Unknown Measurement Noise Research Articles

Practical tracking control of a class of uncertain nonlinear systems and unknown output function

SummaryThis paper investigates the problem of global practical tracking control via dynamic output‐feedback for a family of uncertain nonlinear systems with unknown output function. The nonlinear terms of the system under consideration are assumed to be bounded by an unknown parameter multiplied by a function of unmeasured states. Furthermore, contrary to the previous works, the system output is presented with a multiplicative unknown measurement noise. Based on a high‐gain observer to reconstruct the unmeasured system states and handle the unknown output function, an adaptive output feedback controller is designed to guarantee the reference trajectory tracking. The boundedness of all the closed‐loop signals is verified by Lyapunov analysis and the tracking errors are proved to be sufficiently small prescribed after a finite time. A practical example is given to illustrate the effectiveness of the proposed design scheme.

Vehicle state estimation using a maximum likelihood based robust adaptive extended kalman filter considering unknown white Gaussian process and measurement noise signal

The stochastic nature of noise signals affects the vehicle’s internal states and the outputs, resulting in the difficulty in estimation. The unknown or time-varying nature of noise signals if not taken into account for estimation, the results will diverge and be highly deteriorated. In this paper, a maximum likelihood principle (MLP) based adaptive robust extended kalman filter for estimating the states of the adopted non-linear vehicle model is proposed. An observability test is done for the purpose of estimation. A covariance matching (CM) based robust adaptive high forgetting factor based fault tolerant technique is also employed on the robust adaptive extended and unscented kalman filters for comparison purpose. The Robustness of the filter is analyzed by varying the parameter of the vehicle through a local sensitivity analysis. The results show that the MLP based approach to the extended kalman filter performs well in three simulations for sinusoidal steering, Double Lance Change, J-Turn, Fishhook, Slalom maneuver in comparison to robust adaptive unscented kalman filter. Friction coefficient of 0.8 (dry road) and 0.4 (wet road) is chosen for the simulation. The sideslip angle RMSE value for MLP based estimation is obtained as 2.62e-05, 4.545e-06 for Sine and DLC maneuver.

Simultaneous moving horizon estimation and control for nonlinear systems subject to bounded disturbances

SummaryIn this work, we address the output–feedback control problem for nonlinear systems under bounded disturbances using a moving horizon approach. The controller is posed as an optimisation‐based problem that simultaneously estimates the state trajectory and computes future control inputs. It minimizes a criterion that involves finite backward and forward horizons with respect to the unknown initial state, measurement noises and control input variables. The main novelty of this work relies on linking the lengths of the forward and backward windows with the closed‐loop stability, assuming detectability and decoding sufficient conditions to assure system stabilizability. It leads to a formulation that does not require to be a Control Lyapunov Function for the terminal cost of the controller. Simulation examples are carried out to compare the performance of solving simultaneously and independently the estimation and control problems. Furthermore, the examples show how the controller influences the length of the estimation window through its gain.

An Adaptive Federated Filter Based on Variational Bayes With Application to Multisource Navigation

Information fusion is one of the key technologies in airborne multi-source navigation, where federated filter is widely used due to its simple structure. However, the sensor measurement of multi-source navigation system will become unreliable in some interferential environment, which leads to the state and measurement noise covariance matrix change over time and estimate difficultly. Inaccurate covariance matrice cause the loss of positioning accuracy in traditional federated filter. To address the problems, this paper puts forward an adaptive federal Kalman filtering algorithm based on Variational Bayesian and applies it to the INS/GPS/Terrain/Geomagnetic multi-source navigation system. Simulation and experiment results show that the proposed filter outperforms the traditional federated filter at improving the positioning accuracy under the condition of time-varying or even unknown state and measurement noise covariance matrix, which plays a positive role in UAV multi-source navigation.

An efficient method for estimating time-varying convective heat transfer coefficient based on boundary condition transfer technique

Accurate determination of time-varying convective heat transfer coefficient (CHTC) is the main content of many engineering applications. In view of some problems existing in the determination of time-varying CHTC, this paper develops an estimation scheme using the boundary condition transfer technique. In the new scheme, the estimation of CHTC is transformed into the estimation of known fluid temperature. Then, according to the estimation results of fluid temperature, the discrete values of characteristic variable are weighted comprehensively to obtain the estimated results of time-varying CHTC. Numerical simulation tests are mainly adopted so as to validate the above scheme. The developed scheme is also compared with the traditional method, which can better reveal the performance of the former. Effects of some important parameters such as the number of unknown variables, fluid temperature and measurement noise on the estimation results are illustrated specifically. Results demonstrate that the proposal can effectively determine the time-varying CHTC and improve the computational efficiency. Moreover, the proposed method also reduces the effects of fluid temperature on the forecast results, which is helpful for the accurate determination of time-varying CHTC.

