# sidereon: GNSS and astrodynamics in Elixir ```elixir Mix.install([ {:sidereon, "~> 0.9"} ]) ``` ## About [sidereon](https://hex.pm/packages/sidereon) is the Elixir interface to a GNSS and astrodynamics engine written in Rust. The numerics run in that engine and ship as a precompiled NIF, so there is nothing to compile: this notebook runs as written. Every cell below is self-contained and uses only data embedded here. ## Propagate a satellite and take a look angle Parse a two-line element set (these are real elements for the ISS), run SGP4 to get the sub-satellite point, and compute the azimuth, elevation, and range from a ground station. ```elixir line1 = "1 25544U 98067A 24001.50000000 .00016717 00000-0 10270-3 0 9009" line2 = "2 25544 51.6400 208.8657 0002644 250.3037 109.7782 15.49560812999990" {:ok, iss} = Sidereon.parse_tle(line1, line2) epoch = ~U[2024-01-01 12:00:00Z] {:ok, geo} = Sidereon.geodetic(iss, epoch) %{ catalog_number: iss.catalog_number, sub_lat_deg: Float.round(geo.latitude, 3), sub_lon_deg: Float.round(geo.longitude, 3), altitude_km: Float.round(geo.altitude_km, 1) } ``` ```elixir # London ground station: latitude and longitude in degrees, altitude in meters. station = %{latitude: 51.5, longitude: -0.1, altitude_m: 10.0} {:ok, look} = Sidereon.look_angle(iss, epoch, station) %{ azimuth_deg: Float.round(look.azimuth, 2), elevation_deg: Float.round(look.elevation, 2), range_km: Float.round(look.range_km, 1) } ``` ## Predict passes over a station `Sidereon.predict_passes/5` returns every pass that rises above a minimum elevation in the window, each with rise and set times, peak elevation, and duration. ```elixir window_start = ~U[2024-01-01 00:00:00Z] window_end = DateTime.add(window_start, 1, :day) {:ok, passes} = Sidereon.predict_passes(iss, station, window_start, window_end, min_elevation: 10.0) for p <- passes do %{ rise: Calendar.strftime(p.rise, "%H:%M:%S"), set: Calendar.strftime(p.set, "%H:%M:%S"), peak_elevation_deg: Float.round(p.max_elevation, 1), duration_min: Float.round(p.duration_seconds / 60, 1) } end ``` ## Solve a position from pseudoranges Single-point positioning. Feed `Sidereon.GNSS.Positioning.solve/4` a set of pseudoranges and a precise SP3 ephemeris and it returns a least-squares fix: ECEF and geodetic position, the receiver clock bias, and geometry diagnostics. The SP3 product below is embedded so the cell runs offline; in practice you would load one with `Sidereon.GNSS.SP3.load/1`. ```elixir # GPS L1 pseudoranges (meters) for the satellites in view at the epoch. 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} ] 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 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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) {:ok, solution} = 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: solution.position, rx_clock_s: solution.rx_clock_s, pdop: Float.round(solution.dop.pdop, 2), used_sats: solution.used_sats } ``` ## Screen a conjunction and compute collision probability Parse a CCSDS Conjunction Data Message (CDM), convert it to collision parameters, and compute the probability of collision (Pc) with the Foster method. ```elixir cdm_kvn = """ CCSDS_CDM_VERS = 1.0 CREATION_DATE = 2010-03-12T22:31:12.000 ORIGINATOR = JSPOC MESSAGE_ID = 201113719185 TCA = 2010-03-13T22:37:52.618 MISS_DISTANCE = 715 [m] RELATIVE_SPEED = 14762 [m/s] OBJECT = OBJECT1 OBJECT_DESIGNATOR = 12345 OBJECT_NAME = SATELLITE A REF_FRAME = EME2000 X = 2570.097065 [km] Y = 2244.654904 [km] Z = 6281.497978 [km] X_DOT = 4.418769571 [km/s] Y_DOT = 4.833547743 [km/s] Z_DOT = -3.526774282 [km/s] CR_R = 4.142E+01 [m**2] CT_R = -8.579E+00 [m**2] CT_T = 2.533E+03 [m**2] CN_R = -2.313E+01 [m**2] CN_T = 1.336E+01 [m**2] CN_N = 7.098E+01 [m**2] OBJECT = OBJECT2 OBJECT_DESIGNATOR = 30337 OBJECT_NAME = FENGYUN 1C DEB REF_FRAME = EME2000 X = 2569.540800 [km] Y = 2245.093614 [km] Z = 6281.599946 [km] X_DOT = -2.888612500 [km/s] Y_DOT = -6.007247516 [km/s] Z_DOT = 3.328770172 [km/s] CR_R = 1.337E+03 [m**2] CT_R = -4.806E+04 [m**2] CT_T = 2.492E+06 [m**2] CN_R = -3.298E+01 [m**2] CN_T = -7.5888E+02 [m**2] CN_N = 7.105E+01 [m**2] """ {:ok, cdm} = Sidereon.CCSDS.CDM.parse(cdm_kvn) # Combined hard-body radius of 20 meters. cdm = %{cdm | hard_body_radius_m: 20.0} params = Sidereon.CCSDS.CDM.to_collision_params(cdm) {:ok, equal_area} = Sidereon.Collision.probability(params, method: :equal_area) {:ok, numerical} = Sidereon.Collision.probability(params, method: :numerical) %{ miss_km: Float.round(equal_area.miss_km, 4), pc_equal_area: equal_area.pc, pc_numerical: numerical.pc } ``` ## RF link budget Size a UHF amateur-radio link to the satellite at the look angle computed above: free-space path loss, EIRP, and the resulting link margin. ```elixir fspl_db = Sidereon.RF.fspl(look.range_km, 437.0) eirp_dbw = Sidereon.RF.eirp(30.0, 10.0) margin_db = Sidereon.RF.link_margin(%{ eirp_dbw: eirp_dbw, fspl_db: fspl_db, receiver_gt_dbk: -20.0, other_losses_db: 3.0, required_cn0_dbhz: 30.0 }) %{ fspl_db: Float.round(fspl_db, 1), eirp_dbw: Float.round(eirp_dbw, 1), link_margin_db: Float.round(margin_db, 1) } ``` ## Where to next Full signatures live on [HexDocs](https://hexdocs.pm/sidereon). More notebooks, including a ground-track map and a GNSS positioning walkthrough, live under [`examples/`](https://github.com/neilberkman/sidereon-ex/tree/main/examples).