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क्षण — Sanskrit for the precise instant, the smallest measure of time.
Open, reproducible PNT (positioning, navigation, and timing) resilience simulation with published quantum-sensor performance models.
Kshana (क्षण, Sanskrit: "the precise instant") is an open, reproducible PNT-resilience simulator with quantum-sensor performance models — positioning, navigation, and timing. It compares quantum and classical sensors mostly from published Allan/noise-budget coefficients, with a first-principles cold-atom- interferometer accelerometer layer (Mach–Zehnder phase, quantum projection noise, contrast decay, and vibration coupling) that derives the noise coefficient rather than looking it up; it is not yet a full quantum-physics simulator (Coriolis and light-shift systematics remain coefficient-level — see docs/QUANTUM.md and docs/QUANTUM-MODELS.md).
It quantifies, in hard and reproducible numbers, what quantum clocks, quantum
inertial sensors, and optical time-transfer buy a navigation system over classical
PNT — scored against the operational figures of merit that matter for resilient
navigation. Every result is reproducible from scenario + seed + engine version,
and every sensor parameter is traceable to a published source — consolidated in one
citable table in docs/PROVENANCE.md.
Validated, not asserted. 666/666 AIAA SGP4 vectors to 4.12 mm · Cowell force model 0.08 m vs Orekit 12.2 · Galileo 0.61 m / Swarm-A 0.10 m vs real ESA precise ephemerides · GCRS→ITRS bit-for-bit vs SOFA/ERFA · ML metrics exact vs scikit-learn · 64 of 168 capabilities validated against independent external oracles; 100 honestly labelled Modelled.
One engine, five front doors · SVG
Each row is checked against an independent external oracle (real dataset, independent reference implementation, or published reference vectors) and re-checked in CI (continuous integration). Full 168-row matrix →
| Capability | Result | External oracle | |
|---|---|---|---|
| ✅ | SGP4/SDP4 (Simplified General Perturbations 4 / Simplified Deep-space Perturbations 4, the standard analytic satellite-orbit propagators) propagation | 666/666 vectors, worst 4.12 mm | AIAA 2006-6753 (Vallado; AIAA = American Institute of Aeronautics and Astronautics) + independent sgp4 crate |
| ✅ | Numerical Cowell force model | 0.08 m / 24 h, 275 epochs | Orekit 12.2 DormandPrince853 (CS GROUP) |
| ✅ | Orbit fit vs precise ephemeris | Galileo 0.61 m · Swarm-A 0.10 m | ESA (European Space Agency) / ESOC (European Space Operations Centre) SP3 (Standard Product 3, the precise-orbit format of the IGS — the International GNSS (global navigation satellite system) Service) precise orbits |
| ✅ | GCRS→ITRS (Geocentric Celestial Reference System → International Terrestrial Reference System) frame chain | bit-for-bit vs SOFA (the International Astronomical Union's Standards of Fundamental Astronomy library); ≤ 0.86 m vs SPICE (Spacecraft, Planet, Instrument, C-matrix, Events — the planetary-geometry toolkit) | ERFA (Essential Routines for Fundamental Astronomy, the open port of SOFA)/SOFA + ANISE (Attitude, Navigation, Instrument, Spacecraft, Ephemeris — a pure-Rust SPICE) |
| ✅ | Allan deviations | reproduce reference deviations | NIST SP 1065 (National Institute of Standards and Technology Special Publication 1065) + Stable32 on a real Cs (caesium) clock |
| ✅ | Global navigation satellite system (GNSS) dilution of precision (DOP) · machine-learning (ML) detector metrics | to 1e-6 · to 1e-9 | gnss_lib_py · scikit-learn |
| ✅ | Fisher information · CRLB (Cramér–Rao lower bound) · observability | eigh / CRLB / DOP to 1e-9 | NumPy 2.4.1 (LAPACK, the Linear Algebra PACKage) + Kay (1993) closed forms |
64 Validated · 100 Modelled · 4 Partner — SVG
Free and open source under the GNU AGPL-3.0 (GNU Affero General Public License, version 3)
— with a commercial licence available from Ashforde OÜ (an Estonian private limited
company; OÜ = osaühing) for proprietary/closed integration (see LICENSING.md).
Professionally developed and maintained by Ashforde OÜ; commercial
support, integration, and proprietary extensions available.
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