Dah-Jing Jwo

Adaptive Fuzzy Strong Tracking Extended Kalman Filtering for GPS Navigation

The well-known extended Kalman filter (EKF) has been widely applied to the Global Positioning System (GPS) navigation processing. The adaptive algorithm has been one of the approaches to prevent the divergence problem of the EKF when precise knowledge on the system models are not available. One of the adaptive methods is called the strong tracking Kalman filter (STKF), which is essentially a nonlinear smoother algorithm that employs suboptimal multiple fading factors, in which the softening factors are involved. Traditional approach for selecting the softening factors heavily relies on personal experience or computer simulation. In order to resolve this shortcoming, a novel scheme called the adaptive fuzzy strong tracking Kalman filter (AFSTKF) is carried out. In the AFSTKF, the fuzzy logic reasoning system based on the Takagi-Sugeno (T-S) model is incorporated into the STKF. By monitoring the degree of divergence (DOD) parameters based on the innovation information, the fuzzy logic adaptive system (FLAS) is designed for dynamically adjusting the softening factor according to the change in vehicle dynamics. GPS navigation processing using the AFSTKF will be simulated to validate the effectiveness of the proposed strategy. The performance of the proposed scheme will be assessed and compared with those of conventional EKF and STKF

A practical note on evaluating Kalman filter performance optimality and degradation

This paper presents useful remarks to the readers on the Kalman filter (KF) performance optimality, degradation, and some innovation related parameters. Guidelines for efficient approach for evaluation of the KF performance optimality and sensitivity analysis are presented. Performance degradation due to uncertainty in process and measurement noise statistics is discussed. Consistency check between the filter-calculated covariances versus actual mean square errors are provided, which can be used not only as a verification procedure for the filtering correctness, but also as a approach for making trade-off in designing a suitable Kalman filter. In addition to numerical algorithms, useful Matlab programs are accompanied where necessary to the readers for getting better insight in practical implementation. Exploration of the behaviour of some innovation based parameters useful in adaptive filter and system integrity designs, including covariance of innovation sequence, degree of mismatch (DOM), and degree of divergence (DOD), etc., is also involved.

Navigation Integration Using the Fuzzy Strong Tracking Unscented Kalman Filter

A navigation integration processing scheme, called the strong tracking unscented Kalman filter (STUKF), is based on the combination of an unscented Kalman filter (UKF) and a strong tracking filter (STF). The UKF employs a set of sigma points by deterministic sampling, such that the linearization process is not necessary, and therefore the error caused by linearization as in the traditional extended Kalman filter (EKF) can be avoided. As a type of adaptive filter, the STF is essentially a nonlinear smoother algorithm that employs suboptimal multiple fading factors, in which the softening factors are involved. In order to resolve the shortcoming in traditional approach for selecting the softening factor through personal experience or computer simulation, a novel scheme called the fuzzy strong tracking unscented Kalman filter (FSTUKF) is presented where the Fuzzy Logic Adaptive System (FLAS) is incorporated for determining the softening factor. The proposed FSTUKF algorithm shows promising results in estimation accuracy when applied to the integrated navigation system design, as compared to the EKF, UKF and STUKF approaches.

Applying back-propagation neural networks to GDOP approximation

In this paper, back-propagation (BP) neural networks (NN) are applied to the GPS satellite Geometric Dilution of Precision (GDOP) approximation. The methods using BPNN are general enough to be applicable regardless of the number of satellite signals being processed by the receiver. BPNN is employed to learn the functional relationships firstly, between the entries of a measurement matrix and the eigenvalues and thus generate GDOP, and secondly, between the entries of a measurement matrix and the GDOP, both without inverting a matrix. Consequently, two sets of entries and two sets of output variables, respectively, are used that in total yield four types of mapping architectures. Simulation results from these four architectures are presented. The performance and computational benefit of neural network-based GDOP approximation are explored. . 1. I NTRODUCTION. The navigation accuracy of GPS is normally determined by two causes: the errors in each signal observable, and the geometry formed by the observables employed for positioning or navigation. The GPS measurements are normally corrupted by several error sources, such as ionospheric delay, tropospheric delay, satellite clock and receiver clock osets, receiver noise and multi-path. The Geometric Dilution of Precision, usually referred to as the GDOP, is a geometrically determined factor that describes the eect of geometry on the relationship between measurement error and position determination error. It is used to provide an indication of the quality of the solution. Some receiver hardware may be restricted to processing a limited number of visible satellites. Therefore, it is sometimes necessary to select the satellite subset that oers the best or most acceptable solution. The optimal satellite subset is usually chosen by minimizing the GDOP. Neural networks are trainable, dynamic systems that can estimate input-output functions. They have been applied to a wide variety of problems because they are model-free estimators, i.e. without a mathematical model. The back-propagation neural network (BPNN) has been the most popular learning algorithm throughout all neural applications. BPNN is a neural system with a back-propagation algorithm that can learn input-output functions from a series of samples. It is a gradient-based algorithm, in the sense that the weight update is performed along the direction of the gradient of an appropriate error function. The BPNN is simple and requires a minimal amount of storage.

