Quanbo Ge

Performance Analysis of the Kalman Filter With Mismatched Noise Covariances

The Kalman filter is a powerful state estimator and has been successfully applied in many fields. To guarantee the optimality of the Kalman filter, the noise covariances need to be exactly known. However, this is not necessarily true in many practical applications. Usually, they are either completely unknown or at most partially known. In this technical note, we study performance of the Kalman filter with mismatched process and measurement noise covariances. For this purpose, three mean squared errors (MSEs) are used, namely the ideal MSE (IMSE), the filter calculated MSE (FMSE), and the true MSE (TMSE). The main contribution of this work is that the relationships between the three MSEs are disclosed from two points of views. The first view is about their ordering and the second view is about the relative closeness from the FMSE and TMSE to the IMSE. Using the first view, it is found that for the case with positive (definite) deviation from the truth, the FMSE is the worst and the IMSE is the best. And for the case with negative (definite) deviation, the TMSE is the worst and the best is the FMSE. Using the second view, it is found that the TMSE is relatively closer to the IMSE than the FMSE if the deviation is larger than certain threshold, and the TMSE will be farther away otherwise. Numerical examples further verify these conclusions.

Multisensor Nonlinear Fusion Methods Based on Adaptive Ensemble Fifth-Degree Iterated Cubature Information Filter for Biomechatronics

Performance of the Kalman filter (KF) is degraded when dealing with nonlinear dynamic systems. For a kind of nonlinear biomechatronics system, a fifth-degree ensemble iterated cubature square-root information filter (EsFICIF), which can effectively improve estimation performance, is proposed by combing many estimation schemes. Moreover, the associated multisensor fusion is deeply studied based on this proposed nonlinear filter in this paper. That is, four classic nonlinear fusion methods, which include augmented measurements fusion, weighted measurements fusion, sequential filtering fusion, and distributed filtering fusion, are compared on estimation performance. The motivation of this paper is to extend the work on estimation performance comparison of nonlinear fusion methods based on the conventional extended KF and to validate some basic conclusions existed in the traditional linear data fusion theory based on the proposed EsFICIF. The estimation accuracies of the four nonlinear fusion methods are compared and the exchanging property of measurements update order is also discussed. It is observed that, when the measurement properties are identical, the estimation accuracies of augmented measurements fusion, weighted measurements fusion, and distributed feedback fusion are equivalent, while the sequential filtering fusion does not hold. Furthermore, the exchanging property of the measurements update order of the sequential filtering fusion can no longer be guaranteed. These results further show some basic conclusions existed in linear fusion theory are no longer valid for nonlinear systems and the conclusions based on the EKF are still available for more complex nonlinear filters. Finally, numerical examples are provided to validate the results given in this paper.

Dynamic Balance Optimization and Control of Quadruped Robot Systems With Flexible Joints

This paper investigates dynamic balance optimization and control of quadruped robots with compliant/flexible joints under perturbing external forces. First, we formulate a constrained dynamic model of compliant/flexible joints for quadruped robots and a reduced-order dynamic model is developed considering the robot interaction with the environment through multiple contacts. A dynamic force distribution approach based on quadratic objective function is proposed for evaluating the optimal contact forces to cope with the external wrench, and fuzzy-based adaptive control of compliant/flexible joints for quadruped robots is proposed to suppress uncertainties in the dynamics of the robot and actuators. The dynamic surface control approaches and fuzzy learning algorithms are combined in the proposed framework. All the signals of the closed-loop system have proven to be uniformly ultimately bounded through Lyapunov synthesis. Simulation experiments were performed for a quadruped robot with compliant/flexible joints. The benefits of its tracking accuracy and robustness indicate that the proposed framework is promising for the robots with payload uncertainties and external disturbances.

Analysis on Strong Tracking Filtering for Linear Dynamic Systems

Strong tracking filtering (STF) is a popular adaptive estimation method to effectively deal with state estimation for linear and nonlinear dynamic systems with inaccurate models or sudden change of state. The key of the STF is to use a time-variant fading factor, which can be evaluated based on the current measurement innovation in real time, to forcefully correct one step state prediction error covariance. The strong tracking filtering technology has been extensively applied in many practical systems, but the theoretical analysis is highly lacking. In an effort to better understand STF, a novel analysis framework is developed for the strong tracking filtering and some new problems are discussed for the first time. For this, we propose a new perspective that correcting the state prediction error covariance by using the fading factor can be thought of directly modifying the state model by correcting the covariance of the process noise. Based on this proposed point of view, the conditions for the STF function to be effective are deeply analyzed in a certain linear dynamic system. Meanwhile, issues of false alarm and alarm failure are also briefly discussed for the strong tracking filtering function. Some numerical simulation examples are demonstrated to validate the results.

