Local State Estimates Research Articles

Resilient strategy design for cyber-physical system under active eavesdropping attack

We consider a remote state estimation process under an active eavesdropper for cyber-physical system. A smart sensor transmits its local state estimates to a remote estimator over an unreliable network, which is eavesdropped by an adversary. The intelligent adversary can work in passive eavesdropping mode and active jamming mode. An active jamming mode enables the adversary to interfere the data transmission from sensor to estimator, and meanwhile improve the data reception of itself. To protect the transmission data from being wiretapped, the sensor with two antennas injects noise to the eavesdropping link with different power levels. Aiming at minimizing the estimation error covariance and power cost of themselves while maximizing the estimation error covariance of their opponents, a two-player nonzero-sum game is constructed for sensor and active eavesdropper. For an open-loop case, the mixed Nash equilibrium is obtained by solving an one-stage nonzero-sum game. For a long term consideration, a Markov stochastic game is introduced and a Nash Q-learning method is given to find the Nash equilibrium strategies for two players. Numerical results are provided to show the effectiveness of our theoretical conclusions.

Any Way You Look at It: Semantic Crossview Localization and Mapping With LiDAR

Currently, GPS is by far the most popular global localization method. However, it is not always reliable or accurate in all environments. SLAM methods enable local state estimation but provide no means of registering the local map to a global one, which can be important for inter-robot collaboration or human interaction. In this work, we present a real-time method for utilizing semantics to globally localize a robot using only egocentric 3D semantically labelled LiDAR and IMU as well as top-down RGB images obtained from satellites or aerial robots. Additionally, as it runs, our method builds a globally registered, semantic map of the environment. We validate our method on KITTI as well as our own challenging datasets, and show better than 10 meter accuracy, a high degree of robustness, and the ability to estimate the scale of a top-down map on the fly if it is initially unknown.

A Novel Multi-Area Distribution State Estimation Approach for Active Networks

This paper presents a hierarchically distributed algorithm for the execution of distribution state estimation function in active networks equipped with some phasor measurement units. The proposed algorithm employs voltage-based state estimation in rectangular form and is well-designed for large-scale active distribution networks. For this purpose, as the first step, the distribution network is supposed to be divided into some overlapped zones and local state estimations are executed in parallel for extracting operating states of these zones. Then, using coordinators in the feeders and the substation, the estimated local voltage profiles of all zones are coordinated with the local state estimation results of their neighboring zones. In this regard, each coordinator runs a state estimation process for the border buses (overlapped buses and buses with tie-lines) of its zones and based on the results for voltage phasor of border buses, the local voltage profiles in non-border buses of its zones are modified. The performance of the proposed algorithm is tested with an active distribution network, considering different combinations of operating conditions, network topologies, network decompositions, and measurement scenarios, and the results are presented and discussed.

A novel optimal data fusion algorithm and its application for the integrated navigation system of missile

For Inertial Navigation System (INS)/Celestial Navigation System (CNS)/Global Navigation Satellite System (GNSS) integrated navigation system of the missile, the performance of data fusion algorithms based on the Cubature Kalman Filter (CKF) is seriously degraded when there are non-Gaussian noise and process-modeling errors in the system model. Therefore, a novel method is proposed, which is called Optimal Data Fusion algorithm based on the Adaptive Fading maximum Correntropy generalized high-degree CKF (AFCCKF-ODF). First, the Adaptive Fading maximum Correntropy generalized high-degree CKF (AFCCKF) is proposed and used as the local filter for the INS/GNSS and INS/CNS subsystems to improve the robustness of local state estimation. Then, the local state estimation is fused based on the minimum variance principle and high-degree cubature criterion to get the globally optimal state. Finally, the experimental results verify that the proposed algorithm can significantly improve the robustness of the missile-borne INS/CNS/GNSS integrated navigation system to non-Gaussian noise and process modeling error and obtain the global optimal navigation information.

