Coordinate Conversions

import numpy as np
import gnss_lib_py as glp

ECEF coordintes for N positions can be converted to LLA and back by using functions defined in utils/coordinates.py

# Using the LLA coordinates the Aero/Astro department at Stanford University
x_lla = np.array([[37.427112], [-122.1764146], [16]])
print('Converted ECEF coordinates')
print(glp.geodetic_to_ecef(x_lla))

x_ecef = np.array([[-2700628], [-4292443], [3855152]])
print('Converted LLA coordinates')
print(glp.ecef_to_geodetic(x_ecef))

Converted ECEF coordinates
[[-2700628.97971166]
 [-4292443.61165747]
 [ 3855152.80233124]]
Converted LLA coordinates
[[  37.42711195]
 [-122.17640891]
 [  14.68637162]]

Local NED Frame Conversions

A local North-East-Down (NED) frame of reference can be instantiated by defining the point at the origin of the coordinate frame using either its ECEF position or LLA (w.r.t the WGS-84 ellipsoid) coordinates

# Instantiate using LLA coordinates
local_frame = glp.LocalCoord.from_geodetic(x_lla)
print('NED to ECEF conversion matrix for initialized local frame')
print(local_frame.ned_to_ecef_matrix)

local_frame = glp.LocalCoord.from_ecef(x_ecef)
print('NED to ECEF conversion matrix for initialized local frame')
print(local_frame.ned_to_ecef_matrix)

NED to ECEF conversion matrix for initialized local frame
[[ 0.32364473  0.84641245  0.42289485]
 [ 0.51440859 -0.5325279   0.67215908]
 [ 0.79412713  0.         -0.60775168]]
NED to ECEF conversion matrix for initialized local frame
[[ 0.32364468  0.8464125   0.42289479]
 [ 0.51440862 -0.53252782  0.67215913]
 [ 0.79412713  0.         -0.60775168]]

Once initialized, the local_frame can be used to convert position vectors to NED from ECEF or LLA and vice-versa

ned = local_frame.ecef_to_ned(x_ecef)
print('The converted NED coordinates are')
print(ned)

ecef = local_frame.ned_to_ecef(ned)
print('The converted ECEF coordinates are')
print(ecef)

lla = local_frame.ned_to_geodetic(ned)
print('The converted LLA coordinates are')
print(lla)

The converted NED coordinates are
[[0.]
 [0.]
 [0.]]
The converted ECEF coordinates are
[[-2700628.]
 [-4292443.]
 [ 3855152.]]
The converted LLA coordinates are
[[  37.42711195]
 [-122.17640891]
 [  14.68637162]]

The local_frame can also be used to convert free vectors in the NED frame of reference to free vectors in the ECEF frame of reference

v_vect = np.array([[1], [0], [0]])
v_ned = local_frame.ned_to_ecefv(v_vect)
print('The converted free vector in ECEF is')
print(v_ned)
v_ecef = local_frame.ecef_to_nedv(v_ned)
print('The converted free vector in NED is ')
print(v_ecef)

The converted free vector in ECEF is
[[0.32364468]
 [0.51440862]
 [0.79412713]]
The converted free vector in NED is
[[ 1.00000000e+00]
 [ 3.07393081e-18]
 [-7.83715186e-19]]

Elevation and Aziumth from ECEF Positions

Find elevation and azimuth angle from receiver and satellite ECEF positions.

# load Android Google Challenge data
glp.make_dir("../data")
!wget https://raw.githubusercontent.com/Stanford-NavLab/gnss_lib_py/main/data/unit_test/google_decimeter_2022/device_gnss.csv --quiet -nc -O "../data/device_gnss.csv"
navdata = glp.AndroidDerived2022("../data/device_gnss.csv")
navdata_subset = navdata.where("gps_millis",navdata["gps_millis",0]) # only use data from first timestep

To calculate the elevation and azimuth, pass in the receiver and satellites’ ECEF positions.

pos_sv_m = navdata_subset[["x_sv_m","y_sv_m","z_sv_m"]]
pos_rx_m = navdata_subset[["x_rx_m","y_rx_m","z_rx_m"],0].reshape(-1,1)

calculated_el_az = glp.ecef_to_el_az(pos_rx_m,pos_sv_m)
truth_el_az = navdata_subset[["el_sv_deg","az_sv_deg"]]

We can now compare the calculated elevation and azimuth with their respective “truth” values included in the Google Decimeter Challenge 2022 dataset.

for sat_idx in range(3):
    print(f"SV ID: {int(navdata_subset['sv_id',sat_idx])}")
    print(f"Calculated elevation: {calculated_el_az[0, sat_idx]}, Truth elevation: {truth_el_az[0, sat_idx]}")
    print(f"Calculated azimuth: {calculated_el_az[1, sat_idx]}, Truth azimuth: {truth_el_az[1, sat_idx]}")

SV ID: 2
Calculated elevation: 62.44920476228992, Truth elevation: 62.44920476227796
Calculated azimuth: 43.77300728700859, Truth azimuth: 43.77300728698665
SV ID: 5
Calculated elevation: 27.169886307916364, Truth elevation: 27.16988630793112
Calculated azimuth: 152.993936423783, Truth azimuth: 152.99393642377913
SV ID: 6
Calculated elevation: 25.45246950401311, Truth elevation: 25.45246950400123
Calculated azimuth: 44.140622789726976, Truth azimuth: 44.14062278972148