Low-cost multi-GNSS, single-frequency RTK averaging for marine applications: accurate stationary positioning and vertical tide measurements

Figures & data

Table 1. Maximum allowable uncertainty values for the highest two IHO Orders of survey from S-44 (2020).

Order of Survey:	Special Order	Exclusive Order
Total Horizontal Uncertainty (THU) at a 95% confidence level (m)	±2	±1
Total Vertical Uncertainty (TVU) at a 95% confidence level (m)	$\pm \sqrt{{{0.25}^2+(0.0075\mathrm{ }x\mathrm{ }\mathit{depth})}^2}$	$\pm \sqrt{{{0.15}^2+(0.0075\mathrm{ }x\mathrm{ }\mathit{depth})}^2}$
E.g. TVU at 10 m water depth	±0.26m	±0.17m
E.g. TVU at 30 m water depth	±0.34m	±0.27m

Figure 1. Location of low-cost RTK GNSS trials at Portobello Marine Lab (PML), Dunedin, New Zealand; a) South Island, NZ; b) PML with receiver locations shown (red points), details of each setup in Table 1; c) Example U-blox receiver used in trials; d) MNR1 base station (Trimble R10); e) DUND base station (Trimble Net R9 CORS station); f) A24Y base station (U-blox); g) TITG tide gauge and PML tide staff (ETTS) at wharf; h-j) BBR1 (Trimble R10), BBL1 (U-blox) setup on board R/V Beryl Brewin.

Table 2. Equipment setup at each station, cf. Figure 1.

Station	Terrestrial (fixed) or Marine (moving) installation	Receiver / Antenna	Software (acquisition and processing)	Data rate / observation time days (observation time hours) / logging time (UTC)
MNR1	Terrestrial (fixed)	Trimble R10	TSC3 with Trimble Access 2017.00, TBC v.4 & 5	1Hz / 3 days (55 hrs) / 14th 00:00 – 16th 07:00
DUND	Terrestrial (fixed)	Trimble NetR9 / Trimble TRM57971	CORS: PositioNZ-RT data stream	1Hz / ∼3 days (7 hrs longest continuous timeframe*) / continuous *large data gaps at remote logging computer beginning 14th 10:45.
A24Y	Terrestrial (fixed)	U-blox M8 evaluation kit	U-centre v. 18.11	1Hz / ∼3 days (52 hrs) / 14th 03:00 – 16th 07:00
BBR1	Marine (moving)	Trimble R10	TSC3 with Trimble Access 2017.00, TBC v.4 & 5	1Hz / ∼3 days (49.8 hrs) / 14th 05:10 – 16th 07:00
BBL1	Marine (moving)	U-blox M8 evaluation kit	U-centre v. 18.11	1Hz / ∼3 days (53 hrs) / 14th 02:00 – 16th 07:00
TITG	Terrestrial (fixed)	Waterwatch LS1	Tussock Innovation online portal	0.0033 Hz (5 min) / 3 days / continuous
ETTS	Terrestrial (fixed)	Tide Staff	Manual observation	0.0033 Hz (5 min) for 2x12hr periods over 2 days / 14th 21:00-09:10 and 15th 19:10 − 07:00

Figure 2. Known baseline demonstration of 3D data quality for stage 1 over 7 hrs: green dots are Easting, blue dots are Northing, red dots are Up, grey bars show number of satellites; a) 7.3 km baseline; b) 27.4 km baseline.

Table 3. Comparison of E, N, U values for different baseline lengths and timeframes for stage 1: Horizontal and vertical position quality checks.

Baseline	Baseline	Baseline timeframe	‘position availability’: % of fixed obs used after 0.1m filtering	Max range: E , N , U (m)	1 sigma standard deviation σ: E , N , U (m)
∼7.3km (Figure 1b, 1e & 1f)	DUND – A24Y	3 days : 14 – 16 Sept (including periods with data gaps at DUND CORS site)	99.8%	0.048 , 0.080 , 0.143	0.006 , 0.009 , 0.016
	DUND – A24Y	1 day : 14 Sept (Figure 2)	99.9%	0.021 , 0.040 , 0.063	0.003 , 0.007 , 0.008
∼27.4km (Figure 1d & 1f)	MNR1 – A24Y	3 days : 14 – 16 Sept	85.3%	0.070 , 0.083 , 0.194	0.009 , 0.010 , 0.022
	MNR1 – A24Y	1 day : 14 Sept (Figure 2)	95.4%	0.045 , 0.063 , 0.143	0.008 , 0.010 , 0.015

Figure 3. Tide gauge to tide staff observation comparison check using two twelve hour staff reading periods.

Figure 4. Tide derivation from ∼460 m baseline U-blox A24Y – BBL1 (53 hrs): a) Raw U-blox data and PML data; b) U-blox data raw and with gross spike filter plotted with corresponding PML tide gauge data; c) Raw U-blox and five minute moving average U-blox data; d) Five minute moving average U-blox data plotted with corresponding PML tide gauge data. Note: ‘Vt change / Tide (m)’ on y-axis recognizes raw RTK data (Vt change) and gauge (Tide) comparison.

Figure 5. Tide derivation from ∼7.3 km baseline: Low-cost (a&b), R10 (c&d): DUND – U-blox BBL1 (14 hrs): a) DUND - BBL1 raw and five minute moving average; b) Five minute moving average DUND - BBL1 and PML tide gauge data; and, DUND – R10 BBR1 (∼11hrs, note that the R10 did not start logging until 14th Sept 05:10UTC): c) DUND - BBR1 raw and five minute moving average; b) Five minute moving average DUND - BBR1 and PML tide gauge data. Note: ‘Vt change / Tide (m)’ on y-axis recognizes raw RTK data (Vt change) and gauge (Tide) comparison.

Figure 6. Tide derivation from ∼27.4 km baseline with weather deteriorating from ∼18:00 on 15th Sept visible as an increased variability in raw RTK observations: Low-cost (a&b), R10 (c&d): MNR1 – U-blox BBL1 (49.8 hrs): a) MNR1 - BBL1 raw and ten minute moving average; b) Ten minute moving average MNR1 - BBL1 and PML tide gauge data; and, MNR1 – R10 BBR10 (49.8 hrs): c) MNR1 – R10 raw and 10 min moving average; d) Ten minute moving average MNR1 – BBR1 and PML tide gauge data. Note: ‘Vt change/Tide (m)’ on y-axis recognizes raw RTK data (Vt change) and gauge (Tide) comparison.

Data availability statement

The data that support the findings of this study are available from the corresponding author, Emily Tidey, upon reasonable request.