State Estimation Fusion Research Articles

Fusion State Estimation of CPS Under Quantized Observations and Tampering Attacks

Fusion State Estimation of CPS Under Quantized Observations and Tampering Attacks

A Multimodal Robust Simultaneous Localization and Mapping Approach Driven by Geodesic Coordinates for Coal Mine Mobile Robots

Mobile robots in complex underground coal mine environments are still unable to achieve accurate pose estimation and the real-time reconstruction of scenes with absolute geographic information. Integrated terrestrial-underground localization and mapping technologies have still not been effectively developed. This paper proposes a multimodal robust SLAM method based on wireless beacon-assisted geographic information transmission and lidar-IMU-UWB elastic fusion mechanism (LIU-SLAM). In order to obtain the pose estimation and scene models consistent with the geographic information, the construction of two kinds of absolute geographic information constraints based on UWB beacons is proposed. An elastic multimodal fusion state estimation mechanism is designed based on incremental factor graph optimization. A tightly coupled lidar-inertial odometry is firstly designed to construct the lidar-inertial local transformation constraints, which are further integrated with the absolute geographic constraints by UWB anchors through a loosely coupled approach. Extensive field tests based on coal mine robots have been conducted in scenarios such as underground garages and underground coal mine laneways. The results show that the proposed geodesic-coordinate driven multimode robust SLAM method can obtain absolute localization accuracy within 25 cm with practical robustness and real-time performance in different underground application scenarios. The wireless beacon-assisted geodesic-coordinate transmission strategy can provide a plug-and-play customized solution for precise positioning and scene modeling in complex scenarios of various coal mine robot application.

GNSS-INS-dynamic fusion with robustness to outliers based on external force state estimation

Multi-source information fusion state estimation algorithms are an important means for drones to perceive ego-state, and accurate and robust estimation of external forces is crucial for precise control of quadrotors. This paper proposes a method that integrates a dynamic model into a multi-rate extended Kalman filter (EKF) framework on manifold. By estimating the magnitude of the external force acting on vehicle, meanwhile, a dynamic constraint on velocity loop is established to reduce the discrepancy between the model-predicted motion and the actual motion. Moreover, the estimated external force is integrated into the zero velocity update criterion for zero speed judgment, effectively reducing false detections while improving the accuracy of zero speed state recognition. However, multi-source measurements significantly increase the probability of data signal errors. To address this issue, we use a robust estimation algorithm to improve EKF’s sensitivity to abnormal measurements, flexibly adjusting measurement weights while rejecting unreasonable measurements. Validation with open-source indoor and outdoor datasets shows that our algorithm improves pose estimation performance while maintaining accurate positioning accuracy compared to non-dynamic fusion under the same filtering parameters, particularly in global navigation satellite system short time denied. It provides accurate external force estimation, offering multi-source data support in areas such as human–machine interaction and carrying variable mass payloads.

Multi sensor fusion methods for state of charge estimation of smart lithium-ion batteries

Multi-dimensional sensing is the key characteristic of next generation smart batteries. But the existing researches on multi-sensor fusion methods haven't focused on algorithm mechanism, the global optimal solution has not been built, the superiority has not been proved theoretically. For the first time, this research built the global optimal structure of multi-sensor fusion state estimation algorithm. Specifically, the state of charge (SoC) estimation problem of lithium iron phosphate (LFP) batteries is studied, cooperating with voltage signal, expansion force (EF) signal is introduced. Firstly, a normalization algorithm is introduced to overcome the drift of EF under different cycles and different pre-tightening force. Secondly, the non-monotonic relationship of LFP battery's EF-SoC curve is addressed with a forced monotone transformation method in the transition areas. Then the global optimal multi-sensor fusion method is built, theoretical reductions are carried out to prove the higher precision of multi-sensor fusion methods compared to single-signal methods. Experiments are conducted to verify the effectiveness of the methods, even under the most serious situations, the fusion methods exhibit powerful correction ability, and the root mean square error can be controlled within 3 %. Moreover, the proposed algorithms shows strong tolerance to error sources.

