State Estimate Covariance Research Articles

A consider unscented particle filter with genetic algorithm for UAV multi-source integrated navigation

The unscented particle filter (UPF) combines the advantages of both the unscented Kalman filter and particle filter (PF) algorithms. However, during the fusion of multi-source information for UAV integrated navigation, the UPF may encounter problems related to measurement biases and particle depletion. These issues can lead to algorithm results that are unsatisfactory or divergent. To address these challenges, a novel approach called the consider unscented particle filter with genetic algorithm (GA-CUPF) is proposed. The GA-CUPF algorithm incorporates covariance and co-covariance of biases into the state estimation covariance through the ‘consider’ method employed by the CUPF, and it should be noted that the biases are not estimated in this process. Moreover, the GA-CUPF algorithm enhances the importance probability density of particles to avoid the degeneracy of PF algorithm and improves particle diversity through the application of selection, crossover, and mutation methods in GA. Simulation results demonstrate that the proposed GA-CUPF algorithm can effectively mitigate the adverse effects of measurement biases and particle depletion that the UPF algorithm faces in the UAV navigation system. Additionally, it significantly improves the accuracy of UAV integrated navigation.

Total Variation-Based Distributed Kalman Filtering for Resiliency Against Byzantines

This article proposes a distributed Kalman filter (DKF) with enhanced robustness against Byzantine adversaries. A Byzantine agent is a legitimate network agent that, unlike an honest agent, manipulates information before sharing it with neighbors to impair the overall system performance. In contrast to the literature, the DKF is modeled as a distributed optimization problem where resiliency against Byzantine agents is accomplished by employing a total variation (TV) penalty term. We utilize a distributed subgradient algorithm to compute the state estimate and error covariance matrix updates of the DKF. Additionally, we prove that the proposed suboptimal solution converges to a neighborhood of the optimal centralized solution of the KF with a bounded radius when Byzantine agents are present. Numerical simulations corroborate the theoretical findings and demonstrate the robustness of the proposed DKF against Byzantine attacks.

Low-cost integrated INS/GNSS using adaptive H∞ Cubature Kalman Filter

AbstractWe proposed an adaptive H-infinity Cubature Kalman Filter (AH∞CKF) to improve the navigation accuracy of a highly manoeuvrable unmanned aerial vehicle (UAV). AH∞CKF fuses the Inertial Navigation System (INS) and Global Navigation Satellite System (GNSS) measurements. Traditional state estimation filters like extended Kalman filters (EKF) and cubature Kalman filters (CKF) assume Gaussian noises. However, their performance degrades for non-Gaussian noises and system uncertainties encountered in real-world applications. Thus, designing filters robust to noise and distribution is crucial. AH∞CKF combines H∞CKF design with an added adaptive factor to adjust the state estimation covariance matrix according to measurements by exploiting the square root method to yield more numerically stable results (SrAH∞CKF). We conducted multiple dynamically rich flight tests to validate our claims using a UAV equipped with a commercially well-known GNSS solution. Results show that the SrAH∞CKF state estimation outperforms EKF and CKF methods on average by 90% in various statistical measures.

Adaptive Fuzzy Logic Strong Tracking Based Load Modeling

The randomness and time variability of power load are the main problems in the load modeling, in which the model error and measurement noise greatly affect the modeling accuracy. In this paper, an adaptive fuzzy logic strong tracking based load modeling method is proposed. The problem of load characteristics and parameter identification of load model is transformed into a real-time tracking of load. The optimal model set is first selected from the initial load model set, and according to the mixing probability, the state estimation and error covariance are mixed as the input of the filter. In order to reduce the model error in the parallel filtering, the strong tracking filter (STF) is constructed based on the orthogonality principle. The adaptive fuzzy logic strong tracking filter is constructed by combining the fuzzy logic with the STF to adjust the covariance matrix of the STF according to the change of measurement noise. Moreover, the weights of each sub model are updated in real-time by the parallel filtering, and the sub models are fused to get a comprehensive load model which can reflect the actual load characteristics. The effectiveness of the method is verified by the simulation of IEEE 39-bus system.

