Decentralized State Estimation Research Articles

Decentralized state estimation: An approach using pseudomeasurements and preintegration

This paper addresses the problem of decentralized, collaborative state estimation in robotic teams. In particular, this paper considers problems where individual robots estimate similar physical quantities, such as each other’s position relative to themselves. The use of pseudomeasurements is introduced as a means of modeling such relationships between robots’ state estimates and is shown to be a tractable way to approach the decentralized state estimation problem. Moreover, this formulation easily leads to a general-purpose observability test that simultaneously accounts for measurements that robots collect from their own sensors, as well as the communication structure within the team. Finally, input preintegration is proposed as a communication-efficient way of sharing odometry information between robots, and the entire theory is appropriate for both vector-space and Lie-group state definitions. To overcome the need for communicating preintegrated covariance information, a deep autoencoder is proposed that reconstructs the covariance information from the inputs, hence further reducing the communication requirements. The proposed framework is evaluated on three different simulated problems, and one experiment involving three quadcopters.

Decentralized Moving Horizon Estimation for Large-Scale Networks of Interconnected Unconstrained Linear Systems

This paper addresses the problem of designing a decentralized state estimation solution for a large-scale network of interconnected unconstrained linear time invariant (LTI) systems. The problem is tackled in a novel moving horizon estimation (MHE) framework, while taking into account the limited communication capabilities and the restricted computational power and memory, which are distributed across the network. The proposed design is motivated by the fact that, in a decentralized setting, a Luenberguer-based framework is unable to leverage the full potential of the available local information. A method is derived to solve a relaxed version of the resulting optimization problem. It can be synthesized offline and its stability can be assessed prior to deployment. It is shown that the proposed approach allows for significant improvement on the performance of recent Luenberger-based filters. Furthermore, we show that a state-of-the-art distributed MHE solution with comparable requirements underperforms in comparison to the proposed solution.

Team optimal decentralized estimation by multiple agents with asymmetric information

AbstractIn this paper, we are concerned with the team optimal decentralized state estimation problem where the state is transmitted to a remote agent with packet dropouts and is observed by local agents with additive noises. In particular, the information of the remote agent is available to all local agents with hierarchical relationships, which leads to an asymmetric information structure. The main contribution is to derive the analytical expressions for the team optimal decentralized state estimation. Different from the existing decentralized estimation results, the novelty of the paper is to comprehensively investigate the influence of packet dropouts and additive noises, which occur frequently in networked control systems.

Omni-Swarm: A Decentralized Omnidirectional Visual–Inertial–UWB State Estimation System for Aerial Swarms

Decentralized state estimation is one of the most fundamental components of autonomous aerial swarm systems in GPS-denied areas yet it still remains a highly challenging research topic. Omni-swarm, a decentralized omnidirectional visual-inertial-UWB state estimation system for aerial swarms, is proposed in this paper to address this research niche. To solve the issues of observability, complicated initialization, insufficient accuracy, and lack of global consistency, we introduce an omnidirectional perception front-end in Omni-swarm. It consists of stereo wide-FoV cameras and ultra-wideband sensors, visual-inertial odometry, multi-drone map-based localization, and visual drone tracking algorithms. The measurements from the front-end are fused with graph-based optimization in the back-end. The proposed method achieves centimeter-level relative state estimation accuracy while guaranteeing global consistency in the aerial swarm, as evidenced by the experimental results. Moreover, supported by Omni-swarm, inter-drone collision avoidance can be accomplished without any external devices, demonstrating the potential of Omni-swarm as the foundation of autonomous aerial swarms.

Data-Efficient Collaborative Decentralized Thermal-Inertial Odometry

We propose a system solution to achieve data-efficient, decentralized state estimation for a team of flying robots using thermal images and inertial measurements. Each robot can fly independently, and exchange data when possible to refine its state estimate. Our system front-end applies an online photometric calibration to refine the thermal images so as to enhance feature tracking and place recognition. Our system back-end uses a covariance-intersection fusion strategy to neglect the cross-correlation between agents so as to lower memory usage and computational cost. The communication pipeline uses Vector of Locally Aggregated Descriptors (VLAD) to construct a request-response policy that requires low bandwidth usage. We test our collaborative method on both synthetic and real-world data. Our results show that the proposed method improves by up to 46 % trajectory estimation with respect to an individual-agent approach, while reducing up to 89 % the communication exchange. Datasets and code are released to the public, extending the already-public JPL xVIO library.

