermal system. Nonlinear heat transfer is a quite common issue in this kind of problem. As the thermal properties are temperature-dependent, it is difficult to inversely estimate the input and temperature field. To deal with this problem, a step-renewed scheme is adopted into the weighted optimal two-stage Kalman filter (WOTSKF), forming step-renewed WOTSKF (SR-WOTSKF). This strategy is a marching method, without solving the Jacobian matrix in extended Kalman filter. The feasibility of dealing with the nonlinear inverse heat transfer problem is implemented by comparing WOTSKF and SR-WOTSKF. Then, the weighting factor, initial guess of the input heat flux and measurement noise are changed to investigate their effects on the simultaneous estimation results of heat flux and temperature field. It is found that when the weighting factor is 0.95, the relative error of the estimated heat flux using SR-WOTSKF is approximately 2.73% which is much lower than that using WOTSKF. Results using SR-WOTSKF demonstrate that the estimation results are independent of the initial guess and the estimated heat flux can track the exact one in a short period. An incorrect initial guess causes the initial estimation error of the temperature and heat flux and it makes no sense to following period. When the standard deviations of the measurement noise are adopted as 0.01, 0.10, 0.50 and 1.00, the mean relative error of the heat flux is 2.73%, 4.79%, 7.71% and 9.43%, demonstrating the strong robustness of SR-WOTSKF to resist the measurement noise.

Output Feedback MPC for Nonlinear System in Large Operation Range

This paper studies the output feedback model predictive control (MPC) being suitable to a large operation range of the constrained system represented by a nonlinear model with a bounded disturbance. The model is further parameterized as a multiple linear parameter varying (LPV) state-space equation, each LPV representation being valid around an exclusive equilibrium. Off-line, for each equilibrium, a set of local control laws (in the dynamic output feedback), each having its region of attraction, are calculated. All the control laws for all the equilibriums constitute a lookup table, and all the corresponding regions of attraction take a union. On-line, the real-time control law is searched as one, as per its region of attraction, in the lookup table when the estimated system state moves inside of the union. Once the initial estimation error lies in a pre-specified set, the augmented state is guaranteed to converge to the neighborhood of the target equilibrium, and the constraints on input and output are consistently satisfied. An example is given to illustrate the effectiveness of the proposed algorithm.

Tracking Object’s Pose via Dynamic Tactile Interaction

It is a challenging task to localize and track an in-hand object in robotic domain. Researchers were mainly using the vision as major modality for extracting object’s pose. The vision approaches are fragile when the object is occluded by the robotic arm and hand. To this end, we propose a tactile-based DTI-Tracker (tracking object’s pose via Dynamic Tactile Interaction) approach and formalize the object’s tracking as a filter problem. An Extended Kalman Filter (EKF) is used to estimate the in-hand object pose exploiting the high spatial resolution tactile feedback. Given the initial estimation error, the proposed approach rapidly converges the estimation result to the real pose and the statistic evaluation shows the robustness of the proposed approach. We evaluate this method in physics simulation and real multi-fingered grasping setup while the object is static and movable. The proposed method is a potential tool to foster future research on dexterous manipulation using multifingered robotic hand.

Parameter estimation and control of a fuel cell air supply system based on an improved extended state observer

ABSTRACT Tracking control of the oxygen excess ratio (OER) and keeping the cathode air pressure relatively stable are essential for the operation of polymer electrolyte membrane fuel cell (PEMFC). In automotive fuel cell air supply systems, the cathode air pressure and OER are usually unmeasurable parameters, which makes the air supply system control and fault analysis very difficult. To solve this problem, this paper proposes an extended state observer based on the hyperbolic tangent function (HTF-ESO) to estimate the cathode air pressure of the fuel cell gas supply system, and indirectly obtains the OER according to the estimated cathode pressure, and designs the sliding mode control (SMC) and a first-order active disturbance rejection control (ADRC) for the tracking control of the OER. The simulation results show that the improved HTF-ESO effectively mitigates the initial differential peak phenomenon and reduces the initial estimation error of the cathode air pressure, and the RMSE of the cathode pressure and supply manifold pressure observation errors are reduced by 68% and 20%, respectively, compared with the present unimproved ESO. Compared with the PI, the RSME of the control error after convergence of the designed SMC and ADRC is reduced by 4.3%, and the OER can be restored to the reference value within 1 second, with good dynamic response.

