Kalman Consensus Filter Research Articles

SOC-SOH Estimation and Balance Control Based on Event-Triggered Distributed Optimal Kalman Consensus Filter

The inconsistency in state-of-charge (SOC) for electric vehicle batteries will cause component damage and lifespan reduction of batteries. Meanwhile, the consistency in the state-of-health (SOH) also negatively influences the consensus of SOC. To ensure the consensuses of SOC and SOH simultaneously, this paper introduces an innovative distributed optimal Kalman consensus filter (KCF) approach to battery management systems. In addition, at the stage where sensors transmit information to each other, a new event-triggering mechanism (ETM) based on dynamic information is proposed to reduce communication overhead effectively. Theoretical analysis verifies the optimality of the algorithm. By numerical simulations, the proposed event-triggered distributed optimal KCF (ET-DOKCF) method can improve the performance of SOC-SOH estimation and save communication resources.

Distributed recursive filtering for multi-rate uniform sampling systems with packet losses in sensor networks

The distributed filtering problem is studied for a multi-rate uniform sampling linear discrete system over sensor networks, where packet losses may occur during data exchange between nodes. The multi-rate system is transformed into a single-rate system by using a virtual measurement method. At each sensor node, the estimates received from neighbour nodes are fused by matrix or scalar weighting according to their different estimation accuracy. A distributed recursive filter with the Kalman consensus filter structure is devised based on the fused estimate, where the filtering gain and consensus gain are solved by locally minimising an upper bound of the filtering error covariance. The obtained gains and the upper bound of the covariance depend on a group of free positive scalar parameters. The scalar parameters are optimised by minimising the upper bound of the covariance. It is proved that the upper bound of the covariance of the filter with optimal gains and parameters is smaller than the covariance of the local filter based on sensor measurements. It avoids calculating cross-covariance matrices between nodes and has small computational burden. The exponential boundedness in the mean square of the filtering error is analysed. A target tracking system verifies the effectiveness of the algorithm.

Distributed state estimation with state equality constraints in the presence of packet dropping

In this paper, we investigate distributed Kalman consensus filter with state equality constraints in the presence of packet dropping. Firstly, the unconstrained distributed Kalman filter is designed by utilizing the local measurement information of each sensor node, and then the consensus term is added to it to derive the unconstrained distributed Kalman consensus filter. Secondly, we research the equality constrained distributed Kalman consensus filter based on the projection operator to achieve better filter performance, where the unconstrained estimation gain is calculated by solving a modified algebraic Riccati equation and a Lyapunov equation. Additionally, we design the second type of equality constrained distributed Kalman consensus filter by using time-stamping technology and projection operator to eliminate the effect of the Lyapunov equation in the infinite time domain on the convergence analysis, and its unconstrained estimation gain only requires solving a modified algebraic Riccati equation. Finally, the simulation experiments demonstrate that the equality constrained distributed Kalman consensus filter outperforms the unconstrained filter and that the second type of estimator exhibits superior performance compared to the first.

Recursive Least-Squares Wiener Consensus Filter and Fixed-Point Smoother in Distributed Sensor Networks

Distributed Kalman filter (DKF) is classified into the information fusion Kalman filter (IFKF), i. e. the centralized Kalman filter (CKF), and the Kalman consensus filter (KCF) in distributed sensor networks. The KCF has the advantage to improve the estimate of the state at the sensor node uniformly by incorporating the information of the observations and the filtering estimates at the neighbor nodes. In the first devised KCF, a user adjusts the consensus gain. This paper designs the recursive least-squares (RLS) Wiener consensus filter and fixed-point smoother that do not need to be adjusted in linear discrete-time stochastic systems. In addition to the observation equation at the sensor node, an observation equation is introduced excessively. Here, the new observation is the sum of the filtering estimates of the signals at the neighbor nodes of the sensor node. Thus, it is interpreted that the RLS Wiener consensus estimators incorporate the information of the observations at the neighbor nodes indirectly because the observations are used in the calculations of the filtering estimates. A numerical simulation example shows that the proposed RLS Wiener consensus filter and fixed-point smoother are superior in estimation accuracy to the RLS Wiener estimators.