Signaling Equilibria for Dynamic LQG Games With Asymmetric Information

In this article, we consider a finite-horizon dynamic game with two players who observe their types privately and take actions that are publicly observed. Players' types evolve as conditionally independent, controlled linear Gaussian processes, and players incur quadratic instantaneous costs. This forms a dynamic linear quadratic Gaussian game with asymmetric information. We show that under certain conditions, players' strategies that are linear in their private types, together with Gaussian beliefs, form a perfect Bayesian equilibrium (PBE) of the game. This is a signaling equilibrium due to the fact that future beliefs on players' types are affected by the equilibrium strategies. We provide a backward-forward algorithm to find the PBE. Each step of the backward algorithm reduces to solving an algebraic matrix equation for every possible realization of the state estimate covariance matrix. The forward algorithm consists of Kalman filter recursions, where state estimate covariance matrices depend on equilibrium strategies. We provide necessary and sufficient conditions for the existence of the solution of the algebraic matrix equation for scalar actions. Finally, we present numerical examples.

The Optimal Distributed Kalman Filtering Fusion With Linear Equality Constraint

In this paper, the optimal distributed Kalman filtering fusion with linear equality constraint (LEC) is proposed. When the Kalman filter subject to LEC is applied in state estimation of distributed linear dynamic system, all local error covariance matrices are singular, which is a challenge for most of the existing distributed fusion algorithms. However, the new fusion algorithm is rigorously derived with matrix analysis technique on the Moore-Penrose inverse. Updating state estimate and error covariance matrix, the new fusion algorithm only uses local estimates and their corresponding error covariances. We have proved theoretically that the distributed Kalman filtering with LEC (DKF-LEC) just using all local measurements is equivalent to the centralized Kalman filtering with LEC (CKF-LEC), which means it is optimal. Furthermore, we also prove the optimality of the proposed fusion formula for Kalman filtering with LEC and feedback. In addition, the simulation results show that the proposed fusion formula for Kalman filtering with LEC have the same performance of the centralized Kalman filtering with LEC whether considering feedback or not. It is consistent with the theoretical result that the DKF-LEC is equivalent to CKF-LEC as the estimate of CKF-LEC is disassembled into local estimates in distributed system. And the performance of the new fusion formula for Kalman filtering with LEC and feedback is obviously better than those without feedback.

Attitude anti-interference federal filtering algorithm for MEMS-SINS/GPS/magnetometer/SV integrated navigation system

The attitude measurement systems composed of magnetic, angular rate and gravity sensors in the navigation system of an unmanned aerial vehicle are vulnerable to disturbed magnetic field observations. In this paper, an anti-interference integrated navigation federal Kalman filter is designed with fusing the information of microelectromechanical-system-based strapdown inertial navigation system, gravity field, geomagnetic field and solar vector (direction of sun). The filter works in the mode of fusion reset or no reset according to environmental conditions or manual setting. In addition, the characteristic is discovered that disturbed magnetic field observations can interfere with the state estimation covariance matrixes of quaternions, which in turn affect the fusion update of estimated quaternions in no reset mode of the federal filter. In order to eliminate the effect of magnetic field observations on the attitude information of pitch and roll angles, a method of correction update for a yaw angle component in quaternions using the magnetometer is designed, and an Euler angle information fusion method is developed by constructing a pseudo-covariance matrix of Euler angels in fusion update of the filter. Thus, when there exist disturbed magnetic field observations and the filter is in no reset mode, the estimated pitch and roll angles of the main filter after fusion update are not affected, and the yaw angle estimation errors of the main filter decrease relative to the estimation errors of the sub-filter which is corrected by a magnetometer. The effectiveness of the algorithm is illustrated by a numerical simulation and a semi-physical simulation.