Sequential Fusion Filter for State Estimation of Nonlinear Multi-Sensor Systems with Cross-Correlated Noise and Packet Dropout Compensation

This paper is concerned with the problem of state estimation for nonlinear multi-sensor systems with cross-correlated noise and packet loss compensation. In this case, the cross-correlated noise is modeled by the synchronous correlation of the observation noise of each sensor, and the observation noise of each sensor is correlated with the process noise at the previous moment. Meanwhile, in the process of state estimation, since the measurement data may be transmitted in an unreliable network, data packet dropout will inevitably occur, leading to a reduction in estimation accuracy. To address this undesirable situation, this paper proposes a state estimation method for nonlinear multi-sensor systems with cross-correlated noise and packet dropout compensation based on a sequential fusion framework. Firstly, a prediction compensation mechanism and a strategy based on observation noise estimation are used to update the measurement data while avoiding the noise decorrelation step. Secondly, a design step for a sequential fusion state estimation filter is derived based on an innovation analysis method. Then, a numerical implementation of the sequential fusion state estimator is given based on the third-degree spherical-radial cubature rule. Finally, the univariate nonstationary growth model (UNGM) is combined with simulation to verify the effectiveness and feasibility of the proposed algorithm.

Supervised learning for more accurate state estimation fusion in IoT-based power systems

Concerned with deploying zero-emission energy sources, reducing energy wasted through transmission lines, and managing power supply and demand, monitoring and controlling microgrids have found utter importance. Accordingly, this paper aims to investigate the efficacy of state estimation fusion for a synchronous generator as well as an induction motor in order to ameliorate system monitoring. A third-order nonlinear state-space model, that operates based on actual input data taken from the Smart Microgrid Laboratory, is assumed for each of the electrical machines. The model parameters are set according to the parameters of the electrical machines. A fusion structure based on the internet of things communication network, which is modified to increase uncertainty, is presented for fusing the state estimates. The data fusion topology is distributed and relies on two data fusion models. The first model is a set of state estimators, referred to as data input-feature output model. The second one fuses the estimators’ outputs based on supervised machine learning methods, referred to as feature input-feature output model. The simulation results in MATLAB and Python show the efficiency of linear regression methods compared with other leveraged methods for data fusion. By comparing the results obtained from both simple and complex estimation filters, it can be deduced that combining simple filters, extended Kalman filter in this case, with simple data fusion methods, linear regression in this case, can produce much more accurate results in a short period of time. Besides, this study shows that the averaging operators are unsuitable for estimation fusion by referring to their convexity condition.

Distributed State Fusion Estimation of Multi-Source Localization Nonlinear Systems.

For the state estimation problem of a multi-source localization nonlinear system with unknown and bounded noise, a distributed sequential ellipsoidal intersection fusion estimation algorithm based on the dual set-membership filtering method is proposed to ensure the reliability of the localization system. First, noise with unknown and bounded characteristics is modeled by using bounded ellipsoidal regions. At the same time, local estimators are designed at the sensor link nodes to filter out the noise interference in the localization system. The local estimator is designed using the dual set-membership filtering algorithm. It uses the dual principle to find the minimizing ellipsoid that can contain the nonlinear function by solving the optimization problem with semi-infinite constraints, and a first-order conditional gradient algorithm is used to solve the optimization problem with a low computational complexity. Meanwhile, the communication confusion among multiple sensors causes the problem of unknown correlation. The obtained estimates of local filters are fused at the fusion center by designing a distributed sequential ellipsoid intersection fusion estimation algorithm to obtain more accurate fusion localization results with lower computational cost. Finally, the stability and reliability of the proposed distributed fusion algorithm are verified by designing a simulation example of a multi-source nonlinear system.

Improved Distributed Multisensor Fusion Method Based on Generalized Covariance Intersection

In response to the multitarget tracking problem of distributed sensors with a limited detection range, a distributed sensor measurement complementary Gaussian component correlation GCI fusion tracking method is proposed on the basis of the probabilistic hypothesis density filtering tracking theory. First, the sensor sensing range is extended by complementing the measurements. In this case, the multitarget density product is used to classify whether the measurements belong to the intersection region of the detection range. The local intersection region is complemented only once to reduce the computational cost. Secondly, each sensor runs a probabilistic hypothesis density filter separately and floods the filtering posterior with the neighboring sensors so that each sensor obtains the posterior information of the neighboring sensors. Subsequently, Gaussian components are correlated by distance division, and Gaussian components corresponding to the same target are correlated into the same subset. GCI fusion is performed on each correlated subset to complete the fusion state estimation. Simulation experiments show that the proposed method can effectively perform multitarget tracking in a distributed sensor network with a limited sensing range.