Design of distributed recursive filters based on data compression for sensor networks

This paper is concerned with the distributed filtering problem based on data compression for linear discrete time-varying systems over sensor networks. Two kinds of sensors are considered: one kind only has a measuring capability and communicates measurements, while the other adds a calculating capability and communicates estimates. At each sensor node with calculating capability, a weighted measurement fusion algorithm is employed to compress the measurements of the sensor and its neighbor nodes with only measuring capability; and a weighted state fusion algorithm is employed to compress the estimates from neighbor nodes with calculating capability. Using compressed data, an optimal distributed recursive filter with a Kalman consensus filter form is devised in the linear unbiased minimum variance (LUMV) criterion. Cross-covariance matrices (CCMs) of the filtering errors between sensor nodes are derived. To avoid calculating CCMs, a suboptimal distributed recursive filter is presented, where a covariance intersection fusion algorithm is employed to compress the estimates from neighbor nodes with calculating capability. The filtering and consensus gains are solved to minimize an upper bound of covariance matrix (CM) of the filtering error. It is proved that the filtering error is exponentially bounded in the mean square. Simulations illuminate the effectiveness of proposed algorithms.

Robustness Analysis of Distributed Kalman Filter for Estimation in Sensor Networks.

Motivated by the guaranteed stability margins of linear quadratic regulators (LQRs) and standard Kalman filter (KF) in the frequency domain, this article extends these results to the distributed Kalman-consensus filter (DKCF) for distributed estimation in sensor networks. In particular, we study the robustness margins of DKCF in two cases, one of which is based on the direct target observation while the other uses estimates from neighbor sensors in the network. The loop transfer functions of the two cases are established, and gain and phase margin robustness results are derived for both. The robustness margins of DKCF are improved compared to the single-agent KF. Furthermore, as communication topology varies in sensor networks, graph overall coupling strengths change. We also analyze the correlation between overall coupling strengths and the robustness margins of DKCF.

Distributed estimation of unmanned surface vessel based on Kalman-consensus filter and convolutional neural network

The distributed estimation has important research significance in unmanned systems. This paper investigates the distributed estimation of unmanned surface vessel (USV) via multi-sensor collaboration and 3D object recognition, in which a Knowledge Graph (KG) is constructed to store and represent the estimation results. Kalman-consensus Filter (KCF) and convolutional neural network (CNN) are used to estimate the optimal states of objects, and recognise multiple classes of objects without designing detectors for each class of objects, respectively. The recognition efficiency is improved by dividing the data into pixel blocks whose value is the number of detection points, and a point cloud dataset in different locations and rotations is also provided. Experiments are proposed to show that our method can help the USV accurately perceive entities in the environment, which validates the effectiveness of the proposed algorithm.

Robust control strategy for multi-UAVs system using MPC combined with Kalman-consensus filter and disturbance observer

The stability of formation flight is not only sensitive to external disturbances but also to data observed and transferred between sensors and unmanned aerial vehicles (UAVs). A multi-constrained model predictive control (MPC) strategy, combined with Kalman-consensus filter (KCF) and fixed-time disturbance observer (FTDOB) is developed for the formation control of multiple quadrotors here Firstly, KCF is used to effectively fuse the data shared in the formation with noise and uncertainty, which improves the applicability and robustness of the formation in complex environments. Secondly, FTDOB is able to estimate the external disturbances suffered by the quadrotor in a fixed time and provides real-time compensation for the controller. On this basis, an improved MPC (IMPC) is designed for each UAV of the formation, which improves the computational efficiency while ensuring the asymptotic stability of the system. Eventually, the capability and effectiveness of the proposed strategy are verified by simulation in terms of disturbance rejection and noise suppression, as well as good trajectory tracking of the formation.

