GNSS Multipath Analysis

Table of Contents

• Introduction
• Features
• Installation
  • Prerequisites
  • Installing LaTeX (optional)
• How to run it
• Compatibility
• License
• User arguments
• Examples
  • Run a multipath analysis using a SP3 file and only mandatory arguments
  • Run a multipath analysis using a RINEX navigation file with SNR, a defined datarate for ephemerides and with an elevation angle cut off at 10°
  • Run analysis with several navigation files
  • Run analysis without making plots
  • Run analysis and use the Zstandard compression algorithm (ZSTD) to compress the pickle file storing the results
  • Read a RINEX observation file
  • Read a RINEX navigation file (v.3)
  • Read in the results from an uncompressed Pickle file
  • Read in the results from a compressed Pickle file

Introduction

GNSS Multipath Analysis is a software tool for analyzing the multipath effect on Global Navigation Satellite Systems (GNSS). The core functionality is based on the MATLAB software GNSS_Receiver_QC_2020, but has been adapted to Python and includes additional features. A considerable part of the results has been validated by comparing the results with estimates from RTKLIB. This software will be further developed, and feedback and suggestions are therefore gratefully received. Don't hesitate to report if you find bugs or missing functionality. Either by e-mail or by raising an issue here in GitHub.

Features

• Estimates the code multipath for all GNSS systems (GPS, GLONASS, Galileo, and BeiDou).
• Estimates the code multipath for all available signals/codes in the RINEX file.
• Provides statistics on the total number of cycle slips detected (using both ionospheric residuals and code-phase differences).
• Supports both RINEX navigation files (broadcast ephemerides) and SP3 files (precise ephemerides).
• Supports both RINEX v2.xx and v3.xx observation files.
• Generates various plots, including:
  • Ionospheric delay over time and zenith-mapped ionospheric delay (combined).
  • The multipath effect plotted against time and elevation angle (combined).
  • Bar plot showing multipath RMSE for each signal and system.
  • Polar plot of the multipath effect and Signal-to-Noise Ratio (SNR).
  • Polar plots of SNR and multipath.
  • Polar plot of each observed satellite in the system.
  • SNR versus time/elevation.
• Extracts GLONASS FCN from RINEX navigation files.
• Detects cycle slips and estimates the multipath effect.
• Exports results to CSV and a Python dictionary as a Pickle (both compressed and uncompressed formats are supported).
• Allows selection of specific navigation systems and signal bands for analysis.

Installation

To install the software to your Python environment using pip:

pip install gnssmultipath

Prerequisites

• Python >=3.8: Ensure you have Python 3.8 or newer installed.
• LaTeX (optional): Required for generating plots with LaTeX formatting.

Note: In the example plots, TEX is used to get prettier text formatting. However, this requires TEX/LaTex to be installed on your computer. The program will first try to use TEX, and if it's not possible, standard text formatting will be used. So TEX/LaTex is not required to run the program and make plots.

Installing LaTeX (optional)

• On Ubuntu: sudo apt-get install texlive-full
• On Windows: Download and install from MiKTeX
• On MacOS: brew install --cask mactex

How to Run It

To run the GNSS Multipath Analysis, import the main function and specify the RINEX observation and navigation/SP3 files you want to use. To perform the analysis with default settings and by using a navigation file:

from gnssmultipath import GNSS_MultipathAnalysis

outputdir = 'path_to_your_output_dir'
rinObs_file = 'your_observation_file.XXO'
rinNav_file = 'your_navigation_file.XXN'
analysisResults = GNSS_MultipathAnalysis(rinObs_file,
                                         broadcastNav1=rinNav_file,
                                         outputDir=outputdir)

If you have a SP3 file, and not a RINEX navigation file, you just replace the keyword argument broadcastNav1 with sp3NavFilename_1.

The steps are:

1. Reads in the RINEX observation file
2. Reads the RINEX navigation file or the precise satellite coordinates in SP3-format (depends on what’s provided)
3. If a navigation file is provided, the satellite coordinates will be transformed from Kepler-elements to ECEF for GPS, Galileo and BeiDou. For GLONASS the navigation file is containing a state vector. The coordinates then get interpolated to the current epoch by solving the differential equation using a 4th order Runge-Kutta. If a SP3 file is provided, the interpolation is done by a barycentric Lagrange interpolation.
4. Satellites elevation and azimuth angles get computed.
5. Cycle slip detection by using both ionospheric residuals and a code-phase combination. These linear combinations are given as

$$ \dot{I} = \frac{1}{\alpha-1}\left(\Phi_1 - \Phi_2\right)/\Delta t $$

$$ d\Phi_1R_1 = \Phi_1 - R_1 $$

The threshold values can be set by the user, and the default values are set to $0.0667 [\frac{m}{s}]$ and $6.67[\frac{m}{s}]$ for the ionospheric residuals and code-phase combination respectively.

