kshana 0.14.0

Open hybrid quantum/classical PNT performance simulator

Kshana

क्षण — Sanskrit for the precise instant, the smallest measure of time.
Open, reproducible PNT-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.

Free and open source under Apache-2.0, professionally developed and maintained by Ashforde OÜ — commercial support, integration, and proprietary extensions available.

Status: v0.14.0 · a simulation substrate, not yet a product. A validated, fully reproducible engine spanning the PNT stack — orbit geometry and constellation design, a numerical (Cowell) propagator with a six-perturbation force model, maneuver and trajectory design, time systems, inertial navigation (incl. map-aided and gravity-map-matching alt-PNT), GNSS/INS fusion (loose, tight, UKF, coupled clock+position, 17-state), orbit determination, ARAIM integrity, clocks, advanced time-and-frequency transfer, the GNSS measurement domain, and resilience (jamming + multi-layer spoofing). Honest by design: every figure of merit is labelled validated or not-modeled, and optical-clock figures are space goals on ground hardware (no strontium optical clock has flown). See Capabilities for what it does, What it is / is not for scope, and docs/CAPABILITY.md / docs/VALIDATION.md for per-capability maturity. The overclaim closure ledger docs/CLAIMS-VS-REALITY.md tracks every historical overclaim, how it was resolved, and a CI guard (tests/no_overclaims.rs) that keeps it resolved.

Try it in your browser: the playground runs the engine client-side as WebAssembly — pick a scenario, edit the parameters, and see the result, with nothing uploaded. Build it locally with ./web/build.sh (see web/README.md), or publish it to GitHub Pages via the pages workflow.

New to this? In plain terms: GPS-style satellite signals tell things where they are and what time it is. When those signals are lost (jammed, blocked, or out of view in space), a system has to keep going on its own onboard clock and motion sensors — and they slowly drift. "Quantum" clocks and sensors drift far more slowly. Kshana measures, in honest numbers, how much longer a quantum-equipped system can coast before it exceeds its accuracy limits. New readers should start with the plain-language primer and the glossary.

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Contents

• Why · What it is / is not · Capabilities · Results
• Install & build · Usage (Python, WebAssembly)
• Scenario format · Output · Architecture
• Repository layout · Validation & honesty
• Documentation · FAQ · Troubleshooting
• Roadmap · Contributing · Citing · Versioning & releases · License
• Support & professional services · References

Why

Resilient PNT depends on holding position and time when GNSS is denied or jammed. Quantum sensors promise far slower drift during those outages. There is no good open tool to quantify that advantage honestly and reproducibly — so primes, agencies, and labs each rebuild private one-offs. Kshana aims to be the neutral, citable reference for exactly this question.

The engine knows nothing about "quantum" vs "classical": each sensor is an error model plugged into a common pipeline, so a quantum and a classical device are compared apples-to-apples on the same scenario, with independent noise realizations.

What it is / is not

It is: a deterministic, dependency-light engine spanning the PNT stack — orbit geometry, inertial navigation, GNSS/INS fusion, integrity, clocks, and timing. It runs a scenario (often a GNSS outage), evolves calibrated sensor error models through the appropriate estimator, and scores the result against the operational figures of merit — emitting a reproducible JSON result and an SVG chart, from a Rust library, CLI, Python extension, or in-browser WebAssembly module.

It is not: flight hardware, a quantum-payload design, a full GNSS signal receiver, or a certified avionics product. Quantum-hardware fidelity comes from published error models, not from this tool. The granular maturity of each capability is documented in docs/CAPABILITY.md.

It is not (yet): a full atom-interferometry physics engine (most quantum sensors consume published Allan/noise-budget coefficients; the CAI accelerometer has a first-principles layer — Mach–Zehnder phase, projection noise, contrast decay, and vibration coupling — but Coriolis and light-shift systematics remain a P2 roadmap layer, see ROADMAP.md and docs/QUANTUM-MODELS.md); a GNSS receiver or PVT solver (it models the measurement domain and resilience, not signal acquisition or a least-squares fix); or a mission-design / orbit-determination tool. Owning this scope is deliberate. If you need first-principles cold-atom interferometer error budgets (e.g. CARIOQA-PMP-grade or X-37B-style validation), see the P2 roadmap and get in touch to collaborate.