Outlier accommodation in moving‐horizon state estimation: A risk‐averse performance‐specified approach

SummaryThis paper presents a novel state estimation approach for linear dynamic systems when measurements are corrupted by outliers. Since outliers can degrade the performance of state estimation, outlier accommodation is critical. The standard approach combines outlier detection utilizing Neyman‐Pearson (NP) type tests with a Kalman filter (KF). This approach ignores all residuals greater than a designer‐specified threshold. When measurements with outliers are used (ie, missed detections), both the state estimate and the error covariance matrix become corrupted. This corrupted state and covariance estimate are then the basis for all subsequent outlier decisions. When valid measurements are rejected (ie, false alarms), potentially using the corrupted state estimate and error covariance, measurement information is lost. Either using invalid information or discarding too much valid information can result in divergence of the KF. An alternative approach is moving‐horizon (MH) state estimation, which maintains all recent measurement data within a moving window with a time horizon of length L. In MH approaches, the number of measurements available for state estimation is affected by both the number of measurements per time step and the number of time steps L over which measurements are retained. Risk‐averse performance‐specified (RAPS) state estimation works within an optimization setting to choose a set of measurements that achieves a performance specification with minimum risk of outlier inclusion. This paper derives and formulates the MH‐RAPS solution for outlier accommodation. The paper also presents implementation results. The MH‐RAPS application uses Global Navigation Satellite Systems measurements to estimate the state of a moving platform using a position, velocity, and acceleration model. In this application, MH‐RAPS performance is compared with MH‐NP state estimation.

Improved converted measurement Kalman filter for satellite‐borne multi‐target tracking

This study introduces a special converted measurement Kalman filter (CMKF) algorithm which apply to satellite for tracking target. Typical CMKF applies to radar which measures targets in spherical coordinate system. The new algorithm can be used by satellite which measures target's latitude and longitude. Improved CMKF algorithm tracks target in simple situation but is not able to deal with multi-target and information missing situation. Multiple hypothesis tracking (MHT) can track multi-target accurately and has the ability to initial track and end track at all times. For satellite, MHT use improved CMKF to calculate cost matrix and update the state estimate and estimate covariance. In the simulation, tracking process is simulated by MATLAB. Single target measured by satellite can be tracked accurately by CMKF algorithm. MHT can track multi-target accurately and distinguish the information missing rightly.

A Stability Analysis Framework for Multiantenna Multisensor Cyber-Physical Systems With Rank-Deficient Measurement Matrices

In this paper, we consider a cyber-physical system, where an unstable dynamic plant is monitored by multiple distributed sensors over a wireless communication network. We propose a systematic stability analysis framework for multisensor cyber-physical systems. The proposed framework provides closed-form characterizations of a stability condition for general measurement matrices with rank-deficient cases covered. Utilizing the observable and unobservable cone decomposition of the coordinate transformed system induced by the singular value decomposition of the measurement matrices, we decompose the conventional Riccati recursion of state estimation covariance. Based on the decomposed recursion, we establish closed-form sufficient requirements on the communication resources needed to achieve stabilization of multisensor cyber-physical systems using the Lyapunov drift analysis approach. The proposed framework is also compared with various representative literature and we show that significant performance gains can be achieved.

Highly computationally efficient state filter based on the delta operator

SummaryThe Kalman filter is not suitable for the state estimation of linear systems with multistate delays, and the extended state vector Kalman filtering algorithm results in heavy computational burden because of the large dimension of the state estimation covariance matrix. Thus, in this paper, we develop a novel state estimation algorithm for enhancing the computational efficiency based on the delta operator. The computation analysis and the simulation example show the performance of the proposed algorithm.

Robust Partially Strong Tracking Extended Consider Kalman Filtering for INS/GNSS Integrated Navigation

Unknown biases or perturbations in the INS/GNSS integrated navigation system may produce unforeseeable negative effects when the navigation states are estimated by using the Kalman filtering and its variants. To mitigate these undesirable effects in the INS/GNSS integrated navigation, a novel partially strong tracking extended consider Kalman filtering (PSTECKF) is proposed. In the presented PSTECKF algorithm, the biases are not estimated, but their covariance and co-covariance are incorporated into the state estimation covariance by using a nonlinear “consider” approach. Based on the above, the PSTECKF also partially introduces an adaptive fading factor into the predicted covariance of the states, which excludes the co-covariance between the states and biases, to compensate the nonlinear approximation errors and navigation system covariance uncertainties. Simulation results demonstrate the performance of the proposed PSTECKF for INS/GNSS integrated navigation is superior to that of the EKF and ECKF when the biases or perturbations happen in a navigation system.

