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The effect of errors in the published heights of National GPS Network Active stations

1    Introduction

Recently errors were discovered in the published height coordinates of the Active stations in the Ordnance Survey National GPS Network. These errors have now been corrected and new coordinates for the Active stations issued. An explanation of the cause of the errors and their likely effect on the computed heights of user's stations is given here.

Ordnance Survey is grateful to the Institute of Engineering Surveying & Space Geodesy (IESSG) at the University of Nottingham for their assistance in isolating the errors and testing their magnitude.

2    The cause of the error

A GPS baseline is measured between the phase centres of the two antennas. To relate this baseline to the station markers the vertical height from the station marker to the antenna phase centre must be known. The phase centre is not a physical point that can be measured to, so the offset of the phase centre from a physical point on the antenna must be accounted for during processing.

The antenna heights of all Ordnance Survey Active stations are measured vertically from the station marker to the Antenna Reference Point (ARP) for each antenna, which is usually the base of the antenna mount. For all the Active stations in the Ordnance Survey National GPS Network the station marker is the ARP, so the antenna height is 0.000 m.

The offset from the ARP to the phase centre is then added to the antenna height in the processing software to give the height of the phase centre above the station marker.

The main phase centre offset component is vertical (up) but there are also small horizontal offsets to north and east. There are actually two phase centres in a dual-frequency antenna – one for the L1 frequency and the other for L2, and each phase centre has a different offset.

The phase centre applicable at the time of observation of the satellite signal also varies depending on the elevation of the satellite. Hence, phase centre corrections must be applied in the processing to take this into account. These corrections usually take the form of a mean offset value and a look-up table with additional elevation dependent values quoted for every 5 degrees of elevation, with separate tables for L1 and L2 frequencies.

During the processing to determine the published coordinates of the Active stations it was an error in the input of the elevation dependent values that caused the height errors.

The values come from a file supplied by the International GPS Service (IGS). The file is ftp://igscb.jpl.nasa.gov/pub/station/general/igs_01.pcv. The elevation dependent corrections are quoted every 5 degrees starting at 90 degrees elevation (i.e. vertically upwards) down to 0 degrees elevation (i.e. horizontal).

The error in inputting these values occurred when they were transferred to a different format for use in the GPS processing software used by Ordnance Survey. When the values were transferred to the new format their order was mistakenly reversed so, for example the correction relating to 90 degrees elevation was being applied in the software at 0 degrees.

3    The magnitude of the errors

The error in the elevation dependent corrections translated almost directly to an error in station height. Very small errors were introduced to the horizontal coordinate components but these were of the order of 2 mm or less and well inside the expected noise level of the Active network coordinates.

The height error is different at each station but is correlated with antenna type. The change in the height at each station is given in the table below. The mean height error for each antenna type is also given.

Station	Antenna Type	Station Height Error (m)	Mean Height Error for Antenna Type (m)
DROI	ASH700936E      SNOW	0.012	0.012
INVE	ASH700936E      SNOW	0.013
KING	ASH700936E      SNOW	0.010
LEED	ASH700936E      SNOW	0.012
LOND	ASH700936E      SNOW	0.012
NEWC	ASH700936E      SNOW	0.012
NORT	ASH700936E      SNOW	0.010
NOTT	ASH700936E      SNOW	0.011
OSHQ	ASH700936E      SNOW	0.013
BLAC	LEIAT504        LEIS	0.005	0.006
BLAK	LEIAT504        LEIS	0.006
CARL	LEIAT504        LEIS	0.005
CARM	LEIAT504        LEIS	0.006
COLC	LEIAT504        LEIS	0.005
DARE	LEIAT504        LEIS	0.006
EDIN	LEIAT504        LEIS	0.006
GLAS	LEIAT504        LEIS	0.006
IOMN	LEIAT504        LEIS	0.005
IOMS	LEIAT504        LEIS	0.006
MALG	LEIAT504        LEIS	0.007
PLYM	LEIAT504        LEIS	0.006
SCAR	LEIAT504        LEIS	0.010
TAUN	LEIAT504        LEIS	0.011
THUR	LEIAT504        LEIS	0.008
BUT1	TRM33429.00+GP  DOME	-0.021	-0.023
FLA1	TRM33429.00+GP  DOME	-0.026
GIR1	TRM33429.00+GP  DOME	-0.023
LIZ1	TRM33429.00+GP  DOME	-0.018
LYN1	TRM33429.00+GP  DOME	-0.024
NAS1	TRM33429.00+GP  DOME	-0.025
NFO1	TRM33429.00+GP  DOME	-0.029
SCP1	TRM33429.00+GP  DOME	-0.015
STI1	TRM33429.00+GP  DOME	-0.025
SUM1	TRM33429.00+GP  DOME	-0.017
WOR1	TRM33429.00+GP  DOME	-0.021

The “sense” of the above error values is the old incorrect height minus the new correct height (assumed to be the "truth"), i.e. the given error represents the change that needs to be applied to the new height of a station in order to obtain the old height. Therefore the old published heights for the stations with Ashtech and Leica antennas were too high by 12 mm and 6 mm respectively. The old published heights for the stations with Trimble antennas (the General Lighthouse Authority stations) were too low by 23 mm.

4    The effect of the errors on user’s coordinates

It is impossible to calculate the exact effect of these errors on the coordinates of a user’s station without readjusting the user’s computed GPS baselines. However by making various assumptions a guide to the expected error for a particular combination of antenna types can be given.

Each processed GPS baseline, computed from a user’s station to an Active station, can be used to calculate an ellipsoidal height difference between the two stations. The height of the Active station (assuming it is held fixed in the user’s adjustment) plus the height difference gives a value for the height of the user’s station.

where:	HU	=	Height of user's station;
	HA	=	Height of Active station;
	ΔHAU	=	Height difference from Active station to user's station

When several Active stations are used the final value for H_U can be expressed as:

where:	HAi	=	Height of an Active station;
	ΔHAiU	=	Height difference from an Active station to user's station;
	i	=	Number of active stations used.

                   

In reality the values of ΔH_AiU would be weighted according to the quality of the computed baselines. However, in trying to compute a guide to the error at a user’s station, the quality of an actual baseline cannot be known, so equal weighting of the values for ΔH_AiU has to be assumed.

The error in the Active station heights can now be introduced to the equation:

where:   e_i         =     the error in the Active station height.

So for a particular combination of Active station antennas A₁ to A_i an estimate of the total error introduced at
the user’s station     =    .  Again the sense of this error is from the correct height to the incorrect height.

Using the above formula and the mean error values per antenna type and assuming the nearest Actives to a site are used, estimates of the total error for different combinations of antennas have been calculated and are shown in the table below.

The “Is antenna combination expected in GB” column is based on computing the nearest antennas at every point in a 20 km grid covering the whole country from OSGB36 National Grid coordinates 0,0 to 700000,1260000.

The same algorithm that was used to produce the figures in the table above was used to calculate the expected error when using the nearest 5 Active stations at every point in the 20 km grid. In this case the combined errors were calculated using the individual Active station errors not the mean error per antenna type. These errors were then represented by colours and plotted on a map of GB to indicate where a particular error might be expected. This map is shown below and the errors range from -11 mm to +11 mm. It can be seen that when using the nearest 5 Active stations, the expected error is less than 10 mm in many locations.

 

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