Event-based State Estimation Research Articles

Nonlinear event-based state estimation using particle filter under packet loss

In this research paper, we investigate the problem of remote state estimation for nonlinear discrete systems. Specifically, we focus on scenarios where event-triggered sensor schedules are utilized and where packet drops occur between the sensor and the estimator. In the sensor scheduler, the SOD mechanism is proposed to decrease the amount of data transmitted from the sensor to a remote estimator and the phenomena of packet drops modeled with random variables obeying the Bernoulli distribution. As a consequence of packet drops, the assumption of Gaussianity no longer holds at the estimator side. By fully considering the non-linearity and non-Gaussianity of the dynamic system, this paper develops an event-trigger particle filter algorithm to relieve the communication burden and achieve an appropriate estimation accuracy. First, we derive an explicit expression for the likelihood function when an event trigger occurs and the possible occurrence of packet dropout is taken into consideration. Then, using a special form of sequential Monte–Carlo algorithm, the posterior distribution is approximated and the corresponding minimum mean-squared error is derived. By contrasting the error covariance matrix with the posterior Cramér–Rao lower bound, the estimator’s performance is assessed. An illustrative numerical example shows the effectiveness of the proposed design.

Event-Based State Estimation Against Deception Attacks: A Detection-Based Approach

Event-Based State Estimation Against Deception Attacks: A Detection-Based Approach

Event-Triggered Tracking Control of Nonlinear Systems Under Sparse Attacks and its Application to Rigid Aircraft

This study is aimed at addressing the event-based state estimation and tracking control problems for a class of nonlinear systems, the output of which is measured by multiple sensors, but the adversary can manipulate nearly half of the measurements simultaneously. First, a sampled-data-based event-triggered strategy is developed to reduce unnecessary data transmissions under sparse sensor attacks, and the transmitted data are filtered by a data selector to obtain reliable data. Subsequently, an output-prediction-based continuous-discrete observer is improved so that it can estimate continuous-time system states from the event-triggered output, rather than being limited to time-triggered sampled output. Further, to design a tracking controller with the segmentally differentiable estimated states, a backstepping method incorporating tracking differentiators is proposed. Finally, the effectiveness of the proposed method is demonstrated by applying it in the simulation of a rigid aircraft.

New Event Based H ∞ State Estimation for Discrete-Time Recurrent Delayed Semi-Markov Jump Neural Networks Via a Novel Summation Inequality

Abstract This paper investigates the event-based state estimation for discrete-time recurrent delayed semi-Markovian neural networks. An event-triggering protocol is introduced to find measurement output with a specific triggering condition so as to lower the burden of the data communication. A novel summation inequality is established for the existence of asymptotic stability of the estimation error system. The problem addressed here is to construct an H ∞ state estimation that guarantees the asymptotic stability with the novel summation inequality, characterized by event-triggered transmission. By the Lyapunov functional technique, the explicit expressions for the gain are established. Finally, two examples are exploited numerically to illustrate the usefulness of the new methodology.

Event-based state estimation under constrained bit rate: An encoding–decoding approach

This paper is concerned with the state estimation problem for a class of linear continuous-time systems under bit rate constraints. The data transmission between the sensors and the estimator is implemented through a digital communication network with limited bandwidth. By resorting to the singular value decomposition technique, an event-based encoding strategy is developed to encode the measurement signals into 1-bit codewords so as to reduce network resource consumption. The Zeno phenomenon is first proven to be excluded, and then a sufficient condition is established under which the decoding error is ultimately bounded. Subsequently, a necessary condition is proposed to derive a lower bound of the bit rate below which the decoding error diverges. Moreover, the explicit expression of the desired state estimator is parameterized and the boundedness of the estimation errors is also analyzed. Finally, two simulation examples are presented to validate the effectiveness of the proposed theoretical results.

Event-Based State Estimation of Complex-Valued Neural Networks With Mixed Delays

Event-Based State Estimation of Complex-Valued Neural Networks With Mixed Delays

Towards Event-Based State Estimation for Neuromorphic Event Cameras

In this work, a dynamic information extraction problem for neuromorphic event cameras is investigated from a state estimation perspective. The ego-motion pose estimation task of an event camera is formulated as a state estimation problem for a finite-state hidden Markov model subject to a special event-triggering mechanism. We model the threshold mismatch and the bandwidth limit of the event camera output generalization process as a stochastic event-triggering condition equipped with a state-dependent packet dropout process. For this problem, the recursive expression of the system state conditioned on the event-triggered measurement information is constructed under a suitably designed reference probability measure, based on which the event-based MMSE estimate for the considered estimation problem is further obtained. The effectiveness of proposed results is illustrated by numerical analysis and comparative evaluation of an ego-motion pose estimation example.

