Earth beacon acquisition and tracking under various illumination conditions

EarthbeaconacquisitionandtrackingundervariousilluminationconditionsBarbara Marinoa,Haiping TsoubandTsun-YeeYancaLoyola MarymountUniversit,LosAngeles,CA90045, USAb,cJetPropulsion Lab oratory,Pasadena,CA91109,USAABSTRACTThe use of sun-illuminated Earth images has b een explored to aid in meeting the stringentpointing requirements fordeep space optical downlink telemetry.It has b een shown that fully illuminated Earth images provide a symmetry thateasily lends to the determination of the geo center.Since more often that not, the Earth is only partially illuminatedbythesun,additional work is required to meetthe p ointing requirements underallilluminationconditions.Thispap erdevelops analgorithm for determiningthegeo centerofEarthregardless ofilluminationbythesunusing sub-pixel scanning and a simple thresholding technique.To complete this approach the acquisition algorithmis paired with a tracking technique based on maximum likeliho o d estimation.Results have indicated that the algorithm works well to lo cate and track the p osition of the Earth and, thereby,a receiving station.Results of the exp eriments are presented and compared with other techniques.1.INTRODUCTIONDue to its narrow b eam width, deep space optical downlink telemetry requires micro-radian p ointing accuracy of thespace instruments toward Earth.Algorithms using the sun-illuminated Earth as a b eacon to lo cate the ground-basedtelescop e have b een prop osed.1Since more often than not, the Earth is only partially illuminated, these algorithmswould not b e able to meet the p ointing requirements under all Sun-Earth-Prob e (SEP) angles.This pap er develops an algorithm for determining the geo center of the Earth regardless of the illumination anglewith the sun.Using a Fine Steering Mirror (FSM) capable of radial movement in increments of 1/20th of a pixel,asequenceofEarthimagesistakenbyscanninginorthogonaldirections.Thealgorithmbasedonsub-pixelscans p erformed rst along the Earth-sun axis, and then in the orthogonal direction.To complete this approach theacquisition algorithm is paired with a tracking technique based on maximum likeliho o d estimation.2Section2provides anoverview ofthemathematicalrepresentationofimage dataatariousp ointsduringcapture pro cess.Section3describ es theacquisitionpro cess using sub-pixelscanning,andSection 4maximum likeliho o d based tracking of the translated vector.Numerical results demonstrating its capabilityof sub-pixel acquisition and tracking of fully and partially illuminated Earth images are included in section 5, followed bythe summary in section 6.2.REPRESENTATIONOFIMAGEDTAblo ckdiagram ofthepro cess forcapturing imagesfor theacquisitionandtracking algorithms discussedinthispap er is shown in Figure 1.The functionfl(x; y) represents the continuous Earth image at timet.The pro cess ofcapturing this image using anMNCCD array is represented by a three-step pro cess.The original image assumedto b e degraded by Gaussian optics with zero mean and unityvariance.The intensity of the convolved image is thenintegrated over the area of each pixel in the CCD array resulting in the extended-source imagesl(m; n).The thermalnoiseintro ducedbytheCCDarrayismo deledasanadditivewhiteGaussianrandomdisturbancepro ducingcaptured imagerl(m; n), as follows,rl(m; n)=s)+n);m=12;::: ;M;;::: ;N;(1)Furtherauthorinformation:B. Marino:bmarino@lmu.edu;phone1310338-3947;fax338-2782;LoyolaMary-mountUniversity,DepartmenofElectricalEngineering,7900LoolaBoulevard,LosAngeles,CA90045,USA;H. Tsou:tsou@dsp.jpl.nasa.gov; phone 1 818 354-2393; fax 818 393-1717; Jet Propulsion Lab oratory, California Institute of Technology,4800 Oak Grove Drive, m/s 238-343, Pasadena, CA 91109, USA