Capabilities

Domain	Capability
Orbit & geometry	SGP4/SDP4 propagation (validated to 4.12 mm against all 666 AIAA 2006-6753 vectors); real two-line elements (a committed, date-stamped Celestrak gps-ops snapshot) or synthetic Walker-delta constellations whose mean elements realise the i:T/P/F formula to under 1 km over a 24 h propagation; multi-constellation visibility, dilution of precision, and GNSS availability; a gradient-free constellation-design optimiser, streets-of-coverage minimum-satellite sizing, a multi-constellation comparison tool, and a Walker design sweep that tabulates coverage / PDOP / revisit-time over a planes × satellites grid and reports the Pareto-optimal designs.
Numerical propagator	A Cowell numerical propagator (src/propagator.rs) complementing the analytic SGP4/SDP4 path, with a hierarchical six-perturbation force model (src/forces.rs): two-body + the full J2–J6 zonal field (the exact analytic gradient of its disturbing potential), epoch-driven Sun and Moon third-body gravity (a built-in low-precision ephemeris, no DE/SPK kernel), solar-radiation pressure (cannonball model with a conical umbra+penumbra shadow), atmospheric drag (Vallado piecewise-exponential density, co-rotating atmosphere), and the post-Newtonian Schwarzschild relativistic correction — driven by a choice of two adaptive integrators (RK4 step-doubling or the Dormand–Prince RK5(4) embedded pair). Validated against analytic truth stronger than a cross-tool would give: the unperturbed orbit matches the exact universal-variable Kepler solution to sub-metre over 24 h, energy/angular-momentum conserve to ~1e-9, and each perturbation matches a hand-derived closed-form signature.
Maneuvers & trajectory design	Impulsive ΔV nodes with 6×6 covariance propagation (ECI / LVLH execution-error frames), finite-burn integration checked against the closed-form Tsiolkovsky rocket equation to < 0.01 %, an Izzo-2015 single-revolution Lambert solver, an exact universal-variable Kepler propagator, and a porkchop (launch × arrival) C3 / arrival-V∞ sweep emitted as a JSON contour grid — the performance-simulation layer above GMAT/Orekit, with every Lambert output round-tripped against two-body truth and the porkchop minimum checked against the analytic Hohmann floor.
Time systems	IERS leap-second UTC / TAI / TT / UT1 scales, a Julian-date API, the IAU-2000 Earth Rotation Angle, and GMST-based TEME ↔ ECEF with WGS-84 geodetic frames — plus IAU 2006 precession (Fukushima–Williams) toward an ITRF-precise reduction.
Inertial	Three-axis strapdown INS — quaternion attitude, WGS-84 NED mechanization, coning/sculling compensation, and a deterministic IMU error model (scale-factor, misalignment, g-sensitivity, quantization, drift); a first-principles cold-atom-interferometer accelerometer (Mach–Zehnder phase, quantum projection noise, contrast decay, vibration coupling) that derives the velocity-random-walk coefficient; and a sequential-importance-resampling particle filter for map-aided (terrain-/gravity-referenced) GPS-denied navigation.
Gravity-map / alt-PNT	A cold-atom gravimeter measurement model whose white-noise floor (σ = ASD/√τ) is derived from the CAI accelerometer physics; a low-degree, fully-normalised spherical-harmonic gravity-anomaly field (validated against the closed-form Legendre functions and a hand-derived single-term anomaly) plus synthetic mascons; and a gravity-map-matching particle filter that recovers a GPS-denied track from the anomaly sequence it flies through. A 60-minute GPS-denied benchmark (a ~700 km / one-hour outage where the inertial solution drifts to ~70 km) is recovered to ~145 m (< 500 m) by a hierarchical coarse-to-fine matcher — the ESA NAVISP Quantum Wayfarer target.
Fusion	Loosely-coupled 15-state GNSS/INS error-state EKF with closed-loop feedback (the gnss-ins pack); a tightly-coupled pseudorange update that keeps correcting with fewer than four satellites; a coupled clock + position filter; a general unscented (sigma-point) Kalman estimator for strongly nonlinear measurements; a tightly-coupled GNSS/INS UKF navigator (pseudorange + Doppler) whose force-model orbital coast is validated to 0.77 m RMS over a 30-minute curving LEO pass that includes a 120-second GNSS outage; and a full 17-state tightly-coupled GNSS/INS UKF (position, velocity, attitude error, accelerometer and gyro biases, clock bias and drift) whose quantum-CAI dead-reckoning coasts a 120-second outage on the cold-atom accelerometer's derived velocity-random-walk.
Orbit determination	Recovery of an orbital state [r, v] from ground-station range tracking, composing the two-body + J2 force model and RK4 integrator with a Gauss–Newton batch corrector (determine_orbit_batch, sub-metre / mm·s⁻¹ from noiseless ranges, ~2 m at a 5 m noise floor) and a sequential unscented-filter variant (determine_orbit_sequential).
Integrity	Snapshot and solution-separation (ARAIM-style) RAIM with horizontal/vertical protection levels (HPL/VPL), fault detection & exclusion, and Stanford integrity diagrams; an explicit integrity-risk-budget (MHSS) protection level, including the dual-/multi-constellation constellation-wide fault mode (EU ARAIM / DO-316).
Clock & timing	Two-state Kalman holdover (Joseph-form covariance, NIS/NEES consistency health); Allan-family stability (ADEV / MDEV / TDEV / HDEV) with noise-type-specific confidence intervals and a full IEEE-1139 five-coefficient power-law fit; geometric corrections (Sagnac, GNSS common-view); and the operational transfer methods — TWSTFT with the BIPM Sagnac closed form, GNSS common-view, PPP ionosphere-free time transfer, a free-space optical link with turbulence scintillation, and an inverse-variance clock-ensemble (paper) timescale below the best contributing clock.
GNSS measurement domain	Forward pseudorange / Doppler synthesis with Klobuchar (broadcast) and IONEX / TEC-grid (measured) ionosphere — including an IONEX file parser, time interpolation between maps, and the thin-shell slant-obliquity mapping — Saastamoinen + Niell troposphere, and snapshot RAIM (HPL/VPL).
Resilience	Link-budget jamming (J/S → effective C/N₀ → loss of lock); a stochastic time-spoof detector (Neyman–Pearson / χ²₁ energy test with closed-form and Monte-Carlo P_fa/P_md and a Security FoM of 1 − P_md); and a multi-layer spoof detector fusing a RAIM-consistency parity test (with the common-mode blind spot modelled honestly), an RF AGC-power monitor, and a signal-quality (SQM early-minus-late) monitor.
Interoperability	RINEX-3 multi-GNSS broadcast-ephemeris ingestion (GPS, Galileo, QZSS, BeiDou MEO/IGSO via IS-GPS-200; GLONASS via PZ-90 state-vector RK4) usable as a constellation source (RINEX in, PNT geometry out); a RINEX-3/4 observation parser (pseudorange, carrier phase, Doppler, signal strength); an SP3-c/d precise-ephemeris reader/writer with 9th-order Lagrange interpolation; and CCSDS OEM 2.0 + OMM (mean-elements) export for flight-dynamics tools (GMAT, Orekit, STK).