Magnetometer-Only Kalman Filter Based Algorithms for High Accuracy Spacecraft Attitude Estimation (A Comparative Analysis)

Kalman Filter (KF) based algorithms are the most frequently employed attitude estimation algorithms. Typically, a fully observable system necessitates the use of two distinct sensor types. Therefore, relying on a single sensor, such as a magnetometer, for spacecraft attitude estimation is deemed to be a challenge. The present investigation centers on utilizing magnetometers as the exclusive sensor. Several KF based estimation algorithms have been designed and evaluated to give the designer of spacecraft Attitude and Orbit Control System (AOCS) the choice of a suitable algorithm for his mission based on quantitative measures. These algorithms are capable of effectively addressing nonlinearity in both process and measurement models. The algorithms under examination encompass the Extended Kalman Filter (EKF), Sequential Extended Kalman Filter (SEKF), Pseudo Linear Kalman Filter (PSELIKA), Unscented Kalman Filter (USKF), and Derivative Free Extended Kalman Filter (DFEKF). The comparison of the distinct algorithms hinges on key performance metrics, such as estimation error for each axis, computation time, and convergence rate. The resulting algorithms provide numerous benefits, such as diverse levels of high estimation accuracy (with estimation errors ranging from 0.014o to 0.14o), varying computational demands (execution time ranges from 0.0536s to 0.0584s), and the capability to converge despite large initial attitude estimation errors (which reached 170o). These properties render the algorithms appropriate for utilization by spacecraft designers in all operational modes, supplying high-precision attitude estimations better than (0.5o) despite high magnetometer noise levels, which reached (200 nT).

Fixed-time disturbance observer based robust tracking control of wheeled mobile robot with multiple disturbances

In this article, the problem of robust tracking control for wheeled mobile robot (WMR) with skidding, slipping, and parameter uncertainties is addressed. Through designing double sliding mode variables, a fixed time disturbance observer is developed to estimate the multiple disturbances within a fixed time, and the convergence time is regardless of the initial estimation error of the system. Based on the fixed-time disturbance observer (FTDOB) and the novel power reaching law sliding mode technique, a robust tracking controller is synthesized. The proposed control method eliminates the chattering problem existing in the traditional sliding mode control, and can guarantee the high-precision tracking control performance even in the presence of skidding, slipping and parameter uncertainties. The closed-loop system stability analysis is verified by the Lyapunov stability theory. Meanwhile, simulation comparative results are carried out to illustrate the effectiveness of the proposed control method.

Approximate Optimal Tracking Control for Partially Unknown Nonlinear Systems via an Adaptive Fixed-Time Observer

This paper investigates a novel adaptive fixed-time disturbance observer (AFXDO)-based approximate optimal tracking control architecture for nonlinear systems with partially unknown dynamic drift and perturbation under an adaptive dynamic programming (ADP) scheme. To attenuate the impact of disturbance, a novel AFXDO was designed based on the principle of a fixed-time stable system without prior information of disturbance, making disturbance observer errors converge to zero in a fixed time independent of initial estimation error. Additionally, approximate optimal control is conducted by incorporating the real-time estimation of AFXDO into a critic-only ADP framework to stabilize the dynamics of tracking errors and strike a balance between consumption and performance. In particular, to address the heavy calculation burden and oscillation phenomenon in the traditional actor–critic structure, an improved adaptive update law with a variable learning rate was developed to update the weight for adjusting the optimal cost function and optimal control policy simultaneously, avoiding the initial chattering phenomenon and achieving a prescribed convergence without resorting to dual networks. With the efforts of AFXDO and a weight law with a variable learning rate, the track errors were achieved with fast transient performance and low control consumptions in a fixed time. By revisiting Lyapunov stability, the tracking error and weight estimation error were proven to be uniformly ultimately bounded, and the designed control tended to optimal control. The simulations were carried out on quadrotor tracking to demonstrate the effectiveness of the developed control scheme, which achieves rapid convergence by lower control consumption in 4 s, where the cost function is reduced by 19.13%.

