§ 014. Accuracy of TOPAZ PPK on long baselines (TOPAZ vs BERNESE)

# Intro

Let's evaluate potential accuracy of TOPAZ PPK positioning service on long baseline in static mode.

Why one may need to do such processing? Typical use-case: estimation of own RTK base receiver precise coordinates relative to some permanent CORS station w/ known position.

The problem usually one may face with is distance to nearest permenent station to be used for differential processing. It strongly depends on concrete region and yet it may be equal to few hundred kilometers and even more.

Any PPK engine (even student's diploma software) may give fine results on short base-line in good invironment. But what one may expect on long baseline like 100+ km? What about 200 or 300 km?

It is very challenging task where every short detail (satellite precise orbits and clocks, antenna phase center variations, advanced ionosphere and troposhere estimation, multipath reduction) is to be taken into account if one still whants to get FIXED solution w/ reliable accuracy.

In this article, we'll calculate baseline between IGS stations located 182 km away from each other. High-accurate reference coordinates of these stations are known apriory being previously computed by Bernese GNSS Software run by CODE (Center for Orbit Determination in Europe).

First station in processing session is assumed as base w/ known coordinates (by Bernese). The second one - as "unknonw" rover. Its coordinates are to be estimated. "Unknown" rover coordinates are computed as sum of known base (first station) position and TOPAZ computed base-rover baseline components. Than TOPAZ estimated "rover" coordinates will be compared to apriory known (Bernese) reference coordinates of this "rover" station.

# IGS stations WSRT-DLF1 (182 km)

We'll process IGS stations WSRT and DLF1 located in Netherlands. Distance between stations is about 182 km.

Station raw data (Compact RINEX) my be donwloaded below (24h, 30-sec rate, 09-May-2024):

DLF100NLD_R_20241300000_01D_30S_MO.crx.gz

WSRT00NLD_R_20241300000_01D_30S_MO.crx.gz

# TOPAZ PPK

Let's process these files by TOPAZ. Un-gzip downloaded measurements from WSRT and DLF1 stations. There should be available two files in Compact RINEX format (Hatanaka compressed):

DLF100NLD_R_20241300000_01D_30S_MO.crx

WSRT00NLD_R_20241300000_01D_30S_MO.crx

There is no need to convert CRX to RINEX, TOPAZ may process CRX directly.

Open TOPAZ online PPK processing. Lets' agreed DLF1 station will be known base station while WSRT - "unknown" rover. Select CRX files w/ measurements.

Set up static processing in Settings section. Base coordnates may be kept as is (i.e. aproximate from RINEX) since first of all we're interested in baseline components computed by TOPAZ. Later we will get reference coordinates of DLF1 station and simply add TOPAZ-computed base-rover baseline components in order to get rover position estimation.

Finally, press UPLOAD button. Processing will take some time, please wait. Once processing is completed, one may check information about processed files, antennas, its PCO, input settings and results of PPK computation in form of base-rover baseline components (highlighted in green below).

Input files

General Info

3.05
Hatanaka Compressed (CRX)

3.04
Hatanaka Compressed (CRX)

Date: 2024.05.09
Time: 00:00:0.00
DOY:  130
Week: 2313

Date: 2024.05.09
Time: 00:00:0.00
DOY:  130
Week: 2313

Date: 2024.05.09
Time: 23:59:30.00
DOY:  130
Week: 2313

Date: 2024.05.09
Time: 23:59:30.00
DOY:  130
Week: 2313

LEIAR25.R4      LEIT

LEIAR25.R3      LEIT

0.375400
0.000000
0.000000

0.800000
0.700000
159.100000

0.400000
0.100000
161.700000

Post-Processing Settings

X:  3924698.1156
Y:  301124.8036
Z:  5001904.9952

dX:  -95961.7755
dY:  142179.9426
dZ:  62979.8029

X: 3828736.3401
Y: 443304.7462
Z: 5064884.7981

It is important to ensure precise orbits and clocks (SP3) are used in PPK processing instead of broadcast Ephemeris. SP3 is vital for accurate processing of long baselines. The best accuracy may be achieved if FINAL SP3 product is used. It is available w/ delay about 1 week.

Below are dX,dY,dZ components of baseline between base and rover antennas (L1 Phase Center):

     dX, [m]: -95961,7755
(A)  dY, [m]: 142179,9426
     dZ, [m]:  62979,8029

Let's add these baseline components to a priory known DLF1 station coordinates. Reference coordinates computed by Bernese GNSS Software by CODE (Center for Orbit Determination in Europe) for 09-May-2024 may be found here.