Distributed Kalman Consensus Filter for Estimation With Moving Targets.

Consensus-based distributed Kalman filters for estimation with targets have attracted considerable attention. Most of the existing Kalman filters use the average consensus approach, which tends to have a low convergence speed. They also rarely consider the impacts of limited sensing range and target mobility on the information flow topology. In this article, we address these issues by designing a novel distributed Kalman consensus filter (DKCF) with an information-weighted consensus structure for random mobile target estimation in continuous time. A new moving target information-flow topology for the measurement of targets is developed based on the sensors' sensing ranges, targets' random mobility, and local information-weighted neighbors. Novel necessary and sufficient conditions about the convergence of the proposed DKCF are developed. Under these conditions, the estimates of all sensors converge to the consensus values. Simulation and comparative studies show the effectiveness and the superiority of this new DKCF.

Security and Privacy Protection of Internet of Vehicles Consensus Algorithm Based on Wireless Sensors

Due to its large network scale, open communication environment, unstable wireless network, and other characteristics, it is extremely vulnerable to attacks and causes security problems, resulting in the collapse of the Internet of Vehicles system. The application of the Internet of Vehicles is becoming more and more extensive, but there are still problems such as information security and privacy leakage in the Internet of Vehicles. Through the analysis of the security threats and privacy protection requirements faced by the Internet of Vehicles system, this paper mainly studies information security, vehicle identity privacy, and location privacy in the process of Internet of Vehicles wireless communication. Therefore, it is urgent to conduct research on the information security and privacy protection issues of the Internet of Vehicles. This paper discusses the research on the security and privacy protection of the consensus algorithm for the Internet of Vehicles based on wireless sensors, compares and analyzes the wireless sensor data privacy protection protocols based on sharding technology, Tongtai encryption technology, and perturbation technology, and selects an optimized Kalman consensus filter. The algorithm is applied to the node information exchange of the sensor network, and two filters (low pass and band pass) are used to unify the observations and covariance of the network. Estimation of the sensor network state with and without data packet loss, the effect of system estimation error under different packet loss rates, data privacy protection algorithm performance, vehicle network data communication volume, and confusion factors on algorithm efficiency and the node energy consumption was compared and analyzed. Based on the application of wireless sensors, the estimation error and inconsistency estimation error of the algorithm in this paper finally converge to about 0.5, and both can maintain good stability and have good robustness. In addition, the communication volume of the algorithm in this paper is about 30% of the SCPDA algorithm. The Kalman consensus filtering algorithm reduces the amount of confusing data sent, improves privacy protection, and also achieves lower communication overhead.

Polytopic Robust Distributed Kalman Consensus Filter for Sensor Networks

Distributed estimation is a fundamental task performed by sensor networks, often achieved through the Kalman consensus filter. However, it requires exact models, which is seldom possible in practice since parametric uncertainties are usually unavoidable. We address in this paper the robust distributed filtering problem regarding linear discrete-time systems subject to polytopic uncertainties. We consider uncertainties in all parameter matrices of the target system and sensing models. First, we introduce a centralized filter, obtained as the solution to a min-max optimization problem whose cost function collectively weights all the underlying polytope vertices. Then, we derive a fully distributed version of this filter by applying the hybrid consensus on measurements and information approach. The estimators are recursive and do not rely on numerical solvers, appealing features for real-time applications. We validate our approach and assess its performance with a numerical example, comparing it with other robust distributed strategies.

