Showing papers on "State vector published in 2022"
TL;DR: In this article , an unknown input functional observer design approach was proposed for discrete-time interval type-2 Takagi-Sugeno fuzzy system models subject to measurable and unmeasurable premise variables.
Abstract: This article proposes a novel unknown input functional observer design approach toward discrete-time interval type-2 Takagi–Sugeno fuzzy system models subject to measurable and unmeasurable premise variables. By constructing a new state vector that contains both the unknown inputs and the system states, functional observers are proposed for the cases with measurable and unmeasurable premise variables to estimate this new state vector for unknown input and/or state estimation. The observer design problem is converted into the solvability issue of a linear matrix equation involving observer gain matrices, and the existence conditions of the observers are explicitly obtained based on matrix rank analysis. Meanwhile, instead of solving the intricate Sylvester equation directly, the solution of the simplified matrix equation is employed to derive the observer gains. Moreover, the effectiveness and the superiority of the presented method are demonstrated via two illustrative examples.
18 citations
TL;DR: In this paper , a new adaptive Kalman filter with unknown state noise statistics is proposed to improve the accuracy of the INS/GNSS integrated navigation system, where the measurement noise covariance R is assumed to be known empirically in advance.
13 citations
TL;DR: In this paper , the minimum observability of Boolean control networks (BCNs) is investigated, where an augmented system is proposed to analyze the dynamical trajectories of state pairs, followed by an effective criterion for observability using graphic tools.
13 citations
01 Jan 2022
TL;DR: In this paper, a new notion of stability is introduced, which is called triangular stability, and a prescribed-time controller with guaranteed triangular stability is developed for normal form nonlinear systems with uncertain input gain.
Abstract: In this letter, a new notion of stability is introduced, which is called triangular stability . A system is called triangularly stable if the norm of its state vector is bounded by a decreasing linear function of time such that its intersection point with the time axis can be arbitrarily commanded by the user. Triangular stability implies prescribed-time stability, which means that the nonlinear system is converged to zero equilibrium at an arbitrary finite time. A prescribed-time controller with guaranteed triangular stability is developed for normal form nonlinear systems with uncertain input gain, which is able to reject the disturbances and unmodeled dynamics. Numerical simulations are carried out to visualize the results for second and fourth-order systems.
13 citations
01 Apr 2022
TL;DR: Two novel algorithms are proposed which preserve the system consistency by leveraging the invariant state representation and ensure efficiency by decoupling features from covariance propagation and achieve improved accuracy than a state-of-art filter-based VINS algorithm using FEJ.
Abstract: The invariant extended Kalman filter (IEKF) is proven to preserve the observability property of visual-inertial navigation systems (VINS) and suitable for consistent estimator design. However, if features are maintained in the state vector, the propagation of IEKF will become more computationally expensive because these features are involved in the covariance propagation. To address this issue, we propose two novel algorithms which preserve the system consistency by leveraging the invariant state representation and ensure efficiency by decoupling features from covariance propagation. The first algorithm combines right invariant error states with first-estimates Jacobian (FEJ) technique, by decoupling the features from the Lie group representation and utilizing FEJ for consistent estimation. The second algorithm is designed specifically for sliding-window filterbased VINS as it associates the features to an active cloned pose, instead of the current IMU state, for Lie group representation. A new pseudo-anchor change algorithm is also proposed to maintain the features in the state vector longer than the window span. Both decoupled rightand left-invariant error based VINS methods are implemented for a complete comparison. Extensive Monte-Carlo simulations on three simulated trajectories and real world evaluations on the TUM-VI datasets are provided to verify our analysis and demonstrate that the proposed algorithms can achieve improved accuracy than a state-of-art filter-based VINS algorithm using FEJ.
10 citations
TL;DR: In this paper, a novel algorithm which fuses variational Bayesians into nonlinear filtering is proposed, where position information is augmented to the measurement vector and the measurement functions are divided into linear and nonlinear.