Three-axis high-accuracy spacecraft attitude estimation via sequential extended Kalman filtering of single-axis magnetometer measurements

Magnetometer is a highly advantageous sensor for determining a spacecraft’s attitude. This article provides a solution to the problem of spacecraft attitude estimation using magnetometer measurements only. To ensure full observability of spacecraft attitude states, it is necessary to use at least two types of sensors. Consequently, utilizing a single sensor, such as the magnetometer, poses a significant challenge for any attitude estimation algorithm, including the extended Kalman filter (EKF). Moreover, implementing the EKF algorithm, or any other attitude estimation algorithm, is computationally intensive. To address these issues, an algorithm has been developed that estimates spacecraft attitude angles and attitude rates using a sequential extended Kalman filter (SEKF). This algorithm offers numerous benefits over those found in the literature such as high accuracy, low computational resource requirements, the ability to converge even with large initial attitude and angular velocity estimation errors, and the ability to function even if two of the three measurement channels of the magnetometer are not functioning. With these benefits, the developed SEKF algorithm is capable of operating in all spacecraft operational modes, delivering accurate performance and computation time. In spite of measurements with large noise values, the high accuracy achieved by the SEKF algorithm enables the magnetometer to serve as the sole source of attitude information, even if one or two magnetometer measurement channels are not functioning.

A fast transient tracking differentiator for high-precision motion systems

High-quality velocity signal plays an important role in fast and precise motion systems, but most commercially available motion systems are not commonly equipped with velocity sensors; hence, full access to the system states is impossible. A fast transient tracking differentiator is proposed in this article for obtaining the noise-less time derivative from a noisy measurement. The fast transient tracking differentiator is conceived within the framework of tracking differentiator methodology and is accomplished by integrating a power-like function with a smooth hyperbolic sine function. Tracking differentiator theory and Lyapunov direct method are employed to show the global asymptotic convergence. Advantages of the proposed fast transient tracking differentiator include the easy implementation with intuitive structure and high computational efficiency and faster transient and higher noise attenuation for both small and large initial estimation errors. The proposed fast transient tracking differentiator can be applied to a large class of motion systems by cascading to a robust output feedback proportional–derivative control for fast and high-precision positioning with position measurement only. Numerical simulation and real-time experimental comparisons demonstrate that the proposed approach provides an easygoing model-free output feedback solution for fast and accurate velocity reconstruction and high-performance positioning of uncertain motion systems with position measurement only.

Bias-Corrected Inference of High-Dimensional Generalized Linear Models

In this paper, we propose a weighted link-specific (WLS) approach that establishes a unified statistical inference framework for high-dimensional Poisson and Gamma regression. We regress the parameter deviations as well as the initial estimation errors and utilize the resulting regression coefficients as correction weights to reduce the total mean square error (MSE). We also develop the asymptotic normality of the correction estimates under sparse and non-sparse conditions and construct associated confidence intervals (CIs) to verify the robustness of the new method. Finally, numerical simulations and empirical analysis show that the WLS method is extensive and effective.

Tan-Type BLF-Based Attitude Tracking Control Design for Rigid Spacecraft with Arbitrary Disturbances

This study deals with the problem of disturbances in observer-based attitude tracking control for spacecraft in the presence of inertia-matrix uncertainty and arbitrary disturbance. Following the backstepping control, a tan-type barrier Lyapunov function (BLF)-based attitude tracking control method with prescribed settling time and performance is systematically developed. The proposed control framework possesses three advantages over the existing attitude controllers. Firstly, the singularity problem associated with the use of fractional power in fixed-time control is effectively resolved without employing any command filter or piece-wise continuous function. Secondly, inspired by the concept of the tan-type BLF approach, any desired performance for the attitude tracking error is satisfied. Lastly, the total disturbance, including the system’s uncertainty, external disturbances, and time-derivative of the virtual control, is precisely reconstructed during a predefined time, even if the initial estimation error tends to infinity. Moreover, this time is determined as a tunable gain in the observer. The numerical simulations confirm the superior performance of the proposed control strategy in comparison with the existing pertinent works.

Observer-based iterative learning control for a high relative degree nonlinear system and its application to a vehicular wet-clutch system

In this paper, an observer-based iterative learning control with an output feedback control scheme is proposed for a high relative degree nonlinear system with an unmeasurable control state. Multiple differentiation of measurements can make the control result sensitive to measurement noise when controlling such systems. A convergence analysis was established that can use only lower-order differentiation regardless of the highest-order differentiation, based on the robustness condition to measurement noise and initial estimation error. The application to the vehicular wet-clutch system is presented to illustrate the effectiveness of the proposed method and its learning gain selection. These contributions are verified through theoretical analysis and simulation of the wet-clutch system. The simulation results show the effectiveness of the proposed approach for a class of nonlinear systems with a high relative degree.

