Abstract
Global Navigation Satellite System (GNSS) can be applied for the navigation of the high-orbit satellites. The system observability will change due to the changes in the visible satellite numbers and the spatial geometry between the navigation satellites and the users in the navigation system. The influence of the observability changing is not considered in the traditional navigation filter algorithm. In this paper, an optimized navigation filter method based on observability analysis is proposed. Firstly, a novel criterion for the relative observable degree is proposed for each observation component by making use of observation data from previous and posterior time simultaneously. Secondly, according to the relationship between observability and navigation filter accuracy, a novel optimized navigation filter method is constructed by introducing an adjusting factor based on the relative observable degree. Through the comparative simulations with the traditional Extended Kalman Filter (EKF), the optimized navigation filter method can reduce the estimation error of position and velocity by about 36% and 44% respectively. Therefore, the superiority of the proposed filter optimization algorithm is verified.
Highlights
High-orbit satellites [1] have better performance for ground coverage, safety, and stability compared with low-orbit and medium-orbit ones
We propose a new method for calculating the observable degree of a high-orbit satellite navigation system based on Global Navigation Satellite System (GNSS), which can simultaneously give the relative observability of each state component at each moment and the overall observability of the system; We design an adaptive optimization method of navigation filter based on this observable degree, which maps the observable degree of the state component to a feedback weighting factor to improve the performance of the navigation filter; Based on the GNSS navigation system, we combine the proposed observability calculation method as an adjustment factor of the adaptive filter for filter optimization
In the navigation system of high-orbit satellite based on GNSS, the observation is the pseudo-range measurement between the navigation satellites and the user satellite, and the measurement equation is as follows: ρ j = d j + v j, j = 1, 2
Summary
High-orbit satellites [1] have better performance for ground coverage, safety, and stability compared with low-orbit and medium-orbit ones. Reference [22] defined a method which analyzes the observable degree according to the error attenuation degree of the initial state variables, but the method paid much attention to the initial error covariance and ignored the real-time performance of filter; besides, some studies proposed to use the Fisher information matrix are used to measure the observability of the navigation system in some studies [23,24,25]. It is of great significance to optimize the existing navigation filter algorithm and improve the overall performance of the navigation system of high-orbit satellites based on GNSS with the observability and the observable degree of the navigation system.
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