10 citations
TL;DR: In this article , a novel algorithm which fuses variational Bayesians into nonlinear filtering is proposed, where position information is augmented to the measurement vector and the measurement functions are divided into linear and nonlinear.
10 citations
TL;DR: In this article , the problem of tracking random references and rejecting random perturbations in a quadrotor, both generated by an auxiliary system named exosystem, is solved by extending the deterministic tracking problem to the area of stochastic processes.
Abstract: In this note, the problem of tracking random references and rejecting random perturbations in a quadrotor, both generated by an auxiliary system named exosystem, is solved by extending the deterministic tracking problem to the area of stochastic processes. Besides, it is considered that only a part of the state vector of the quadrotor is available through measurements. As a consequence, the state vector of the plant must be estimated in order to close the control loop. On this basis, a controller to track random references and to reject random perturbations is developed by combining a Kalman filter to estimate the references and perturbations of an exosystem and an observer to estimate the states of a quadrotor. Besides, to obtain a more practical controller, the analysis is carried out in discrete time. Numerical simulations are used in a quadrotor to confirm the validity and effectiveness of the proposed control.
9 citations
TL;DR: In this paper , a new filter with a linear structure was proposed to achieve nonlinear tracking by integrating information in the polar coordinate system, where the state vectors composed of the range, bearing and their differentials were constructed to make the measurement equations linear.
6 citations
TL;DR: In this paper , the problem of designing the interval observer for the system described by a linear discrete-time model under external disturbances and measurement noises was considered, and the relations involved in designing an interval observer, which has minimal dimensions and estimates the prescribed linear function of the original system state vector, were obtained.
Abstract: In this paper, we consider the problem involved when designing the interval observer for the system described by a linear discrete-time model under external disturbances and measurement noises. To solve this problem, we used the reduced order model of the initial system, which is insensitive or has minimal sensitivity to the disturbances. The relations involved in designing the interval observer, which has minimal dimensions and estimates the prescribed linear function of the original system state vector, were obtained. The theoretical results were illustrated by a practical example.
5 citations
TL;DR: In this article, the authors proposed to use the notion of centerpoint, which is an extension of the median in higher dimensions, instead of the Tverberg partition of points, to compute a safe point.
01 Jan 2022
TL;DR: In this article, an unknown input zonotopic Kalman filter-based interval observer for discrete-time linear time-invariant systems is proposed, where a change of coordinates decoupling the state and unknown inputs is often used.
Abstract: This letter proposes an unknown input zonotopic Kalman filter-based interval observer for discrete-time linear time-invariant systems. In such contexts, a change of coordinates decoupling the state and the unknown inputs is often used. Here, the dynamics are rewritten into a discrete-time linear time-invariant descriptor system by augmenting the state vector with the unknown inputs. A zonotopic outer approximation of the feasible state set is then obtained with a prediction-correction strategy using the information from the system dynamics, known inputs and outputs. Bounds for both the state and unknown inputs are obtained from this zonotopic set. The efficiency of the proposed interval observer is assessed with numerical simulations.
TL;DR: In this article , the estimation and correction of non-line-of-sight (NLOS) induced errors within the vector tracking (VT) framework was investigated. But the estimation of NLOS-induced bias has not been thoroughly investigated in the VT framework.
Abstract: Position and location constitute critical context for Internet of Things (IoT) devices. Global navigation satellite systems (GNSSs) are the primary apparatus providing precise position and location information for IoT devices in outdoor environments. However, in dense urban areas, non-line-of-sight (NLOS) signals will induce large errors in GNSS pseudorange measurements due to the additional signal transmission paths. The vector tracking (VT) technique utilizing a Kalman filter (KF) to estimate navigation solutions has been investigated in NLOS detection, and its advantages have been demonstrated. However, the estimation of NLOS-induced bias has not been thoroughly investigated in the VT framework. In this article, we focus on the estimation and correction of NLOS-induced errors within the VT framework. First, graph optimization (GO) instead of a KF is incorporated with VT to optimize the estimation of navigation solutions. The NLOS-induced bias is then added to the VT state vector as the variable for real-time estimation. Compared with the KF-VT method, in GO-VT, the state transformation and the measurement model are regarded as constraints to optimize the state vector estimation. Hence, the GO-VT framework is more flexible than the KF approach in dealing with state vector changes. An iterative process is conducted to solve for the optimization results; a multiple-correlator scheme is employed in GO-VT to provide the initial values of the NLOS-induced bias. Three collected GPS L1 data sets (static and dynamic) are used to evaluate the proposed method. The statistical results support the conclusion that GO-VT with state augmentation achieves superior position estimation in urban areas.
