OrbitsNot yet on GitHubSource: docs/SSV.md

GNSS beyond the constellation: the gnss-ssv kind

Advisory only. Modelled results from stated inputs and a simulated truth; not a certification, a flight-qualified figure or a service-volume claim for any system. Kshana transmits nothing.

The gnss-ssv kind answers: for a spacecraft above, around or far past the GNSS orbits, how many GNSS signals can it use, how strong are they, how good is the geometry, and what can an onboard filter do with them? It has three modes, chosen by which table the scenario has: [shell], [trajectory] or [navigation] (with an optional [formation]).

Status: MODELLED. The availability sweeps are compared with the ICG Space Service Volume booklet under a pre-registration; see what the comparison shows before relying on any number.

Public sources#

  • The Interoperable Global Navigation Satellite Systems Space Service Volume, United Nations Office for Outer Space Affairs, ST/SPACE/75 (1 November 2018), prepared by the International Committee on GNSS (ICG), Working Group B: the method (annex B), the orbital elements of every constellation (annex C), the transmit beamwidths and powers (tables B2, B6, B8, 4.2), the user antennas (table B10), and the published availability tables. It is itself a simulation. Fetched by xval/gnss-ssv/fetch.sh (pinned SHA-256), never vendored.
  • U.S. Coast Guard Navigation Center, GPS Block IIR and IIR-M antenna panel patterns (Marquis, 2014): the measured L1 panel patterns used only to judge the parametric stand-in (bar S7). Fetched, never vendored, no pattern data committed.
  • The constants of the model (gravity, Earth rotation, free-space loss, noise density) are standard; the Gallagher plasmasphere density law, the Chapman layer and the radio refractivity profile are published forms, used with stated simple parameters (see src/ssv/limb.rs).

Shell mode: the booklet's global metric#

[shell] places a user on a sphere (default 36,000 km altitude with a nadir-pointing hemispherical antenna, the upper SSV; or 8,000 km with an omnidirectional antenna, the lower SSV) on a 2,562-point icosphere grid and counts, over 14 days at 1-minute steps, the share of (user, epoch) pairs with at least one and at least four signals, per constellation and combined, and the longest outage at the worst user. The sweep uses the closed-form visibility interval in central angle (a beam cone, Earth blockage by the 6378 km sphere plus 50 km, the user hemisphere and the RF range limit) and runs in seconds in a release build; a property test checks it against the general geometric predicate.

Signal availability for a user on a sphere at 36000 km altitude with a hemisphere antenna, from a real run of engine v0.38.0 on scenarios/gnss-ssv-shell.toml (a reduced run: 162 users, 3 days, 10 min steps), at a 20 dB-Hz threshold. For each constellation and band, two bars: the share of (user, epoch) pairs with at least one signal and with at least four. Combined, L1: 99.4 % at least one, 73.2 % at least four, longest outage below four signals 160 min. Combined, L5: 100.0 % at least one, 99.9 % at least four, longest outage below four signals 20 min. MODELLED: a modelled study from stated inputs, not a measurement and not a service-volume claim for any system. The reduced size is not the booklet comparison. Advisory: analysis output from a research and engineering tool, not type-approved navigation equipment and not a safety-of-life service.Signal availability for a user on a sphere at 36000 km altitude with a hemisphere antenna, from a real run of engine v0.38.0 on scenarios/gnss-ssv-shell.toml (a reduced run: 162 users, 3 days, 10 min steps), at a 20 dB-Hz threshold. For each constellation and band, two bars: the share of (user, epoch) pairs with at least one signal and with at least four. Combined, L1: 99.4 % at least one, 73.2 % at least four, longest outage below four signals 160 min. Combined, L5: 100.0 % at least one, 99.9 % at least four, longest outage below four signals 20 min. MODELLED: a modelled study from stated inputs, not a measurement and not a service-volume claim for any system. The reduced size is not the booklet comparison. Advisory: analysis output from a research and engineering tool, not type-approved navigation equipment and not a safety-of-life service.