Neural Network Aided Adaptive Extended Kalman Filtering Approach for DGPS Positioning

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.

ARMA Neural Networks for Predicting DGPS Pseudorange Correction

In this paper, the Auto-Regressive Moving-Averaging (ARMA) neural networks (NNs) will be incorporated for predicting the differential Global Positioning System (DGPS) pseudorange correction (PRC) information. The neural network is employed to realize the time-varying ARMA implementation. Online training for real-time prediction of the PRC enhances the continuity of service on the differential correction signals and therefore improves the positioning accuracy. When the PRC signal is lost, the ARMA neural network predicted PRC would temporarily provide correction data with very good accuracy. Simulation is conducted for evaluating the ARMA NN based DGPS PRC prediction accuracy. A comparative performance study based on two types of ARMA neural networks, i.e. Back-propagation Neural Network (BPNN) and General Regression Neural Network (GRNN), will be provided.

Fuzzy Adaptive Unscented Kalman Filter for Ultra-Tight GPS/INS Integration

This paper presents a sensor fusion method based on the combination of adaptive unscented Kalman filter (UKF) and Fuzzy Logic Adaptive System (FLAS) for the ultra-tightly coupled GPS/INS integrated navigation. The UKF employs a set of sigma points by deterministic sampling, such that the linearization process is not necessary, and therefore the error caused by linearization as in the traditional extended Kalman filter (EKF) can be avoided. The adaptive algorithm has been one of the approaches to prevent divergence problem of the filter when precise knowledge on the system models are not available. Through the use of fuzzy logic, the FLAS has been incorporated into the AUKF as a mechanism for timely detecting the dynamical changes and implementing the on-line tuning of the factors in the weighted covariance matrices by monitoring the innovation information so as to maintain good estimation accuracy and tracking capability. The performance assessment for UKF and FUKF are carried out.

Particle swarm optimization for GPS navigation Kalman filter adaptation

Purpose – The purpose of this paper is to conduct the particle swarm optimization (PSO)‐assisted adaptive Kalman filter (AKF) for global positioning systems (GPS) navigation processing. Performance evaluation for the PSO‐assisted Kalman filter (KF) as compared to the conventional KF is provided.Design/methodology/approach – The position‐velocity also knows as constant velocity process model can be applied to the GPS KF adequately when navigating a vehicle with constant speed. However, when an abrupt acceleration motion occurs, the filtering solution becomes very poor or even diverges. To avoid the limitation of the KF, the PSO can be incorporated into the filtering mechanism as dynamic model corrector. The PSO is utilized as the noise‐adaptive mechanism to tune the covariance matrix of process noise and overcome the deficiency of KF. In other words, PSO‐assisted KF approach is employed for tuning the covariance of the GPS KF so as to reduce the estimation error during substantial maneuvering.Findings – Th...

Fuzzy adaptive interacting multiple model unscented Kalman filter for integrated navigation

In this paper, application of fuzzy interacting multiple model unscented Kalman filter (FUZZY-IMMUKF) approach to integrated navigation processing for maneuvering vehicle is presented. The unscented Kalman filter (UKF) employs a set of sigma points through deterministic sampling, such that the linearization process is not necessary, and therefore the error caused by linearization as in the traditional extended Kalman filter (EKF) can be avoided. Fuzzy logic adaptive system (FLAS) is employed to determine the lower and upper bounds of the system noise through fuzzy inference system (FIS). The use of interacting multiple model (IMM), which describes a set of switching models, finally provides the suitable value of process noise covariance. Consequently, the resulting sensor fusion strategy can efficiently deal with the nonlinear problem in vehicle navigation. The proposed FUZZY-IMMUKF algorithm shows significant improvement in navigation estimation accuracy as compared to the UKF and interacting multiple model unscented Kalman filter (IMMUKF) approaches.

Efficient DOP calculation for GPS with and without altimeter aiding

Geometric Dilution Of Precision (GDOP) is a factor that describes the effect of geometry on the relationship between measurement error and position determination error. It is used to provide an indication of the quality of the solution. Conventional closed-form GDOP calculation formula applied to all possible combinations of visible satellites is rather time consuming, especially as the number of satellites grows. Approximations, such as the maximum volume method, are faster but optimum selection is not guaranteed. In this paper, a more concise but efficient solution for the calculation of GDOP value in the case of four Global Positioning System (GPS) satellites is firstly reviewed and then extended to cover the other forms of dilution of precision (DOP) values, including vertical DOP (VDOP) and horizontal DOP (HDOP). Secondly, a review and extension of the conventional solution is performed in the case of three GPS satellites aided by an altimeter. Based on the ideas gained from these two approaches, a simpler closed-form DOP formula for three GPS satellites aided by an altimeter is derived. The advantage of the proposed formulation is that it is simpler and thus reduces the computational load in comparison to the conventional one.