TL;DR: In this article , an image reconstruction algorithm of EMT based on fractional Kalman filter (FKF) is proposed, where the image reconstruction process is regarded as the state estimation process of FKF.
TL;DR: In this article , a constrained state estimation method is proposed by incorporating the pseudomeasurements into the nonlinear filtering process, where the cubature Kalman filter is employed to handle the high-dimensional filtering problem and the strong nonlinearity involved in pseudomeasures.
Abstract: Proportional navigation (PN) guidance laws have been commonly applied to homing missile systems guiding the missile to its target. When the target is stationary and its location is known a priori, the state of the missile is subjected to a destination constraint, which contains extra information on missile state that can help increase tracking performance. This article concerns with the constraint modeling and the state estimation with a destination constraint imposed by PN guidance law in 3-D space. Constraint models corresponding to three representative PN guidance laws: pure PN, true PN, and generalized PN, are presented using the state augmentation method, which stacks the states at the previous and current time steps in one state vector to express the constraint relationships. For cases where the destination information is noisy and the parameters of the guidance law, i.e., the navigation constant and the bias angle, are not known a priori, the unknown parameters are estimated along with the missile state in the state vector in an augmentation way. Based on the formulations of constraint models, the construction of pseudomeasurements is carried out. A constrained state estimation method is proposed by incorporating the pseudomeasurements into the nonlinear filtering process. In this method, a sequential process framework is employed and the cubature Kalman filter is used to handle the high-dimensional filtering problem and the strong nonlinearity involved in pseudomeasurements. Numerical experiments in three scenarios are performed to demonstrate the validity of the proposed models along with the estimation method.
TL;DR: In this article , a multivariate state estimation technique with the dynamic process memory matrix is proposed to warn the failure risk of the engine bleed air system (BAS), which is one of the important systems for civil aircraft, and its operating state directly affects the operational safety of the aircraft.
Abstract: The engine bleed air system (BAS) is one of the important systems for civil aircraft, and its operating state directly affects the operational safety of the aircraft. The effective risk warning of the BAS is critical to improving aircraft safety and operators’ profits; thus, a multivariate state estimation technique with the dynamic process memory matrix is proposed to warn the failure risk of the bleed air system. First, to obtain the optimal estimation value of the observation vector, the memory matrix is formed by searching for the first vectors that are similar to each input observation vector from the healthy data pool that can cover the common working space. Then, the similarity function is defined to quantitatively measure the deviation between the observed vector and the estimated vector, and the amount of risk information contained in each variable is quantified by the analytic hierarchy process. Finally, the dynamic threshold different from the traditional engineering experience threshold is designed, based on the idea of interval estimation. The developed approach is validated on an Airbus A320-series aircraft with quick access recorder data for one year. The results show that the proposed strategy can provide an effective risk warning for the abnormal state of the BAS before a failure occurs.
17 Mar 2022
TL;DR: In this article , an extended Kalman filter for estimating the coordinates and yaw angle of the consumer is presented. But the accuracy of this algorithm is limited by the limiting filtering errors of the state vector.
Abstract: The development of positioning algorithms for indoor navigation systems does not lose its relevance due to the constant improvement and widespread distribution of such systems. This article discusses the positioning algorithm for a complex system based on ultra-wideband signals and inertial sensors of a smartphone. The algorithm is an extended Kalman filter for estimating the coordinates and yaw angle of the consumer. In this study, analytical estimates of the limiting filtering errors of the state vector are presented in comparison with estimates obtained from the dispersion matrices of filtering errors. A comparison of these estimates allows us to conclude that the algorithm is suitable for real navigation conditions.
