GNSS Measurement Simulator

The GNSS measurement simulator is used to generate raw GNSS observables from an input file containing the simulated navigation solution of the receiver and an associated ephemeris file retrievied from CDDIS. The GNSS measurement simulator then uses this information to generate raw GNSS observables.

Why use a software-based measurement simulator

I developed this GNSS measurement simulator during my PhD with obvious reasons as to why I needed it. Some of the reasons behind it include:

• The simulator allows comprehensive, repeatable, and cost-effective multi-system multiconstellation GNSS testing.
• User motion and measurement generation can be tightly integrated and easily customisable in a software-based measurement simulator.
• Allows for ease of testing and evaluating a navigation scheme easy under different conditions leading to faster turn around times.
• Multiple GNSS receivers can easily be simulated, making it easy to develop and assess relative positioning systems such as RTK and PPK alongside GNSS attitude solutions.
• Low maintenace costs. GNSS hardware simulators are heavy and expensive units and require expensive licenses and upgrades to keep up to date.
• Better control of the receiver dynamics. The level of control of the receiver dynamics in a hardware simulator is fairly limited. In [3], it was shown that double differenced code residuals were affected by large biases during turns or when the aircraft experienced rapid accelerations. As a result, the receiver lost lock. It was argued that the operation of the receiver tracking loops was the cause of the increased residuals to cope with the level of dynamics experienced by the receiver. Since the methods used within a receiver are proprietary, it was difficult to identify the exact cause. This makes a software-based GNSS simulator an attractive alternative to a hardware-based one since the receiver dynamics can be added or removed as desired by the user.

Measurement Models

In the simulator, for a given frequency band i (here eliminated for brevity) the pseudorange $P_r^s$, Doppler frequency $D_r^s$, and carrier phase (given as phase range) measurements between a satellite s and a receiver r are given by:

$P_r^s = \rho_r^s + c(dt_r(t_r)-dT_s(T_s))+I_r^s + T_r^s + M_P + \epsilon(\rho)$

$D_r^s = -\frac{fi}{c} \left([v_{es}^e(T_s) - v_{er}^e(t_r)]^T \cdot e_r^s + c\left( \frac{\partial t_r(t_r)}{\partial t} - \frac{\partial T_s(T_s)}{\partial t} \right) + \dot{I}_r^s + \dot{T}_r^s \right) + \epsilon(f_D)$

$\Phi_r^s = \rho_r^s + c(dt_r(t_r)-dT_s(T_s)) - I_r^s + T_r^s + \lambda (\delta\phi + N_r^s) +\epsilon(\Phi)$

where:

$\rho_r^s$ - Geometric range from the receiver to the satellite [m]

$dt_r(t_r)$ - Receiver clock offset at signal reception time [s]

$dT_s(T_s)$ - Satellite clock offset at signal transmission time [s]

$I_r^s$ - Ionospheric delay [m]

$T_r^s$ - Tropospheric delay [m]

$\delta\phi = \phi_{r,0} - \phi_{s,0}$

$N_r^s$ - Integer ambiguity term

$\epsilon(\rho)$ - Random thermal noise in range measurements [m]

$\epsilon(f_D)$ - Includes multipath effects and random noise in Doppler measurements [Hz]

$\epsilon(\Phi)$ - In addition to carrier phase noise, this terms also admits satellites and receiver's antenna phase centre offset and variation, any receiver displacement due to earth tides, and phase wind-up

The measurement generation mechanism is shown in the figure below:

Carrier power to noise density

In addition to the measurements above, the simulator also outputs the carrier power to noise density ratio given by:

$C/N_0 = P_r + G_a - N_0 + \epsilon(C/N_0)$

where:

$P_r$ - is the received signal power from a satellite at the antenna input [dBW]

$N_0$ - is the thermal noise power component in a 1-Hz bandwidth [dBW]

$G_a$ - is the antenna gain toward a satellite [dBic]

Further, the thermal noise power is modelled using:

$N_0 = 10\cdot log_{10}(k\cdot(T_{ant} + T_{amp}))$

where:

$T_{ant}$ - antenna equivalent noise temperature ~ $100 K$

$T_{amp}$ - is the amplifier noise temperature [K] that is determined from the amplifier noise figure $N_f$

$k$ - is the Boltzmann's constant

In the simulator, the $C/N_0$ measurements for a particular satellite will vary depending on the satellite elevation angle due to differences in path loss and the satellite and receiver gain pattern [1]. The antenna gain variation with satellite elevation angle for the simulated receiver is shown in the figure below. And the $C/N_0$ realisations are also shown for the simulated receiver.

Thermal Noise

In the simulator, thermal noise affecting the pseudorange measurements is modelled as white noise with a standard deviation varying with the carrier power to noise density ratio. This is given by:

$\epsilon(\rho) = N(0,\sigma_e^2(C/N_0))$

$\sigma_e = b_0 + b_1\cdot\exp(-\frac{C/N_0-b_2}{b_3})$

Results using the model above are shown in the figure below. The figure shows the multiconstellation pseudorange noise obtained using Hatch filter residuals from multiconstellation dataset.

Other Models

For a detailed description of other error models including:

• Residual Ionospheric error model
• Residual Tropospheric error model
• Multipath model
• Receiver clock error model

The user is directed to [1] and [2].

Usage

1. To fetch ephemeris files, it is recommended to use the fetch.py script. This will store any retrieved files in the CDDIS folder. For additional information, please refer to Fetching files

References

[1] Mwenegoha, H. A., Moore, T., Pinchin, J. and Jabbal, M. (2020) ‘A Model-based Tightly Coupled Architecture for Low-Cost Unmanned Aerial Vehicles for Real-Time Applications’, IEEE Access.

[2] Mwenegoha, H. A., Moore, T., Pinchin, J. and Jabbal, M. (2019) ‘Enhanced Fixed Wing UAV Navigation in Extended GNSS Outages using a Vehicle Dynamics Model and Raw GNSS Observables’, in Proceedings of the 32nd International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2019). Miami, Florida, pp. 2552–2565.

[3] Pinchin, J. (2011) GNSS Based Attitude Determination for Small Unmanned Aerial Vehicles. University of Canterbury