Minimum-Variance Unbiased Unknown Input and State Estimation for Multi-Agent Systems by Distributed Cooperative Filters

Simultaneous seismic input and state estimation with optimal sensor placement for building structures using incomplete acceleration measurements

For nonlinear discrete systems with dual unknown inputs, there are many limitations regarding previous nonlinear filters. This paper proposes two new, improved square-root cubature Kalman filtering (ISRCKF) algorithms to estimate system states and dual unknown inputs. Improved square-root cubature Kalman filtering 1 (ISRCKF1) introduces an innovation that first obtains the unknown input estimates from the measurement equation, then updates the innovation to derive the unknown input estimates from the state equation, then uses the already obtained estimates of the dual unknown inputs to correct the one-step estimate of the state, and finally the minimum variance unbiased estimate of the state is obtained. Improved square-root cubature Kalman filtering 2 (ISRCKF2) builds a unified innovation feedback model, then applies the minimum variance unbiased estimation (MVUE) criterion to obtain the estimates of system states and dual unknown inputs, refining a more concise recursive filter but requiring stronger assumptions. Finally, simulation results demonstrate that the above two algorithms can achieve the optimal estimates of system states and dual unknown inputs simultaneously, and ISRCKF2 further enhances the accuracy of both state and dual unknown inputs estimation, which verifies the validity of the proposed algorithms.

Input and state estimation for linear systems with a rank-deficient direct feedthrough matrix

This paper presents a system augmentation-based unbiased minimum-variance input and state estimation for systems with unknown inputs which can be reconstructed with a multi-step delay. An estimable input generating model (EIGM)-based system augmented approach is proposed to facilitate the filter design. It is shown that, via this new filtering approach the optimal unknown input and state estimation can be simultaneously achieved through the previously proposed robust two-stage Kalman filter (RTSKF). An illustrative example is given to show the effectiveness of the proposed results.

This paper addresses the problem of the joint estimation of system state and generalized sensor bias (GSB) under a common unknown input (UI) in the case of bias evolution in a heterogeneous sensor network. First, the equivalent UI-free GSB dynamic model is derived and the local optimal estimates of system state and sensor bias are obtained in each sensor node; Second, based on the state and bias estimates obtained by each node from its neighbors, the UI is estimated via the least-squares method, and then the state estimates are fused via consensus processing; Finally, the multi-sensor bias estimates are further refined based on the consensus estimate of the UI. A numerical example of distributed multi-sensor target tracking is presented to illustrate the proposed filter.

In this paper, the event-based state and unknown input estimation (SUIE) problem is investigated for a class of stochastic systems subject to parameter uncertainties and stochastic nonlinearities. For the purpose of reducing the energy consumption in data transmission, an event-triggering protocol is employed to regulate whether the current measurement is transmitted by the sensor. Utilising the event-triggered measurement, a recursive estimator is constructed to concurrently estimate the state and the unknown input. The upper bounds of estimation error covariances are given explicitly for both the state and the unknown input estimates. By means of the completing-the-square technique and Lagrange multiplier method, the estimator gain matrices are designed which minimise the obtained upper bounds. Finally, a numerical example is given to show the effectiveness of the proposed SUIE method.

For the direct feedthrough system where unknown input affects both process equation and measurement equation, an unscented recursive three-step filter based unbiased minimum-variance (URTSF-UMV) estimation algorithm is proposed. The algorithm is based on the unbiased minimum-variance (UMV) method and uses statistical linearisation technology to approximate the nonlinear system and the nonlinear measurement function to linear regression form. The estimation of unknown input is obtained from innovation through weighted least-squares (WLS) estimation. The approximate linear regression form allows us to process the nonlinear system with unknown input direct feedthrough by using the UMV state estimation framework, and derive the filter by minimising the trace of the state error covariance of the measurement update under the unbiased condition. The URTSF-UMV requires that the unknown input distribution matrix is full column rank. We use the full rank decomposition method to deal with the nonlinear system containing the unknown input rank-deficient distribution matrix. The effectiveness of the URTSF-UMV algorithm is demonstrated through an illustrative simulation example.

Estimating unknown inputs in indoor heating, ventilation, and air conditioning (HVAC) systems, particularly under the influence of diverse environmental constraints and time-varying relative humidity, presents a significant challenge. A viable solution is to employ a weighted least squares approach for estimating unknown inputs, which utilizes an unbiased minimum variance (UMV) estimator in conjunction with an unscented Kalman filter (UKF)-based nonlinear filtering technique. This allows for the simultaneous estimation of the system’s state and the unknown inputs. To accurately represent the real-life nonlinear thermal profile influenced by these uncertain inputs, it is essential to adopt an RC network-based mathematical modeling approach that captures the system’s dynamic behavior over time. The integration of the UMV-based optimal estimator with the UKF culminates in the proposed unscented Kalman filter with unbiased minimum variance for unknown inputs (UKF-UMV-UI) estimation algorithm. Extensive experimentation with the proposed UKF-UMV-UI algorithm has been conducted in a laboratory-scale realistic environment, dealing with uncertain and challenging unknown inputs. The results of the investigation indicate that the proposed method outperform the unscented Kalman filter with unknown input (UKF-UI) by 41.64% and 35.85% in Cumulative Mean Squared Error (CuMSE) for two distinct measurement conditions, respectively.