Design of False Data Injection Attack on Distributed Process Estimation

Herein, design of false data injection attack on a distributed cyber-physical system is considered. A stochastic process with linear dynamics and Gaussian noise is measured by multiple agent nodes, each equipped with multiple sensors. The agent nodes form a multi-hop network among themselves. Each agent node computes an estimate of the process by using its sensor observation and messages obtained from neighboring nodes, via Kalman-consensus filtering. An external attacker, capable of arbitrarily manipulating the sensor observations of some or all agent nodes, injects errors into those sensor observations. The goal of the attacker is to steer the estimates at the agent nodes as close as possible to a pre-specified value, while respecting a constraint on the attack detection probability. To this end, a constrained optimization problem is formulated to find the optimal parameter values of a certain class of linear attacks. The parameters of linear attack are learnt on-line via a combination of stochastic approximation based update of a Lagrange multiplier, and an optimization technique involving either the Karush-Kuhn-Tucker (KKT) conditions or online stochastic gradient descent. The problem turns out to be convex for some special cases. Desired convergence of the proposed algorithms are proved by exploiting the convexity and properties of stochastic approximation algorithms. Finally, numerical results demonstrate the efficacy of the attack.

A Topology Optimization Method for Reducing Communication Overhead in the Kalman Consensus Filter

Distributed estimation and tracking of interested objects over wireless sensor networks (WSNs) is a hot research topic. Since network topology possesses distinctive structural parameters and plays an important role for the performance of distributed estimation, we first formulate the communication overhead reduction problem in distributed estimation algorithms as the network topology optimization in this paper. The effect of structural parameters on the algebraic connectivity of a network is overviewed. Moreover, aiming to reduce the communication overhead in Kalman consensus filter (KCF)-based distributed estimation algorithm, we propose a network topology optimization method by properly deleting and adding communication links according to nodes’ local structural parameters information, in which the constraint on the communication range of two nodes is incorporated. Simulation results show that the proposed network topology optimization method can effectively improve the convergence rate of KCF algorithm and achieve a good trade-off between the estimate error and communication overhead.

Analysis of Distributed Wireless Sensor Systems with a Switched Quantizer

In this article, a switched quantizer is proposed to solve the bandwidth limitation application problem for distributed wireless sensor networks (WSNs). The proposed estimator based on switched quantitative event-triggered Kalman consensus filtering (KCF) algorithm is used to monitor the aircraft cabin environmental parameters when suffering packet loss and path loss issues during the communication process for WSN. The quantization error of the novel switched quantizer structure is bounded, and the corresponding stability theory for the quantitative estimation approach is proved. Compared with other methods, the simulation results for the introduced method verify that the environmental parameters can be estimated accurately and timely and reduce the burden of network communication bandwidth.

Event-triggered optimal Kalman consensus filter with upper bound of error covariance

In this paper, we present an event-triggered optimal Kalman consensus filter (EOKCF) for state estimation in distributed wireless sensor networks. The local message is exchanged only when the local estimation violates a predetermined Send-on-Delta (SoD) data transmission condition in order to reduce the amount of data transfer. The neighboring measurement and estimation information are integrated into the consensus filter, and a recursive upper bound of the error covariance is derived for uncertainties of interval communication from the event-based systems. The optimal Kalman gain and consensus gain matrices are obtained by minimizing the upper bound of state error covariance. The Crameˇr−−Rao lower bound (CRLB) of the state estimates is also introduced to measure the mean-square estimation error performance. The effectiveness of event-triggered communication protocol and the advantages of filtering performance of EOKCF are demonstrated using Monte Carlo simulations on a target tracking application in a distributed sensor network.

Event‐triggered Kalman consensus filter for sensor networks with intermittent observations

SummaryThis article investigates the event‐triggered Kalman consensus filtering (ET‐KCF) problem for distributed sensor networks with intermittent observations. First, a novel ET consensus filtering structure is designed for sensor networks with intermittent observations. With the proposed consensus filtering structure, a new ET mechanism that is more efficient than the existed ones is designed to schedule transmissions of local estimates. Then, an optimal ET‐KCF in the sense of minimum mean‐square error is developed. For reducing the computational complexity of filtering algorithm, a suboptimal ET‐KCF is further proposed. Moreover, the stability of the suboptimal ET‐KCF is analyzed. Simulation results verify the validity and superiority of the proposed method.

