Current section
Files
Jump to
Current section
Files
examples/gnss_positioning.livemd
# GNSS Positioning
```elixir
Mix.install([
{:sidereon, "~> 0.9"}
])
```
## Load a precise ephemeris
A precise SP3 product (from an IGS or MGEX analysis center) gives each
satellite's position and clock on a fixed time grid. Here it is embedded as a
string so this notebook runs offline; in practice you would download one from a
public archive and load it with `Sidereon.GNSS.SP3.load/1`. This trimmed product
holds six GPS satellites on 2020-06-24.
```elixir
sp3_data = """
#cP2020 6 24 9 45 0.00000000 19 TRACK IGb14 FIT GRGS
## 2111 259200.00000000 900.00000000 59024 0.0000000000000
+ 6 G08G10G16G18G20G21 0 0 0 0 0 0 0 0 0 0 0
+ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
+ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
+ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
+ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
++ 4 4 4 4 4 4 0 0 0 0 0 0 0 0 0 0 0
++ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
++ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
++ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
++ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
%c M cc GPS ccc cccc cccc cccc cccc ccccc ccccc ccccc ccccc
%c cc cc ccc ccc cccc cccc cccc cccc ccccc ccccc ccccc ccccc
%f 0.0000000 0.000000000 0.00000000000 0.000000000000000
%f 0.0000000 0.000000000 0.00000000000 0.000000000000000
%i 0 0 0 0 0 0 0 0 0
%i 0 0 0 0 0 0 0 0 0
/* CNES/CLS/GRGS - TOULOUSE,FRANCE - Contact : igs-ac@cls.fr
/* PCV:IGS14_2108 OL/AL:FES2012 NONE NN ORB:CoN CLK:CoN
/* CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
/* CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
* 2020 6 24 9 45 0.00000000
PG08 4643.904912 -24162.558516 -9650.049610 -38.635183
PG10 17886.671789 3039.006353 -19391.393793 -380.478330
PG16 3673.608258 -18933.969815 17839.814705 -174.352223
PG18 23700.127530 6507.753313 10093.688366 228.808891
PG20 21015.602926 12381.822675 -10856.524893 527.448122
PG21 26299.269767 -2460.995007 716.844563 15.508264
* 2020 6 24 10 0 0.00000000
PG08 5254.320976 -24937.345008 -6980.386897 -38.636691
PG10 19010.269319 4866.851618 -17921.084337 -380.488198
PG16 4860.112779 -17100.303698 19364.987730 -174.356395
PG18 22418.061092 6785.447511 12538.206018 228.818132
PG20 21540.808052 13373.630254 -8364.466576 527.447968
PG21 26177.802655 -2146.941378 3560.974533 15.512752
* 2020 6 24 10 15 0.00000000
PG08 5710.564170 -25453.105280 -4188.721104 -38.638443
PG10 20115.189466 6485.476927 -16142.894217 -380.498119
PG16 6226.321564 -15204.115225 20546.504507 -174.360500
PG18 20889.343380 7160.242478 14767.111628 228.827365
PG20 21908.611100 14137.388789 -5730.669927 527.447926
PG21 25760.514626 -1769.431822 6343.514786 15.516981
* 2020 6 24 10 30 0.00000000
PG08 6042.284075 -25684.525952 -1323.814227 -38.640412
PG10 21159.408012 7879.460815 -14087.964262 -380.507982
PG16 7759.098529 -13294.312785 21364.232984 -174.364502
PG18 19148.071571 7657.452624 16742.023312 228.836711
PG20 22085.133601 14686.270178 -2999.737823 527.447449
PG21 25067.475736 -1296.107146 9017.301047 15.521531
* 2020 6 24 10 45 0.00000000
PG08 6283.596097 -25614.361768 1564.242656 -38.641756
PG10 22100.268611 9041.937175 -11792.020438 -380.517890
PG16 9436.967444 -11417.672716 21804.746560 -174.368582
PG18 17234.002467 8295.952772 18428.910848 228.845896
PG20 22041.002117 15040.256156 -217.934016 527.447614
PG21 24126.033756 -698.817607 11537.888708 15.525474