State-of-charge estimation for second-life lithium-ion batteries based on cell difference model and adaptive fading unscented Kalman filter algorithm

Abstract Lithium-ion batteries retired from electric vehicles can provide considerable economic benefits when they are retired for secondary use. However, retired batteries after screening and restructuring still face the problem of inaccurate battery pack state-of-charge (SOC) estimation due to the existence of extreme inconsistency. To solve this problem, an adaptive fading unscented Kalman filtering (AFUKF) algorithm based on the cell difference model (CDM) is proposed in this paper for improving the accuracy of SOC estimation of retired lithium-ion battery packs. Firstly, an improved CDM based on a hypothetical Rint model is developed based on a second-order resistor/capacitor equivalent circuit model. Secondly, an AFUKF algorithm is developed to improve the adaptability and robustness of local state estimation against process modelling errors. Finally, characteristic data are obtained by conducting discharge tests on the screened retired lithium-ion batteries under specific operating conditions. The proposed method can improve the accuracy of SOC estimation of retired lithium-ion battery packs and provide a new idea for SOC estimation of retired lithium-ion battery packs, as shown by the simulated real experimental data.

Encryption scheduling for remote state estimation under an operation constraint

In remote state estimation, data transmitted by a sensor through a wireless communication channel may be overheard by an eavesdropper. One possible way to avoid information leakage is to encrypt the transmitted data all the time. However, this may impose an extra operation energy burden on the sensor. In this paper, we investigate the optimal encryption scheduling in order to protect data privacy and ensure estimation accuracy under an energy constraint. Specifically, the sensor computes its local state estimate and then quantizes it using a non-subtractively dithered quantizer. Before each transmission, the sensor determines whether encrypting the data or not in order to strike a balance between data privacy and estimation accuracy. As the information about eavesdropper is unknown to the estimator, we introduce the concept of eavesdropper-invariant schedules and derive associated structural results. In addition, we propose a practical algorithm that compares a finite number of points to obtain an ε-optimal encryption schedule. Numerical examples are provided to illustrate performance benefits of the proposed methods.

Fixed-Time Projection Algorithm for Distributed Constrained Optimization on Time-Varying Digraphs

This article studies the distributed convex optimization problem with a common decision variable, a global inequality constraint, and local constraint sets over a time-varying multiagent network, the objective function of which is a sum of agents’ local convex cost functions. To solve such problem, a penalty-based distributed continuous-time subgradient algorithm with time-varying gain is developed for each agent to seek the saddle point of the penalty Lagrangian function. It is shown that an exact primal optimal solution can be obtained with certain assumption on time-varying gain. Moreover, the proposed algorithm adopts fixed-time projection scheme to ensure that for any initial state value, each local state estimate converges to its convex constraint set within fixed time. Finally, numerical examples are provided to show the effectiveness of the theoretical results.

Globally exponentially stable single beacon underwater navigation with unknown sound velocity estimation

Single beacon navigation methods with unknown effective sound velocity (ESV) have recently been proposed to solve the performance degeneration induced by ESV setting error. In these methods, a local linearization-based state estimator, which only exhibits local convergence, is adopted to estimate the navigation state. When the initial ESV setting error or vehicle initial position error is large, the local linearization-based state estimators have difficulty guaranteeing the filtering convergence. With this background, this paper proposes a linear time-varying single beacon navigation model with an unknown ESV that can realize global convergence under the condition of system observability. A Kalman filter is adopted to estimate the model state, and the corresponding stochastic model is inferred for the application of the Kalman filter. Numerical simulation confirms that the proposed linear time-varying single beacon navigation model can realize fast convergence in the case of a large initial error, and has superior steady-state performance compared with the existing methods.

Distributed Cubature Kalman Filter with Performance Comparison for Large-scale Power Systems

This paper studies a distributed cubature Kalman filter algorithm for the dynamic state estimation of a large-scale power system, which is interconnected and consists of some sub-areas. Using the hybrid measurements, each subsystem runs the proposed algorithm independently and in parallel to forecast and estimate its local state, which helps in reducing the whole execution time and the communication load without a central coordinator. The edge measurements and the exchanged information with the neighboring subsystems are utilised to correct the local state estimation of each subsystem, which makes this algorithm improve some known methods in literature. Simulation results of the IEEE 118-bus system are provided to demonstrate the performance of the proposed algorithm by comparing it with the distributed methods based on the extended Kalman filter and unscented Kalman filter.