CRD file by CODE provides computed coordinates tagged to geodetical marker point (geodetic reference monument). These coordinates are:

     X, [m]: 3924697.57159
(B)  Y, [m]:  301125.34545  
     Z, [m]: 5001905.37891

We need to convert these coords to L1_PC. First, let's take into account distance between marker and Antenna Reference Point (ARP). RINEX file section [ANTENNA: DELTA H/E/N] is filled by zeros so marker position is equal to ARP. Next, we need to convert ARP position to L1_PC using Antenna Phase Center Offsets (PCO). LEIAR25.R3 LEIT antenna (installed on DLF1 station) PCO are the following:

      North:   0.4 mm
(C)   East:    0.1 mm
      Up:    161.7 mm

North and East components may be neglected (sub-millimeter). Up component is to be added to ARP Height being converted to meters (LLA format). Just in case, one may use MEONMAP service for coordinates transformations.

      X, [m]: 3924697.57159        Lat, [deg]: 51.986021742451705
(D)   Y, [m]:  301125.34545   =>   Lon, [deg]: 4.387465412205929
      Z, [m]: 5001905.37891        Alt,   [m]: 75.819 + 0.1617 = 75.9807

Finally, DLF1 L1_PC coordinates (converted back to XYZ format) are:

      X, [m]: 3924697.6711
(E)   Y, [m]:  301125.3531
      Z, [m]: 5001905.5065

Well, next we'll add baseline components computed by TOPAZ to DLF1 L1_PC coordinates. What in turn will give us "unknown" rover WSRT coordinates of antenna L1_PC.

      X, [m]: 3924697,6711 -  95961,7755 = 3828735,8956
(F)   Y, [m]:  301125,3531 + 142179,9426 =  443305,2957
      Z, [m]: 5001905,5065 +  62979,8029 = 5064885,3094

# Compare w/ Reference Coordinates

But how far this estimation is from reference coordinates of WSRT station computed by CODE / Bernese? Let's check it!

In order to compare Bernese / CODE coordinates of WSRT station w/ TOPAZ computed, we need to convert reference WSRT station coordinates to L1_PC. Procedure is absolutely similar to what we did above for DLF1 station.

WSRT station marker precise coordinates are:

X, [m]: 3828735.57500   
Y, [m]:  443305.26849  
Z, [m]: 5064884.89771

Next, take into account antenna height from RINEX header:

i.e. add antenna height taken from RINEX header [ANTENNA: DELTA H/E/N] to geodetical altitude previously converted from XYZ to LLA (BLH) format:

X, [m]: 3828735.57500      Lat, [deg]: 52.91461385152348
Y, [m]:  443305.26849  =>  Lon, [deg]: 6.604510502407136
Z, [m]: 5064884.89771      Alt, [m]:   82,278 + 0,3754 = 82,6534

At next step, apply LEIAR25.R4 LEIT antenna PCO to get position of L1_PC. East and North components are neglected.

North:   0.8 mm
East:    0.7 mm
Up:    159.1 mm

Lat, [deg]: 52.91461385152348
Lon, [deg]: 6.604510502407136
Alt, [m]:   82,6534 + 0,1591 = 82,8125

Or being converted to XYZ by MEONMAP service:

X, m:  3828735.8952
Y, m:   443305.3056
Z, m:  5064885.3243

Now we can do direct comparison of reference by CODE / Bernese and TOPAZ PPK coordinates of WSRT antenna L1 Phase Center:

       TOPAZ             Bernese (CODE)    DELTA
X, m:  3828735,8956      3828735,8952      -0,0004
Y, m:   443305,2957       443305,3056       0,0099
Z, m:  5064885,3094      5064885,3243       0,0149

Not BAD! TOPAZ estimated baseline components with 3D accuracy better than 1.8 cm being compared w/ precise reference coordinates estimated by Bernese GNSS Software for IGS network. Just to remind, distance between base and rover is 182 km.

# Summary

One may estimate precise rover position in static mode on long baselines (100+ km) with accuracy down to 1-2 centimeters with help of TOPAZ PPK online service. It may help in reckoning own RTK base coordinates using permanent CORS station (IGS, NGS, local provider) even if reference is located far away.

For sure such results may be get only when using good GNSS antenna with minimal multipath located in perfect environment w/o shadings and obstacles. Both rover and base measurements files must contain at least dual frequency pseudorange and carrier phase observations for at least several GNSS systems (L1-Only UBLOX receivers is not the case).