On Preconditioning of Decentralized Gradient-Descent When Solving a System of Linear Equations

This article considers solving an overdetermined system of linear equations in peer-to-peer multiagent networks. The network is assumed to be synchronous and strongly connected. Each agent has a set of local data points, and their goal is to compute a linear model that fits the collective data points. In principle, the agents can apply the decentralized gradient-descent method (DGD). However, when the data matrix is <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ill-conditioned</i> , DGD requires many iterations to converge and is unstable against system noise. We propose a decentralized preconditioning technique to mitigate the deleterious effects of the data points’ conditioning on the convergence rate of DGD. The proposed algorithm converges <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">linearly</i> , with an improved convergence rate than DGD. Considering the practical scenario where the computations performed by the agents are corrupted, we study the robustness guarantee of the proposed algorithm. In addition, we apply the proposed algorithm for solving decentralized state estimation problems. The empirical results show our proposed state predictor’s favorable convergence rate and robustness against system noise compared to prominent decentralized algorithms.

Reachability-Based False Data Injection Attacks and Defence Mechanisms for Cyberpower System

With the push for higher efficiency and reliability, an increasing number of intelligent electronic devices (IEDs) and associated information and communication technology (ICT) are integrated into the Internet of Things (IoT)-enabled smart grid. These advanced technologies and IEDs also bring potential vulnerabilities to the intelligent cyber–physical smart grid. State estimation, as a primary step of system monitoring and situational awareness, is a potential target for attackers. A number of other smart grid applications, such as voltage stability assessment and contingency screening, utilize state estimation results as input data. False data injection (FDI) is a specific way to attack state estimation by manipulating input data. Existing research mainly focuses on the mathematical analysis of FDI attacks; however, in these methods, discussions of reachability requirements to compromise measurements considering cyberinfrastructure are limited. Reachability is defined as a measure that estimates the number of hosts to compromise for the possible FDI. Most of the existing FDI attack methods require the simultaneous manipulation on multiple measurement devices in different substations, in order to bypass the bad data detection, which may be impractical. In this paper, a new type of reachability-based FDI attack considering the cybernetwork with a practical attack is proposed and validated on two IEEE test systems. The corresponding defence mechanisms are (a) decentralized state estimation (DSE), (b) DSE with additional backup computational nodes, (c) communication network rerouting, and (d) intrusion detection system, and they were developed and presented with validation for two IEEE test systems with superior performance for an IoT-enabled intelligent smart grid system.

Decentralized FLL-Assisted PLL Design for Robust GNSS Carrier Tracking

This letter presents a decentralized state estimation framework for FLL-assisted PLL design to enhance the GNSS carrier tracking loop capability. Different from the existing centralized structure that fuses the FLL and PLL measurements via a collective filter, this architecture allows the measurements to be distributively filtered in the local state estimators. Thus, the global carrier state can be updated by combining the local estimates through weighting matrices. The proposed decentralized carrier tracking framework ensures high precision phase performance against noisy measurements and preserves intrinsically wider pull-in range in the presence of large Doppler errors, simultaneously. Demonstrative simulations are provided to show that the decentralized framework exhibits excellent robustness against weak signal and high dynamic conditions as compared with the existing centralized carrier tracking method.

Decentralized Low-Rank State Estimation for Power Distribution Systems

This article considers the low-observability state estimation problem in power distribution networks and develops a decentralized state estimation algorithm leveraging the matrix completion methodology. Matrix completion has been shown to be an effective technique in state estimation that exploits the low dimensionality of the power system measurements to recover missing information. This technique can utilize an approximate (linear) load flow model, or it can be used with no physical models in a network where no information about the topology or line admittance is available. The direct application of matrix completion algorithms requires solving a semi-definite programming (SDP) problem, which becomes computationally challenging for large networks. We therefore develop a decentralized algorithm that capitalizes on the popular proximal alternating direction method of multipliers (proximal ADMM). The method allows us to distribute the computation among different areas of the network, leading to a scalable algorithm. By doing all computations at individual control areas and only communicating with neighboring areas, the algorithm eliminates the need for data to be sent to a central processing unit and thus increases efficiency and contributes to the goal of autonomous control of distribution networks. We illustrate the advantages of the proposed algorithm numerically using standard IEEE test cases.

Pause-and-Go Self-Balancing Formation Control of Autonomous Vehicles Using Vision and Ultrasound Sensors

In this work, we implement a decentralized and noncooperative state estimation and control algorithm to autonomously balance a team of robots in a circular formation pattern. The group of robots includes a leader periodically moving at a constant steering angle and a set of followers that, by only leveraging intermittent and noisy proximity measurements, independently implement a fully decentralized state estimation control algorithm to determine and adjust their relative position with closest neighbors. The algorithm is conducted in a pause-and-go sequence, where, during the pause, each robot stops to gather and process the information coming from the measurements, estimate the relative phase with respect to the others, and identify its closest pursuant. During the go, each robot accelerates to space from its closest pursuant and then to move at a constant speed when the desired spacing is achieved. The algorithm is tested in an unprecedented experiment on a custom-made low-cost caster-wheeled robotic framework featuring sonar and vision sensors mounted on a rotating platform to estimate the proximity distance to closer neighbors. The control scheme, which does not necessitate cooperation and is capable of coping with uncertain and intermittent sensor feedback data, is shown to be effective in balancing the robot on the circle even when, at a steady state, no feedback sensor data are available.