Distributed Multi-Object Tracking Under Limited Field of View Sensors

We consider the challenging problem of tracking multiple objects using a distributed network of sensors. In the practical setting of nodes with limited field of views (FoVs), computing power and communication resources, we develop a novel distributed multi-object tracking algorithm. To accomplish this, we first formalise the concept of label consistency, determine a sufficient condition to achieve it and develop a novel \textit{label consensus approach} that reduces label inconsistency caused by objects' movements from one node's limited FoV to another. Second, we develop a distributed multi-object fusion algorithm that fuses local multi-object state estimates instead of local multi-object densities. This algorithm: i) requires significantly less processing time than multi-object density fusion methods; ii) achieves better tracking accuracy by considering Optimal Sub-Pattern Assignment (OSPA) tracking errors over several scans rather than a single scan; iii) is agnostic to local multi-object tracking techniques, and only requires each node to provide a set of estimated tracks. Thus, it is not necessary to assume that the nodes maintain multi-object densities, and hence the fusion outcomes do not modify local multi-object densities. Numerical experiments demonstrate our proposed solution's real-time computational efficiency and accuracy compared to state-of-the-art solutions in challenging scenarios. We also release source code at https://github.com/AdelaideAuto-IDLab/Distributed-limitedFoV-MOT for our fusion method to foster developments in DMOT algorithms.

Anomaly Resilient Relative Pose Estimation for Multiple Nonholonomic Mobile Robot Systems

This article addresses the resilient relative pose estimation problem for multiple mobile robot systems against abnormal sensor measurements. Motivated by the fact that in real implementations, sensors used for neighboring robot detection, such as stereo camera, laser range finder, etc., may suffer from unpredictable anomalies, a resilient relative pose estimation approach is proposed such that each robot can obtain satisfactory relative pose estimates of its neighbors for further coordination algorithm design. In the proposed approach, the optimal Kalman estimate is decomposed as a weighted sum of local state estimates, based on which a convex optimization problem is formulated to generate the resilient estimation. Unlike most of the existing approaches investigating similar problems, which assume that the statistics or the bound of anomalies is known in advance, our proposed approach is not limited by this assumption. The effectiveness of the proposed method has been validated by numerical simulations and real robot experiments. It has been demonstrated that the proposed approach is comparable to the Kalman filter in the absence of sensor anomalies, while boundedness of the relative pose estimation error can be guaranteed under abnormal observations.

Fusion estimation for a class of multi-rate power systems with randomly occurring SCADA measurement delays

In this paper, the fusion estimation problem is investigated for a class of multi-rate power systems with randomly occurring delays in supervisory control and data acquisition (SCADA) measurements. The power system is measured by the SCADA and the phasor measurement unit (PMU), and the state updating period of the power system is allowed to be different from the sampling periods of the SCADA and the PMU. The phenomenon of the randomly occurring SCADA measurement delays is characterized by a set of Bernoulli distributed random variables. To facilitate the state estimator design, a new approach is developed to transform the multi-rate power system into single-rate one. First, two local state estimators are designed, respectively, based on the SCADA and the PMU measurements such that upper bounds of the local estimation error covariances are guaranteed at each sampling instant, and such upper bounds are subsequently minimized by appropriately designing the gains of both local state estimators. Then, the asynchronous estimates from the local state estimators are fused by recurring to the covariance intersection fusion scheme. Finally, a simulation experiment is carried out on the IEEE 14-bus system to illustrate the effectiveness of the proposed fusion estimation scheme.

Local Decomposition of Kalman Filters and its Application for Secure State Estimation

This article is concerned with the secure state estimation problem of a linear discrete-time Gaussian system in the presence of sparse integrity attacks. <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbf {m}$</tex-math></inline-formula> sensors are deployed to monitor the state and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbf {p}$</tex-math></inline-formula> of them can potentially be compromised by an adversary, whose data can be arbitrarily manipulated by the attacker. We show that the optimal Kalman estimate can be decomposed as a weighted sum of local state estimates. Based on these local estimates, we propose a convex optimization based approach to generate a more secure state estimate. It is proved that our proposed estimator coincides with the Kalman estimator with a certain probability when all sensors are benign. Besides, we establish a sufficient condition under which the proposed estimator is stable against the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbf {(p,m)}$</tex-math></inline-formula> -sparse attack. A numerical example is provided to validate the secure state estimation scheme.