Vehicle state estimation based on extended Kalman filter and radial basis function neural networks

To improve the reliability of vehicle state parameter estimation, a vehicle state fusion estimation method based on dichotomy is proposed. An extended Kalman filter algorithm is designed based on the vehicle 3 degrees of freedom dynamic model. Meanwhile, considering the influence of dynamic model and sensor noise and its coefficient selection on the estimation results, a radial basis function neural network estimation algorithm is designed. To further improve the reliability of the estimation algorithm, a method of estimation algorithm fusion is proposed based on the idea of mutual compensation between model- and data-driven estimation algorithms. The weights of the estimation results of different algorithms are assigned through the dichotomy. The redundancy and fusion of estimation algorithms can improve estimation performance. The effectiveness of the fusion method is verified by the co-simulation of MATLAB/Simulink and CarSim, and the real vehicle test. The results show that the change trend of the estimation result is consistent with the actual state parameters change trend, and the estimation accuracy after algorithm fusion is significantly improved compared to a single extended Kalman filter or radial basis function.

Global state estimation under sequential measurement fusion for clustered sensor networks with cross-correlated measurement noises

In practical multi-sensor fusion estimation, both the expensive communication burden of long-distance connection sensor networks and cross-correlated noises are usually inevitable, and need to be taken into account. To adequately address these difficulties, a global fusion estimation problem is studied for clustered sensor networks with cross-correlated measurement noises. To begin, we derive direct and indirect sequential measurement fusion (SMF) schemes as fusion rules, relying on whether a weighted least square method is used directly for the arriving measurements. We discover that the direct SMF has lower computational complexity than the indirect SMF, but the estimation accuracy of the latter is higher when the number of sensors exceeds three. Then, a globally indirect sequential measurement fusion estimation (GISMF) algorithm is proposed by using the indirect SMF, which is more computationally efficient and suitable for asynchronous fusion than that of batch fusion estimation. Accuracy relations among the GISMF, the batch state fusion estimation, and the centralized Kalman fuser (CKF) are proved. Moreover, the equality of the estimation accuracy between the GISMF and the CKF is also performed if all the measurement noises are mutually independent or if the measurement noises are only cross-correlated within the same cluster. Finally, several simulation results are implemented to show the effectiveness of the presented algorithm.

Multi-IMU Based Alternate Navigation Frameworks: Performance & Comparison for UAS

On-board state estimation is a persistent challenge to fielding unmanned aerial systems (UAS), particularly when global positioning system (GPS) measurements are not available. The dominant estimation tool remains the extended Kalman filter (EKF) applied to an inertial measurement unit (IMU). The growing availability of low-cost commercial-grade IMUs raises questions about how to best improve sensor readings into an estimate when measurements are available from multiple IMUs. This paper evaluates four different approaches to attitude estimation from multiple IMU measurements and their application in high dynamic motion. The four approaches are fusion of measurements (virtual IMU), fusion of state estimates (Federated KF), feedback fusion state estimate (Feedback Federated KF), and an EKF design incorporating the additional measurements (Augmented KF); these correspond to fusion before, within, or after state estimation. The performance of the approaches are quantified for varying IMU number theoretically and experimentally. The experiments use on-board autopilot hardware implementations of the estimators during maneuvers in a motion capture volume and flights on-board an Unmanned Aerial Systems (UAS) implementation, with the peak and root-mean-square (RMS) errors used to quantify accuracy. The RMS error results indicate that the feedback federated Kalman Filter using five IMUs returns 38% compared to general federated Kalman Filter using 37% accuracy improvement over a single IMU. This improvement compares to a 19% improvement for virtual IMU and 9% improvement for the Augmented KF respectively. These results indicate that both the Federated KF approach achieves the lowest RMS error relative to the virtual IMU and augmented KF approaches and inform the design of multi-IMU UAS pose estimators.

Event-Triggered Globally Sequential Fusion Estimation for Clustered Wireless Sensor Networks With Variational Bayesian

This paper concentrates on a globally sequential fusion state estimation problem for clustered wireless sensor networks (WSNs). Therein, frequent data communications in WSN will significantly increase energy consumption and communication burden, and it needs to be taken into account. To reduce unnecessary data transmissions and save energy, an event-triggered mechanism that decides whether the current measurement should be transmitted or not, therefore, is introduced. Then a novel variational Bayesian based event-triggered sequential measurement fusion (VB-ESMF) estimator is proposed to produce the local fused results of the clustered WSNs, where the variational Bayesian approach is used to infer the measurement noise covariance matrices of pseudo measurement noises. Therein, the local fused measurements of the clusters in the clustered WSNs are used sequentially by the remote fusion center, and thus a global fusion state estimation, which is globally optimal when all measurements are transmitted successfully, is computed. Additionally, certain boundedness and convergence conditions of the proposed estimator are derived, and an expected compromise between communication rate and estimation accuracy can be obtained by properly turning the trigger threshold. Finally, the effectiveness of both the VB-ESMF estimation and the globally sequential fusion state estimation is illustrated by simulation results.