6. Multipath estimates get computed by making a linear combination of the code and phase observation. PS: A dual frequency receiver is necessary because observations from two different bands/frequency are needed.

$$MP_1 = R_1 - \left(1+\frac{2}{\alpha - 1}\right)\Phi_1 + \left(\frac{2}{\alpha - 1}\right)\Phi_2$$

where $R_1$ is the code observation on band 1, $\Phi_1$ and $\Phi_2$ is phase observation on band 1 and band 2 respectively. Furthermore $\alpha$ is the ratio between the two frequency squared

$$\alpha=\frac{{f}^2_1}{{f}^2_2}$$

7. Based on the multipath estimates computed in step 6, both weighted and unweighted RMS-values get computed. The RMS value has unit meter, and is given by

$$RMS=\sqrt{\frac{\sum\limits_{i=1}^{N_{sat}}\sum\limits_{j=1}^{N_{epohcs}} MP_{ij}}{N_{est}}}$$

For the weighted RMS value, the satellite elevation angle is used in a weighting function defined as

$$w =\frac{1}{4sin^2\beta}$$

for every estimates with elevation angle $\beta$ is below $30^{\circ}$ and $w =1$ for $\beta > 30^{\circ}$.

8. Several plot will be generated (if not set to FALSE):

   • Ionospheric delay wrt time and zenith mapped ionospheric delay (combined)

     

   • The Multipath effect plotted wrt time and elevation angle (combined)

     

   • Barplot showing RMS values for each signal and system

     

   • Polar plot of the multipath effect as function of elevation angle and azimuth

     

   • Polar plot of each observed satellite in the system

     

   • Signal-To-Noise Ratio (SNR) plotted wrt time and elevation angle (combine)

     

   • Polar plot of Signal-To-Noise Ratio (SNR)

     

9. Exporting the results as a pickle file which easily can be imported into python as a dictionary
10. The results in form of a report get written to a text file with the same name as the RINEX observation file.
11. The estimated values are also written to a CSV file by default

    

User arguments

The GNSS_MultipathAnalysis function accepts several keyword arguments that allow for detailed customization of the analysis process. Below is a list of the first five arguments:

• rinObsFilename (str): Path to the RINEX 3 observation file. This is a required argument.

• broadcastNav1 (Union[str, None], optional): Path to the first RINEX navigation file. Default is None.

• broadcastNav2 (Union[str, None], optional): Path to the second RINEX navigation file (if available). Default is None.

• broadcastNav3 (Union[str, None], optional): Path to the third RINEX navigation file (if available). Default is None.

• broadcastNav4 (Union[str, None], optional): Path to the fourth RINEX navigation file (if available). Default is None.

More...

• sp3NavFilename_1 (Union[str, None], optional): Path to the first SP3 navigation file. Default is None.

• sp3NavFilename_2 (Union[str, None], optional): Path to the second SP3 navigation file (optional). Default is None.

• sp3NavFilename_3 (Union[str, None], optional): Path to the third SP3 navigation file (optional). Default is None.

• desiredGNSSsystems (Union[List[str], None], optional): List of GNSS systems to include in the analysis. For example, ['G', 'R'] to include only GPS and GLONASS. Default is all systems (None).

• phaseCodeLimit (Union[float, int, None], optional): Critical limit that indicates cycle slip for phase-code combination in m/s. If set to 0, the default value of 6.667 m/s will be used. Default is None.

• ionLimit (Union[float, None], optional): Critical limit indicating cycle slip for the rate of change of the ionospheric delay in m/s. If set to 0, the default value of 0.0667 m/s will be used. Default is None.

• cutoff_elevation_angle (Union[int, None], optional): Cutoff angle for satellite elevation in degrees. Estimates with elevation angles below this value will be excluded. Default is None.

• outputDir (Union[str, None], optional): Path to the directory where output files should be saved. If not specified, the output will be generated in a sub-directory within the current working directory. Default is None.

• plotEstimates (bool, optional): Whether to plot the estimates. Default is True.

• plot_polarplot (bool, optional): Whether to generate polar plots. Default is True.

• include_SNR (bool, optional): If set to True, the Signal-to-Noise Ratio (SNR) from the RINEX observation file will be included in the analysis. Default is True.

• save_results_as_pickle (bool, optional): If True, the results will be saved as a binary pickle file. Default is True.

• save_results_as_compressed_pickle (bool, optional): If True, the results will be saved as a binary compressed pickle file using zstd compression. Default is False.

• write_results_to_csv (bool, optional): If True, a subset of the results will be exported as a CSV file. Default is True.

• output_csv_delimiter (str, optional): The delimiter to use for the CSV file. Default is a semicolon (;).

• nav_data_rate (int, optional): The desired data rate for ephemerides in minutes. A higher value speeds up processing but may reduce accuracy. Default is 60 minutes.

• includeResultSummary (Union[bool, None], optional): Whether to include a detailed summary of statistics in the output file, including for individual satellites. Default is None.

• includeCompactSummary (Union[bool, None], optional): Whether to include a compact overview of statistics in the output file. Default is None.

• includeObservationOverview (Union[bool, None], optional): Whether to include an overview of observation types for each satellite in the output file. Default is None.

• includeLLIOverview (Union[bool, None], optional): Whether to include an overview of LLI (Loss of Lock Indicator) data in the output file. Default is None.