Cooperative Output-Feedback Secure Control of Distributed Linear Cyber-Physical Systems Resist Intermittent DoS Attacks.

This article studies a cooperative output-feedback secure control problem for distributed cyber-physical systems over an unreliable communication interaction, which is to achieve coordination tracking in the presence of intermittent denial-of-service (DoS) attacks. Under the switching communication network environment, first, a distributed secure control method for each subsystem is proposed via neighborhood information, which includes the local state estimator and cooperative resilient controller. Second, based on the topology-dependent Lyapunov function approach, the design conditions of secure control protocol are derived such that cooperative tracking errors are uniformly ultimately bounded. Interestingly, by exploiting the topology-allocation-dependent average dwell-time (TADADT) technique, the stability analysis of closed-loop error dynamics is presented, and the proposed coordination design conditions can relax time constraints on interaction topology switching. Finally, two numerical examples are presented to demonstrate the effectiveness of the theoretical results.

Parameter Identification Method Based on Mixed-Integer Quadratic Programming and Edge Computing in Power Internet of Things

With the rapid development of power Internet of Things, its scale is becoming larger and larger. Many advanced applications depend on the accuracy of network model and state estimation, and the accuracy of network model and state estimation largely depends on network parameter error. Therefore, a parameter identification and estimation method based on mixed-integer quadratic programming (MIQP) and edge computing is proposed. Firstly, a “cloud-tube-edge-end” architecture of power Internet of Things is proposed, and the edge computing layer collects terminal data and conducts data analysis, which greatly reduces the computing pressure of cloud center. In this architecture, the local state estimation is used to limit the branch with error data in a specific range to prevent the measurement errors in other ranges from affecting the local estimation process. Then, the parameter identification model is transformed into MIQP model, and a penalty factor is introduced into the optimization model to identify the parameter error and measurement error in the process of minimizing the objective function. Finally, data encryption, identity authentication, and other methods are used in edge computing to achieve network security protection, so as to avoid network attacks and information leakage in the process of data transmission. The proposed method is tested and analyzed in IEEE 14-bus test system. The results show that the proposed method can accurately determine and identify the error data in a certain probability in the actual operation of the power grid, which is convenient for the controller to find out the wrong data in time and determine the source of the error data, so as to set a reasonable data value.

Distributed Reinforcement Learning for Cyber-Physical System With Multiple Remote State Estimation Under DoS Attacker

In this paper, we consider cyber-physical system (CPS) with multiple remote state estimation under denial-of-service (DoS) attack in infinite time-horizon. The sensors monitor the system and send their local state estimate to remote estimators by choosing the local channels in “State 0” or “State 1”. The aim of sensors is to find policies for choosing local channel in a specific state to transmit message to minimize the total estimation error covariance on account of energy-saving in an infinite time-horizon. The DoS attacker aims to achieve the opposite goal by choosing channels to attack or not. The games between sensors and DoS attacker under two different structures of public information are investigated, that is the open-loop case (where sensors and attacker cannot observe others' behaviors) and the closed-loop case (where sensors and attacker can observe the others' behaviors causally). For the open-loop case with assumption that the DoS attacker can get the information from the remote estimators to the sensors, the distributed reinforcement learning algorithms for sensors and attacker based on local information are proposed to find their Nash equilibrium policies, respectively. Further, we consider in closed loop case that the DoS attacker cannot get the information from the remote estimators to the sensors which leads to asymmetric information between the sensors and attacker. To derive Nash equilibrium policies for sensors and attacker, we convert the original game into a belief-based continuous-state stochastic game. The convergence of distributed reinforcement learning method is proved. Some simulations are presented to demonstrate its effectiveness.