In this paper, we consider the problem of designing a special type of observer to estimate the state and unknown input disturbance for linear time-invariant positive systems. Although positive observers have been designed for positive systems, they are unable to estimate the states when unknown inputs or disturbances are present in the systems. To realize simultaneous estimation of states and unknown inputs, we first design positive unknown input observers (PUIO) for positive linear systems, which is the main contribution of this paper. Then, we provide a procedure to estimate the unknown disturbance. The PUIO design can be performed with the aid of a positive stabilization scheme via LMI. A critical step in the design process is the requirement of imposing a condition on positivity of the generalized inverse of a certain design matrix. We show that this can easily be accomplished with the aid of a unique result, which makes the design of PUIO possible. An alternative LMI with less restrictive assumption is also included to design PUIO. Finally, theoretical results are supported by numerical examples.

In the context of structural and industrial asset monitoring and twinning, the estimation of unknown inputs – typically reflecting the loads acting onto a system – stands as a critical factor in ensuring both the safety and performance of engineered systems. This research introduces a novel approach for inferring such unknown inputs from observed outputs, focusing particularly on dynamical systems, whether characterized by known or learned dynamics. Our proposed approach is situated within the framework of Imitation Learning from Observation (ILfO), which is here recast in the context of dynamical systems’ estimation. Our primary objective is to infer estimates of input signals on the basis of real-world measured outputs. The problem is formulated as a Partially Observable Markov Decision Process (POMDP), and we address it by utilizing established planning algorithms specifically tailored for ILfO applications. To address the POMDP, we harness the effectiveness and robustness of the cross-entropy method. We first verify the efficacy of the proposed approach on simulated case studies involving dynamical systems possessing well-defined dynamics. The proposed method is further validated on a practical scenario involving experimental data from a scaled wind turbine blade, leveraging dynamics learned through the Neural Extended Kalman Filter (Neural EKF) technique; an approach which leverages deep learning for inferring the dynamics of a system when this is imprecisely known. These examples demonstrate the flexibility of the proposed approach for use with systems featuring different degrees of prescribed dynamics. • A new perspective of input estimation, embedded within Imitation Learning from Observation methodology. • Recast the input estimation problem as a Partially Observable Markov Decision Process. • Integration of learning-based dynamics models.

This paper proposes an unknown input root mean square cubature Kalman filter algorithm, which is applied to the fault diagnosis of nonlinear systems with unknown input. Firstly, a standard linear regression equation with unknown input is constructed, and orthogonal trigonometric decomposition is combined to solve the equation to improve the estimation accuracy of unknown input. In addition, in order to improve the numerical stability of algorithm, the root mean square algorithm is introduced into the error covariance matrix calculated from the unknown input estimation and state estimation results. Secondly, the root mean square value of the sliding window of residual obtained from the difference between the measured value and the estimated value is computed to judge whether the actuator has a fault. The generalized regression neural network is used for fault identification. Finally, a single link manipulator system is taken for simulation verification.

The robot localization problem is typically solved using state estimation techniques, where process and sensing inaccuracies are invariably present. Moreover, disturbances in the sensing and actuating mechanisms add to the uncertainties. Any system may degrade over time, and its parameter values may be ambivalently known. Cumulatively, all these sources of errors and uncertainties are considered as unknown inputs. This work aims to address the unknown inputs using a robust state (pose in the robot localization problem) estimator. The proposed robust state estimator deals with the unknown inputs such that the solution of the estimator is constrained in a way that warrants unbiased state estimates in the presence of the unknown inputs. This article explores the formulation of these constraints and the development of a constrained state estimator for a system, where the unknown inputs appear in both the state transition map (i.e., system model) and the state-output map (i.e., measurement model). The theoretical development of such a strategy stems from the localization problem of a wheeled mobile robot. The residuals of the constrained state estimator developed contain information about the unknown inputs. We conceive a recursive least squares strategy to estimate the unknown inputs simultaneously with the states using this information. Using simulations and experimental studies, we demonstrate the adequacy of our strategy for a differential drive robot.

This brief investigates the issue of state estimation and unbounded unknown input reconstruction for a class of one-sided Lipschitz nonlinear interconnected systems with uncertain output and mismatched unknown input distribution matrix. Based on descriptor augmentation strategy and coordinate transformation, the effect of measurement noise and matched unknown input parts are firstly decoupled. Then, a novel multi-intermediate estimator-assisted unknown input observer is constructed to estimate state and mismatched unknown input. In addition, sufficient conditions in linear matrix inequality (LMI) form is derived to guarantee the stability of the observer and to facilitate observer parameter tuning. Finally, a simulation example is provided to illustrate the effectiveness and merits of the proposed methods.

This article presents a new approach to estimation of unknown inputs and faults in a class of nonlinear systems. The approach is based on the design of a cascade connection of two sliding mode observers. The first is used for estimation of state and unknown inputs and the second is used for fault detection. An important feature of the proposed approach is that the state trajectories do not leave the sliding manifold even in presence of unknown disturbances and faults. This allows for faults and disturbances to be reconstructed based on information retrieved from the equivalent output injection signal. The proposed approach is used to reconstruct unknown disturbances and faults in nonlinear model of Vertical Take-Off and Landing (VTOL) aircraft system.

In this paper, the problem of attack detection and defense for linear time-invariant systems with disturbances is studied. Unlike existing attack detection mechanisms, a new attack detection mechanism under disturbances is designed by output errors, whose trigger can be determined as attacks rather than disturbances. To solve the unobservable problem of the system under attacks, an augmented system and its auxiliary outputs are constructed until the observer matching condition is satisfied. Using estimates of augmented system states and unknown inputs, a state feedback controller is designed to defend against network attacks and ensure system stability. Theoretical analysis and simulation results verify the feasibility of the scheme.