Each capability is reachable as a Rust API, a runnable scenario kind, or both. Maturity per capability — validated, runnable, or library — is tracked in docs/CAPABILITY.md.

Results

Each scenario compares a quantum sensor against its classical counterpart through a ~1.8 h GNSS outage. Numbers are reproducible (scenario + seed + version).

Dead-reckoning position error during a GNSS outage: the quantum sensor (blue) stays flat near the spec; the classical sensor (red) diverges to tens of kilometres. Generated by Kshana from scenarios/imu-deadreckoning.toml.

Pack	Scenario	Quantum	Classical
1 — Clock holdover	clock-holdover.toml (20 ns spec)	optical clock holds the full outage	CSAC breaches the spec mid-outage
2 — Inertial dead-reckoning	imu-deadreckoning.toml (100 m spec)	cold-atom: ~41 m, holds full outage	nav-grade: breaches in ~350 s → tens of km
3 — Time transfer (optical inter-satellite link)	timetransfer.toml	optical: ~0.3 mm ranging	RF (TWSTFT): ~150 mm ranging
4 — Hybrid fusion (capstone)	hybrid-pnt.toml	full position+timing for the whole outage	position-limited at ~350 s

The capstone shows the fusion thesis: optical inter-satellite time-transfer keeps even a classical clock locked, isolating the inertial sensor as the classical suite's weak link — i.e. quantum inertial + optical timing together.