Stochastic Game in Linear Quadratic Gaussian Control for Wireless Networked Control Systems Under DoS Attacks

Recently, the security problem of wireless networked control systems (WNCSs) has become critical. In this article, we focus on strategies designing problem for sensor and denial-of-service (DoS) attacker in WNCS based on linear quadratic Gaussian (LQG) cost. In this scenario, a sensor measures the output of the system and transmits its local state estimate to the remote estimator via an unreliable channel which may suffer interference from an intelligent DoS attacker. In each step, the sensor demands to determine the power to transmit its packet data, at the same time, the attacker needs to determine the interference power to degrade the performance of the WNCS. To analyze this interactive decision-making process, we construct a two-player zero-sum stochastic game and propose an improved LQG cost considering energy-efficient factors. Then, for continuous power-level setting, we discuss the existence and the structure of equilibrium strategies of the sensor&#x2013;attacker game. For a discrete power set, an algorithm is developed to solve equilibrium strategies for both players. Finally, we present an example to illustrate our results.

Remote State Estimation in the Presence of an Active Eavesdropper

We consider remote state estimation in the presence of an active eavesdropper. A sensor forward local state estimates to a remote estimator over a network, which may be eavesdropped by an intelligent adversary. Aiming at improving the eavesdropping performance efficiently, the adversary may adaptively alternate between an eavesdropping and an active mode. In contrast to eavesdropping, the active attack enables the adversary to sabotage the data transfer to the estimator, and improve the data reception to itself at the same time. However, launching active attacks may increase the risk of being detected. As a result, a tradeoff between eavesdropping performance and stealthiness arises. We present a generalized framework for active eavesdropping and propose a criterion based on the packet reception rate at the estimator to evaluate the stealthiness of the eavesdropper. Moreover, the tradeoff is formulated as a constrained Markov decision process. After deriving a sufficient condition under which at least one stationary policy satisfies the stealthiness constraint and also bounds the eavesdropping performance, we develop an optimal attack policy for the eavesdropper and focus on the structural analysis of the optimal policy. Furthermore, numerical examples are provided to illustrate the developed results.

Optimal Scheduling of Multiple Sensors Over Lossy and Bandwidth Limited Channels

This work considers the sensor scheduling for multiple dynamic processes. We consider $n$ linear dynamic processes, the state of each process is measured by a sensor, which transmits their local state estimates over wireless channels to a remote estimator with certain communication costs. In each time step, only a portion of the sensors is allowed to transmit data to the remote estimator and the packet might be lost due to unreliability of the wireless channels. Our goal is to find a scheduling policy which coordinates the sensors in a centralized manner to minimize the total expected estimation error of the remote estimator and the communication costs. We formulate the problem as a Markov decision process. We develop an algorithm to check whether there exists a deterministic stationary optimal policy. We show the optimality of monotone policies, which saves computational effort of finding an optimal policy and facilitates practical implementation. Nevertheless, obtaining an exact optimal policy still suffers from curse of dimensionality when the number of processes are large. We further provide an index-based heuristics to avoid brute force computation. Numerical examples are presented to illustrate our theoretical results.

Optimal Design of Islanded Microgrids Considering Distributed Dynamic State Estimation

This article proposes an optimal zone clustering algorithm of islanded microgrids (IMG) based on supply adequacy taking into account the dynamic performance of distributed state estimation units. The IMG is partitioned into several localized, yet coupled zones, where each zone is responsible for its local state estimate and performs data fusion to reach consensus for shared state variables between zones. The technique proposes a novel algorithm to optimally define the placement of the virtual boundaries of the zones by minimizing the potential power transfer between adjacent zones. The proposed algorithm adopts the distributed particle filter (DPF) technique for the state estimation process. The proposed algorithm also has the ability to come up with one optimal configuration considering different events and scenarios that might occur in the IMG. Monte Carlo simulations demonstrate the efficacy of the proposed technique in the presence of severely corrupted measurements and state values as well as displaying tolerance to major load changes within the IMG. The DPF shows similar performance when compared to its centralized implementation while also providing computational savings by a factor of the number of zones.