Decentralization of Phasor-Aided State Estimation Using Local State Vector Extension

Distributed state estimation (DSE) and bad data (BD) processing have become increasingly important for the analysis and operation of large-scale power networks. This paper develops a new strategy for decentralized phasor-aided state estimation (DPHASE) to improve the performance of BD processing and, hence, the accuracy of DSE results. Given the recent availability of PMUs, the DPHASE strategy is developed using a parallel multi-stage hybrid approach. The practical challenges in the approach are identified and attributed to the difference between the sets of buses for SCADA- and PMU-based state estimates in sub-areas. Phasor-aided normalized residuals are locally unobtainable and the fusion of local state estimates is unattainable. These challenges are effectively resolved by extending local state vectors. Comparative case studies are performed using the proposed and conventional DSE strategies. The study results confirm that the proposed DPHASE strategy improves the accuracy and robustness of the DSE results under various test network and data measurement conditions.

Lithium-ion battery diagnostics and prognostics enhanced with Dempster-Shafer decision fusion

Prognostics is the discipline of predicting the remaining useful life of a component or system in order to optimize the maintenance planning or the mission execution. Prognostics-enabled systems likely reduce the overall life-cycle cost and increase the reliability. In the Bayesian estimation framework, the widely used techniques are the traditional Kalman filter, along with its non-linear extensions, and the particle filter. Each technique has different advantages. This paper investigates the fusion of prognostic results from different techniques in order to achieve a more trustworthy remaining useful life (RUL) prediction, as measured by a reduction in uncertainty. Models for extended Kalman filter (EKF) and particle filter (PF) are developed from the feature data. The results from EKF and PF are then fused using an application of Dempster-Shafer theory (DST). Separate models are utilized for EKF and PF in order to introduce multi-model prognostics and to optimize the performance of each technique for both diagnosis and RUL prediction. Prognostics is triggered when degradation is detected by diagnosis. DST is then applied to the prognostic results from EKF and PF. The result of DST is a density function whose performance can be compared with that of EKF and PF. DST allows for the fusion of multiple sensors and state estimates. The proposed method is verified with the prognosis of a set of lithium-ion batteries.

Coordinated target tracking of two UAVs based on game theory approach and Lyapunov guidance vector fields

Considering the problems of the lack of tracking the intelligent target, which is “smart” enough to escape from the detection by maximizing the estimation error in the current tracking methods by multi-UAVs, a cooperative control method for tracking intelligent target by two UAVs is proposed based on Lyapunov guidance vector field. The mathematical model of an intelligent target is established. According to the multi-UAV distributed intelligent target state fusion estimation method, the target state information is obtained to control two UAVs to circle the target through the Lyapunov guidance vector method. The simulation results demonstrated that the method enables two UAVs to track the intelligent target stably and improve the intelligent target’s positioning accuracy effectively

Three State Estimation Fusion Methods Based on the Characteristic Function Filtering.

There are three state estimation fusion methods for a class of strong nonlinear measurement systems, based on the characteristic function filter, namely the centralized filter, parallel filter, and sequential filter. Under ideal communication conditions, the centralized filter can obtain the best state estimation accuracy, and the parallel filter can simplify centralized calculation complexity and improve feasibility; in addition, the performance of the sequential filter is very close to that of the centralized filter and far better than that of the parallel filter. However, the sequential filter can tolerate non-ideal conditions, such as delay and packet loss, and the first two filters cannot operate normally online for delay and will be invalid for packet loss. The performance of the three designed fusion filters is illustrated by three typical cases, which are all better than that of the most popular Extended Kalman Filter (EKF) performance.

A Fast Covariance Union Algorithm for Inconsistent Sensor Data Fusion

We consider a challenging scenario in this research, where the sensors may receive spurious sensor data, potentially causing inconsistent state estimates. Covariance union (CU) is a fault-tolerant algorithm that can deal with inconsistent state estimation fusion. However, existing CU algorithms suffer from high computational costs due to optimizing nonlinear cost functions when generating fusion weights. To overcome this deficiency, an efficient CU algorithm named fast covariance union (FCU) is developed. We have proved that the fusion weight of FCU can be optimally generated by a closed-form algorithm without optimizing any nonlinear cost function, leading to better fusion efficiency. In addition, the FCU algorithm ensures the fused estimate be consistent as long as one of the estimates is consistent. Finally, the Monte Carlo simulation results show that the FCU algorithm has higher computational efficiency than the existing CU algorithms and handles the spurious sensor data fusion effectively.