An Improved Strong Tracking Cubature Kalman Filter for GPS/INS Integrated Navigation Systems.

The cubature Kalman filter (CKF) is widely used in the application of GPS/INS integrated navigation systems. However, its performance may decline in accuracy and even diverge in the presence of process uncertainties. To solve the problem, a new algorithm named improved strong tracking seventh-degree spherical simplex-radial cubature Kalman filter (IST-7thSSRCKF) is proposed in this paper. In the proposed algorithm, the effect of process uncertainty is mitigated by using the improved strong tracking Kalman filter technique, in which the hypothesis testing method is adopted to identify the process uncertainty and the prior state estimate covariance in the CKF is further modified online according to the change in vehicle dynamics. In addition, a new seventh-degree spherical simplex-radial rule is employed to further improve the estimation accuracy of the strong tracking cubature Kalman filter. In this way, the proposed comprehensive algorithm integrates the advantage of 7thSSRCKF’s high accuracy and strong tracking filter’s strong robustness against process uncertainties. The GPS/INS integrated navigation problem with significant dynamic model errors is utilized to validate the performance of proposed IST-7thSSRCKF. Results demonstrate that the improved strong tracking cubature Kalman filter can achieve higher accuracy than the existing CKF and ST-CKF, and is more robust for the GPS/INS integrated navigation system.

Discrete-time state estimation for stochastic polynomial systems over polynomial observations

This paper presents a solution to the mean-square state estimation problem for stochastic nonlinear polynomial systems over polynomial observations confused with additive white Gaussian noises. The solution is given in two steps: (a) computing the time-update equations and (b) computing the measurement-update equations for the state estimate and error covariance matrix. A closed form of this filter is obtained by expressing conditional expectations of polynomial terms as functions of the state estimate and error covariance. As a particular case, the mean-square filtering equations are derived for a third-degree polynomial system with second-degree polynomial measurements. Numerical simulations show effectiveness of the proposed filter compared to the extended Kalman filter.

Dynamic input estimation and shape sensing for a nonlinear beam based on distributed fiber bragg grating sensor network

In the area of structural health monitoring, input estimation and shape sensing play an important role. This paper proposes a method to estimate dynamic input and reconstruct dynamic shape at the same time for a nonlinear beam system based on strain measurement by distributed fiber bragg grating(FBG) sensor network. In the process of estimating the magnitude and location of input, shape can be monitored at the same time. For a nonlinear beam system, the proposed method is based on cubature Kalman filter (CKF) and a nonlinear estimator. There are three steps to fulfill task. First, the state equations of structures are constructed and discretized. Second, CKF is used to suppress noise and reconstruct dynamic shape. Finally, the residual innovation sequences, priori state estimate, gain matrix and innovation covariance generated by CKF are used to estimate input. To verify the novel method, experiment of a nonlinear beam is employed and results show that the method has an excellent performance to estimate dynamic input and reconstruct dynamic shape.

A collision-free motion planning method by integrating complexity-reduction SLAM and learning-based artificial force design

Abstract In order to generally deal with the rotor-type UAV’s collision-free motion planning problem in the unknown static environment, we propose a non-holonomic solution via integration of the KF-based SLAM technique and governing force design. The traditional SLAM is modified and reduced as a low-complexity form according to the fact that too early detected obstacle information can be regarded as nearly frozen after sufficient correction. The artificial force terms are designed in a intuitive and smart way, through employment of the wall-following rule and lessons from historical and current experience, which are taught by the bat’s predation process. Further, they are converted to the real-time thrust vector expectation. Multiple simulation tests in both continuous and discrete scenes indicate that: (1) using slight sacrifice on the state estimate covariance can exchange pronounced reduction on structural complexity of the complete SLAM in return; (2) the LBAFD can not only mitigate limitations on the path oscillation, no passage between closely spaced obstacles and goal unreachability, but also lead to a high flying and exploration efficiency; (3) the integrated method demonstrates a relatively stable performance under different parameter settings and is even unconcerned to the surrounding characteristics.