Maximum correntropy criterion variational Bayesian adaptive Kalman filter based on strong tracking with unknown noise covariances

The performance of the current state estimation will degrade in the existence of slow-varying noise statistics. To solve the aforementioned issues, an improved strong tracking maximum correntropy criterion variational-Bayesian adaptive Kalman filter is presented in this paper. First of all, the inverse-Wishart distribution, as the conjugate-prior, is adopted to model the unknown and time-varying measurement and process noise covariances, then the noise covariances and system state are estimated via the variational Bayesian method. Secondly, the multiple fading-factors are obtained and evaluated to modify the prediction error covariance matrix to address the problems associated with inaccurate error estimation. Finally, the maximum correntropy criterion is employed to correct the filtering gain, which improves the filtering performance of the proposed algorithm. Simulation results show that the proposed filter exhibits better accuracy and convergence performance compared to other existing algorithms.

Nonsmooth funnel transformation function-based discrete-time sliding-mode control with deterministic performance margin for servo systems

This paper proposes a nonsmooth funnel transformation function-based discrete-time sliding-mode control strategy for the discrete-time servo systems with unknown frictions and disturbances. For obtaining a more accurate discrete-time system model, a filter-based adaptive identification algorithm (FAIA) is introduced, where the unknown measurement noises are considered. Based on the identified system model and a novel discrete-time nonsmooth funnel transformation function (improving the tracking performances), a discrete-time sliding-mode surface is designed to confine the tracking error to a smaller funnel region compared with the predefined one, which has a deterministic performance margin related to the upper bound of the lumped disturbance. Furthermore, selections of steady-state funnel boundary and sliding-mode surface parameter can be guided theoretically according to the upper bound of the lumped disturbance. Experimental results show that the tracking error is guaranteed in the predefined funnel with a deterministic performance margin by using the proposed control strategy.

Sparse Bayesian technique for load identification and full response reconstruction

Most load identification methods require that the load location is known in advance. A sparse Bayesian framework is proposed in this study to identify the force location and time history simultaneously and then reconstruct the responses with consideration of the uncertainties of the input force and response measurement. The prior distribution of the unknown forces is assumed to be the product of multiple independent Gaussian distributions of each individual potential force. Then, the most probable values of the unknown forces, measurement noise, and variances of the forces are derived and iteratively calculated by a self-adaptive posterior maximization strategy. In such a way, the estimated force vector is nonzero merely at the positions where loads are applied, and it thus possesses the sparsity in space. Consequently, the input forces are located and quantified simultaneously, and the full-field structural responses are sequentially reconstructed with suppressed uncertainties. The proposed approach is applied to numerical and experimental examples. The results demonstrate that the technique is able to identify the force and reconstruct the responses accurately.

Leader–follower consensus for nonlinear multi-agent systems with unknown measurement sensitivities

In this paper, the leader–follower consensus problem is investigated for a class of lower-triangular nonlinear multi-agent systems with unknown measurement sensitivities. By developing a dual-domination gain method, a distributed compensator is proposed for each follower by utilising the output information of the follower and its neighbour agents. Based on the compensator, an output feedback control law is designed to achieve consensus. These two gains are used to deal with the unknown measurement noises and nonlinear terms, respectively. Then the consensus problem is transformed into a stability problem by introducing an appropriate state transformation. Based on the Lyapunov stability theory, it is proved that the states of the leader and followers can achieve consensus asymptotically. In the end, numerical simulations are provided to verify the correctness of the proposed consensus algorithm.

A Robust Distributed Interval Observer for LTI Systems

In this article, the state estimation problem of a continuous-time linear time-invariant system is investigated for the situation with unknown external disturbance and measurement noise. A robust distributed interval observer is designed, which consists of a group of sensors communicating with others through a directed graph where each sensor can only access partial information from the output of the plant. The communication among the sensors together with the heterogeneity and undetectability of the sensors result in some stringent requirements on the robust distributed interval observer construction. To resolve these restrictions, the internally positive representation originated from a single agent system is introduced into the robust distributed interval observer. After presenting detailed design and analysis, numerical simulations are demonstrated to verify the theoretical results.

Memory-Event-Triggered Fault Detection of Networked IT2 T-S Fuzzy Systems.

