Kalman filter application to mitigate the errors in the trajectory simulations due to the lunar gravitational model uncertainty

17th Brazilian Colloquium on Orbital Dynamics

Gonçalves, L.D.^1 ; Rocco, E.M.^1 ; De Moraes, R.V.^1,2 ; Kuga, H.K.^1

Instituto Nacional de Pesquisas Espaciais, INPE, São José dos Campos, Brazil^1

Universidade Federal de São Paulo, UNIFESP, São José dos Campos, Brazil^2

关键词: Computational effort;    Filter applications;    Gravitational model;    Gravitational potential;    Spacecraft trajectories;    Spherical harmonics;    Trajectory simulation;    Velocity increments;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/641/1/012029/pdf
DOI  :  10.1088/1742-6596/641/1/012029

来源: IOP

【 摘 要 】

This paper aims to simulate part of the orbital trajectory of Lunar Prospector mission to analyze the relevance of using a Kalman filter to estimate the trajectory. For this study it is considered the disturbance due to the lunar gravitational potential using one of the most recent models, the LP100K model, which is based on spherical harmonics, and considers the maximum degree and order up to the value 100. In order to simplify the expression of the gravitational potential and, consequently, to reduce the computational effort required in the simulation, in some cases, lower values for degree and order are used. Following this aim, it is made an analysis of the inserted error in the simulations when using such values of degree and order to propagate the spacecraft trajectory and control. This analysis was done using the standard deviation that characterizes the uncertainty for each one of the values of the degree and order used in LP100K model for the satellite orbit. With knowledge of the uncertainty of the gravity model adopted, lunar orbital trajectory simulations may be accomplished considering these values of uncertainty. Furthermore, it was also used a Kalman filter, where is considered the sensor's uncertainty that defines the satellite position at each step of the simulation and the uncertainty of the model, by means of the characteristic variance of the truncated gravity model. Thus, this procedure represents an effort to approximate the results obtained using lower values for the degree and order of the spherical harmonics, to the results that would be attained if the maximum accuracy of the model LP100K were adopted. Also a comparison is made between the error in the satellite position in the situation in which the Kalman filter is used and the situation in which the filter is not used. The data for the comparison were obtained from the standard deviation in the velocity increment of the space vehicle.