Unscented Kalman Filter based RAIM for GNSS Receivers FDE
Bocheng Zhu, Fanchen Meng, Peking University, China
Location: Grand Ballroom G
With the extensive application and popularization of GPS, it makes remarkable contributions to scientific applications and engineering services. Currently, two emerging constellations (BDS, Galileo) as well as the recovery of GLONASS, the multi-constellation GNSS is undergoing dramatic development with better performance. Once all four systems are fully deployed, about 120 satellites will be available for GNSS users. If all the visible satellites are used for position resolving, it will burden the receiver processor significantly. Satellite selection plays a crucial role in decreasing computational complexity for receivers with limited processing units and enhancing positioning accuracy by optimal satellite geometric distribution. The objective of this research is to improve GNSS accuracy, availability and reliability in multi-constellation. Reliability enhancement usually depends on statistical tests for receiver autonomous integrity monitoring (RAIM) and fault detection and exclusion (FDE) in order to detect and exclude erroneous outliers. It is here extended by fast satellite selection algorithm and RAIM for GNSS performance enhancement in multi-constellation. In addition, the method combining satellite selection and RAIM has not appeared in existing literatures and provides a new way for modern navigation in multi-constellation.
The technology of data fusion is rapidly evolving in multi-constellation. The most mature technique used in data fusion is the Kalman Filter (KF), which is a stochastic estimator that is typically used to solve various estimation problems and that is applied to a linear process. Various approximations have been developed for KF, such as Extended Kalman Filter (EKF), which is based on a first-order linearization of the nonlinear stochastic system models with the assumption of Gaussian distributed noises, to overcome the nonlinear filtering problems in multi-constellation. While the EKF might suffer from the performance degradation and divergence problem due to the linearization process. If the filter is ill-conditioned due to modeling error, incorrect tuning of the covariance matrices, or initialization, and the subsequent estimation error will affect the linearization error. In turn, the latter will affect the estimation process and is known as a filter divergence. The technology of data fusion adopted by EKF might suffer from the performance degradation and divergence problem due to the linearization process. In order to solve above concerns, the model of orthogonal triangular decomposition of augmented unscented Kalman filter (AUKF) is employed for data fusion to avoid the issues linked with modeling error and noise uncertainties. The AUKF is used to address nonlinear state estimation in the context of control theory. In various circumstances where there are uncertainties in the system model and noise description, and the assumptions on the statistics of disturbances are violated since in numerous practical situations, the availability of a precisely known model is unrealistic due to the fact that in the modelling step, some phenomena are disregarded and a way to take them into account is to consider a nominal model affected by uncertainty. The advantage of this filtering approach is that no assumptions are made regarding the statistical proprieties of the disturbance, and the filter is designed to minimize the estimation error due to the worst-case estimation error rather than the covariance of the estimation error. When undergoing data filter, we could ensure the non-negative qualitative of state covariance matrix and improve the numerical stability of filtering and not increase the amount of filter calculation by AUKF simultaneously. Moreover, when dealing with parameter estimation, we could greatly reduce the amount of computational complexity with the insurance of high accuracy and reliability.
In this paper, we concentrate on dealing with multi-outliers in multi-constellation. Moreover, the proposed method is also suitable for single constellation with one or more outliers. We innovatively combine fast satellite selection and RAIM for GNSS reliability enhancement, including rejection of possible outliers and selecting satellites with quasi-optimal geometric distribution, especially treating for the special cases of GEO/IGSO satellite in BDS. At the same time, we make full use of data fusion superiorities of AUKF for smoothing and performance guaranteeing. The availability of RAIM is also introduced in case the influence of bad geometric distribution. Global and local test monitoring will be achieved after fast satellite selection for FDE. In summary, we can achieve fairly good performance in modern navigation combining fast satellite selection and RAIM by AUKF.
Satellite selection, i.e., selecting a subset from all visible satellites, is a vital solution to improve positioning accuracy and lessen receiver computational complexity, especially for those with limited processing capability. Traditional optimal satellite selection algorithm is full of complexity with respect to matrix inversion directly and numerous period calculations, which restricts the implementation of real-time positioning significantly. We propose a new fast satellite selection algorithm for multi-constellation, which is based on both Newton’s identities for Geometric Dilution of Precision (GDOP) fast computation and optimal satellite geometric distribution for less cycle calculation. Meantime, special situation of GEO and IGSO in BDS is considered compared with other main systems, i.e., GPS, GLONASS and Galileo. An effective closed-form formula is used for GDOP approximation, avoiding conventional matrix inversion. Meantime, we reduce computational cycles with auxiliary optimal satellite geometric distribution, which also considers the special cases of GEO/IGSO in BDS. What we have to be observant is that BDS is different from GPS for the high orbit satellite of GEO and IGSO with low angular velocity, which aims to the enhancement of navigation and positioning in the Asia-Pacific region, and GPS is mainly composed by MEO. Concerning the fact that the GEO/IGSO of BDS are high orbit satellite with low angular velocity, especially for the GEO who has lower angular velocity, has influence on the structure of the positioning model. The detailed expression of GEO/IGSO/MEO for positioning is given with extra analysis of Dilution of Precision (DOP). In addition, fast satellite selection algorithm also lays foundation for RAIM, contributing to false detection and exclusion (FDE) deeply.
With respect to RAIM, we use the Protection Level (PL) to determine the availability of receivers. The PL is a function involving satellite geometry, the Minimum Detectable Bias (MDB), which is derived from the probability of missed detection, the threshold for failure detection and statistical hypothesis about measurements such as error distribution and one-sigma thermal noise. The probability of false alert is used to determine the threshold of residual weighted sum of squared errors (WSSE). This threshold combining with the probability of missed detection is used to determine MDB. The Horizontal Protection Level (HPL) is then deduced by projecting the detectable error from the measurement domain to the position domain by the geometry factor. Generally, WSSE presents a chi-square distribution when there are no outliers and the measurement errors are Gaussian random variable (GRV). Otherwise, WSSE is a noncentrality chi-square distribution with the noncentrality parameters lambda consisting of weighted matrix and residual vector.
The novelty in this paper is that we can improve positioning accuracy and lessen receiver computational complexity by fast satellite selection, depending on both Newton’s identities and optimal satellite geometric distribution, especially treating for the special cases of GEO/IGSO satellite in BDS. In addition, we are able to implement robust data fusion by AUKF with numerical stability of filtering. More available and reliable navigation will be achieved by FDE in RAIM, according to global monitoring and local monitoring in conjunction with fast satellite selection. The simulation results demonstrate that satellite selection, AUKF and RAIM yield a significant enhancement in GNSS accuracy, availability, continuity and reliability, which reveals good potential as alternative navigation techniques in modern multi-constellation.