Reference

General GNSS References

The GNSS in gnss_lib_py stands for Global Navigation Satellite System(s). The following is a list of references that might be helpful in learning more about GNSS:

• Global Positioning System: Signals, Measurements, and Performance by Pratap Misra and Per Enge.

• Positioning, Navigation, and Timing Technologies in the 21st Century edited by Y. Jade Morton, Frank van Diggelen, James J. Spilker Jr, Bradford W. Parkinson, Sherman Lo, and Grace Gao.

• Understanding GPS/GNSS: Principles and Applications edited by Elliott D. Kaplan and Christopher J. Hegarty.

• “GPS: An Introduction to Satellite Navigation” by Frank van Diggelen found on YouTube: a playlist of online classes that teach a broad overview of GNSS topics.

• “GPS” by Bartosz Ciechanowski found at ciechanow.ski/gps: a visually-appealing and interactive blog post about some of the basic principles of GNSS positioning.

Reference Documents for GNSS Standards

GNSS constellations and receivers use standardized file formats to transfer information such as estimated receiver coordinates, broadcast ephemeris parameters, and precise ephimerides. The parsers in gnss_lib_py are based on standard documentation for the GNSS constellations and file types, which are listed below along with their use in gnss_lib_py.

• Rinex v2.11 (version format document retrieved on 2nd July, 2023): for parsing broadcast navigation ephimerides.

• Rinex v3.05 (version format document retrieved on 2nd July, 2023): for parsing broadcast navigation ephimerides.

• Rinex v4.00 (version format document retrieved on 2nd July, 2023): currently not supported by gnss_lib_py.

• NMEA (reference manual retrieved on 23rd June, 2023): for parsing NMEA files with GGA and RMC messages.

• SP3: used to determine SV positions for precise

• GLONASS ICD (retrieved from this link retrieved on 27th June, 2023): for determining GLOASS SV states from broadcast satellite positions, velocities, and accelerations.

Details about NavData Class

We use a custom class NavData in gnss_lib_py for storing measurements and state estimates. Along with the standard naming convention for measurements and state estimates, the NavData class provides modularity between different datasets, algorithms and functions for visualization and metric calculation.

Using our custom NavData class has the following advantages:

• Our implementation uses string labels to intuitively access and set values in the underlying array. Eg. data['row_name'] = row_values. This prevents mistakenly accessing the wrong row while using measurements

• Our implementation uses np.ndarray as the underlying data data storage object, which is faster than pd.DataFrame. The speed increase over Pandas’ pd.DataFrame is illustrated in the timing_comparisons example notebook.

• We have implemented custom methods for adding new rows (measurement types), adding new columns (time stamps of data), deleting rows and columns and creating copies, including subsets

• We have also implemented custom methods for returning subsets where given equality and inequalities are satisfied

• NavData also has implementations to loop over a larger NavData column-wise and loop over subsets grouped over time

• NavData also supports string valued entries, which are stored numerically in the underlying array. We provide methods so that accessing string valued rows takes strings as inputs and outputs. Users don’t have to worry about the internal handling of string values

However, NavData is maintained as part of gnss_lib_py and might not have all desired functionality that more mature libraries, like pandas and numpy might have. As a workaround, since the underlying storage is in np.ndarray and we provide functions for handling strings, you can implement your own methods using a combination of numpy methods and NavData methods.

Timing Conventions

We use four different time formats in gnss_lib_py:

• gps_millis : The number of milliseconds that have elapsed since the start of the GPS epoch on January 6th, 1980. This time format is continuous and is not adjusted with leap seconds. This time is stored as a single number that is a double int or float, depending on the context.

• unix_millis : The number of milliseconds that have elapsed since the start of the Unix epoch on January 1st, 1970. This time format is not continuous and is adjusted with leap seconds. This time is also stored as a single number that is a double int or float.

• utc_timestamp : UTC time, which is stored as a timestamp using the datetime library. This time format is not continuous and is adjusted with leap seconds.

• gps_week and gps_tow : The GPS week since the start of the GPS epoch on January 6th, 1980 and the time of that week in seconds.

Of these four time formats, we use gps_millis as the default time that measurements and state estimates correspond to. Conversions between all these time formats are provided in the utils/time_conversion.py file.