In this article, a networked fault detection (FD) problem is investigated for interval type-2 T-S fuzzy systems. A novel adaptive memory-event-triggered mechanism (METM) is proposed by introducing historical information of the measured output in a prescribed sliding window. The current measured output in the traditional event-triggered mechanism is replaced by a weighting function-based historical information. As a result, the data releasing rate can be effectively reduced and maltriggering events aroused by unknown abrupt disturbance or measurement noise can be avoided as well. Meanwhile, an adaptive threshold depending on the historical information is utilized to further adjust the data releasing rate. The FD filter is designed and derived in terms of linear matrix inequalities to guarantee the H∞ performance of fault detected systems. Finally, a hardware-in-loop simulation experiment platform is built to manifest the effectiveness of the proposed METM-based FD method.

Leader-Follower Asymptotic Consensus Control of Multiagent Systems: An Observer-Based Disturbance Reconstruction Approach.

In this article, a leader-follower asymptotic consensus control strategy is developed for a class of linear multiagent systems (MASs) with unknown external disturbances and measurement noises. First, the preconditions, the minimum phase condition (MPC) and observer matching condition (OMC), are discussed in detail, and an equivalent result under these two preconditions is given. In this way, the corresponding results from Corless and Tu (1998) are improved. Meanwhile, a reduced-order observer is designed for a constructed augmented system to estimate the system states and noises of each agent. Next, with the help of a traditional interval observer, a novel unknown disturbance reconstruction method is developed, and the reconstruction can converge to the unknown disturbance asymptotically and decouple from the control input. The subsequent asymptotic consensus is accomplished by utilizing an observer-based control scheme, with its design satisfying the so-called separation principle. Finally, two simulation examples are given to verify the effectiveness and show the advantages of the proposed methods.

Temporally-adaptive Robust Data-driven Sparse Voltage Sensitivity Estimation for Large-scale Realistic Distribution Systems with PVs

This letter proposes a new robust data-driven sparse voltage sensitivity estimation approach for large-scale distribution systems with PVs. It has a high statistical efficiency to mitigate the impacts of PV stochasticity and unknown measurement noise under various system operating conditions. A new adaptively-weighted <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> sparsity-promoting regularization is developed, exploiting the temporal characteristic of time-varying sensitivities for better accuracy. The <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> regularization is used to mitigate collinearity impacts. The Huber loss function and a concomitant scale estimate are adopted to mitigate the impacts of unknown and non-Gaussian noise. These techniques are implemented in a fast recursive parallel computing framework. The proposed estimator is tested by quasi-static time series simulations of a large three-phase unbalanced system with PVs and various discrete time-delayed control devices. Results validate the superior robustness and efficiency of the proposed estimator over existing alternatives.

Analysis and Design of Active Disturbance Rejection Control With an Improved Extended State Observer for Systems With Measurement Noise

This article presents a new method that employs the active disturbance rejection control (ADRC) paradigm to handle the control problem for a class of nonlinear systems with unknown disturbances and measurement noise. An improved extended state observer (ESO) is devised to separate disturbance estimation from state reconstruction and a new parameter is used to adjust disturbance-rejection performance independently. This increases the flexibility of system design and makes the gain of the improved ESO (IESO) small compared to that of a conventional ESO in the ADRC. A low-pass filter is added to the IESO. This changes the slope of the magnitude curve of the Bode diagram from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$-20$</tex-math></inline-formula> dB/dec to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$-40$</tex-math></inline-formula> dB/dec at high frequencies for measurement noise, which improves the noise-suppression performance. Comparison with a conventional ESO reveals the superiority of the IESO in disturbance rejection and noise suppression. The presented method is validated by simulation and experimental results.

Extended kernel Risk-Sensitive loss unscented Kalman filter based robust dynamic state estimation

The traditional unscented Kalman filter (UKF) with mean square error (MSE) criterion for dynamic state estimation (DSE) is sensitive for unknown non-Gaussian noise and outliers. Leading to biased state estimates. This paper proposes a novel robust UKF with extended kernel risk-sensitive loss (EKRSL) for DSE considering unknown non-Gaussian process and measurement noises. Instead of MSE criterion, a novel robust EKRSL via the generalized Gaussian density is defined in KRSL framework, and we further develop a new robust UKF using the EnKRSL(called EKRSL-UKF). To obtain the recursive form of EKRSL-UKF, the statistical linear regression model is used and the fixed-point iteration is further utilized to iteratively get the optimal state estimate. An error constrained method is also introduced to restrict the error to address the numerical instability problem caused by large outliers. Furthermore, an enhanced EKRSL-UKF is established by using an exponential function of innovation to improve the estimation accuracy in the presence of noise uncertainties. Numerical results carried out on the IEEE 39-bus test system demonstrate that the proposed method can achieve desired robustness without loss of estimation accuracy under various conditions.