Design and Evaluation of an Invariant Extended Kalman Filter for Trunk Motion Estimation With Sensor Misalignment

Understanding human motion is of critical importance for health monitoring and control of assistive robots, yet many human kinematic variables cannot be directly or accurately measured by wearable sensors. In recent years, invariant extended Kalman filtering (InEKF) has shown a great potential in nonlinear state estimation, but its applications to human poses new challenges, including imperfect placement of wearable sensors and inaccurate measurement models. To address these challenges, this article proposes an augmented InEKF design which considers the misalignment of the inertial sensor at the trunk as part of the states and preserves the group affine property for the process model. Personalized lower-extremity forward kinematic models are built and employed as the measurement model for the augmented InEKF. Observability analysis for the new InEKF design is presented. The filter is evaluated with three subjects in squatting, rolling-foot walking, and ladder-climbing motions. Experimental results validate the superior performance of the proposed InEKF over the state-of-the-art InEKF. Improved accuracy and faster convergence in estimating the velocity and orientation of human, in all three motions, are achieved despite the significant initial estimation errors and the uncertainties associated with the forward kinematic measurement model.

Cyber Attack Detection and Isolation for a Quadrotor UAV With Modified Sliding Innovation Sequences

Common vulnerabilities in typical intelligent cyber-physical systems such as unmanned aerial vehicles (UAVs) can be easily exploited by cyber attackers to cause serious accidents and harm. For successful UAV operations, security against cyber attacks is imperative. In this paper, we propose a modified sliding innovation sequences (MSIS) detector, based on the extended Kalman filter optimal state estimation, for a dynamic quadrotor system to detect cyber attacks inflicted on both its actuators and sensors in real time. These cyber attacks include random attacks, false data injection (FDI) attacks and denial-of-service (DoS) attacks. The MSIS detector computes the operator norm of the normalized innovation (residual) sequence within a sliding time window and triggers the alarm if the value is above the preset threshold. For a quadrotor undergoing rapid turns in a complex trajectory, the detector observes a reduced false alarm rate as compared to other state estimation-based detectors. To address the initial estimation error problem, we implement an iteration procedure to initiate and calibrate the detector. By evaluating the sample covariance of the normalized innovation sequence, the MSIS detector has the capability to isolate cyber attacks. Finally, simulation results of a quadrotor in a periodic, complex trajectory flight are provided to verify the effectiveness of the MSIS detection and isolation method.

Disturbance Observer-Based Tracking Controller for Uncertain Marine Surface Vessel

In this study, a novel control framework is proposed to improve the tracking performance of uncertain marine vessels which work in enhanced sea states. The proposed control strategy is based on incorporating a fixed-time nonlinear disturbance observer (FTNDO) in a fixed-time convergent backstepping control. More specifically, the FTNDO is developed to reconstruct the total uncertainties due to the system uncertainty and unknown time-varying exterior disturbances. In comparison with the existing disturbance observers, the FTNDO guarantees that the estimation errors will converge to the origin within a predefined time even if the initial estimation errors tend toward infinity. This feature is quite important in the closed-loop system stability analysis as the separation principle does not hold in nonlinear systems. Besides, it does not require the restricting assumption that the upper bound of the lumped uncertainty or its time derivative has to be bounded or known. A backstepping control with a compensation control part is then designed to make the tracking errors converge to the origin within a finite time regardless of initial tracking errors. The compensation control is developed by means of the estimated signal and applied to totally reject the total uncertainty. The global fixed-time stabilization of the closed-loop system is investigated through the Lyapunov stability criterion. Numerical simulation results conducted on an uncertain marine surface vessel confirm the superior control performance and efficiency of the planned method in comparison with the existing disturbance observer-based tracking control strategies.

Various damper forces and dynamic excitation nonparametric identification with a double Chebyshev polynomial using limited fused measurements

By introducting a double Chebyshev polynomial as a general nonparametric model for various nonlinear restorying forces (NRFs) and an updated observation equation, and with the help of an Updated Extended Kalman filter with unknown input (UEKF-UI) algorithm and a data fusion technology, a nonparametric identification approach for both NRFs at multiple locations and excitation for multi-degree-of-freedom (MDOF) lumped mass structures is presented. In order to investigate the generality of the proposed identification method, both numerical and experimental studies on different MDOF structure models equipped with a shape memory alloy (SMA) damper and/or a magnetorheological (MR) damper mimicking different types of nonlinearities that widely exist in practical engineering structures under unknown excitation are carried out. Identification results considering different initial estimation errors and measurement noise show that the NRF provided by different types of dampers at multiple locations, excitation and unmeasured dynamic responses can be identified nonparametrically with acceptable accuracy.