State Estimation for Hybrid VSC Based HVDC/AC Transmission Networks

As the integration of High Voltage Direct Current (HVDC) systems on modern power networks continues to expand, challenges have appeared in different fields of the network architecture. In the Supervisory, Control and Data Acquisition (SCADA) field, software and toolboxes are expected to be modified to meet the new network characteristics. Therefore, this paper presents a unified Weighted Least Squares (WLS) state estimation algorithm suitable for hybrid HVDC/AC transmission systems, based on Voltage Source Converter (VSC). The mathematical formulas of the unified approach are derived for modelling the AC, DC and converter coupling components. The method couples the AC and DC sides of the converter through power and voltage constraints and measurement functions. Two hybrid power system test cases have been studied to validate this work, a 4-AC/4-DC/4-AC network and Cigre B4 DC test case network. Furthermore, comparison between the fully decentralized state estimation and the unified method is provided, which indicated an accuracy improvement and error reduction.

Decentralized state estimation and diagnosis of p-time labeled Petri nets systems

This paper proposes a state estimation technique in a decentralized context for time dependent systems. The plant of the studied system is modeled by P-time labeled Petri nets (P-TLPN) and the set of events is partitioned into a set of observable and unobservable ones, leading to a partial observation configuration. Indeed, the observation is distributed over a set of distinct sites which have their own local vision of the system. Moreover, some event are indistinguishable as the same label can be associated with the same transition adding another source of non-determinism. Thus, thanks to a global coordinator helped by the consideration of the timing factor, the local information transmitted via the different sites will be exploited to assess the set of states consistent with the current considered observation. The developed technique is an iterative procedure coupled with a time feasibility analysis (i.e., schedulability) conducted for particular firing sequences allowing to explain the considered observation, called time explanations. A diagnosis procedure aiming at evaluating the occurrence of particular faults for each behavior is also provided.

Multi-Agent system-based decentralized state estimation method for active distribution networks

This paper deals with the state estimation problem in Active Distribution Networks. With energy deregulation and the emergence of renewable energy sources, more distributed generation is integrated into distribution networks which increases their complexity. To be able to manage, control and take appropriate decisions on power networks, it is necessary to have accurate real-time measurements to perform state estimation. However, the use of classical methods for state estimation, on complex distribution networks, reveal instantly their limits. To handle these systems complexity, a new decentralized multi-agent-based approach is proposed. This allows us to split systems into smaller parts whose estimation is easier and faster. Finally, Artificial Bee Colony algorithm is adopted for state estimation. Our approach is tested on IEEE 6-bus, 14-bus and 30-bus. Results show a dramatic decrease in the computational burden, thus a faster estimation on large systems. This demonstrates the effectiveness of the proposed strategy.

Decentralized State Estimation of Combined Heat and Power System Considering Communication Packet Loss

In order to obtain an accurate state estimation of the operation in the combined heat and power system, it is necessary to carry out state estimation. Due to the limited information sharing among various energy systems, it is practical to perform state estimation in a decentralized manner. However, the possible communication packet loss is seldomly considered among various energy systems. This paper bridges this gap by proposing a relaxed alternating direction method of multiplier algorithm. It can also improve the computation efficiency compared with the conventional alternating direction of the multiplier algorithm. Case studies of two test systems are carried out to show the validity and superiority of the proposed algorithm.

Forming Distributed State Estimation Network From Decentralized Estimators

In this paper, we focus on the distributed state estimation of nonlinear systems comprised of several subsystems. We assume that a decentralized state estimation system already exists for the nonlinear system, where the local estimators can be of different types. In order to achieve improved estimation performance, the existing decentralized estimators may be connected together via a communication network to form a distributed state estimation network. We propose a systematic approach to take advantage of the existing decentralized estimators potentially of different types to form a distributed state estimation network without performing a complete redesign of the estimation system. Specifically, a compensator is designed for each subsystem, and is connected to the corresponding decentralized estimator to obtain an augmented estimator (AE). The AEs for the subsystems communicate with each other to exchange subsystem state estimates and measurements via a communication network every sampling time. We derive sufficient conditions on the convergence and boundedness of the estimation error of the proposed distributed estimation network. The proposed approach is demonstrated via the application to two chemical process examples and one hybrid tank plant.

