State-of-charge estimation of lead-acid batteries using an adaptive extended Kalman filter

Constraints can provide additional aids to a multi-sensor integrated navigation system and hence can increase accuracy of the solution and enhance reliability of the system. To integrate the constraints with the data from the sensors, the traditional integration Kalman filter (IKF) needs to be reconstructed. A new algorithm, the so-called constrained adaptive robust integration Kalman filter (CARIKF) is presented, which implements adaptive integration upon the robust direct fusion solution. In the algorithm the raw observations from all heterogeneous sensors are corrected by the pseudoobservations derived from state equality constraint. The posterior covariances of the corrected observations are subsequently estimated upon the robust maximum-likelihood-type estimation (M-estimation) theory. The fusion state and its covariance are solved for all sensors further in the least squares (LS) sense. The pseudoobservations are constructed according to the estimated state and its covariance. They are further combined with the dynamic model of the host platform in an adaptive Kalman filter (AKF), from which a reliable and accurate navigation solution can be then obtained. A state constraint model is proposed upon Newton's forward differential extrapolation numerical method. To demonstrate performance of the CARIKF algorithm, simulations have been conducted in different dynamic and observation scenarios. Several algorithms are compared to evaluate the validity and efficiency of the CARIKF. The results show that the CARIKF is superior to other algorithms and can significantly improve the precision and reliability of the integrated solution.

Equality Constrained Robust Measurement Fusion for Adaptive Kalman-Filter-Based Heterogeneous Multi-Sensor Navigation

Radial basis function neural network aided adaptive extended Kalman filter for spacecraft relative navigation

Integration of Global Positioning System (GPS) and Inertial Navigation System (INS) technologies can overcome the drawbacks of the individual systems. One of the advantages is that the integrated solution can provide continuous navigation capability even during GPS outages. However, bridging the GPS outages is still a challenge when Micro-ElectroMechanical System (MEMS) inertial sensors are used. Methods being currently explored by the research community include applying vehicle motion constraints, optimal smoother, and artificial intelligence (AI) techniques. In the research area of AI, the neural network (NN) approach has been extensively utilised up to the present. In an NN-based integrated system, a Kalman filter (KF) estimates position, velocity and attitude errors, as well as the inertial sensor errors, to output navigation solutions while GPS signals are available. At the same time, an NN is trained to map the vehicle dynamics with corresponding KF states, and to correct INS measurements when GPS measurements are unavailable. To achieve good performance it is critical to select suitable quality and an optimal number of samples for the NN. This is sometimes too rigorous a requirement which limits real world application of NN-based methods. The support vector machine (SVM) approach is based on the structural risk minimisation principle, instead of the minimised empirical error principle that is commonly implemented in an NN. The SVM can avoid local minimisation and over-fitting problems in an NN, and therefore potentially can achieve a higher level of global performance. This paper focuses on the least squares support vector machine (LS-SVM), which can solve highly nonlinear and noisy black-box modelling problems. This paper explores the application of the LS-SVM to aid the GPS/INS integrated system, especially during GPS outages. The paper describes the principles of the LS-SVM and of the KF hybrid method, and introduces the LS-SVM regression algorithm. Field test data is processed to evaluate the performance of the proposed approach.

Novel Hybrid of LS-SVM and Kalman Filter for GPS/INS Integration

A Comparison of Extended Kalman Filter, Sigma-Point Kalman Filter, and Particle Filter in GPS/INS Sensor Fusion

The extended Kalman filter, when employed in the GPS receiver as the navigation state estimator, provides optimal solutions if the noise statistics for the measurement and system are completely known. In practice, the noise varies with time, which results in performance degradation. The covariance matching method is a conventional adaptive approach for estimation of noise covariance matrices. The technique attempts to make the actual filter residuals consistent with their theoretical covariance. However, this innovation-based adaptive estimation shows very noisy results if the window size is small. To resolve the problem, a multilayered neural network is trained to identify the measurement noise covariance matrix, in which the back-propagation algorithm is employed to iteratively adjust the link weights using the steepest descent technique. Numerical simulations show that based on the proposed approach the adaptation performance is substantially enhanced and the positioning accuracy is substantially improved.

Neural Network Aided Adaptive Extended Kalman Filtering Approach for DGPS Positioning

GPS navigation state processing using the extended Kalman filter provides optimal solutions (in the mean square sense) if the noise statistics for the measurement and system are completely known. Covariance matching method is a conventional adaptive approach for estimation of noise covariance matrices. This innovation-based adaptive estimation shows noisy result if the window size is small. To overcome the problem, the fuzzy method combined with NN to identify the noise covariance matrix is proposed. The structure of FNN can automatically identify the fuzzy rules and tune the membership functions by modifying the connection weights of the network using back-propagation algorithm. Numerical simulations show that the adaptation accuracy based on the proposed approach is substantially improved.

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Hung-Chih Huang

Papers

Neural Network Aided Adaptive Extended Kalman Filtering Approach for DGPS Positioning

GPS Navigation Using Fuzzy Neural Network Aided Adaptive Extended Kalman Filter

Fuzzy neural network aided adaptive Kalman filtering for GPS navigation