Effect of PDOP on Performance of Kalman Filters for GNSS-Based Space Vehicle Position Estimation

Abstract

A theoretical performance analysis of Kalman Filters for Global Navigation Satellite System GNSS-based space vehicle position estimation in varying Position Dilution of Precision (PDOP) conditions is presented. The PDOP indicates the possible accuracy of GNSS measurements using Least Square Estimation (LSE). The Kalman Filter combines the knowledge of the vehicle motion with the GNSS measurements and then provides better accuracy than the LSE. For the same nonlinear vehicular motion and PDOP condition, the ratio of average position error and noise standard deviation varies depending on the type of Kalman Filter used. The presented theoretical analysis explains and characterizes this behavior for four Kalman Filters, which are the Extended Kalman Filter (EKF), the Unscented Kalman Filter (UKF) and two newly developed Unscented Type Kalman Filters. The experiment shows that for highly nonlinear space vehicle motion, the performance of the UKF is better than the EKF in high PDOP conditions and all the filters perform similarly for low PDOP conditions. For a space vehicle with lower nonlinearity in the motion, the performances of all the filters are indistinguishable for any PDOP condition.

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GPS Solutions
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