Event-triggered optimal and suboptimal distributed Kalman consensus filters for sensor networks

This paper studies the distributed Kalman consensus filtering problem based on the event-triggered (ET) protocol for linear discrete time-varying systems with multiple sensors. The ET strategy of the send-on-delta rule is employed to adjust the communication rate during data transmission. Two series of Bernoulli random variables are introduced to represent the ET schedules between a sensor and an estimator, and between an estimator and its neighbor estimators. An optimal distributed filter with a given recursive structure in the linear unbiased minimum variance criterion is derived, where solution of cross-covariance matrix (CCM) between any two estimators increases the complexity of the algorithm. In order to avert CCM, a suboptimal ET Kalman consensus filter is also presented, where the filter gain and the consensus gain are solved by minimizing an upper bound of filtering error covariance. Boundedness of the proposed suboptimal filter is analyzed based on a Lyapunov function. A numerical simulation verifies the effectiveness of the proposed algorithms.

Velocity-Varying Target Tracking of Mobile Sensor Network Based on Flocking Control

Existing coupled distributed estimation and motion control strategies of mobile sensor networks present limitations in velocity-varying target tracking. Therefore, a velocity-varying target tracking algorithm based on flocking control is proposed herein. The Kalman-consensus filter is utilized to estimate the position, velocity and acceleration of a target. The flocking control algorithm with a velocity-varying virtual leader enables the position of the center of the mobile sensor network to converge to that of the target. By applying an effective cascading Lyapunov method, stability analysis is performed. Simulation results are provided to validate the feasibility of the proposed algorithm.

Freshness constraints of an age of information based event-triggered Kalman consensus filter algorithm over a wireless sensor network

This paper presents the design of a new event-triggered Kalman consensus filter (ET-KCF) algorithm for use over a wireless sensor network (WSN). This algorithm is based on information freshness, which is calculated as the age of information (AoI) of the sampled data. The proposed algorithm integrates the traditional event-triggered mechanism, information freshness calculation method, and Kalman consensus filter (KCF) algorithm to estimate the concentrations of pollutants in the aircraft more efficiently. The proposed method also considers the influence of data packet loss and the aircraft’s loss of communication path over the WSN, and presents an AoI-freshness-based threshold selection method for the ET-KCF algorithm, which compares the packet AoI to the minimum average AoI of the system. This method can obviously reduce the energy consumption because the transmission of expired information is reduced. Finally, the convergence of the algorithm is proved using the Lyapunov stability theory and matrix theory. Simulation results show that this algorithm has better fault tolerance compared to the existing KCF and lower power consumption than other ET-KCFs.

An Optimal Kalman-Consensus Filter for Distributed Implementation Over a Dynamic Communication Network

With the rising number of applications for sensor networks comes a need for more accurate cooperative fusion algorithms. In this paper, a distributed and optimal state estimator is presented for implementation through a dynamically switching, yet strongly connected, directed communication network to cooperatively estimate the state of a dynamic system. The Kalman-Consensus filter approach is used to incorporate a consensus protocol of neighboring state estimates into the traditional Kalman filter. It has been known that the main difficulty associated with implementing such an optimal solution is its fully coupled covariance matrix. Presented is a distributed computation of the covariance matrix at every node achieved by taking advantage of its independence from state estimates. Reductions to the distributed covariance computations are achieved through shared processing made available by the strongly connected digraph. Should the digraph change over time, a distributed topology estimation algorithm is included to facilitate the implementation of the proposed Kalman-Consensus filters. Together, these advances render a distributed and optimal solution to the consensus-based cooperative Kalman filter design problem. Convergence and stability of the proposed algorithms are analyzed and analytically concluded with performance verified through simulation of an illustrative example.