01 Jan 2022
TL;DR: In this paper , an unknown input zonotopic Kalman filter-based interval observer for discrete-time linear time-invariant systems is proposed, where a change of coordinates decouples the state and the unknown inputs.
Abstract: This letter proposes an unknown input zonotopic Kalman filter-based interval observer for discrete-time linear time-invariant systems. In such contexts, a change of coordinates decoupling the state and the unknown inputs is often used. Here, the dynamics are rewritten into a discrete-time linear time-invariant descriptor system by augmenting the state vector with the unknown inputs. A zonotopic outer approximation of the feasible state set is then obtained with a prediction-correction strategy using the information from the system dynamics, known inputs and outputs. Bounds for both the state and unknown inputs are obtained from this zonotopic set. The efficiency of the proposed interval observer is assessed with numerical simulations.
TL;DR: In this article , the authors study the evolution of a two-state system that is monitored continuously but with interactions with the detector tuned so as to avoid the Zeno affect. And they obtain analytic results for the distribution of number of detector events and the time-evolution of the probability distribution.
Abstract: We study the evolution of a two-state system that is monitored continuously but with interactions with the detector tuned so as to avoid the Zeno affect. The system is allowed to interact with a sequence of prepared probes. The post-interaction probe states are measured and this leads to a stochastic evolution of the system’s state vector, which can be described by a single angle variable. The system’s effective evolution consists of a deterministic drift and a stochastic resetting to a fixed state at a rate that depends on the instantaneous state vector. The detector readout is a counting process. We obtain analytic results for the distribution of number of detector events and the time-evolution of the probability distribution. Earlier work on this model found transitions in the form of the steady state on increasing the measurement rate. Here we study transitions seen in the dynamics. As a spin-off we obtain, for a general stochastic resetting process with diffusion, drift and position dependent jump rates, an exact and general solution for the evolution of the probability distribution.
TL;DR: In this article , the dual, neural, extended Kalman filter (DNEKF) and the state model compensation neural (SNN) are synthesized to compensate for modeling errors in the EKF-based multirate sensor fusion.
Abstract: Sensor fusion plays a critical role in improving estimation accuracy of process quality variables. In this article, the dual, neural, extended Kalman filter (DNEKF) and the state model compensation neural, extended Kalman filter (SNEKF) are synthesized to compensate for modeling errors in the extended Kalman filter (EKF)-based multirate sensor fusion. Specifically, fusion is performed in the presence of irregularly sampled, slow-rate measurements with time-varying time delays. The proposed algorithm estimates the state and neural network parameters simultaneously through state vector augmentation. The estimated parameters of the state model compensation neural network (SNN) are shared between the DNEKF and SNEKF. It is demonstrated through two numerical examples that the proposed algorithm effectively reduces the estimation error under different conditions. In addition, it successfully improves the critical industrial quality variable estimation accuracy from the fast-rate soft sensor for over 20%, in terms of the mean squared error, demonstrating its advantages.
TL;DR: In this paper , a Gaussian student t-mixed distribution (GSTM) with Bernoulli random variable is utilized to describe the differenced measurement noise, and the state vector, intermediate random variables (IRV), mixed probability and BRV are simultaneously inferred by introducing variational Bayesian (VB) technique.
Abstract: The filtering issue of a nonlinear system with colored non-stationary heavy-tailed measurement noise (CNSHMN) is addressed in this study via designing a new Gaussian approximate filter. By utilizing the state expansion method and the measurement difference method, the nonlinear filtering problem with the one-step delayed state and the white non-stationary heavy-tailed measurement noise (NSHMN) after the difference is turned into the traditional nonlinear filtering problem with NSHMN. A Gaussian student t-mixed distribution (GSTM) with Bernoulli random variable is utilized to describe the differenced measurement noise. The state vector, intermediate random variables (IRV), mixed probability and Bernoulli random variable (BRV) are simultaneously inferred by introducing variational Bayesian (VB) technique. Target tracking simulation examples reveal that the proposed filter is superior to the existing methods in the nonlinear filtering issue of CNSHMN.