* 2020 6 24 11 0 0.00000000
PG08 6471.529324 -25234.155183 4424.947554 -38.642177
PG10 22896.131923 9974.623387 -9294.735744 -380.527755
PG16 11230.846890 -9617.105625 21861.506015 -174.372582
PG18 15191.136796 9087.282030 19798.684014 228.855179
PG20 21752.562074 15225.214120 2567.564373 527.447459
PG21 22969.651026 45.186775 13864.197409 15.529722
* 2020 6 24 11 15 0.00000000
PG08 6644.360327 -24544.616731 7208.313715 -38.643219
PG10 23507.988002 10687.523653 -6639.037631 -380.537732
PG16 13105.095965 -7930.108701 21534.895433 -174.377072
PG18 13066.149231 10035.038521 20827.696867 228.864441
PG20 21202.891348 15271.756854 5309.432624 527.447520
PG21 21636.563260 952.305394 15959.053118 15.534059
* 2020 6 24 11 30 0.00000000
PG08 6839.902243 -23555.650675 9865.783600 -38.644720
PG10 23900.971736 11198.322998 -3870.373323 -380.547626
PG16 15018.822256 -6387.464812 20832.117593 -174.381097
PG18 10906.724082 11134.589308 21498.159124 228.873724
PG20 20382.574992 15213.927788 7960.972253 527.447536
PG21 20168.317061 2031.899012 17789.631146 15.538108
* 2020 6 24 11 45 0.00000000
PG08 7093.820244 -22286.025531 12351.111011 -38.645281
PG10 24045.725638 11531.498375 -1035.945281 -380.557547
PG16 16927.393599 -5012.236439 19766.958053 -174.385107
PG18 8759.860313 12373.107746 21798.447374 228.883076
PG20 19290.210666 15087.759974 10476.882192 527.447233
PG21 18608.242309 3285.876753 19327.806335 15.542220
* 2020 6 24 12 0 0.00000000
PG08 7438.042916 -20762.704119 14621.192800 -38.647002
PG10 23919.560682 11717.183156 1816.071269 -380.567404
PG16 18784.088401 -3819.088286 18359.430195 -174.389524
PG18 6670.210753 13729.937789 21723.310519 228.892428
PG20 17932.623680 14929.762015 12814.016152 527.447354
PG21 16999.913180 4708.560403 20550.418405 15.546299
* 2020 6 24 12 15 0.00000000
PG08 7899.334503 -19019.862023 16636.833344 -38.647763
PG10 23507.373783 11789.829543 4637.317275 -380.577286
PG16 20541.815806 -2813.957336 16635.315598 -174.393761
PG18 4678.519090 15177.272097 21273.965621 228.901739
PG20 16324.780780 14775.387488 14932.114622 527.446948
PG21 15385.647811 6286.819595 21439.461249 15.550671
* 2020 6 24 12 30 0.00000000
PG08 8498.085463 -17097.635989 18363.427105 -38.649562
PG10 22802.289648 11786.720063 7380.034276 -380.587160
PG16 22154.836702 -1994.074300 14625.615492 -174.397842
PG18 2820.214554 16681.118608 20458.082166 228.911022
PG20 14489.402694 14657.545765 16794.499670 527.447051
PG21 13805.092069 8000.463976 21982.204956 15.554459
* 2020 6 24 12 45 0.00000000
PG08 9247.369015 -15040.654467 19771.547156 -38.650484
PG10 21806.004803 11746.384064 9997.833858 -380.596890
PG16 23580.419142 -1348.326156 12365.929519 -174.402246
PG18 1124.218120 18202.518914 19289.654667 228.920337
PG20 12456.286563 14605.211454 18368.720568 527.447006
PG21 12293.927824 9822.872282 22171.258698 15.558791
* 2020 6 24 13 0 0.00000000
PG08 10152.299669 -12896.410588 20837.430270 -38.651742
PG10 20528.822194 11706.977946 12446.442268 -380.606741
PG16 24780.366877 -857.936737 9895.777935 -174.406704
PG18 -387.994051 19698.971935 17788.765433 228.929616
PG20 10261.360393 14642.186916 19627.138333 527.447150
PG21 10882.740798 11721.833118 22004.581485 15.563408
* 2020 6 24 13 15 0.00000000
PG08 11209.716830 -10713.543221 21543.351971 -38.652897
PG10 18989.375629 11704.688739 14684.410767 -380.616599
PG16 25722.366833 -497.431201 7257.882649 -174.411115
PG18 -1703.034135 21126.008215 15981.241263 228.938925