Event-based state and fault estimation for stochastic nonlinear system with Markov packet dropout

This paper investigates the event-based state and fault estimation problem for stochastic nonlinear system with Markov packet dropout. By introducing the fictitious noise, the fault is augmented to the system state. Then combining the unscented Kalman filter (UKF) with event-triggered and Markov packet dropout, the modified UKF is proposed to estimate the state and fault. Meanwhile, the stochastic stability of the proposed filter is also discussed. Finally, two simulation results illustrate the performance of the proposed method.

An Efficient Event-Based State Estimator for Linear Discrete-Time System With Multiplicative Measurement Noise

This letter addresses an event-based state estimation for a linear discrete-time system with a remote estimator, when measurements are affected by multiplicative noise. An innovation-based scheduling scheme is used to communicate measurements from the sensor to the remote estimator. A maximum a posteriori estimator is employed to deal with multiplicative noise, enabling the recursive equations for the updated state and its covariance. The sensor to estimator communication rate is derived in terms of a predefined threshold that is used to trigger the sensor measurement. The results proposed are validated using a numerical example and Monte Carlo simulations.

Distributed Event Triggering Algorithm for Multi-Agent System over a Packet Dropping Network.

The availability of wireless networked control systems (WNCSs) has increased the interest in controlling multi-agent systems. Multiple feedback loops are closed over a shared communication network in such systems. An event triggering algorithm can significantly reduce network usage compared to the time triggering algorithm in WNCSs, however, the control performance is insecure in an industrial environment with a high probability of the packet dropping. This paper presents the design of a distributed event triggering algorithm in the state feedback controller for multi-agent systems, whose dynamics are subjected to the external interaction of other agents and under a random single packet drop scenario. Distributed event-based state estimation methods were applied in this work for designing a new event triggering algorithm for multi-agent systems while retaining satisfactory control performance, even in a high probability of packet drop condition. Simulation results for a multi-agent application show the main benefits and suitability of the proposed event triggering algorithm for multi-agent feedback control in WNCSs with packet drop imperfection.

Intermittent dynamic event-triggered state estimation for delayed complex networks based on partial nodes

In this paper, the intermittent dynamic event-based state estimation problem is investigated for a class of delayed complex dynamic networks (CDNs). The estimate is implemented based on the measurements from a fraction of network nodes. In the framework of aperiodic intermittent measurement outputs, a dynamic event-triggered mechanism is introduced to save communication resources and reduce actuation burden. The aim of this work is to design a dynamic event-based state estimator by adopting intermittent dynamic event-triggered (IDET) strategy, such that the dynamics of estimation error system is exponentially stable. By resorting to Halanay inequality and switched system method, the sufficient conditions are derived for ensuring the existence of the desired state estimator, and are characterized by the ratio of the average working time to the average rest time. In the meanwhile, the estimator gains for partial nodes are explicitly obtained by solving some matrix inequalities. Furthermore, it is also proven that Zeno behavior can be excluded under the proposed IDET strategy. Finally, a numerical simulation is provided to verify the effectiveness of the derived results.

Worst-Case Stealthy Attacks on Stochastic Event-Based State Estimation

This article considers the worst-case stealthy attack strategies on stochastic event-based state estimation. Smart sensors equipped with local event-triggered Kalman filters are used to transmit innovations. Contrary to classic Kalman filters, the transmitted innovation screened by the stochastic decision rule does not follow a Gaussian distribution. A type of distribution called complete Gaussian crater is defined and analyzed, which is essential for designing stealthy attacks. The evolution of the estimation error covariance under attacks is obtained. Stealthy attacks that yield the greatest estimation errors under constraints on transmission rates and probability distributions are obtained and analyzed. The system performance degradation caused by different attacks is evaluated via simulations.

Learning hidden Markov models for linear Gaussian systems with applications to event-based state estimation

This work attempts to approximate a linear Gaussian system with a finite-state hidden Markov model (HMM), which is found useful in dealing with challenges in designing networked control systems An indirect approach is developed, where a state-space model (SSM) is firstly identified for a Gaussian system and the SSM is then used as an emulator for learning an HMM. In the proposed method, the training data for the HMM are obtained from the data generated by the SSM through building a quantization mapping. Parameter learning algorithms are designed to learn the parameters of the HMM, through exploiting the periodical structural characteristics of the HMM. The convergence and asymptotic properties of the proposed algorithms are analyzed. The HMM learned using the proposed algorithms is applied to event-triggered state estimation, and numerical results on model learning and state estimation demonstrate the validity of the proposed algorithms.

Event-based state and unknown input estimation for uncertain systems with stochastic nonlinearities

ABSTRACT 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.

