Test Dataset 1 - Residual Stacking

Standard deviation of residuals - Comparison between different periods

Residuals have been stacked over three different periods in 2000. After the first period, there have been some changes in antenna and receiver with respect to the second and third, or main, period. The three main periods are

Day 110-117 2000 (8 days)
The Dutch stations Delft, Eijsden and Terschelling used different antenna and receivers compared to the other two periods.
Day 200-207 2000 (8 days)
Actually, the antenna and receiver in Delft has been changed during the middle (day 205) of the 2nd period. Therefore, results for Delft are analysed for 5 days directly before the change (day 199-204) and 5 days directly after the change (day 206-211).
Day 297-311 2000 (15 days). This is the main period.

Three different antenna designs, and three different receiver types, were analysed. The antenna design mainly influenced the elevation dependent phase delay. The standard deviation of the residuals depends mainly on the receiver type and amount of multipath at the site. The receivers that are analysed are

TRIMBLE 4700 Trimble 4700 CORS reference station receiver, 12 channel, operating at a 1 Hz sample rate, data decimated to 30 sec.
AOA SNR-12 RM AOA Turbo-Rogue, rack-mounted, 12 channel receiver, operating at a 30 sec sample rate. The phase and code data is smoothed within the receiver; a second degree polynomial is fitted to the phase data over a period of not more than 10 second.
AOA SNR-12 ACT AOA Turbo-Rogue, rack-mounted, 12 channel receiver, using the "Benchmark ACT ™" technology tracking all three signals (C1, P1 and P2), operating at a 30 sec sample rate. The phase and code data is smoothed within the receiver; a second degree polynomial is fitted to the phase data over a period of not more than 10 second.

The standard deviation of the residuals is plotted as function of elevation in 1 degree steps in [mm]. Plotted are

Emperical standard deviation (computed from the residuals) - blue lines
Emperical standard deviation (computed from the residuals) after correction for multipath - green lines
Formal error of the residuals (computed from the co-variance matrix), - red lines

for different receivers and periods.

Period 1 day 110-117 2000 (8 days)	Period 2 day 200-207 2000 (8 days)	Period 3 (main period) day 297-311 2000 (15 days)
Delft (DELF) AOA SNR-12 RM AOAD/M_T DUTD	Delft (DELF) AOA SNR-12 RM AOAD/M_T DUTD	In Delft the receiver and antenna where changed during the middle of the 2nd period. In the middle column (to the left) is plotted day 199-204. In the middle column on the next row is plotted day 206-211.
	Delft (DELF) TRIMBLE 4700 TRM29659.00 UNAV	Delft (DELF) TRIMBLE 4700 TRM29659.00 UNAV
Eijsden (EIJS) AOA SNR-12 RM AOAD/M_T DUTD	Eijsden (EIJS) TRIMBLE 4700 TRM29659.00 UNAV	Eijsden (EIJS) TRIMBLE 4700 TRM29659.00 UNAV
Terschelling (TERS) AOA SNR-12 RM AOAD/M_T DUTD	Terschelling (TERS) TRIMBLE 4700 TRM29659.00 UNAV	Terschelling (TERS) TRIMBLE 4700 TRM29659.00 UNAV
Westerbork IGS (WSRT) AOA SNR-12 ACT AOAD/M_T DUTD	Westerbork IGS (WSRT) AOA SNR-12 ACT AOAD/M_T DUTD	Westerbork IGS (WSRT) AOA SNR-12 ACT AOAD/M_T DUTD
Westerbork IGS and AGRS use the same antenna, but are different receivers.	Westerbork AGRS (WSRA) TRIMBLE 4700 AOAD/M_T DUTD	Westerbork AGRS (WSRA) TRIMBLE 4700 AOAD/M_T DUTD
Kootwijk IGS (KOSG) ROGUE SNR-12 RM AOAD/M_B DUTD	Kootwijk IGS (KOSG) ROGUE SNR-12 RM AOAD/M_B DUTD	Kootwijk IGS (KOSG) ROGUE SNR-12 RM AOAD/M_B DUTD
Kootwijk IGS and AGRS use the same antenna, but are different receivers.	Kootwijk AGRS (KOSA) TRIMBLE 4700 AOAD/M_B DUTD	Kootwijk AGRS (KOSA) TRIMBLE 4700 AOAD/M_B DUTD

Click on the pictures to enlarge.

The following can be concluded from these results

The emperical standard deviation (after correction for multipath) as function of elevation is the same for receivers of the same type and design, irrespective of the period
The emperical standard deviation after correction for multipath is always smaller than the emperical standard deviation before correction, and the difference is the largest for sites with large multipath, see also the multipath maps
The standard deviations of the Turbo-Rogues, which smooth internally their phase data, is smaller than the standard deviation of the Trimbles.
The standard deviation of the AOA SNR-12 ACT is better than the standard deviation of its predecessor the AOS SNR-12 RM
The emperical standard deviation (after correction for multipath) has a similar behaviour to the formal standard deviation of the residuals, but fine tuning of the elevation dependent weighting function in the analysis is advised. So far, we used 1/cos(z)² as elevation dependent weighting function for all receivers, assuming a standard deviation of 1 mm for the raw phase observables (i.e. 3 mm for the ionosphere free linear combination that we are using).
The formal standard deviation of the residuals can be fitted reasonably well by a function of the type a + b*cos(z)²
Kootwijk and Westerbork use two different receivers, connected to the same antenna by means of antenna slitters, which is an ideal situation for comparing receivers
Results are very similar from one period to another, as long as the same receiver is used
The main differences are in the zenith, which is caused by lack of observations in the zenith direction
There is unexplained behaviour in Westerbork IGS for the first period

Different elevation dependent weighting for receivers in the GPS processing software should be investigated.