A Novel Fifth-Degree Cubature Kalman Filter for Real-Time Orbit Determination by Radar

Zhaoming Li,Dan Ding,Yurong Liao,Wenge Yang

doi:10.1155/2017/8526804

Abstract

A novel fifth-degree cubature Kalman filter is proposed to improve the accuracy of real-time orbit determination by ground-based radar. A fully symmetric cubature rule, approaching the Gaussian weighted integral of a nonlinear function in general form, is introduced, and the specific points and weights are calculated by matching the monomials of degree not greater than five with the exact values. On the basis of the above rule, a novel fifth-degree cubature Kalman filter, which can achieve a higher accuracy than UKF and CKF, is derived under the Bayesian filtering framework. Then, to describe the nonlinear system more accurately, the orbital dynamics equation with J2 perturbation is used as the state equation, and the nonlinear relationship between the radar measurement elements and orbital states is built as the measurement equation. The simulation results show that, compared with the traditional third-degree algorithm, the proposed fifth-degree algorithm has a higher accuracy of orbit determination.

Highlights

With the increasing number of satellites launched into orbit every year, the monitoring and cataloguing of satellites play an important role in improving the rate of utilisation of space resources and alleviating the pressure on orbit resources
A novel fifth-degree cubature Kalman filter is proposed to improve the accuracy of real-time orbit determination by ground-based radar
As a type of sensor in space surveillance systems, groundbased radar is equipped without considering the influence of the weather and other special circumstances, and the use of its measurement data for real-time orbit determination is a key technology in space target tracking [1, 2]

Summary

Introduction

With the increasing number of satellites launched into orbit every year, the monitoring and cataloguing of satellites play an important role in improving the rate of utilisation of space resources and alleviating the pressure on orbit resources. The aforementioned methods tend to be restricted when the system has strong nonlinearity with high dimensionality For the latter, the Gaussian pdf is approximated using the deterministic sampling approach, which mainly includes the unscented transform (UT) and spherical-radial rule (SRR). The unscented Kalman filter (UKF) [10, 11] and cubature Kalman filter (CKF) [12,13,14] are obtained by embedding UT and SRR into the Bayesian filtering framework, respectively, these have a wide range of applications in engineering [15,16,17,18,19,20], but these two types of algorithm have only third-degree filtering accuracy, which is required to be further improved. The proposed filtering method, which can achieve a higher accuracy compared to that with UKF and CKF, is deduced by embedding the novel fifthdegree cubature rule into the Bayesian filtering framework.

The Traditional Cubature Kalman Filter

Fifth-Degree Cubature Rule and Cubature Filtering Algorithm

Mathematical Model for Orbit Determination

The Numerical Experiment

Conclusion