Least square estimation of the bias of the measured distance between the two GRACE satellites and production of a new KBRL1B-X files versions based on GPS observations



Gravity Recovery and Climate Experiment (GRACE) satellite gravimetry mission launched in March 2002 based on its twin gravimetric satellites makes application of both High-Low (HL) and Law-Low (LL) gravimetric techniques possible. The LL is based on Satellite-to-Satellite Tracking (SST) via the one way two frequencies K-Band-Ranging between the two GRACE satellites. As a result of combination of LL and HL structures via geodesy community following gravity observables are developed: (1) Potential Difference between the two GRACE satellites based on Line of Sight (LOS) velocity using energy integral method. (2) Projection of the gravitational acceleration difference of the two GRACE satellites along the LOS, using LOS acceleration. The latter observable which can provide finer details is one of the important observation quantities of the GRACE mission. Application of this observable as a boundary data for local and regional modeling of the Earth’s gravity field provides valuable information about short and medium wavelength spectrums of the field. One of the necessary parameters for the production of this boundary data from the GRACE satellite gravimetry mission is the “inter-satellite range ?” with the bias ?b, which can be obtained from KBRL1B-X data files with 0.2 Hz rate. The unknown bias of ?, caused by phase ambiguity of the observed distance between the two GRACE satellites, is the main problem facing the application of the aforementioned information as boundary data. This issue has forced the GRACE data user’s community to compute ? at its epoch of observations from the position vectors of the two satellites, which off course has much less accuracy than the K-band measuring distance instrument. Considering the importance of the range measurement ? as boundary data for the gravimetric boundary value problems, in this paper we have offered a least squares based method for the estimation of the unknown bias ?b based on onboard GPS measurements.
Our method is based on the following steps: (1) Application of LL-SST data of GRACE mission and removal of the associated systematic errors. (2) Computation of the bias of the inter-satellite range and its accuracy via the difference between measured biased distance ? and the distance computed from GPS derived position vectors of the two satellites. (3) Detection of the occurred cycle slips within the inter-satellite range ? from the jumps in the computed biases for the consequent epochs of observations, and determination of time spans without cycle slip. (4) Computation of the range biases from the weighted mean of the computed bias for every time span without cycle slip. (5) Computation of bias free distances for every KBR observation epoch using the estimated bias from the previous step. (6) Replacing the computed bias free ranges in the original KBRL1B-X data files. Our numerical computations show that the computed bias free range based on our aforementioned method is much more accurate than direct application of the GPS derived position vectors. Besides the longer the time span without cycle slip the more accurate estimation of bias can be obtained. Finally, using the proposed method in this paper a new version of KBRL1B-X file bias free inter-satellite range observations for the time period 2002-2006 is computed.