Trajectory mode: along an orbit#

[trajectory] flies the user on a Keplerian orbit (a preset: leo, meo, geo, heo (the booklet's table 5.10) or lunar-transfer, or elements) and reports, per band and constellation, availability of one and four signals, outage durations, signals in view, best C/N0, dilution of precision (median, 95th percentile, worst), links received through the main lobe and through sidelobes, and an optional time series and CSV.

  • Transmit pattern ([transmit] pattern): booklet (constant power inside the reference off-boresight angle), parametric (a labelled stand-in: 3 dB per degree beyond the reference angle to a floor 25 dB below the main lobe; not any system's measured pattern) or table (a measured pattern you supply: pattern_csv or inline pattern_text; the Block IIR/IIR-M panel patterns can be extracted with xval/gnss-ssv/extract_patterns.py).
  • Receive antennas: omni, hemisphere, or the booklet's table-B10 high-gain and patch antennas, nadir or zenith; each link uses the antenna with the higher gain.
  • Limb-ray medium ([atmosphere]): a Chapman ionosphere, a plasmasphere (Gallagher 1988 form, plasmapause at L = 4.5, tapered below 1,500 km) and a neutral atmosphere (bending about 1.33 degrees at the surface, oxygen absorption, defocusing) integrated along the straight ray. Reports slant TEC, the plasmaspheric part, excess delay, tangent altitude and the links lost to grazing. Straight-ray integration: bending is reported, not iterated.
  • Weak-signal receiver ([receiver] weak_signal): coherent and non-coherent integration, data-bit limit, aiding and pilot channels, Doppler search; the acquisition threshold at the stated detection and false-alarm probabilities and the carrier and code tracking thresholds replace the fixed C/N0 threshold (10 to 25 dB-Hz range). Reuses the engine's acquisition and tracking-loop models.
Signals along one high Earth orbit (perigee 497 km, apogee 58622 km, period 18.8 h), from a real run of engine v0.38.0 on scenarios/gnss-ssv-heo.toml, band L1. Top: the best carrier-to-noise density among the signals in view, against the 20 dB-Hz threshold. Middle: the number of signals in view from all constellations, from 4 to 55 along the sampled points. Of the links received, 2252 came through a main lobe and 696 through sidelobes, using a labelled parametric stand-in pattern, not any system's measured pattern. Median PDOP 67, 95th percentile 358. MODELLED: a modelled study from stated inputs, not a measurement and not a service-volume claim for any system. Advisory: analysis output from a research and engineering tool, not type-approved navigation equipment and not a safety-of-life service.Signals along one high Earth orbit (perigee 497 km, apogee 58622 km, period 18.8 h), from a real run of engine v0.38.0 on scenarios/gnss-ssv-heo.toml, band L1. Top: the best carrier-to-noise density among the signals in view, against the 20 dB-Hz threshold. Middle: the number of signals in view from all constellations, from 4 to 55 along the sampled points. Of the links received, 2252 came through a main lobe and 696 through sidelobes, using a labelled parametric stand-in pattern, not any system's measured pattern. Median PDOP 67, 95th percentile 358. MODELLED: a modelled study from stated inputs, not a measurement and not a service-volume claim for any system. Advisory: analysis output from a research and engineering tool, not type-approved navigation equipment and not a safety-of-life service.

[navigation] flies a high-orbit or lunar-transfer craft and runs a nine-state extended Kalman filter (position, velocity, receiver clock bias and drift, a solar-radiation-pressure scale) on pseudoranges. Truth is integrated with point-mass gravity, J2, Sun and Moon third-body and radiation pressure with a cylindrical Earth shadow; the filter models gravity, J2 and the third bodies and estimates the radiation pressure. Pseudoranges come from the same link geometry and C/N0 threshold as the sweeps; their noise grows as the C/N0 falls; the medium's excess delay (with [atmosphere]) is added and not modelled by the filter. The report separates the part of the run inside the GNSS orbits (below 20,000 km altitude) from the part above, gives the longest gap with no measurement and the mean normalised estimation error squared (about 3 for a consistent position block). The Sun and Moon are low-precision circular stand-ins.

