This paper introduces a novel methodology for robust intersatelliteranging and attitude measurement planning via a case study of two lowEarth orbit small satellites ying in formation. The relative positionmodel express the curvilinear coordinates dynamics of the Follower inthe Leader centered local frame, and includes deterministic eects ofthe J2 acceleration. The relative attitude model express the linearizeddynamics of the Euler angles from the Leader centered local frame tothe Follower body frame and includes the Gravity-Gradient torque. Theatmospheric air density is modeled as a stochastic process perturbingboth accelerations and torques. Its means and variances are calibratedvia Monte-Carlo simulations of a high-delity Truth model. Measuredintersatellite ranges and relative attitudes are processed along a niteperiod of time via a Kalman lter to produce estimates of a twelve statesvector of relative position and attitude and of their rates. The estimationerror covariance matrix at the nal time possess a known upper boundfunction of the observability and noise controllability Gramians.First an optimal ranging strategy is developed by nding the rangingnoise variance prole that minimizes the upper bound. The minimiza-tion is subject to a time integral constraint on the noise variance that isderived from a laser energy budget. This results in a remarkably shortsequence of ranging epoch times. Then that problem is extended tothe maximization of the upper bound with respect to the atmosphericdensity variance prole. The density variance is assumed to satisfy atime integral constraint, derived from nite energy considerations andquantied through Monte-Carlo simulations. The problems are solvedthrough numerical iterative schemes and their solutions consist of veryfew ranging acquisition times, atmospheric density impulses, along withthe corresponding optimized intensities. The combined solution to bothproblems thus provides a robust laser ranging planning over a given win-dow of time. Robustness is here in terms of guaranteed performanceson the estimation error covariance matrix at the nal time: its upperbound is designed for the worst-case atmospheric density prole alongthe scheduled trajectory. The proposed design has got appealing prac-tical features such as: very few ranging epoch times compared withcontinuous ranging, for a given overall laser energy budget; very fewprocess noise impulses, compared with continuous process noise, for agiven overall noise energy. Extensive simulations are performed that verify the algorithms convergence and validate the proposed approach.Extensive Monte-Carlo simulations are also presented to compare theperformances of Kalman lters designed via the proposed approach withothers based on continuous measurement and process noise.
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