TL;DR: In this paper , an observer-based feedback controller for quasi-linear systems when the entire state vector is unavailable for measurement is proposed. But, the design of a state feedback and the state observer can be carried out independently, and general complete parameterisation of the state feedback controller is also established.
Abstract: This paper designs an observer-based feedback controller for quasi-linear systems when the entire state vector is unavailable for measurement. First, based on the solution of a type of generalised Sylvester equations, general complete parameterisation of the full-order observer is proposed. Second, the traditional separation principle is applied to the quasi-linear systems. In other words, the design of a state feedback and the design of a state observer can be carried out independently. Further, general complete parameterisation of the state feedback controller is also established. Finally, numerical examples and simulations are adopted to verify the effectiveness of the proposed method.
TL;DR: Hysteresis Identification via Reversal Points (HIRP) as mentioned in this paper uses the points at which the displacement across the joint reverses as a surrogate, reducing the number of state variables and making the state variables more continuous.
TL;DR: In this paper , the joint estimation and virtual sensing of structures are reformulated on a Bayesian probabilistic foundation, focusing on data-driven uncertainty quantification and propagation, and the joint posterior distribution of the latent states and the noise parameters is characterized, and a BEM strategy is established to search for the most probable values iteratively.
TL;DR: In this article , a multilayer loosely-coupled, local-global, and step-optimized MF5DCKF (Multisensor Federated fifth-degree Cubature Kalman filter) state estimation algorithm for the small UAV is presented.
Abstract: Aimed at improving the nonlinear integrated navigation solution performance of multiple low-cost sensors fusion, this paper presents a multilayer loosely-coupled, local-global, and step-optimized MF5DCKF (Multisensor Federated fifth-degree Cubature Kalman filter) state estimation algorithm for the small unmanned aerial vehicle (UAV). This method establishes a multilayer nonlinear integrated navigation model composed of the nonlinear attitude and heading reference system (AHRS) error model, strapdown inertial navigation system/global positioning system (SINS/GPS) error model, and strapdown inertial navigation system/barometer (SINS/BARO) error model to enhance the robustness and richness of the navigation module. Further, based on the above navigation models, a loosely-coupled error state fusion frame is designed to obtain the local convergent state vector. Simultaneously, a three-layer fifth-degree Cubature Kalman filter is proposed to improve the local state estimation accuracy. Subsequently, to optimize the estimated local state, this paper presents a novel distributed MF5DCKF scheme fusing the local state vector to calculate the global optimal state parameters in a step-optimized process. The experimental flight test results show that the proposed algorithm achieves a higher state solution accuracy and a better convergent performance compared with some conventional multisensor fusion algorithms. The new algorithm framework can provide applicability and reliability for the small UAV during the flight.
26 Jun 2022
TL;DR: In this article , the convergence of Bayes-optimal orthogonal/vector approximate message-passing (AMP) to a fixed point in the large system limit is proved.
Abstract: This paper proves the convergence of Bayes-optimal orthogonal/vector approximate message-passing (AMP) to a fixed point in the large system limit. The proof is based on Bayes-optimal long-memory (LM) message-passing (MP) that is guaranteed to converge systematically. The dynamics of Bayes-optimal LM-MP is analyzed via an existing state evolution framework. The obtained state evolution recursions are proved to converge. The convergence of Bayes-optimal orthogonal/vector AMP is proved by confirming an exact reduction of the state evolution recursions to those for Bayes-optimal orthogonal/vector AMP.
TL;DR: In this paper , an enhanced affine projection algorithm (APA) is proposed to improve the filter performance in aspects of convergence rate and steady-state estimation error, since the adjustment of the input-vector number can be an effective way to increase the convergence ratio and to decrease the estimation error at the same time.