An onboard nine-state filter on a transfer from low orbit toward the Moon, from a real run of engine v0.38.0 on scenarios/gnss-ssv-nav-lunar.toml (289 epochs, 13 points drawn). On a log axis, the true position error and the filter's own one-sigma bound against time since the start. Inside the GNSS orbits the position RMS is 1.4 m; above them it is 90 m, with the final error 184 m at 193,330 km altitude with 1 measurement. Mean normalised estimation error squared over the whole run is 4.4 (about 3 for a consistent position block). Truth and filter share their Sun and Moon stand-ins. MODELLED: a modelled study from stated inputs, not a measurement and not a service-volume claim for any system. Advisory: analysis output from a research and engineering tool, not type-approved navigation equipment and not a safety-of-life service.An onboard nine-state filter on a transfer from low orbit toward the Moon, from a real run of engine v0.38.0 on scenarios/gnss-ssv-nav-lunar.toml (289 epochs, 13 points drawn). On a log axis, the true position error and the filter's own one-sigma bound against time since the start. Inside the GNSS orbits the position RMS is 1.4 m; above them it is 90 m, with the final error 184 m at 193,330 km altitude with 1 measurement. Mean normalised estimation error squared over the whole run is 4.4 (about 3 for a consistent position block). Truth and filter share their Sun and Moon stand-ins. MODELLED: a modelled study from stated inputs, not a measurement and not a service-volume claim for any system. Advisory: analysis output from a research and engineering tool, not type-approved navigation equipment and not a safety-of-life service.

Formation mode: relative navigation#

[formation] (needs [navigation] for the chief) adds deputies offset in true anomaly. Each craft runs the absolute filter; the deputy's position relative to the chief is estimated by subtracting the independent absolute estimates and by a relative filter on single-differenced pseudoranges of the signals both craft track. The report gives both, the baseline, and the number of signals tracked in common.

Relative navigation of 2 deputies around a chief on a high orbit, from a real run of engine v0.38.0 on scenarios/gnss-ssv-formation-heo.toml (401 epochs). For each deputy, two bars: the relative position RMS from subtracting the two independent absolute estimates, and from the relative filter on single-differenced pseudoranges. Baseline 0.8 km: 5.1 m and 1.2 m. Baseline 2.0 km: 4.1 m and 2.1 m. The absolute filter is not consistent here: mean normalised estimation error squared 187 against about 3 for a consistent filter, so its stated uncertainty is far too small. MODELLED: a modelled study from stated inputs, not a measurement and not a service-volume claim for any system. Advisory: analysis output from a research and engineering tool, not type-approved navigation equipment and not a safety-of-life service.Relative navigation of 2 deputies around a chief on a high orbit, from a real run of engine v0.38.0 on scenarios/gnss-ssv-formation-heo.toml (401 epochs). For each deputy, two bars: the relative position RMS from subtracting the two independent absolute estimates, and from the relative filter on single-differenced pseudoranges. Baseline 0.8 km: 5.1 m and 1.2 m. Baseline 2.0 km: 4.1 m and 2.1 m. The absolute filter is not consistent here: mean normalised estimation error squared 187 against about 3 for a consistent filter, so its stated uncertainty is far too small. MODELLED: a modelled study from stated inputs, not a measurement and not a service-volume claim for any system. Advisory: analysis output from a research and engineering tool, not type-approved navigation equipment and not a safety-of-life service.

What the comparison with the booklet shows#

Bars were pre-registered (xval/gnss-ssv/PREREGISTRATION.md, addenda 1 to 5) before the full-size run; results in xval/gnss-ssv/RESULTS.md, cells in results-*.json, pinned by tests/ssv_booklet_results.rs, misses included.

bar what run 1 (pre-registered reading) GLONASS-angle variant (diagnostic)
S0 minimum radiated power, 13 signals, within 0.1 dB MET MET
S1 upper SSV geometry (table B4) NOT MET (43 of 52 cells) all 52 cells in tolerance
S2 lower SSV (table 5.2) NOT MET (48 of 52) all 52
S3 upper SSV with 15/20/25 dB-Hz (table B9) NOT MET (122 of 155) 153 of 155
S4 six GEO missions NOT MET (132 of 156) all 156
S5 HEO mission NOT MET (18 of 26) 21 of 26
S6 lunar mission MET NOT MET (23 of 26)
S7 parametric pattern against measured GPS L1 panel patterns NOT MET (RMS 6.3 to 8.8 dB against 3 dB) n/a

