Inverse Covariance Intersection Research Articles

Cubature Kalman fusion filtering under stochastic communication protocol: Tackling dynamical bias, scheduling probability and channel noise

The paper addresses the problem of cubature Kalman fusion filtering (CKFF) for nonlinear systems subject to dynamical bias and stochastic communication protocol (SCP). To account for the engineering practice of networked environment, the channels from sensors to filters, affected by Gaussian channel noise, are considered in the system model incorporating dynamical bias. With the purpose of reducing communication load and enhancing resource utilization efficiency, the SCP is adopted for information transmissions, where the scheduling probability is allowed to deviate within bounds from its designated value owing to possible implementation errors. The objective of this paper is to design a CKFF algorithm in spite of the presence of dynamical bias, channel noise and SCP with uncertain scheduling probability. Specifically, the local filter is constructed such that an upper bound on the filtering error covariance (FEC) is calculated through the resolution of matrix difference equations, and the filter gain is subsequently designed to minimize this upper bound. Then, the local filters are fused by utilizing the inverse covariance intersection fusion rule. Moreover, the boundedness of the FEC’s upper bound is also investigated using the matrix theory. The feasibility and effectiveness of the proposed CKFF approach are demonstrated through a simulation experiment.

Distributed fusion filtering for multi-sensor nonlinear networked systems with multiple fading measurements via stochastic communication protocol

This paper studies the distributed fusion filtering (DFF) issue for a class of nonlinear delayed multi-sensor networked systems (MSNSs) subject to multiple fading measurements (MFMs) under stochastic communication protocol (SCP). The phenomenon of MFMs occurs randomly in the network communication channels and is characterized by a diagonal matrix with certain statistical information. In order to decrease the overload of communication network and save network resources, the SCP that can regulate the information transmission between sensors and estimators is adopted. The primary aim of the tackled problem is to develop the DFF method for nonlinear delayed MSNSs in the presence of MFMs and SCP based on the inverse covariance intersection fusion rule. In addition, the local upper bound (UB) of the filtering error covariance (FEC) is derived and minimized by means of suitably designing the local filter gain. Moreover, the boundedness analysis regarding the local UB is proposed with corresponding theoretical proof. Finally, two simulation examples with comparative illustrations are given to display the usefulness and feasibility of the derived theoretical results.

The GM-JMNS-CPHD Filtering Algorithm for Nonlinear Systems Based on a Generalized Covariance Intersection.

Some fusion criteria in multisensor and multitarget motion tracking cannot be directly applied to nonlinear motion models, as the fusion accuracy applied in nonlinear systems is relatively low. In response to the above issue, this study proposes a distributed Gaussian mixture cardinality jumping Markov-cardinalized probability hypothesis density (GM-JMNS-CPHD) filter based on a generalized inverse covariance intersection. The state estimation of the JMNS-CPHD filter combines the state evaluation of traditional CPHD filters with the state estimation of jump Markov systems, estimating the target state of multiple motion models without knowing the current motion models. The performances of the generalized covariance intersection (GCI)GCI-GM-JMNS-CPHD and generalized inverse covariance intersection (GICI)GICI-GM-JMNS-CPHD methods are evaluated via simulation results. The simulation results show that, compared with algorithms such as Sensor1, Sensor2, GCI-GM-CPHD, and GICI-GM-CPHD, this algorithm has smaller optimal subpattern assignment (OSPA) errors and a higher fusion accuracy.

Distributed asynchronous measurement system fusion estimation based on inverse covariance intersection algorithm

For state estimation of multi-source asynchronous measurement systems with measurement missing phenomena, this paper proposes a distributed sequential inverse covariance intersection (DSICI) fusion algorithm based on conditional Kalman filtering method. It is mainly divided into synchronized state space module, local filtering module and fusion estimation module. The missing measurements occurring in the system are modelled and described by a set of random variables obeying a Bernoulli distribution. The synchronized state space module uses a state iteration method to synchronize the asynchronous measurement system at the moment of measurement update and it ensures the integrity of the measurement information. The local filtering module uses a conditional Kalman filtering algorithm for filter estimation. The reliability of the local filtering results is guaranteed because the local estimator designs a method to interact information with the domain sensors. The fusion estimation module designs a DSICI fusion algorithm with higher accuracy and satisfying consistency, which fuses the filtering results provided by each sensor when the relevant information between multiple sensors is unknown. Simulation examples demonstrate the excellent performance of the proposed algorithm, with a 33% improvement in accuracy over existing algorithms and an iteration time of less than 3 ms.

An Efficient Implementation Method for Distributed Fusion in Sensor Networks Based on CPHD Filters.