Robust measurement fusion steady-state estimator design for multisensor networked systems with random two-step transmission delays and missing measurements

In this paper, we study the centralized fusion (CF) and weighted measurement fusion (WMF) robust steady-state Kalman filtering problem for a class of multisensor networked systems with mixed uncertainties including multiplicative noises, two-step random delays, missing measurements, and uncertain noise variances. By using a model transformation approach consisting of augmented approach, de-randomization approach and fictitious noise approach, the original multisensor system under study is converted into a multi-model multisensor system with only uncertain noise variances. By introducing an augmented state vector, and applying the weighted least squares (WLS) algorithm, the CF and WMF systems are obtained. According to the minimax robust estimation principle, based on the worst-case fusion systems with conservative upper bounds of uncertain noise variances, the CF and WMF robust steady-state Kalman estimators (predictor, filter, and smoother) are presented in a unified framework. Their robustness is proved by using a combination method consisting of augmented noise approach, matrix representation approach of quadratic form, and Lyapunov equation approach, the so-called robustness is concerned with the design of a filter such that for all admissible uncertainties, the actual fused steady-state estimation error variances of the estimators are guaranteed to have the corresponding minimal upper bounds. The accuracy relations among the robust local and fused steady-state Kalman estimators are proved. An example with application to autoregressive (AR) signal processing is proposed, which shows that the robust fusion signal estimation problems can be solved by the robust fusion state estimation method. Simulation example shows the effectiveness and correctness of the proposed method.

Temperature Sequential Data Fusion Algorithm Based on Cluster Hierarchical Sensor Networks.

The process of extracting gold by biological oxidation involves oxidizing the refractory high-sulfur and high-arsenic ore with the help of bacteria to decompose the wrapping material of gold to extract the gold. Therefore, maximizing the activity of bacteria will directly affect the efficiency of gold extraction, for which it is particularly important to maintain the pulp temperature in the oxidation tank at the optimal bacteria breeding temperature. However, gold mines are generally located in mountainous areas, and the large temperature difference between day and night in winter, coupled with the influence of wind and snow, creates variations in the temperature in the oxidation tank. The traditional temperature measurement method cannot fully reflect the temperature change of the oxidation tank. As a multi-field application method, sensor information fusion can effectively address the problem of pulp temperature measurement. First, we analyzed the heat transfer principle inside the oxidation tank, and designed the cluster hierarchical sensor network according to the spatial position of each oxidation tank and the environmental interference factors. The network structure is divided into three layers; the bottom of the sensor to collect pulp temperature data shows a spiral distribution in the inner wall of the oxidation tank. Each cluster head node sensor is used as an intermediate layer to complete local measurement fusion estimation. Finally, the fusion center is taken as the upper layer to realize the global state fusion estimation. Secondly, in the data processing of the bottom temperature sensor, the traditional unscented Kalman filter (UKF) algorithm is improved and the fading memory matrix is added to improve the identification of nonlinear modeling errors. The sequential observation fusion estimator (SOFE) algorithm is embedded in the measurement update to improve the performance of local measurement fusion. Finally, in the global state fusion estimation, the sequential analysis is combined with the inverse covariance intersection, and the sequential analysis and inverse covariance intersection-global state fusion estimation (SICI-GSFE) algorithm is proposed. Through calculation and simulation, the results show that the external interference can be reduced by combining all the temperature state estimations, and the accuracy of the best global temperature state estimation is improved.

Distributed State Estimation for Dynamic Positioning Systems with Uncertain Disturbances and Transmission Time Delays

The dynamic positioning system of unmanned underwater vehicles (UUVs) is a complex and large-scale system mainly due to the nonlinear dynamics, uncertainty in model parameters, and external disturbances. With the aid of the bio-inspired computing (BIC) method, the designed three-dimensional (3D) spatial positioning system is used for enlarging communication constraints and increasing signal coordination processing. With the growing of measurement scales, the issue of the networked high-precision positioning has been developed rapidly. Then, an information fusion estimation approach is presented for the distributed networked systems with data random transmission time delays and lost and disordered packets. To reduce the communication burden, an adaptive signal selection scheme is employed to reorganize the measurement sequence, and the parameter uncertainties as well as cross-correlated noise are used to describe the uncertain disturbances. Moreover, a reoptimal weighted fusion state estimation is designed to alleviate the information redundancy and maintain higher measurement accuracy. An illustrative example obtained from the 3D spatial positioning system is given to validate the effectiveness of the proposed method.