Input Forces Estimation for Nonlinear Systems by Applying a Square-Root Cubature Kalman Filter.

This work presents a novel inverse algorithm to estimate time-varying input forces in nonlinear beam systems. With the system parameters determined, the input forces can be estimated in real-time from dynamic responses, which can be used for structural health monitoring. In the process of input forces estimation, the Runge-Kutta fourth-order algorithm was employed to discretize the state equations; a square-root cubature Kalman filter (SRCKF) was employed to suppress white noise; the residual innovation sequences, a priori state estimate, gain matrix, and innovation covariance generated by SRCKF were employed to estimate the magnitude and location of input forces by using a nonlinear estimator. The nonlinear estimator was based on the least squares method. Numerical simulations of a large deflection beam and an experiment of a linear beam constrained by a nonlinear spring were employed. The results demonstrated accuracy of the nonlinear algorithm.

Mean‐square filtering for polynomial discrete‐time systems with Poisson noises

The discrete-time state estimation problem for a class of stochastic non-linear polynomial systems confused with Poisson noises over linear observations is presented in this study. The filtering problem is solved computing the time-update and measurement-update equations for the state estimate and error covariance matrix. A finite number of filtering equations can be obtained by expressing the conditional expectations of polynomial terms as functions of the estimate and error covariance. The finite-dimensional filtering equations are explicitly derived in a closed form for third degree polynomial systems. Numerical simulations are performed for a third degree polynomial system and the performance of the designed filter is compared to the performances of the filter designed for polynomial systems confused with additive white Gaussian noises and the extended Kalman filter.

MIMO Precoding for Networked Control Systems with Energy Harvesting Sensors

In this paper, we consider a MIMO networked control system with an energy harvesting sensor, where an unstable MIMO dynamic system is connected to a controller via a MIMO fading channel. We focus on the energy harvesting and MIMO precoding design at the sensor so as to stabilize the unstable MIMO dynamic plant subject to the energy availability constraint at the sensor. Using the Lyapunov optimization approach, we propose a closed-form dynamic energy harvesting and dynamic MIMO precoding solution, which has an event-driven control structure. Furthermore, the MIMO precoding solution is shown to have an eigenvalue water-filling structure, where the water level depends on the state estimation covariance, energy queue and the channel state, and the sea bed level depends on the state estimation covariance. The proposed scheme is also compared with various baselines and we show that significant performance gains can be achieved.

A New Method for State of Charge Estimation of Lithium-Ion Battery Based on Strong Tracking Cubature Kalman Filter

The estimation of state of charge (SOC) is a crucial evaluation index in a battery management system (BMS). The value of SOC indicates the remaining capacity of a battery, which provides a good guarantee of safety and reliability of battery operation. It is difficult to get an accurate value of the SOC, being one of the inner states. In this paper, a strong tracking cubature Kalman filter (STCKF) based on the cubature Kalman filter is presented to perform accurate and reliable SOC estimation. The STCKF algorithm can adjust gain matrix online by introducing fading factor to the state estimation covariance matrix. The typical second-order resistor-capacitor model is used as the battery’s equivalent circuit model to dynamically simulate characteristics of the battery. The exponential-function fitting method accomplishes the task of relevant parameters identification. Then, the developed STCKF algorithm has been introduced in detail and verified under different operation current profiles such as Dynamic Stress Test (DST) and New European Driving Cycle (NEDC). Making a comparison with extended Kalman filter (EKF) and CKF algorithm, the experimental results show the merits of the STCKF algorithm in SOC estimation accuracy and robustness.