gnssTroposphere

Tropospheric delay model for GNSS signals

Since R2026a

Description

The gnssTroposphere object stores the tropospheric delay model to use while calculating the receiver position using the receiverposition function.

Creation

Syntax

tropo = gnssTroposphere

tropo = gnssTroposphere(delaymodel)

Description

tropo = gnssTroposphere create a tropospheric delay model object with no delay model.

tropo = gnssTroposphere(delaymodel) specifies the delay model.

example

Input Arguments

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`delaymodel` — Delay model
`"none"` (default) | `"saastamoinen"`

Delay model, specified as a one of these options:

"none" — Use no delay model.
"saastamoinen" — Use the Saastamoinen delay model.

This argument sets the DelayModel property.

Data Types: char | string

Properties

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`Delay Model` — Delay model
`"none"` (default) | `"saastamoinen"`

Delay model, specified as a one of these options:

"none" — Use no delay model.
"saastamoinen" — Use the Saastamoinen delay model. For more information, see Saastamoinen Delay Model.

Data Types: char | string

Examples

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Calculate Receiver Positions with Ionospheric and Tropospheric Delays

Open Live Script

Read the data from a RINEX navigation and observation messages. These RINEX files contain GNSS data for March 29, 2025.

navFileName = "GODE00USA_R_20250880000_01D_GN.rnx";
obsFileName = "GODE00USA_R_20250880800_01H_30S_MO.rnx";
[rnxnavdata,rnxnavhdr] = rinexread(navFileName);
[rnxobsdata,rnxobshdr] = rinexread(obsFileName);

Create ionosphere and troposphere delay models. Use the Klobuchar model for the ionosphere delay model with the GPS alpha and beta coefficients from the header file.

ionoParams = rnxnavhdr.IonosphericCorrections;
alpha = ionoParams(1).Parameters;
beta = ionoParams(2).Parameters;
ionoDelayModel = gnssIonosphere("klobuchar",alpha,beta);
tropoDelayModel = gnssTroposphere("saastamoinen");

Create the GNSS options for estimating the receiver position.

opts = gnssoptions(Ionosphere=ionoDelayModel,Troposphere=tropoDelayModel);

Get the GNSS measurements for the GPS satellites using the RINEX navigation and observation messages. Show the data for the first three time steps.

gpsData = gnssmeasurements(rnxobsdata.GPS,rnxnavdata.GPS);
gpsData(1:3,:)

ans=3×8 timetable
            Time            SatelliteID    Pseudorange                SatellitePosition                SatelliteClockBias    PseudorangeRate          SatelliteVelocity          SatelliteClockDrift    EphemerisAccuracy
    ____________________    ___________    ___________    _________________________________________    __________________    _______________    _____________________________    ___________________    _________________

    29-Mar-2025 08:00:00         1         2.4375e+07      -2.126e+07    -1.4117e+07     7.4018e+06        0.00019738              NaN          -471.47    -855.01      -2983        1.8076e-11                 2        
    29-Mar-2025 08:00:00         2          2.566e+07     -2.0524e+07    -1.6951e+07    -2.4589e+06       -0.00020789              NaN           429.94     23.954    -3140.9         9.436e-12                 2        
    29-Mar-2025 08:00:00         3         2.2235e+07     -1.2415e+07    -9.5047e+06      2.132e+07         0.0006808              NaN           578.88    -2675.8    -837.42        3.5243e-12                 2

Calculate the receiver positions by using the GPS measurements and the options specified by the gnssoptions object. Show the receiver positions for the first three time steps.

[recPos,recVel,hdop,vdop,info] = receiverposition(gpsData,opts);
recPos(1:3,:)

ans = 3×3

   39.0217  -76.8268   13.7420
   39.0217  -76.8269   13.0003
   39.0217  -76.8268   12.2894

More About

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Saastamoinen Delay Model

The Saastamoinen delay model calculates the tropospheric time delay on GNSS signals as they pass through the troposphere using this procedure [3].

Calculate the total pressure.
$P = 1013.25 \times {(1 - 2.2557 \times 10^{- 5} \times h_{r})}^{5.2568},$
where h_r is the geodetic height above mean sea level (MSL) of receiver r, in meters. This is approximated by the ellipsoidal height which is equivalent to the receiver altitude estimate.
Calculate the total temperature, in Kelvin.
$T = 15.0 - 6.5 \times 10^{- 3} h_{r} + 273.15$
Calculate the partial pressure, in hPa.
$p = 6.108 \exp {\frac{17.15 T - 4684.0}{T - 38.45}} \times \frac{h_{r e l}}{100},$
where h_rel is the relative humidity. gnssTroposphere assumes a constant relative humidity value of 70%.
Calculate the Saastamoinen tropospheric delay , in meters. The delay is comprised of wet and hydrostatic delay components.
$\begin{array}{l} T_{r, w e t}^{s} = \frac{1}{\cos (z)} (0.002277 (\frac{1255}{T} + 0.05) p) \\ T_{r, h y d r o}^{s} = \frac{1}{\cos (z)} \frac{0.0022768 P}{1 - 0.0026 \cos (2 ϕ_{r}) - 0.00000028 h_{r}}, \\ T_{r}^{s} = T_{r, w e t}^{s} + T_{r, h y d r o}^{s}, \end{array}$
where:
- z — Zenith angle, in radians, defined as $z = \frac{π}{2} - e l_{r}^{s}$ .
- $e l_{r}^{s}$ — Elevation angle of satellite s with respect to receiver r, in radians.
- ϕ_r — Latitude of the receiver r, in radians.

References

[1] Takasu, T. RTKLIB ver. 2.4.2 Manual, Appendix E.5, April 29, 2013. https://www.rtklib.com/prog/manual_2.4.2.pdf.

[2] International GNSS Service (for Daily 30-Second GPS Broadcast Ephemeris Data, NASA Crustal Dynamics Data Information System (CDDIS), Greenbelt, MD, USA, March 29, 2024; accessed March 29, 2024). https://dx.doi.org/10.5067/GNSS/gnss_daily_n_001.

[3] International GNSS Service (for Hourly 30-Second Observation Data, NASA Crustal Dynamics Data Information System (CDDIS), Greenbelt, MD, USA, March 29, 2024; accessed March 29, 2024). https://dx.doi.org/10.5067/GNSS/gnss_hourly_o_001.

gnssTroposphere

Description

Creation

Syntax

Description

Input Arguments

`delaymodel` — Delay model
`"none"` (default) | `"saastamoinen"`

Properties

`Delay Model` — Delay model
`"none"` (default) | `"saastamoinen"`

Examples

Calculate Receiver Positions with Ionospheric and Tropospheric Delays

More About

Saastamoinen Delay Model

References

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Version History

See Also

gnssTroposphere

Description

Creation

Syntax

Description

Input Arguments

delaymodel — Delay model "none" (default) | "saastamoinen"

Properties

Delay Model — Delay model "none" (default) | "saastamoinen"

Examples

Calculate Receiver Positions with Ionospheric and Tropospheric Delays

More About

Saastamoinen Delay Model

References

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using MATLAB® Coder™.

Version History

See Also

`delaymodel` — Delay model
`"none"` (default) | `"saastamoinen"`

`Delay Model` — Delay model
`"none"` (default) | `"saastamoinen"`

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.