A highly efficient implementation method for distributed fusion in sensor networks based on CPHD filters is proposed to address the issues of unknown cross-covariance fusion estimation and long fusion times in multi-sensor distributed fusion. This method can effectively and efficiently fuse multi-node information in multi-target tracking applications. Discrete gamma cardinalized probability hypothesis density (DG-CPHD) can effectively reduce the computational burden while ensuring computational accuracy similar to that of CPHD filters. Parallel inverse covariance intersection (PICI) can effectively avoid solving high-dimensional weight coefficient convex optimization problems, reduce the computational burden, and efficiently implement filtering fusion strategies. The effectiveness of the algorithm is demonstrated through simulation results, which indicate that PICI-GM-DG-CPHD can substantially reduce the computational time compared to other algorithms and is more suitable for distributed sensor fusion.

Inverse-Covariance-Intersection-Based Distributed Estimation and Application in Wireless Sensor Network

In a sensor network, estimation performance may degrade when unknown correlations among local estimates are not addressed carefully. This article presents a novel distributed estimation algorithm based on inverse covariance intersection (ICI) for effectively solving the cross-correlation and dynamic state estimation problems in a wireless sensor network. The intermediate results of a set of consensus filters running in parallel are utilized to realize a global fusion of estimates, which involves all agents' local estimates and improves the estimation accuracy. Meanwhile, the global consistency of the proposed algorithm can be guaranteed theoretically since the fusion process considers all local estimates jointly and in a unified way. Furthermore, besides the asymptotic performance, the boundedness and consistency of the fused estimate can be achieved under finite iterations, which demonstrates its robustness and potential in practical applications. A cooperative target tracking problem illustrates the performance of the proposed algorithm.

Distributed resilient fusion filtering for nonlinear systems with multiple missing measurements via dynamic event-triggered mechanism

This paper investigates the distributed resilient fusion filtering (DRFF) issue under inverse covariance intersection (ICI) fusion criterion and dynamic event-triggered mechanisms (DETMs), where the physical plant is described by stochastic nonlinear multi-sensor networked systems (MSNSs) with time-varying system parameters and multiple missing measurements (MMMs). The measurements from various sensor nodes to the fusion center may undergo the missing data, where this phenomenon is depicted by means of random variables governed by certain statistical principles. In addition, the DETM is adopted to regulate the communication process from each sensor node to fusion center, which can alleviate the network transmission situations with communication overload and energy consumption limitation. The purpose of the addressed issue is to construct a set of local resilient filters (LRFs) for stochastic nonlinear MSNSs with MMMs via the DETM, which can guarantee that the minimized upper bounds are derived and the desirable filter gain with easy-to-implementation form is given. Subsequently, via the obtained LRFs, a unified framework of the DRFF approach is formulated through using the ICI fusion criterion. In addition, the monotonicity analysis of the obtained upper bound in regard to the triggered parameter is examined by providing rigorous theoretical proof. Finally, the simulations with comparison experiment are provided to illustrate the validity of presented DRFF technique.

Distributed Estimation With Iterative Inverse Covariance Intersection

For distributed estimation in sensor network systems, intractable correlation among local estimates has a great impact on the accuracy and consistency of the fused estimate. An inconsistent or over conservative estimate would lead to degradation of estimation performance or even estimation divergence. In this brief, a distributed iterative diffusion estimation algorithm based on inverse covariance intersection (ICI) technique is proposed to address the unknown correlation and yield an estimate with uncertainty close to the true mean square error. The proposed algorithm is referred to as iterative ICI (It-ICI), which leverages the iteration of fusions that is only executed locally. Every sensor node only combines estimates from its neighbors. By iterations, the local information can be propagated to the entire sensor network and the accuracy can be incrementally improved. The fused estimate is proved to be unbiased with bounded covariance provided that the local filters’ estimates are unbiased and bounded. The performance of the proposed distributed estimation algorithm is illustrated by a collaborative target tracking problem in terms of enhanced tracking accuracy and consistency.

Gaussian Mixture Cardinalized Probability Hypothesis Density(GM-CPHD): A Distributed Filter Based on the Intersection of Parallel Inverse Covariances

A distributed GM-CPHD filter based on parallel inverse covariance crossover is designed to attenuate the local filtering and uncertain time-varying noise affecting the accuracy of sensor signals. First, the GM-CPHD filter is identified as the module for subsystem filtering and estimation due to its high stability under Gaussian distribution. Second, the signals of each subsystem are fused by invoking the inverse covariance cross-fusion algorithm, and the convex optimization problem with high-dimensional weight coefficients is solved. At the same time, the algorithm reduces the burden of data computation, and data fusion time is saved. Finally, the GM-CPHD filter is added to the conventional ICI structure, and the generalization capability of the parallel inverse covariance intersection Gaussian mixture cardinalized probability hypothesis density (PICI-GM-CPHD) algorithm reduces the nonlinear complexity of the system. An experiment on the stability of Gaussian fusion models is organized and linear and nonlinear signals are compared by simulating the metrics of different algorithms, and the results show that the improved algorithm has a smaller metric OSPA error than other mainstream algorithms. Compared with other algorithms, the improved algorithm improves the signal processing accuracy and reduces the running time. The improved algorithm is practical and advanced in terms of multisensor data processing.