Joint Estimation of Mass and Center of Gravity Position for Distributed Drive Electric Vehicles Using Dual Robust Embedded Cubature Kalman Filter

The accurate estimation of the mass and center of gravity (CG) position is key to vehicle dynamics modeling. The perturbation of key parameters in vehicle dynamics models can result in a reduction of accurate vehicle control and may even cause serious traffic accidents. A dual robust embedded cubature Kalman filter (RECKF) algorithm, which takes into account unknown measurement noise, is proposed for the joint estimation of mass and CG position. First, the mass parameters are identified based on directly obtained longitudinal forces in the distributed drive electric vehicle tires using the whole vehicle longitudinal dynamics model and the RECKF. Then, the CG is estimated with the RECKF using the mass estimation results and the vertical vehicle model. Finally, different virtual tests show that, compared with the cubature Kalman algorithm, the RECKF reduces the root mean square error of mass and CG by at least 7.4%, and 2.9%, respectively.

Design and experimental validation of an adaptive fast-finite-time observer on uncertain electro-hydraulic systems

This paper presents the design of an adaptive fast-finite-time extended state observer for electro-hydraulic actuator systems. First, the system model is divided into three parts, and fast-finite-time state observers are designed independently for each part. This guarantees the fast-finite-time uniform ultimate boundedness of the estimation errors. Then, based on the designed state observers and without neither any knowledge about the upper bounds of the uncertainties nor their derivative, supplementary observers are presented to estimate the unknown terms. Rigorous analyses of the proposed strategy are provided through the Lyapunov approach. The suggested adaptive framework can improve the convergence rate for zones both far from the equilibrium points and around them. The adaptive gains are computed based on the straightforward evaluation of the absolute value of the observation errors, thus their values are valid in real life applications, achieving finite-time estimate of both the full state variables as well as uncertainties. Comparative simulations are presented to analyze the effectiveness of the proposed observers with and without unknown measurement noise. Finally, the effectiveness of the proposed approach in real-life conditions is demonstrated through experimental studies.

Optimal reduced‐order interval observer design for uncertain continuous‐time linear systems

AbstractThis article investigates the reduced‐order interval observer (R‐IO) design technique for continuous‐time linear systems with unknown external disturbances and measurement noises. First, we propose a coupled R‐IO structure with more design degrees of freedom, and it can be directly applied not only to solve the difficulty of the error system cooperativity construction but to relax the constraint on the sensor measurement noises. Second, the R‐IO existence condition is derived as a set of matrix equations (MEs), and a complete solution, explicitly showing the available design parameters, to such an R‐IO is further obtained by solving the MEs. Third, using the solution, an integrated optimization indicator of the R‐IO performance is built as the valid selection mechanism of these parameters. Finally, the efficiency of the obtained results is illustrated through a numerical example and a practical example.

Strong tracking square-root modified sliding-window variational adaptive Kalman filtering with unknown noise covariance matrices

The Kalman filter’s performance deteriorates in the existence of slowly time-varying and unknown measurement and process noise covariances. A simplified strong tracking square-root modified sliding window variational adaptive Kalman filter is proposed for the aforementioned challenges in this paper. A modified slidingwindow variational adaptive Kalman filtering is designed in the proposed algorithm capable of correcting and smoothing the previous states in accordance with the latter states and reducing the number of backward iterations to improve the filtering accuracy and computational efficiency of the algorithm. The multiple fading factors have been constructed to correct the one-step predicted error covariance matrix. Moreover, the square root decomposition approach is developed for decomposing the error covariance matrices to eliminate numerical rounding errors. The simulation results demonstrate that the proposed algorithm exhibits superior tracking capacity of the one-step predicted error covariance matrix and filtering accuracy compared with the existing filters.

Variational Bayesian Estimator for Mobile Robot Localization With Unknown Noise Covariance

This article studies mobile robot localization with unknown noise covariance. The AprilTag is used as landmarks and observed using the onboard camera. The system model is created based on the mobile robot motion and AprilTag measurements. The unknown measurement noise covariance is considered as a random matrix satisfying an inverse Wishart distribution. A variational Bayesian estimator is proposed to estimate the robot pose, AprilTag locations, and measurement noise covariance, where the Rao–Blackwellized estimator is developed for robot pose and AprilTag location estimation, and variational Bayesian approximation is adopted for measurement noise covariance estimation. Simulations and experiments are conducted to validate the effectiveness of the proposed method.