Abstract: An enhanced affine projection algorithm (APA) is proposed to improve the filter performance in aspects of convergence rate and steady-state estimation error, since the adjustment of the input-vector number can be an effective way to increase the convergence rate and to decrease the steady-state estimation error at the same time. In this proposed algorithm, the input-vector number of APA is adjusted reasonably at every iteration by comparing the averages of the accumulated squared errors. Although the conventional APA has the constraint that the input-vector number should be integer, the proposed APA relaxes that integer-constraint through a pseudo-fractional method. Since the input-vector number can be updated at every iteration more precisely based on the pseudo-fractional method, the filter performance of the proposed APA can be improved. According to our simulation results, it is demonstrated that the proposed APA has a smaller steady-state estimation error compared to the existing APA-type filters in various scenarios.
TL;DR: Hardware implementation of the study of nature of this functional dependence of the state violation and its restoration in the automated mode of operation of the integrated tool will allow the creation of a computer-integrated hardware solution for the identification of objects that interact by approaching and touching their surfaces.
Abstract: The article defines the relevance of modeling the parameters of spatial location of an abstract object when performing various functions. Thus, modeling makes it possible to determine object movement trajectories both during industrial application in technological processes and when used to create bionic objects, for example, the action of artificial limbs, correction of the movement trajectory of an object with spatial orientation defects.
The main goal of research was to substantiate the analytical models of object movement, taking into account spatial coordinate systems, according to which coordinate transformations are carried out during the functioning of an abstract object of various applications.
The creation of a sensory complex to compensate for violations of limb functions based on the justification of analytical models of vector field of main systems of the object, characteristic of its vital activity, can solve the possibility of real actions of an abstract biotechnical object in interaction with other objects of the external environment. It is necessary to compare the idealized parameters of vector fields with the real current characteristics of the object under study and to determine the difference as a differential function that corresponds to diagnostic parameters of state of object's limbs trajectory. Or when applied in industrial conditions, errors in the reproduction of the movement trajectory are taken into account.
As a result, the study of nature of this functional dependence of the state violation and its restoration in the automated mode of operation of the integrated tool will allow the creation of a computer-integrated hardware solution for the identification of objects that interact by approaching and touching their surfaces.
Thus, determining the positioning of TONTOR step in the space of movement of objects and during their interaction provides the possibility of the functioning of each abstract object when performing various types of work.
At the same time, it is necessary to significantly develop the base of physical and mathematical models that determine the vector fields of objects in dynamics over a certain time, taking into account the TONTOR step of the phantom and real spaces of the existence and operation of the object. Thus, hardware implementation of this hypothesis increases the accuracy of identification of objects interactions with a human limb, regardless of its condition, and the accuracy of determining their relative location in space.
TL;DR: In this paper , the authors describe the architecture of a vector-tracking algorithm, using a real-time Global Navigation Satellite System (GNSS) array-antenna receiver, which is based on an Error-Position-State formulation as proposed in (Lashley, 2009).
Abstract: This paper describes the architecture of a vector-tracking algorithm, using a real-time Global Navigation Satellite System (GNSS) array-antenna receiver, which is based on an Error-Position-State formulation as proposed in (Lashley, 2009). The tracking algorithm is tested and validated in real-time scenarios, which includes a simulative GNSS environment in the laboratory, as well as outdoor testing, whereby the functionality of the system can be determined. In order to improve the robustness of the receiver an exploitation of the Direction of Arrival (DoA) measurements is implemented, which allows the exclusion of unauthentic or unwanted signals in the Kalman Filter updating process. An error vector based on comparison and statistically testing of the measured DoAs against the expected DoAs (Meurer et al., 2016), which can be obtained by geometric calculation of the receivers position and attitude, is generated and contains information about the credibility of each tracking channel. Manipulating the measurement covariance matrix of the central navigation Kalman filter with this error vector will decrease the contribution of incredible channels not only to the Position/Velocity/Timing (PVT) solution, but also to the tracking loops, because of the vector tracking feedback.