Comparison of various orbit fitting methods
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ABCDEFGHIJKLMNOPQRSTUVWXYZ
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NOAA-1 satellite
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3
Without noise and without filters
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Semi-major axisEccentricityInclination
Longitude of Ascending Node
Argument of Periaspsis
Mean Anomaly
True Anomaly
6
Original7826.0065380.0031531101.754195.737352.864117.261117.5816062
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lambert’s7826.0076170.00315285439101.7540051195.7370024352.8587926N/A228.0702912
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error0.001078719931-0.00000024561020640.0000050950779950.000002404946997-0.005207441205N/A110.488685
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interpolation
7825.8459480.00402097791101.7540051195.7370024274.6642297N/A228.0702912
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error-0.16059019020.00086787791030.0000051261999940.000002383121-78.19977028N/A110.488685
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ellipse fit7826.0077240.003152843631101.7540051195.7369982352.8584817N/A117.5815259
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error0.00118607965-0.00000025636917410.000005103477989-0.000001757641598-0.005518304091N/A-0.000080320183
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With ±15 km noise and without filters
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Semi-major axisEccentricityInclination
Longitude of Ascending Node
Argument of Periaspsis
Mean Anomaly
True Anomaly
23
Original7826.0065380.0031531101.754195.737352.864117.261117.5816062
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25
lambert’s11227.916680.3283752827102.0735998195.6536403175.1020099N/A182.5706796
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error3401.910140.32522218270.3195998273-0.08335972322-177.7619901N/A64.98907341
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interpolation
9745.0499580.3418359186101.4740385195.6027827206.9570237N/A182.5706796
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error1919.043420.3386828186-0.2799615134-0.1342172611-145.9069763N/A64.98907341
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ellipse fit7825.5953450.003072602139101.7530423195.740244354.598912N/A115.8803747
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error-0.4111929776-0.00008049786122-0.0009576733220.0032440023871.734912039N/A-1.701231503
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With ±15 km noise and with filters
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Triple Moving Average Window: 3
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Savitzky-Golay Window: 5, Degree: 3
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Semi-major axisEccentricityInclination
Longitude of Ascending Node
Argument of Periaspsis
Mean Anomaly
True Anomaly
43
Original7826.0065380.0031531101.754195.737352.864117.261117.5816062
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lambert’s7989.0640590.1119213668101.7700613195.647977175.0497895N/A193.2307752
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error163.05752120.10876826680.01606132028-0.08902295674-177.8142105N/A75.649169
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interpolation
7970.0659470.1062632544101.8251156195.6374327200.9399207N/A193.2307752
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error144.05940880.10311015440.07111563852-0.09956734932-151.9240793N/A75.649169
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ellipse fitN/AN/AN/AN/AN/AN/AN/A
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errorN/AN/AN/AN/AN/AN/AN/A
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GPS BIIA-23 satellite
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Without noise
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Semi-major axisEccentricityInclination
Longitude of Ascending Node
Argument of Periaspsis
Mean Anomaly
True Anomaly
60
Original26560.214190.014295554.405884.841774.4543193.5934193.214967
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ellipse fit26560.214050.0142955004354.4058003784.8417005474.45431618N/A193.2149811
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error-0.00014452059990.00000000043321570120.00000037105190390.00000053504919610.0000161830137N/A0.00001408581301
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With ±25 km noise
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Semi-major axisEccentricityInclination
Longitude of Ascending Node
Argument of Periaspsis
Mean Anomaly
True Anomaly
71
Original26560.214190.014295554.405884.841774.4543193.5934193.214967
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73
ellipse fit26560.24870.0143406090554.4061899684.8412238774.4677905N/A193.2061393
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error0.03451234220.000045109049750.0003899552505-0.00047613007280.01349049991N/A-0.008827768532
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Cryosat-2 satellite
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Without noise
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Semi-major axisEccentricityInclination
Longitude of Ascending Node
Argument of Periaspsis
Mean Anomaly
True Anomaly
82
Original7096.697190.000508892.0287282.8216298.018862.050562.10202
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ellipse fit7096.6971840.000508806585592.0286993282.8215975298.017019N/A62.10097751
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error-0.0000062294602690.000000006585528474-0.0000007008637937-0.000002476512009-0.001781039787N/A-0.001042492515
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With ±25 km noise
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Semi-major axisEccentricityInclination
Longitude of Ascending Node
Argument of Periaspsis
Mean Anomaly
True Anomaly
93
Original7096.697190.000508892.0287282.8216298.018862.050563.50963214
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ellipse fit7096.6449160.000600510541792.02001597282.8178511288.5858713N/A71.64106096
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error-0.05227350570.00009171054166-0.008684027102-0.003748901516-9.432928691N/A8.13142882
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