Between these four time formats, all major applications of GNSS-based state estimation should be covered and any of these time formats can be used interchangeably.

Standard Naming Conventions

In large part our conventions follow from the naming patterns in Google’s derived datasets for the Google Decimeter challenge

GNSS measurement naming conventions are as follows:

• trace_name : (string) name for the trace

• rx_name : (string) name for the receiver device

• gps_millis : (float) milliseconds that have elapsed since the start of the GPS epoch on January 6th, 1980. gps_millis is the common method for time that we expect in many functions and must be created to use some of the algorithms.

• gps_week : (int) GPS weeks since the start of the GPS epoch on January 6th, 1980. The NOAA CORS website maintains a helpful reference calendar.

• gps_tow : (float) time of receiving signal as measured by the receiver in seconds since start of GPS week (Sunday at midnight). This time includes leap seconds

• unix_millis : (int) milliseconds that have elapsed since January 1, 1970 at midnight (midnight UTC) and not counting leapseconds.

• gnss_id : (string) GNSS identification using the constellation name in lowercase, possible options are gps, galileo glonass, beidou, qzss, sbas, irnss, etc.

• sv_id : (int) satellite vehicle identification number

• gnss_sv_id : (string) combination of gnss_id and sv_id in a three character string. The first character is the upper case letter for the satellite system identifier defined in the RINEX 3.04 specification (e.g. G for gps, R for glonass, E for galileo, C for Beidou, etc.) followed by a two digit SV ID.

• signal_type (string) Identifier for signal type, eg. l1 for GPS L1 signal, e5 for Galileo’s E5 signal or b1i for BeiDou’s B1I signal. The string is expected to consist of lowercase letters and numbers.

• tx_sv_tow (float) measured signal transmission time as sent by the space vehicle/satellite and in seconds since the start of the gps week.

• x_sv_m : (float) satellite ECEF x position in meters at best estimated true signal transmission time.

• y_sv_m : (float) satellite ECEF y position in meters at best estimated true signal transmission time.

• z_sv_m : (float) satellite ECEF z position in meters at best estimated true signal transmission time.

• el_sv_deg : (float) Elevation of satellite in degrees in relation to the receiver’s position.

• az_sv_deg : (float) Azimuth of satellite in degrees in relation to the receiver’s position.

• vx_sv_mps : (float) satellite ECEF x velocity in meters per second at estimated true signal transmission time.

• vy_sv_mps : (float) satellite ECEF y velocity in meters per second at estimated true signal transmission time.

• vz_sv_mps : (float) satellite ECEF z velocity in meters per second at estimated true signal transmission time.

• b_sv_m : (float) satellite clock bias in meters.

• b_dot_sv_mps : (float) satellite clock bias drift in meters per second.

• raw_pr_m : (float) raw, uncorrected pseudorange in meters.

• corr_pr_m : (float) corrected pseudorange according to the formula: corr_pr_m = raw_pr_m + b_sv_m - intersignal_bias_m - iono_delay_m - tropo_delay_m

• raw_pr_sigma_m : (float) uncertainty (standard deviation) of the raw, uncorrected pseuodrange in meters.

• intersignal_bias_m : (float) inter-signal range bias in meters.

• iono_delay_m : (float) ionospheric delay in meters.

• tropo_delay_m : (float) tropospheric delay in meters.

• cn0_dbhz : (float) carrier-to-noise density in dB-Hz

• accumulated_delta_range_m : accumulated delta range in meters.

• accumulated_delta_range_sigma_m : uncertainty in the accumulated delta range in meters.

State estimate naming conventions are as follows:

• gps_millis : (float) milliseconds that have elapsed since the start of the GPS epoch on January 6th, 1980. gps_millis is the common method for time that we expect in many functions and must be created to use some of the algorithms.

• x_rx_m : (float) receiver ECEF x position estimate in meters.

• y_rx_m : (float) receiver ECEF y position estimate in meters.

• z_rx_m : (float) receiver ECEF z position estimate in meters.

• v_rx_mps : (float) receiver total velocity estimate in meters per second.

• vx_rx_mps : (float) receiver ECEF x velocity estimate in meters per second.

• vy_rx_mps : (float) receiver ECEF y velocity estimate in meters per second.

• vz_rx_mps : (float) receiver ECEF z velocity estimate in meters per second.