A further scenario, orbit-gnss-challenged.toml, derives GNSS availability from orbital geometry rather than hand-authored windows: a spacecraft inside the GNSS shell is propagated against a GPS-like Walker constellation, and the visible-satellite count (line-of-sight, Earth-occultation, elevation mask) sets the fix state at each step. Over a day the user is in fix only ~59% of the time; the quantum clock holds a 5 ns timing solution through every gap (availability 1.0), the chip-scale clock only ~0.83.

The constellation can also be given as real two-line element sets. A full TLE (line 1 + line 2) is propagated with the full SGP4/SDP4 model — including atmospheric drag and the deep-space lunar-solar and 12 h / 24 h resonance terms that matter for ~12 h GNSS orbits — validated against the official AIAA 2006-6753 vectors to a worst-case ≈ 4 mm. scenarios/orbit-sgp4-gps.toml ships a real Celestrak gps-ops snapshot of the operational GPS constellation (2021-07-28, 30 satellites) and requires valid TLE checksums — two-line element sets are open data from the US Space Force / 18th Space Defense Squadron catalogue, redistributed by Celestrak (Dr T. S. Kelso, celestrak.org); refresh with scripts/fetch_tles.sh. A line-2-only block keeps the analytic two-body propagation (scenarios/orbit-real-tle.toml); the two forms can be mixed in one constellation. A constellation can equally be built from a block of RINEX-3 GPS broadcast-ephemeris records — the format a receiver decodes — propagated by the IS-GPS-200 user algorithm and fed through the same geometry (scenarios/orbit-rinex.toml).

Install & build

Requires a Rust toolchain (≥ 1.75; developed on 1.93).

git clone https://github.com/AshfordeOU/kshana
cd kshana
cargo build --release
cargo test          # all tests pass

Usage

Run any scenario; the CLI dispatches on the scenario's kind field and writes a <scenario>.result.json and a <scenario>.chart.svg next to it:

cargo run -- scenarios/clock-holdover.toml
cargo run -- scenarios/imu-deadreckoning.toml
cargo run -- scenarios/timetransfer.toml
cargo run -- scenarios/hybrid-pnt.toml
cargo run -- scenarios/orbit-gnss-challenged.toml
cargo run -- scenarios/orbit-sgp4-gps.toml
cargo run -- scenarios/orbit-rinex.toml
cargo run -- scenarios/integrity-raim.toml

# Export a propagated constellation to an SP3-c precise-ephemeris file:
cargo run -- scenarios/orbit-sgp4-gps.toml --export-sp3 gps.sp3

# Export the constellation's mean elements to a CCSDS OMM catalogue (one OMM
# message per TLE-defined satellite, with its real NORAD id / COSPAR designator):
cargo run -- scenarios/orbit-sgp4-gps.toml --export-omm gps.omm

Interoperability role. Kshana is the performance-simulation layer that sits alongside the post-processing toolchain, not a replacement for it: feed its RINEX output into RTKLIB or gLAB for a position solution, and use its SP3 output as a precise-orbit product for tools like Ginan — Kshana answers what resilience a given PNT architecture buys before you have real signals, in formats those tools already ingest (--export-sp3, or export_sp3 = true in an orbit scenario, writes <scenario>.sp3). The same orbit can be published as standards-track CCSDS OMM mean elements (--export-omm, or export_omm = true, writes <scenario>.omm) — one OMM 502.0 KVN message per TLE-defined satellite, carrying each object's real NORAD catalogue number, COSPAR international designator, and epoch, for any OMM-aware consumer instead of a bespoke two-line element set.

Example output (clock holdover — note the Integrity and Security figures of merit):

scenario c827e5d40d25 | quantum holdover 6600s p95 0.0ns integrity 1.000 security 0.997 | classical holdover 2610s p95 19.7ns integrity 1.000 security 0.000
wrote scenarios/clock-holdover.result.json and scenarios/clock-holdover.chart.svg

The optical clock's tight detection floor keeps security 0.997; the chip-scale clock's own noise over the monitoring window exceeds the 20 ns spec, so it has no spoof-detection margin (security 0.000). The orbit scenario additionally reports a geometry block — fraction of samples with a fix, and best/median PDOP and position accuracy — alongside the clock result.