PG20 7945.502154 14786.067388 20547.437547 527.446927
PG21 9596.077666 13660.568119 21485.446350 15.567441
* 2020 6 24 13 30 0.00000000
PG08 12408.203090 -8540.094231 21877.887705 -38.653740
PG10 17214.054103 11772.219589 16673.782838 -380.626446
PG16 26381.110092 -235.841125 4497.421430 -174.415665
PG18 -2815.928687 22438.854161 13898.209721 228.948171
PG20 5553.165699 15047.451338 21113.054383 527.446839
PG21 8451.716682 15598.904800 20622.361836 15.572148
* 2020 6 24 13 45 0.00000000
PG08 13728.433306 -6421.809657 21836.058871 -38.653666
PG10 15236.146433 11937.412720 18380.709769 -380.636302
PG16 26739.150669 -38.100050 1661.268176 -174.419882
PG18 -3730.115104 23594.121838 11575.562442 228.957546
PG20 3130.863904 15429.429881 21313.510668 527.447015
PG21 7460.170730 17494.563735 19428.952908 15.577088
* 2020 6 24 14 0 0.00000000
PG08 15143.837640 -4400.549449 21419.364822 -38.654444
PG10 13094.736367 12222.060725 19776.006518 -380.646060
PG16 26787.476793 133.425531 -1202.769329 -174.424084
PG18 -4457.109220 24551.458779 9053.334699 228.966797
PG20 725.565911 15927.378707 21144.644989 527.446993
PG21 6624.436243 19304.522499 17923.801627 15.580392
* 2020 6 24 14 15 0.00000000
PG08 16621.549904 -2512.864913 20635.703989 -38.655549
PG10 10833.387063 12640.950613 20835.640171 -380.655943
PG16 26525.779980 317.327470 -4046.704331 -174.428345
PG18 -5015.857646 25275.093632 6375.012002 228.975990
PG20 -1616.930248 16529.064324 20608.733434 527.446900
PG21 5939.995958 20986.417129 16130.246267 15.584692
EOF
"""
{:ok, sp3} = Sidereon.GNSS.SP3.parse(sp3_data)
```
## Query satellite positions
`Sidereon.GNSS.SP3.position/3` interpolates the grid to any epoch. Positions are
ITRF/IGS ECEF meters.
```elixir
{:ok, state} = Sidereon.GNSS.SP3.position(sp3, "G08", ~N[2020-06-24 12:00:00])
radius_km =
:math.sqrt(state.x_m ** 2 + state.y_m ** 2 + state.z_m ** 2) / 1000.0
%{
position_m: {state.x_m, state.y_m, state.z_m},
clock_s: state.clock_s,
radius_km: Float.round(radius_km, 1)
}
```
The radius lands near the ~26,560 km GPS orbit. Sweep an arc to watch the
satellite move:
```elixir
base = ~N[2020-06-24 12:00:00]
for minutes <- 0..60//15 do
epoch = NaiveDateTime.add(base, minutes * 60, :second)
{:ok, s} = Sidereon.GNSS.SP3.position(sp3, "G08", epoch)
{epoch, Float.round(s.x_m / 1000.0, 1), Float.round(s.y_m / 1000.0, 1),
Float.round(s.z_m / 1000.0, 1)}
end
```
## Single-point positioning
`Sidereon.GNSS.Positioning.solve/4` recovers a receiver position from one epoch
of pseudoranges against the SP3 product (or a parsed broadcast navigation
source). A mixed-constellation observation set is solved together with one
receiver clock per system; the ionosphere and troposphere corrections, the
elevation mask, and satellite rejection are all configurable.
```elixir
# GPS L1 pseudoranges (meters), one per satellite in view.
observations = [
{"G08", 23_825_519.8},
{"G10", 22_717_690.1},
{"G16", 20_478_653.4},
{"G18", 21_768_335.2},
{"G20", 21_248_327.7},
{"G21", 20_808_709.8}
]
{:ok, sol} =
Sidereon.GNSS.Positioning.solve(sp3, observations, ~N[2020-06-24 12:00:00],
initial_guess: [4_500_000.0, 500_000.0, 4_500_000.0, 0.0]
)
%{
position_ecef_m: sol.position,
geodetic: sol.geodetic,
rx_clock_s: sol.rx_clock_s,
pdop: Float.round(sol.dop.pdop, 2),
used_sats: sol.used_sats
}
```
See `Sidereon.GNSS.Positioning` for the full option list and the solution
fields, and `Sidereon.GNSS.RTK`, `Sidereon.GNSS.PrecisePositioning`, and
`Sidereon.GNSS.DGNSS` for the RTK, PPP, and DGNSS solvers.