The booklet is internally inconsistent about GLONASS's reference off-boresight angle: tables B2 and B6 print 20 and 28 degrees, table 4.2 prints 26 and 34. Run 1 used the first (what the pre-registration named); almost every miss in S1 to S5 is GLONASS. The variant, committed to as a diagnostic before it was run, uses the second, and then the upper SSV, lower SSV and GEO missions agree cell for cell, outages included. The variant does not replace run 1. No row is VALIDATED: the booklet is a simulation, the verdict rule requires S0 to S3 under the pre-registered reading, and the remaining misses (GPS L1 at 20 dB-Hz, HEO Galileo, QZSS and NavIC, the lunar GLONASS rows) are not explained.

The recorded comparison of the space-user availability model with the public Space Service Volume booklet, from the committed results of the pre-registered run (xval/gnss-ssv/results-run1.json, written by the ssv_booklet_check example of engine v0.38.0). Bar by bar, the cells within tolerance: S0 13 of 13 (MET); S1 43 of 52 (NOT MET); S2 48 of 52 (NOT MET); S3 122 of 155 (NOT MET); S4 132 of 156 (NOT MET); S5 18 of 26 (NOT MET); S6 26 of 26 (MET); S7 0 of 20 panel patterns (NOT MET). Only S0 and S6 are met under the pre-registered reading. A diagnostic variant that uses the booklet's other GLONASS angles brings S1, S2 and S4 to every cell, but does not replace the run of record. No ledger row is VALIDATED. Advisory: analysis output from a research and engineering tool, not type-approved navigation equipment and not a safety-of-life service.The recorded comparison of the space-user availability model with the public Space Service Volume booklet, from the committed results of the pre-registered run (xval/gnss-ssv/results-run1.json, written by the ssv_booklet_check example of engine v0.38.0). Bar by bar, the cells within tolerance: S0 13 of 13 (MET); S1 43 of 52 (NOT MET); S2 48 of 52 (NOT MET); S3 122 of 155 (NOT MET); S4 132 of 156 (NOT MET); S5 18 of 26 (NOT MET); S6 26 of 26 (MET); S7 0 of 20 panel patterns (NOT MET). Only S0 and S6 are met under the pre-registered reading. A diagnostic variant that uses the booklet's other GLONASS angles brings S1, S2 and S4 to every cell, but does not replace the run of record. No ledger row is VALIDATED. Advisory: analysis output from a research and engineering tool, not type-approved navigation equipment and not a safety-of-life service.

Running it#

kshana scenarios/gnss-ssv-shell.toml            # the upper SSV, reduced size
kshana scenarios/gnss-ssv-heo.toml              # a HEO, parametric sidelobes, limb medium
kshana scenarios/gnss-ssv-lunar-weak.toml       # lunar transfer, weak-signal receiver design
kshana scenarios/gnss-ssv-nav-lunar.toml        # onboard EKF on the way to the Moon
kshana scenarios/gnss-ssv-formation-heo.toml    # formation relative navigation
cargo run --release --example ssv_booklet_check # the full pre-registered comparison (about 12 minutes)

Every bundled scenario is cut down to run in seconds; the full-size comparison is the example above. The same kind runs from Python (kshana.run), the browser (WebAssembly), the MCP server (run_scenario, inline text only: pattern_csv is a file source and is refused, use pattern_text) and the plugins.

Limits#

  • MODELLED: nothing here was compared with measured on-orbit GNSS reception. The booklet is a simulation.
  • Keplerian two-body orbits for the GNSS constellations and for the user in the sweeps; the lunar transfer is a two-body ellipse, not a propagated trajectory.
  • The medium is a stated simple model with straight-ray integration; it is not a space-weather forecast.
  • The navigation filter is a design study: no manoeuvres, no attitude, no multipath, and the truth shares its Sun and Moon ephemerides with the filter.