Robust Sequential Fusion Estimation Based on Adaptive Innovation Event-Triggered Mechanism for Uncertain Networked Systems.

In order to reduce the transmission pressure of the networked system and improve its robust performance, an adaptive innovation event-triggered mechanism is designed for the first time, and based on this mechanism, the robust local filtering algorithm for the multi-sensor networked system with uncertain noise variances and correlated noises is presented. To avoid calculating the complex error cross-covariance matrices, applying the sequential fusion idea, the robust sequential covariance intersection (SCI) and sequential inverse covariance intersection (SICI) fusion estimation algorithms are proposed, and their robustness is analyzed. Finally, it is verified in the simulation example that the proposed adaptive innovation event-triggered mechanism can reduce the communication burden, the robust local filtering algorithm is effective for the uncertainty generated by the unknown noise variances, and two robust sequential fusion estimators show good robustness, respectively.

Distributed resilient fusion filtering for nonlinear systems with random sensor delay under round-robin protocol

In this paper, we address the distributed resilient fusion filtering (DRFF) problem for a class of nonlinear multi-sensor networked systems (MSNSs) with random sensor delay (RSD) under round-robin protocol (RRP). The RSD is depicted by the Bernoulli random variable with known occurrence probability. In order to relieve the network congestion, the RRP that can deal with information overload issue of the transmission process from sensor to the estimator is utilised. The major objective of this paper is that the resilient fusion filter is designed for nonlinear MSNSs with RSD and RRP in the light of the inverse covariance intersection approach, where the local upper bound regarding the filtering error covariance is obtained and then minimised by suitably exploiting the local filter gain. Finally, a simulation example that can show the validity of the provided DRFF algorithm is presented.

Consistent fusion method with uncertainty elimination for distributed multi-sensor systems

In this study, the elimination of correlated errors with an unknown correlation in distributed fusion is investigated, and a consistent fusion method for distributed multi-sensor systems is proposed. Unlike most existing fusion methods, the proposed method guarantees the consistency of fusion results without requiring system model parameters or adopting conservative strategies. First, a universal bijection is used to quantify the uncertainty in the estimates to be fused based on the entropy of the independent scalars. Second, the correlated errors caused by unknown mutual information and common process noise are treated as avoidable uncertainties. The avoidable uncertainty is then estimated by using a similarity function based on the Kullback–Leibler divergence. Finally, the avoidable uncertainty is separated from the fusion results by employing a conditional probability model to avoid correlated errors. This method is proven to be unbiased, consistent, and more accurate than the well-known covariance intersection method and the inverse covariance intersection method. The simulation results further verify the superiority of the proposed method in terms of the consistency, accuracy, and ability to limit cumulative errors in sequential fusion processes.

Electric Vehicle State Parameter Estimation Based on DICI-GFCKF

To improve the estimation accuracy of the state parameters of distributed electric vehicles, a double inverse covariance intersection generalized fifth-order cubature Kalman filter (DICI-GFCKF) es-timation algorithm is proposed. Based on the fifth-order cubature Kalman filter algorithm, the generalized cubature rule is used to directly obtain the weight and cubature point of the algorithm. Then, the inverse covariance intersection (ICI) data fusion algorithm is introduced and combined with the generalized fifth-order CKF, and the double inverse covariance intersection-generalized fifth-order cubature Kalman filter is derived. The algorithm is applied to estimate the state parameters of distributed electric vehicles. Finally, the simulation and the vehicle experiment show that the algorithm not only improves the estimation accuracy and stability but also reduces the influence of the system model nonlinearity on the algorithm, and has good effectiveness and robustness.

Data fusion based wireless temperature monitoring system applied to intelligent greenhouse

In intelligent greenhouses, wireless sensor networks with uneven temperature distribution and low collection efficiency may lead to poor monitoring effects in real time. To improve the performance of the temperature monitoring system in intelligent greenhouses, a real-time fusion strategy for a hierarchical wireless sensor network (WSN) is proposed. The designed WSN has three layers. In the bottom, sensors collect and preprocess the temperature data of the greenhouse by an improved unscented Kalman filter. In the middle layer, each cluster-head sensor, as a local fusion center, is used to fuse the data collected from the bottom sensors by a parallel inverse covariance intersection fusion algorithm. In the top, a global fusion center is utilized to fuse the temperature data from the middle layer to reflect the global temperature of the greenhouse by an improved extreme learning machine algorithm. The designed algorithm applied in each layer ensures the efficiency and accuracy of data fusion in real time. Simulation results show that the designed fusion strategy effectively improves the fusion accuracy and realizes the real-time fusion. The performance of the designed temperature monitoring system is greatly improved.

