Research On Relative Orbit Determination Of Low Earth Orbit Formation Flying Satellite Using Spaceborne GPS

With the development of GPS positioning and orbit determination technology and the improvement of accuracy, spaceborne GPS relative orbit determination has become an effective way for Leo Earth Orbit (LEO) satellites. The precision of relative orbit can be achieved by cm or mm level. Similar to the ground GPS, spaceborne GPS will be affected by errors such as phase center delay, ionospheric delay, and problems such as ambiguity should be handled to improve the accuracy. Meanwhile, data process for spaceborne GPS is more complicated than that for the ground GPS, since the constellation shifts more quickly and the visible GPS satellites are less.The main research contents and innovations are as follows:1. Based on the characteristics of spaceborne GPS observation data, detailed analyses of the visibility, DOP and C/No value were made. The orbit and clock errors were fitted using Chebyshev method. The gross errors and cycle slips were detected using multiple methods including phase-peudorange combinations, ionospheric residuals, and M-W combinations.2. Approaches to antenna mean phase center offsets (PCOs) and variations (PCVs) for spaceborne GPS were studied. Different ways to handle satellite phase center offsets were compared. GPS transmitter and receiver PCVs were extended to nadir angle beyond14°for IGS products and zenith angle beyond80°for NGS products, respectively. GFZ products and the corresponding coordinate transformations were analyzed. Impacts of phase center corrections on the relative positioning of Gravity Recovery and Climate Experiment (GRACE) were analyzed. Studies show that, the IGS absolute model and GFZ products should be used for the satellite and receiver phase center corrections, respectively.3. A modified ionospheric correction method and the corresponding approximate algorithm for spaceborne single-frequency GPS users were proposed in this study. Single Layer Model (SLM) mapping function for spaceborne GPS was analyzed. SLM mapping functions at different altitudes were calculated. Ionospheric Pierce Point (IPP) trajectories of the GRACE satellite were computed at the single layer height of500km. The modified Klobuchar model and scale factors were used to compute the fractional ionospheric corrections above the GRACE altitudes, and calculation results were validated using dual-frequency observations. Study shows that the single layer height needs to be changed from350km to500km according to the altitude of GRACE. Approximate forms of Earth angle and slant factor developed for modified Klobuchar model are applicable to GRACE, with accuracy adequate to preserve the essential elements required to compute ionospheric delays. Results show that the modified Klobuchar model corrects more than80%on average of the ionospheric delays for the test data.4. Correction methods and impacts of the ionospheric dalays and Differential Code Biases (DCBs) were discussed. The LEO satellites were infuenced only by the ionosphere above the orbit, and the fractional total electron content (TEC) above the receiver can be obtained from the TEC above the Earth and a scale factor. Methods to determine scale factors were implemented and further developed, based on Global Ionosphere Maps (GIM), Klobuchar model and modified Klobuchar model. Receiver DCB values were achieved at the same time. Methods were validated using flight data from the GRACE mission. Results show that scale factors are influenced by the receiver altitude, TECs along the line of sight and the ionospheric correction method. In a given case, scale factors obtained using GIM are more regular, while those obtained using Klobuchar model and modified Klobuchar model are closely related to TECs. However, all these correction methods are benefitial to GPS orbit determination.5. The determination methods of initial orbits, float solutions and ambiguities were analyzed. Wide-lane ambiguity resolution methods suitable to spaceborne GPS were discussed. The AMBiguity Decorrelation Adjustment (LAMBDA) method for spaceborne GPS was analyzed, too. Results show that, the success rates of the wide-lane ambiguity resolutions for GRACE A and B using the rounding method were over60%; the success rate of the wide-lane ambiguity resolutions using the ionospheric model was about70.2%for the test data. The precision of the fixed solutions can be improved using LAMBDA method.6. The basic principle and observation model for K-Band Ranging (KBR) system were analyzed. Combined GPS/KBR model was proposed based on the comparison between KBR model and double difference GPS model. Unit weight standard deviation of KBR was derived from the signal to noise ratio (SNR) and carrier to noise density ratio (C/No) analysis. Relative orbits were determinined using bidirectional Kalman filter based on double difference GPS and GPS/KBR observation equations. Ambiguities were solved using LAMBDA methods without and with KBR constraint. Study shows that KBR can be used as a new observation type and the GPS solutions can be improved. It also shows that KBR is beneficial to fixing ambiguities, and the relative orbit determination error is no more than3cm (Root Mean Square) for the test data.