• ax_rx_mps2 : (float) receiver ECEF x acceleration estimate in meters per second squared.

• a_rx_mps2 : (float) receiver total acceleration estimate in meters per second squared.

• ay_rx_mps2 : (float) receiver ECEF y acceleration estimate in meters per second squared.

• az_rx_mps2 : (float) receiver ECEF z acceleration estimate in meters per second squared.

• b_rx_m : (float) receiver clock bias in meters.

• b_dot_rx_mps : (float) receiver clock bias drift rate in meters per second.

• lat_rx_deg : (float) receiver latitude position estimate in degrees.

• lon_rx_deg : (float) receiver longitude position estimate in degrees.

• alt_rx_m : (float) receiver altitude position estimate in meters. Referenced to the WGS-84 ellipsoid.

• heading_rx_rad : (float) receiver heading estimate in radians, clockwise from North, where to 0 radians is North, pi/2 radians is East and so on. Assumed to be radians in the range between 0 and 2pi.

Receiver ground truth naming conventions are as follows:

• gps_millis : (float) milliseconds that have elapsed since the start of the GPS epoch on January 6th, 1980. gps_millis is the common method for time that we expect in many functions and must be created to use some of the algorithms.

• x_rx_gt_m : (float) receiver ECEF x ground truth position in meters.

• y_rx_gt_m : (float) receiver ECEF y ground truth position in meters.

• z_rx_gt_m : (float) receiver ECEF z ground truth position in meters.

• v_rx_gt_mps : (float) receiver total velocity ground truth in meters per second.

• vx_rx_gt_mps : (float) receiver ECEF x velocity ground truth in meters per second.

• vy_rx_gt_mps : (float) receiver ECEF y velocity ground truth in meters per second.

• vz_rx_gt_mps : (float) receiver ECEF z velocity ground truth in meters per second.

• a_rx_gt_mps2 : (float) receiver total acceleration estimate in meters per second squared.

• ax_rx_gt_mps2 : (float) receiver ECEF x acceleration ground truth in meters per second squared.

• ay_rx_gt_mps2 : (float) receiver ECEF y acceleration ground truth in meters per second squared.

• az_rx_gt_mps2 : (float) receiver ECEF z acceleration ground truth in meters per second squared.

• lat_rx_gt_deg : (float) receiver ground truth latitude in degrees.

• lon_rx_gt_deg : (float) receiver ground truth longitude in degrees.

• alt_rx_gt_m : (float) receiver ground truth altitude in meters. Referenced to the WGS-84 ellipsoid.

• heading_rx_gt_rad : (float) receiver heading ground truth in radians, clockwise from North, where to 0 radians is North, pi/2 radians is East and so on. Assumed to be radians in the range between 0 and 2pi.

Module Level Function References

All functions and classes are fully documented in the linked documentation below.

• algorithms
  • fde module
  • gnss_filters module
  • residuals module
  • snapshot module
• navdata
  • navdata module
  • operations module
• parsers
  • android module
  • clk module
  • google_decimeter module
  • nmea module
  • rinex_nav module
  • rinex_obs module
  • smartloc module
  • sp3 module
• utils
  • constants module
  • coordinates module
  • dop module
  • ephemeris_downloader module
  • file_operations module
  • filters module
  • gnss_models module
  • sv_models module
  • time_conversions module
• visualizations
  • plot_map module
  • plot_metric module
  • plot_skyplot module
  • style module

Testing References

All tests and test cases are fully documented in the linked documentation below.

• algorithms
  • test_fde module
  • test_gnss_filters module
  • test_residuals module
  • test_snapshot module
• navdata
  • test_navdata module
  • test_operations module
• parsers
  • test_android module
  • test_clk module
  • test_google_decimeter module
  • test_nmea module
  • test_rinex_nav module
  • test_rinex_obs module
  • test_smartloc module
  • test_sp3 module
• utils
  • test_coordinates module
  • test_dop module
  • test_ephemeris_downloader module
  • test_file_operations module
  • test_filters module
  • test_gnss_models module
  • test_sv_models module
  • test_time_conversions module
• visualizations
  • test_plot_map module
  • test_plot_metric module
  • test_plot_skyplot module
  • test_style module

Additional Indices

• Index

• Module Index