A novel collaborative multiscale weighting factor‐adaptive Kalman filtering method for the time‐varying whole‐life‐cycle state of charge estimation of lithium‐ion batteries

Accurate state of charge (SOC) estimation is essential for the whole-life-cycle safety guarantee and protection of lithium-ion batteries, which is quite difficult to realize. In this study, a novel weighting factor-adaptive Kalman filtering (WF-AKF) method is proposed for the accurate estimation of SOC with a collaborative model for parameter identification. An improved bipartite electrical equivalent circuit (BEEC) model is constructed to describe the dynamic characteristics combined with the mathematical correction of the time-varying factors. The model parameters are identified online, corresponding to various SOC levels and temperature conditions. Considering the internal resistances, ambient temperature, and complex current rate variations, an adaptive multi-time scale iterative calculation model is constructed and combined with the real-time estimation and correction strategies. The maximum closed-circuit voltage (CCV) traction error is 0.36% and 0.24% for the main pulse-current charging and discharging processes, respectively. The proposed WF-AKF algorithm stabilizes the large initial SOC estimation error by tracking the actual value with a maximum error of 0.46% under the complex working condition. The SOC estimation is accurate and robust to the time-varying characteristics and working conditions even when the initial error is large, providing a safety protection theory for lithium-ion batteries.

Disturbance observer-based constrained attitude control for flexible spacecraft

This paper investigates the difficult issue of fixed-time constrained attitude control for a flexible spacecraft under the influence of the system uncertainties, environmental disturbance and abrupt actuator faults. The contributions of the proposed control framework are twofold. Firstly, an observer is presented to precisely reconstruct the uncertain dynamics within a fixed time regardless of the initial estimation error while the settling time is given as a specific parameter. Secondly, using a combination of prescribed performance control (PPC) and barrier Lyapunov function (BLF) approaches, a simple structure constrained attitude control for flexible spacecraft is proposed while desired performance specifications for both quaternion and rotation velocity are indirectly achieved by constraining the sliding manifold. A distinctive feature of the suggested control framework is that the settling time of the closed-loop system is finite and explicitly expressed as two tunable gains even when abrupt actuators faults happen. Numerical simulations substantiate the ability of the offered control to effectively accomplish favorable attitude maneuver under the negative effect of the inertia matrix uncertainty, external disturbances, flexible structures vibration and actuators faults.

Efficient Simultaneous Spacecraft Attitude and Orbit Estimation via Neural Networks

Spacecraft attitude and orbit estimation are considered very important tasks for nearly every spacecraft. The full state estimation process is usually done using the Extended Kalman Filter (EKF). Nonlinearities associated with spacecraft model, measurement model, and disturbance models represent a serious obstacle for EKF to be implemented on-board a spacecraft. In order to overcome this problem, two neural networks architecture are developed. They are the direct architecture and the cross-feeding architecture. The first one can estimate the spacecraft orbital states but it has a degraded accuracy for the spacecraft representing attitude states. A modification of the direct architecture is made to enable simultaneous estimation of spacecraft attitude and orbit states and named as cross-feeding architecture. The cross-feeding architecture has outperformed the EKF. It has the same accuracy as the EKF, with less than half of its execution time. An EKF is used to provide data set for training and validation of the neural networks solution. In order to avoid overfitting and enhance network generalization, 15% of the EKF data set is used to validate the solution. The developed algorithms have the ability to deal with initial high estimation errors without using any small angle approximation. Thus, the developed algorithms can work in all the spacecraft operational modes.

Stochastic stability of decentralized Kalman filter for nonlinear systems

SummaryIn this paper, stochastic stability of a decentralized Kalman filter (DKF) for nonlinear systems and a bound on the sum of square of predicted estimation error are examined of a single node. A Lyapunov analysis approach is used to show that the predicted estimation error of the nonlinear DKF is stochastically stable and exponentially bounded in mean square, if the system is observable, controllable and the initial estimation error is bounded. Moreover, it is validated by the numerical simulations. The numerical results show that the sum of square of the predicted estimation error is bounded above.