Analyzing the Unscented Kalman Filter Robustness for Orbit Determination through Global Positioning System Signals

Abstract

The nonlinear unscented Kalman filter (UKF) is evaluated for the satellite orbit determination problem, using Global Positioning System (GPS) measurements. The assessment is based on the robustness of the filter. The main subjects for the evaluation are convergence speed and dynamical model complexity. Such assessment is based on comparing the UKF results with the extended Kalman filter (EKF) results for the solution of the same problem. Based on the analysis of such criteria, the advantages and drawbacks of the implementations are presented. In this orbit determination problem, the focus is to analyze UKF convergence behavior using different sampling rates for the GPS signals, where scattering of measurements will be taken into account. A second aim is to evaluate how the dynamical model complexity affects the performance of the estimators in such adverse situation. After solving the real-time satellite orbit determination problem using actual GPS measurements, through EKF and UKF algorithms, the results obtained are compared in computational terms such as complexity, convergence, and accuracy.

An investigation on cubature Kalman filter performance for orbit determination application

“…The forces model is convenient for implementation in orbit determination because it adds low computational cost, when the gain in the results accuracy is analyzed [15,24]. The pseudo-range vector was corrected to the first order, regarding ionosphere.…”

“…The observation may be collected by ground station networks or space navigation systems, as the GPS. The later provides standard precision around tens of meters, and the (15)…”

“…The variables are placed in the inertial reference frame: is the position vector; , the velocity vector; , the modeled perturbing accelerations (here, only the essential set of perturbations was added, allowing the CKF to be analyzed without any significant loss [24]: geopotential [25]; direct solar radiation pressure [26]; and third-body point mass effect of the Sun and the Moon [27]); w v , the white noise vector, with covariance ; b , the user satellite GPS clock bias; d , the user satellite GPS clock drift; and w d , the noise associated with the GPS clock. The GPS receiver clock offset was beforehand obtained and used to correct the pseudo-ranges, so that these are free from errors derived from receiver clock offset [15].…”

“…Therefore, the main contribution of this paper is to analyze the CKF behavior for the highly nonlinear orbit determination problem, based on the robustness of the filter, concerning convergence speed when the measurements are scattered. The CKF results will be compared to the UKF results [15] for the same problem, in computational terms such as time of convergence and performance. According to these criteria, the advantages and drawbacks of the implementations will be presented.…”

The Particle Filter Sample Impoverishment Problem in the Orbit Determination Application

“…The force model comprises perturbations due to geopotential up to order and degree 50 × 50; direct solar radiation pressure; and Sun-Moon gravitational attraction. This model of forces is suitable for implementation in orbit determination because of the low computational cost added compared to the improvement in the results accuracy [22][23][24]. The pseudorange measurements were corrected to the first order with respect to ionosphere.…”