when altimeter data are mixed with reduced networks o f range data, the fewer range data points are used, the smaller should be the value o f altimeter sigma, L e., the larger should be the altimeter weight so that the solution becomes more constrained.
To understand the influence o f the data standard deviations in the solution w e have to remember that each altimeter measurement is multiplied by a weight factor coa = 1/ ^a^’ and each PRARE measurement is multiplied by a factor cOp = 1/ Gp^ = l/(0.07m )2 = 200. Therefore if Ga =1 m each PRARE measurement has a weight 200 times larger than each altimeter measurement. In the case o f the PRARE3 data set, composed o f 54 points, the PRARE data w ill have a weight equal to 200 x 54 = 10 800 , much larger than the 2900 altimeter measurements. In the solution P3A where Ga = 0.3 m the total altimeter weight becomes 2900 / (0.3^) = 32000 therefore dominating the solution.
3
- The third configuration is composed o f 7 passes from two stations, 3011 and 7834 (PRARE4), maintaining a gap o f about two days during which no tracking data are available (Figure 8.8). The solution computed with only these data (P4) is very similar to the previous solution computed with 5 passes from only one station. The differences to the reference orbit reveal the same along-track pattern with larger errors in the area with no tracking data (Figure 8.16). Again the addition o f altimetry (P4A) reduces the errors by a factor o f 3 in both T and R directions removing the along track error pattern in the middle o f the arc (Figure 8.17).4
- The fourth configuration is constituted by 8 passes from the same stations (Figure 8.9). The main difference relative to the previous configuration is that now the largest interval during which there are no tracking data is reduced to about one day. The orbit computed with only this PRARE data (P5) is now much better determined with a uniform error distribution along the arc (Figure 8.18). The addition o f altimetry (P5A) apparently does not im prove the accuracy o f the solution (Figure 8 .19), but the solved-for parameters are better determined, revealing smaller correlations between them. In this solution a slightly larger altimeter sigma was used (0.5 m), but the solution with sigma = 0.3m is equivalent.5 - The last configuration is formed by 8 passes from station 3003, the last pass being at the beginning o f the third day (Figure 8.10). Therefore there are no tracking data for the last 22 hours o f the arc. An orbit was computed with only these tracking data (P6), solving for the start vector, solar radiation coefficient and two drag coefficients, one for the first day and another for the last two days. The differences o f this solution to the
reference orbit are presented in Figure 8.20. It is evident that the errors increase very quickly towards the end o f the arc, showing that these solutions are not reliable at any time after the time corresponding to the last pass. This confirms a well known result that ephemerides computed by fitting to tracking data cannot be extrapolated outside the tracking interval.
The addition o f altimeter data (P6A) does not solve the problem (Figure 8.21). A s in the previous solution the along-track errors have a large increase towards the end o f the arc. The conclusions are that altimetry data are a very helpful tracking data type to fill gaps of range data but not to extrapolate range data for more than a few hours after the last pass.
To assess the feasibility o f using altimeter data alone, a solution was computed using altimetry data alone and using a set of starting values giving range rms o f 280 metres and an altimeter rms (filtered residuals) of 2.14 m. After the adjustment to altimetry data alone the rms became 306 m for range and 0.59 m for altimeter. The differences o f this solution to the reference are as large as 0.6 km along-track and 1.3 km across-track. However the radial difference is only 0.75 m. These results leave no doubt about the weakness o f the along track and total absence o f across-track information in altimeter data.
From these results several conclusions can be withdrawn.
Altimeter data alone cannot be used as tracking data for orbit determination. In spite o f the w eakness o f this data type when used alone, only a few passes o f range data are sufficient to add the necessary along-track information to obtain a stable and reliable solution.
The results show that altimetry can fill gaps o f range data covering periods as long as two days. It is important to note that these gaps should be between passes o f range data and not for exam ple at the end o f the arc. This means that altimetry can only be used to interpolate range data, but not to extrapolate.
The application to ERS-1 o f these results obtained for SEA SA T, is lim ited to the existence o f a suitable geopotential model for this satellite. This model should produce ERS-1 orbits with similar accuracy to SEASAT orbits derived with GEM Tl. This means that the rms range residuals for a 3-day arc tracked by a suitable network o f laser stations, should be about 0.6m. If the actual model gives an rms o f fit larger than this by a certain amount, the results w ill have to be scaled by the same amount
The results presented in chapter 9 show that the present models for ERS-1 yield orbits with rms range residuals about three times these figures (= 1.5 m). This constitutes a serious limitation for the scientific applications o f ERS-1 data requiring satellite positions
at decimetre accuracy. This indicates the need for the development o f short arc techniques whereby precise orbits can be obtained over regions o f particular interest that are tracked by several stations. This is the subject o f chapter 10 where the research carried out during this project on the development o f short arc methods is presented.