Multi-Sensor Fusion Positioning Method Based on Batch Inverse Covariance Intersection and IMM

For mass application positioning demands, the current single positioning sensor cannot provide reliable and accurate positioning. Herein, we present batch inverse covariance intersection (BICI) and BICI with interacting multiple model (BICI-IMM) multi-sensor fusion positioning methods, which are based on the batch form of the sequential inverse covariance intersection (SICI) fusion method. Meanwhile, it is proved that the BICI is robust. Compared with SICI, BICI-IMM reduces estimation error variance of the motion model and has less conservativeness. The BICI-IMM algorithm improves the accuracy of local filtering by interacting with multiple models and realizes global fusion estimation based on BICI. The validity of the BICI and BICI-IMM algorithm are demonstrated by two simulations and experiments in the open and semi-open scenes, and its positioning accuracy relations are shown. In addition, it is demonstrated that the BICI-IMM algorithm can improve the positioning accuracy in the actual scenes.

Distributed GM-CPHD Filter Based on Generalized Inverse Covariance Intersection

In this paper, we propose a distributed Gaussian mixture cardinalized probability hypothesis density (GM-CPHD) filter based on generalized inverse covariance intersection that fuses multiple node information effectively for multi-target tracking applications. Covariance intersection (CI) is a well-known fusion method that produces a conservative estimate of the joint covariance regardless of the actual correlation between the different nodes. Inverse covariance intersection (ICI) is the updated version to obtain fusion results that guarantee consistency and less conservative than CI. However, the ICI is not extended to multi-sensor multi-target tracking system yet. Since the ICI formula can be re-structured as naïve fusion with covariance inflation in Gaussian pdf, this method was applied to the GM-CPHD with generalization. The formula for random finite set (RFS) fusion was derived in the same way as the conventional generalized covariance intersection (GCI) based fusion. The simulation results for multi-target tracking show that the proposed algorithm has smaller optimal sub-pattern assignment (OSPA) errors than naïve fusion and the GCI-based fusions.

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.

1-point RANSAC UKF with Inverse Covariance Intersection for Fault Tolerance.

The fault tolerance estimation method is proposed to maintain reliable correspondences between sensor data and estimation performance regardless of the number of valid measurements. The proposed method is based on the 1-point random sample consensus (RANSAC) unscented Kalman filter (UKF), and the inverse covariance intersection (ICI)-based data fusion method is added to the update process in the proposed algorithm. To verify the performance of the proposed algorithm, two analyses are performed with respect to the degree of measurement error reduction and accuracy of generated information. In addition, experiments are conducted using the dead reckoning (DR)/global positioning system (GPS) navigation system with a barometric altimeter to confirm the performance of fault tolerance in the altitude. It is confirmed that the proposed algorithm maintains estimation performance when there are not enough valid measurements.

Data Fusion With Inverse Covariance Intersection for Prior Covariance Estimation of the Particle Flow Filter

The prior covariance estimation method based on inverse covariance intersection (ICI) is proposed to apply the particle flow filter. The proposed method has better estimate performance and guarantees consistent estimation results compared with previous works. ICI is the recently developed method of ellipsoidal intersection and is used to get the combined estimate of prior covariance. This method integrates the sample covariance estimate, which is unbiased but usually with high variance, together with a more structured but typically a biased target covariance through fusion gains. For verifying the performance of the proposed algorithm, analysis and simulations are performed. Through the simulations, the results are given to illustrate the consistency and accuracy of the proposed algorithm’s estimation and target tracking performance.

Decentralized data fusion with inverse covariance intersection

In distributed and decentralized state estimation systems, fusion methods are employed to systematically combine multiple estimates of the state into a single, more accurate estimate. An often encountered problem in the fusion process relates to unknown common information that is shared by the estimates to be fused and is responsible for correlations. If the correlation structure is unknown to the fusion method, conservative strategies are typically pursued. As such, the parameterization introduced by the ellipsoidal intersection method has been a novel approach to describe unknown correlations, though suitable values for these parameters with proven consistency have not been identified yet. In this article, an extension of ellipsoidal intersection is proposed that guarantees consistent fusion results in the presence of unknown common information. The bound used by the novel approach corresponds to computing an outer ellipsoidal bound on the intersection of inverse covariance ellipsoids. As a major advantage of this inverse covariance intersection method, fusion results prove to be more accurate than those provided by the well-known covariance intersection method.