Adaptive Cubature Strong Tracking Information Filter Using Variational Bayesian Method

Abstract For most practical nonlinear state estimation problems, the conventional nonlinear filters do not usually work well for some cases, such as inaccurate system model, sudden change of state-interested and unknown variance of measurement noise. In this paper, an adaptive cubature strong tracking information filter using variational Bayesian (VB) method is proposed to cope with these complex cases. Firstly, the strong tracking filtering (STF) technology is used to integrally improve performance of cubature information filter (CIF) aiming at the first two cases and an iterative scheme is presented to effectively evaluate a strong tracking fading factor. Secondly, the VB method is introduced to iteratively evaluate the unknown variance of measurement noise. Finally, the novel adaptive cubature information filter is obtained by perfectly combining the STF technology with the VB method, where the variance estimation provided by the VB method guarantees normal running of the strong tracking functionality.

Flexible Fusion Structure-Based Performance Optimization Learning for Multisensor Target Tracking

Compared with the fixed fusion structure, the flexible fusion structure with mixed fusion methods has better adjustment performance for the complex air task network systems, and it can effectively help the system to achieve the goal under the given constraints. Because of the time-varying situation of the task network system induced by moving nodes and non-cooperative target, and limitations such as communication bandwidth and measurement distance, it is necessary to dynamically adjust the system fusion structure including sensors and fusion methods in a given adjustment period. Aiming at this, this paper studies the design of a flexible fusion algorithm by using an optimization learning technology. The purpose is to dynamically determine the sensors’ numbers and the associated sensors to take part in the centralized and distributed fusion processes, respectively, herein termed sensor subsets selection. Firstly, two system performance indexes are introduced. Especially, the survivability index is presented and defined. Secondly, based on the two indexes and considering other conditions such as communication bandwidth and measurement distance, optimization models for both single target tracking and multi-target tracking are established. Correspondingly, solution steps are given for the two optimization models in detail. Simulation examples are demonstrated to validate the proposed algorithms.

Cubature Kalman Fusion For Bearings-Only Tracking Networks

Abstract In this paper, we study the nonlinear data fusion problem for a kind of Bearings-only tracking network system with correlations among measurement noises. As a result, a decentralized cubature Kalman fusion algorithm is proposed by using an information filtering form (CIF) of cubature Kalman filter (CKF) and a noise de-correlation way. Based on the CIF and an augmented measurement, a centralized cubature Kalman fusion algorithm is firstly established and a problem on computational performance is pointed out. In order to improve computational performance of the centralized fusion method, the noise de-correlation technology is used to obtain a functionally equivalent Bearings-only tracking fusion system without the noise correlations, namely the variance of an augmented measurement noise is diagonalized. Accordingly, the proposed decentralized fusion method based on the CIF can be used to achieve a more effective tracking fusion estimate.

Flexible Fusion Structure for Air Task Networks

For the UAV(unmanned aerial vehicle) air task networks, a new kind of flexible fusion structure method is proposed to improve the flexibility of data processing of the target tracking fusion system in this paper. When the system performance parameters are affected by the internal or external causes to be changed, this flexible structure method can auto-adjust the allocation of system resources to achieve the optimal results of target tracking task. Firstly, the performance evaluation of the target tracking system is analyzed. Secondly, the advantages of the new method and the applying process of it are explained. And finally, based on the models of system resources, such as sensors, data communication bandwidth and system processors, we compare the advantages and disadvantages of the flexible fusion structure with that of the fixed fusion structure. Some analytical results show that the flexible fusion structure is efficient.

Adaptive Quantized Estimation Fusion Using Strong Tracking Filtering and Variational Bayesian

In this paper, adaptive quantized state estimation fusion is deeply studied. To approach the model mismatching problem induced by random quantization, some quantized Kalman filters have been presented in the previous work, such as the quantized Kalman filter with strong tracking filtering (QKF-STF), the variational Bayesian adaptive quantized Kalman filter (VB-AQKF), and a centralized fusion frame-based complex quantized filter called variational Bayesian adaptive QKF-STF (VB-AQKF-STF). Based on the previous work for the single sensor system, a distributed complex quantized filter is designed in this paper. A novel quantized Kalman filter based on multiple-method fusion scheme (QKF-MMF) is proposed. Similar to the VB-AQKF-STF, the QKF-MMF can also realize joint estimation on the state and the quantization error covariance under the distributed fusion frame. Furthermore, it extends the single sensor results to multisensor tracking systems by using centralized and distributed fusion frames. Two multisensor quantized fusion estimators are proposed for a parallel structure with main-secondary processors in the fusion center. The weighted fusion and embedded integration ways are deeply applied to design the multisensor quantized fusion methods. The proposed work can perfect the quantized estimation algorithms and provide different choices for practical engineering applications.