Recursive State and Random Fault Estimation for Linear Discrete Systems under Dynamic Event-Based Mechanism and Missing Measurements

This paper is concerned with the event-based state and fault estimation problem for a class of linear discrete systems with randomly occurring faults (ROFs) and missing measurements. Different from the static event-based transmission mechanism (SETM) with a constant threshold, a dynamic event-based mechanism (DETM) is exploited here to regulate the threshold parameter, thus further reducing the amount of data transmission. Some mutually independent Bernoulli random variables are used to characterize the phenomena of ROFs and missing measurements. In order to simultaneously estimate the system state and the fault signals, the main attention of this paper is paid to the design of recursive filter; for example, for all DETM, ROFs, and missing measurements, an upper bound for the estimation error covariance is ensured and the relevant filter gain matrix is designed by minimizing the obtained upper bound. Moreover, the rigorous mathematical analysis is carried out for the exponential boundedness of the estimation error. It is clear that the developed algorithms are dependent on the threshold parameters and the upper bound together with the probabilities of missing measurements and ROFs. Finally, a numerical example is provided to indicate the effectiveness of the presented estimation schemes.

On stochastic and deterministic event-based state estimation

This paper investigates the problem of remote event-based state estimation for a linear discrete-time plant. Both stochastic and deterministic event-based transmission policies are considered for the systems implemented with smart sensors, where local Kalman filters are embedded. Based on the concept of generalized closed skew normal distributions, the exact probability density functions of the remote event-based state estimation processes are provided. With the properties of smart sensors, the explicit form of the remote event-based state estimators can be derived, without involving numerical integration. In addition, in the case of scalar plants, the estimation and transmission performances under different kinds of event-based scheduling policies are compared theoretically. An important inequality on a truncated covariance of some particular multivariate Gaussian distribution is proved, which builds a bridge between performances of the two event-based policies. Based on this inequality, it is proved that for any considered stochastic event-based transmission policy, there always exists a deterministic counterpart that leads to better estimation performance using the same communication and computational resources. Numerical simulations are provided to illustrate the theoretical results.

Dynamic event-based state estimation for delayed artificial neural networks with multiplicative noises: A gain-scheduled approach

This study is concerned with the state estimation issue for a kind of delayed artificial neural networks with multiplicative noises. The occurrence of the time delay is in a random way that is modeled by a Bernoulli distributed stochastic variable whose occurrence probability is time-varying and confined within a given interval. A gain-scheduled approach is proposed for the estimator design to accommodate the time-varying nature of the occurrence probability. For the sake of utilizing the communication resource as efficiently as possible, a dynamic event triggering mechanism is put forward to orchestrate the data delivery from the sensor to the estimator. Sufficient conditions are established to ensure that, in the simultaneous presence of the external noises, the randomly occurring time delays with time-varying occurrence probability as well as the dynamic event triggering communication protocol, the estimation error is exponentially ultimately bounded in the mean square. Moreover, the estimator gain matrices are explicitly calculated in terms of the solution to certain easy-to-solve matrix inequalities. Simulation examples are provided to show the validity of the proposed state estimation method.

Event-Based State Estimation With Multiplicative Measurement Noise and Correlated Additive Noises

This letter examines a state estimation with event-based transmissions for a linear discrete-time system when multiplicative noise affects the measurements while the additive noises of process and measurements of the sensor are correlated with each other. A general event-based technique is applied to produce the measurements at event-triggering instants and the sum of Gaussians approach is used at remote estimator to address the computation of state estimate when measurements are unavailable. The two-step predicted probability density function with Gaussian assumption is used to derive the recursive equations for the state estimate and its covariance matrix when the correlation between additive noises is at the same epoch. The results proposed are validated by a numerical example.

Optimized state estimation for nonlinear dynamical networks subject to fading measurements and stochastic coupling strength: An event-triggered communication mechanism

This paper is concerned with the design of event-based state estimation algorithm for nonlinear complex networks with fading measurements and stochastic coupling strength. The event-based communication protocol is employed to save energy and enhance the network transmission efficiency, where the changeable event-triggered threshold is adopted to adjust the data transmission frequency. The phenomenon of fading measurements is described by a series of random variables obeying certain probability distribution. The aim of the paper is to propose a new recursive event-based state estimation strategy such that, for the admissible linearization error, fading measurements and stochastic coupling strength, a minimum upper bound of estimation error covariance is given by designing the estimator gain. Furthermore, the monotonicity relationship between the trace of the upper bound of estimation error covariance and the fading probability is pointed out from the theoretical aspect. Finally, a simulation example is used to show the effectiveness of developed state estimation algorithm.

Event-Triggered State Estimation of Linear Systems Using Moving Horizon Estimation

In this brief, a problem of event-triggered state estimation for networked linear systems is investigated. We consider that the stochastic system disturbances and noise are bounded and moving horizon estimation (MHE) is used to handle these constraints. We establish an event-based state estimation mechanism that aims to provide good state estimates while reducing the frequencies of both the evaluation of the state estimator and networked communication between the plant and the estimator. An event-triggering condition is used to govern the evaluation of the MHE-based estimator and the use of networked communication. An MHE-based estimator is designed to provide state estimates when there is an event. Stability analysis of the estimation error dynamics is carried out for the proposed event-triggered estimation mechanism. The effectiveness and the applicability of the proposed method are demonstrated through numerical simulations and an experiment.