• use_LaTex (bool, optional): If True, LaTeX will be used for rendering text in plots, requiring LaTeX to be installed on your system. Default is True.

Output

• analysisResults (dict): A dictionary containing the results of the analysis for all GNSS systems.

Compatibility

• Python Versions: Compatible with Python 3.8 and above.
• Dependencies: All dependencies will be automatically installed with pip install gnssmultipath.

License

This project is licensed under the MIT License - see the LICENSE file for details.

Some simple examples on how to use the software:

Run a multipath analysis using a SP3 file and only mandatory arguments

from gnssmultipath import GNSS_MultipathAnalysis

rinObs_file = 'OPEC00NOR_S_20220010000_01D_30S_MO_3.04'
SP3_file    = 'SP3_20220010000.eph'
analysisResults = GNSS_MultipathAnalysis(rinex_obs_file=rinObs_file, sp3NavFilename_1=SP3_file)

Run a multipath analysis using a RINEX navigation file with SNR, a defined datarate for ephemerides and with an elevation angle cut off at 10°

from gnssmultipath import GNSS_MultipathAnalysis

# Input arguments
rinObs_file = 'OPEC00NOR_S_20220010000_01D_30S_MO_3.04'
rinNav_file = 'BRDC00IGS_R_20220010000_01D_MN.rnx'
output_folder = 'C:/Users/xxxx/Results_Multipath'
cutoff_elevation_angle = 10  # drop satellites lower than 10 degrees
nav_data_rate = 60  # desired datarate for ephemerides (to improve speed)

analysisResults = GNSS_MultipathAnalysis(rinex_obs_file=rinObs_file,
                                         broadcastNav1=rinNav_file,
                                         include_SNR=True,
                                         outputDir=output_folder,
                                         nav_data_rate=nav_data_rate,
                                         cutoff_elevation_angle=cutoff_elevation_angle)

Run analysis with several navigation files

from gnssmultipath import GNSS_MultipathAnalysis

outputdir = 'path_to_your_output_dir'
rinObs = "OPEC00NOR_S_20220010000_01D_30S_MO_3.04_croped.rnx"

# Define the path to your RINEX navigation file
rinNav1 = "OPEC00NOR_S_20220010000_01D_CN.rnx"
rinNav2 = "OPEC00NOR_S_20220010000_01D_EN.rnx"
rinNav3 = "OPEC00NOR_S_20220010000_01D_GN.rnx"
rinNav4 = "OPEC00NOR_S_20220010000_01D_RN.rnx"

analysisResults = GNSS_MultipathAnalysis(rinObs,
                                         broadcastNav1=rinNav1,
                                         broadcastNav2=rinNav2,
                                         broadcastNav3=rinNav3,
                                         broadcastNav4=rinNav4,
                                         outputDir=outputdir)

Run analysis without making plots

from gnssmultipath import GNSS_MultipathAnalysis

rinObs_file = 'OPEC00NOR_S_20220010000_01D_30S_MO_3.04'
SP3_file    = 'SP3_20220010000.eph'
analysisResults = GNSS_MultipathAnalysis(rinex_obs_file=rinObs_file, sp3NavFilename_1=SP3_file, plotEstimates=False)

Run analysis and use the Zstandard compression algorithm (ZSTD) to compress the pickle file storing the results

from gnssmultipath import GNSS_MultipathAnalysis

rinObs_file = 'OPEC00NOR_S_20220010000_01D_30S_MO_3.04'
SP3_file    = 'SP3_20220010000.eph'
analysisResults = GNSS_MultipathAnalysis(rinex_obs_file=rinObs_file, sp3NavFilename_1=SP3_file, save_results_as_compressed_pickle=True)

Read a RINEX observation file

from gnssmultipath import readRinexObs

rinObs_file = 'OPEC00NOR_S_20220010000_01D_30S_MO_3.04'
GNSS_obs, GNSS_LLI, GNSS_SS, GNSS_SVs, time_epochs, nepochs, GNSSsystems, \
        obsCodes, approxPosition, max_sat, tInterval, markerName, rinexVersion, recType, timeSystem, leapSec, gnssType, \
        rinexProgr, rinexDate, antDelta, tFirstObs, tLastObs, clockOffsetsON, GLO_Slot2ChannelMap, success = \
        readRinexObs(rinObs_file)

Read a RINEX navigation file (v.3)

from gnssmultipath import Rinex_v3_Reader

rinNav_file = 'BRDC00IGS_R_20220010000_01D_MN.rnx'
navdata = Rinex_v3_Reader().read_rinex_nav(rinNav_file, data_rate=60)

Read in the results from an uncompressed Pickle file

from gnssmultipath import PickleHandler

path_to_picklefile = 'analysisResults.pkl'
result_dict = PickleHandler.read_pickle(path_to_picklefile)

Read in the results from a compressed Pickle file

from gnssmultipath import PickleHandler

path_to_picklefile = 'analysisResults.pkl'
result_dict = PickleHandler.read_zstd_pickle(path_to_picklefile)