Article Index

Research Activities

The routine data processing and analyses are enlarged by several additional research activities. The current subjects of interest are shortly described in following sub-sections

Advanced Analyses of the post fit observation residuals

DORIS residuals are usually presented as range-rate residuals (in mm/s), but they can be expressed as phase count residuals (mm) as well. The basic relation between the range-rate and the count residuals is simple: the range-rate residual multiplied by the length of the observation time interval is equal to the count residual. The situation is more complicated due to the frequently switched chained/unchained observation mode. The observations with different time intervals are usually acquired (and processed) together. It is thus desirable to analyze the residuals of both types of observations separately, i.e., to distinguish the mixed “short” 7 s or 9 s observation intervals (unchained mode) and the “long” 10 s observation intervals (chained mode), or at least to pay attention to their ratio. Note that if observations with different time intervals are processed together, there is a difference between the minimization of the sum of squared range-rate residuals and the minimization of the sum of squared count residuals. In the GOP solution, the sum of squared count residuals is minimized. All results described in this chapter are derived from the daily GOP single-satellite solutions with adjusted orbits, station coordinates, ZTD and beacon frequency offsets but with fixed ERP.

A profound and detailed comparison of the “short” and “long” measurement accuracy based on the analysis of post-fit residuals is difficult, since both types of observations are processed together. The amount of the short observation intervals is usually too low to be processed separately. The presented approach can thus give only an approximate estimation of the relation between the measurement precision and the length of the observation interval. The approximate computation of the post fit residual RMS of the chained and unchained observations σc , σu (eq. 4)

(4a)   σu = √( (Σe2 / nu)*(n / n - u))
(4b)   σc = √( (Σe2 / nc)*(n / n - u))

was used to compare the residuals of both types of the measurement, where 'e' are post-fit residuals referring to unchained or chained observations, n is the total number of observations, nu the number of unchained observations, nc the number of chained observations, and u the total number of estimated parameters. The fact, that the short (unchained) observations have higher range-rate residuals but lower count residuals than the long ones (chained), makes it clear that the measurement noise partly depends on the length of the observation time interval. We may, as a simple approximation, explain the accuracy of the count measurements as the result of a combination of two uncorrelated processes, where the first one is independent and the second one dependent on the count interval. More specifically, we may write the variance of the count measurements in the form (eq. 5)

(5)   σ2 = σ12 + (Tσ2)2

where σ1 is related to the phase measurement noise while σ2 relates to the frequency dependent noise and T is the count interval. We may thus write (eq. 6)

(6a)   σu2 = σ12 + Tu2 σ22

(6b)   σc2 = σ12 + Tc2 σ22

where Tu (Tc) is the time interval of the unchained (chained) observation. We may then use the post-fit residual RMS computed using eq. 1 as the estimate of the observation standard deviation for the short and long observation intervals. The system of the two equations (eq.6) can be then solved for the two noise components σ1 and σ2. The values obtained by this procedure for the time period 2002-2008 are similar for all satellites except for SPOT-2. The unchained observations of SPOT-2 are based on a 9 s time interval, while unchained observations of the other satellites have 7 s time interval. The standard deviation σ2 ranges between 0.225 and 0.257 mm/s for all satellites except for SPOT-2, where σ2 is 0.307 mm/s. On the other hand, σ1 is lower in the case of SPOT-2 (2.57 mm) than for the other satellites (2.77-3.16 mm). Fig. 9 shows the corresponding average values for each year of the analyzed time interval. The estimated relations between constant and time-dependent term are very similar, except for SPOT-2.

Spot-5 and South Atlantic Anomaly

The SAA is based on the geometry of the Van Allen radiation belts. The Van Allen radiation belts are symmetric with the Earth's magnetic axis, which is tilted with respect to the Earth's rotational axis by an angle of ~11 degrees. Because of this tilt, the inner Van Allen belt is closest to the Earth's surface over the south Atlantic ocean, and farthest from the Earth's surface over the north Pacific ocean.

Height offset for chosen South American stations, behavior from 2003.0 to 2010.5 Fig 2. Height offset for chosen South American stations, behavior from 2003.0 to 2010.5
Daily behavior of the estimated frequency offset for Master beacons. SPOT-5 and Envisat Fig 3. Daily behavior of the estimated frequency offset for Master beacons. SPOT-5 and Envisat

The analysis of single-satellite solutions disclosed a SPOT-5 specific abnormality, related with the well known South Atlantic magnetic Anomaly (SAA). The effect of the SSA on the Jason-1 DORIS observation has been well known, but the significant effect on the SPOT-5 observations is an original discovery of GOP analyses center. The estimated station height and other related parameters, derived from SPOT-5 single-satellite solution, are significantly biased. Fig. 2 shows the differences between the weekly estimated station coordinates, using the SPOT-5 single-satellite solution and the combined solution GOP31. The highest bias was found in the station height, where the differences between both solutions reached the highest values for South America stations Cachoeira Paulista (-205 mm), Arequipa (-74 mm) and Santiago (-68 mm). In addition, the bias is getting higher during the time, as documented by Fig. 2. The horizontal positions show the largest absolute differences (from 30 to 45 mm) for the same stations and also for Kourou.

Corresponding differences were similarly detected also in comparison between estimated ZTD (Zenithal Troposphere delay) and GNSS ZTD and confirmed by analyses of the estimated frequency offset. Figure 3 shows the daily behavior of the estimated oscillator frequency offset, displayed for the master beacons (equipped with atomic clock). The behavior for SPOT-5 (affected by SAA) and Envisat (not significantly affected) is completely different. In the case of SPOT-5, frequency is strongly rising during flight through the SAA area. This part of the daily arc corresponds to the observation time span of the station Kourou (KRVB).