Decentralized state estimation of combined heat and power systems using the asynchronous alternating direction method of multipliers

State estimation is a statistical method used to obtain accurate estimates of system operating states. It has been used to provide essential operating data for analysis, control and optimization in various energy supply systems. In a combined heat and power system, it is impractical to perform a state estimation procedure in a pool due to the information gap between the different energy sectors. To handle this problem, a decentralized state estimation algorithm based on the asynchronous alternating direction method of multipliers for a whole combined heat and power system is proposed. A dynamic state estimation model for a combined heat and power system is formulated considering the spatiotemporal quasidynamics of the network of heating pipelines. A framework based on the alternating direction method of multipliers is then proposed to solve the state estimation model in a decentralized way. First, an alternating estimation strategy is employed to solve district heating network subproblems to address the nondifferentiable and nonlinear constraints involved. Second, an asynchronous framework is employed to implement the alternating direction method of multipliers to reduce the idle time in the calculation of the subproblems and improve the overall computational efficiency. Case studies show that the proposed algorithm can still provide accurate estimates of the states of the integrated system even though it is decentralized. Compared to the standard implementation of the alternating direction method of multipliers, the proposed framework offers improved computational efficiency.

Decentralized Load Estimation for Distribution Systems Using Artificial Neural Networks

In this paper we present a decentralized state estimation method to support real-time Volt/Var optimization in distribution network with high penetration of distributed generation. The network is divided into sub-areas according to the location of the generation units and the mutual information (MI) between the states of interest and the available measurements. The proposed decentralized state estimation scheme only relies on local information and on a limited amount of information from neighboring areas. In each area, an artificial neural network (ANN) is used to estimate the loads consumptions. The proposed approach is tested using a modified IEEE 34-node test feeder. The effectiveness of the method is validated on a Hardware-In-the-Loop (HIL) simulation platform. To evaluate the accuracy and efficiency of the proposed decentralized approach we compared the results obtained to a centralized and a totally local approach.

Robust decentralised state estimation for formation flying spacecraft

In this study, a robust decentralised state estimation algorithm named decentralised Huber-based cubature filtering (DHCF) for formation flying spacecraft is proposed. In this algorithm, a decentralised architecture is designed, in which each deputy estimates its relative state with respect to the chief based on its own exteroceptive sensor measurement. The relative motion equation considering the non-spherical influence of the earth is derived. The relative measurements' information contain not only the line-of-sight between the deputy and the chief, but also the ranges among the deputies, which improves the redundancy of the relative navigation task. A set of cubature points are selected using spherical-radial rule to map the probability distribution, which is more accurate than the linearisation of the extended Kalman filter (EKF). The non-Gaussian noise in formation is approximated by Gaussian mixture models. To deal with the non-Gaussian noise, the Huber technique is used in measurement update of each deputy and the extra measurement uncertainty caused by linearisation is compensated. Simulation results indicate that the proposed DHCF provides better performance in state estimation accuracy and robustness when compared to decentralised EKF and decentralised cubature Kalman filtering in the presence of non-Gaussian measurement noise.

Decentralized three-phase distribution system static state estimation based on phasor measurement units

This paper presents a novel approach for static state estimation in electrical distribution systems, in which the state variables to be estimated are branch currents in rectangular coordinates. Branch current and voltage phasors are measured from a reduced number of PMUs located along a non fully observable electrical distribution system with radial topology. For the non-monitored buses, load pseudo-measurements are considered as a set of inequality constraints varying between upper and lower limits, which are adjusted during the safety barrier interior point optimization solution process (SBIPM). In order to track daily load variations, the initial load limits for the next time interval are obtained from the actual estimated loads at the non-monitored buses, considering the percentage of power variation at the exit of each lateral feeder. At each iteration of the SBIPM solution process, if any load is set to its corresponding limit, then a new limit margin is set accordingly, meaning that at the end of the solution process all the non-monitored loads are within specified bounds. The distribution network is also subdivided into subsystems considering a PMU allocation procedure in which each lateral feeder is estimated individually, yielding a naturally decentralized state estimator. In this decentralization context, priority loads, such as hospitals, police stations, telecom centers and places with high load density concentration can be considered as monitored subareas, exploring the radial topology of the distribution system. Tests are conducted on IEEE 33 bus test feeder and compared with an existing method in the literature to show the effectiveness of the proposed algorithm. Another simulation was conducted on a long lateral feeder of 57 bus in order to show the possibility of using the proposed technique for large scale distribution systems.

Decentralized State Estimation for Hybrid AC/DC Microgrids

This paper presents a decentralized state estimation (SE) for the newly emerging hybrid ac/dc microgrid. The microgrid consists of an ac and a dc network which are connected via the interlinking ac/dc converter. The proposed SE is able to estimate the state variables of both networks in a decentralized way that the estimation is separately conducted while only limited information is exchanged during the process. The dual decomposition approach is adopted as the decentralized technique in this paper. Simulation results suggest that the proposed decentralized SE performs comparably to the centralized SE for the hybrid ac/dc microgrids in terms of accuracy, convergence, and robustness.