Read these two numbers carefully. security is an analytic spoof-detectability bound derived from each clock's stability — it is meaningful only against a configured spoofing scenario and is not a multi-satellite RAIM detector. integrity here is the filter's self-consistency (fraction of outage samples inside its own k-sigma bound), not an aviation HPL/VPL integrity figure. See docs/INTEGRITY.md.

For genuine receiver-autonomous integrity, the integrity scenario kind (scenarios/integrity-raim.toml) runs real snapshot and solution-separation (ARAIM-style) RAIM over the propagated constellation geometry: it computes horizontal/vertical protection levels (HPL/VPL) per epoch and reports the fraction of epochs that meet the configured alert limits, with a Stanford integrity diagram for error-vs-PL classification.

Python

An optional Python extension (PyO3, abi3) wraps the same engine. Build and install it with maturin:

pip install maturin
maturin develop --features python   # or: maturin build --features python

import json, kshana

result = json.loads(kshana.run(open("scenarios/clock-holdover.toml").read()))
print(result["quantum"]["fom"]["integrity"])

# json, svg, and a one-line summary at once:
result_json, chart_svg, summary = kshana.run_full(open("scenarios/orbit-gnss-challenged.toml").read())
print(kshana.version(), summary)

Wheels are built for Linux, macOS, and Windows by the wheels workflow on each release tag.

WebAssembly

The engine also runs in the browser via wasm-pack:

wasm-pack build --target web -- --features wasm

import init, { run, chart_svg, version } from "./pkg/kshana.js";
await init();
const result = JSON.parse(run(tomlText));
console.log(version(), result.classical.fom.timing_p95_ns);

Scenario format

Scenarios are declarative TOML. A top-level kind selects the pack (clock is the default if omitted; inertial, timetransfer, hybrid, fusion, gnss-ins, orbit, gnss-sim, integrity, spoof, jamming, sweep, sweep-nd). Common fields: seed, a [time] grid, a [gnss] availability timeline (the outage driver), and per-sensor blocks with provenance strings citing the source of every figure. Example (clock):

seed = 42
threshold_ns = 20.0
[time]
step_s = 10.0
duration_s = 7200.0
[gnss]
windows = [
  { t0 = 0.0,   t1 = 600.0,  state = "nominal" },  # 10 min GNSS sync
  { t0 = 600.0, t1 = 7200.0, state = "denied"  },  # ~1.8 h outage
]
[clock_quantum]
id = "optical-sr-lattice"
provenance = "Strontium optical lattice clock, space-oriented goal sigma_y(1s)=1e-15 (arXiv:1503.08457)"
y0 = 5.0e-17
q_wf = 1.0e-30   # white FM:  q_wf = sigma_y(1s)^2
q_rw = 0.0       # random-walk FM
drift = 0.0      # linear aging (per second)
[clock_classical]
id = "csac-sa45s"
provenance = "Microchip SA65 / SA.45s CSAC datasheet sigma_y(1s)=3e-10"
y0 = 5.0e-10
q_wf = 9.0e-20
q_rw = 0.0
drift = 0.0

Optional fields (off when absent): a clock may add flicker_floor (1/f FM Allan floor); an inertial sensor may add gyro_bias and q_arw (gyro bias and angular random walk), and bias_instability and q_aa (the Allan bias-instability floor and acceleration random walk) — together a single-axis (1-DOF) accelerometer error budget (VRW/ARW and bias-instability). This is the error budget the shipped inertial scenario pack runs. Separately, the library now carries a verified 3-axis strapdown navigator (src/inertial/{attitude,mechanization,imu_errors}.rs): quaternion attitude with coning/sculling compensation, a full NED mechanization (Earth-rate and transport-rate terms, WGS-84 Somigliana gravity), and a deterministic IMU error model in which scale-factor, misalignment, g-sensitivity, quantization, and rate-ramp are modelled (IEEE Std 952-1997 §A.2; Groves 2013 §4.3). That 3-axis path is now wired into a runnable loosely-coupled GNSS/INS pack (kind = "gnss-ins"): a 15-state error-state EKF disciplines the strapdown solution against noisy fixes while GNSS is up, then coasts through the outage, reporting the fused horizontal error against the open-loop free-INS coast. A tightly-coupled pseudorange update is also available (it forms the innovation in the range domain, so it keeps correcting with fewer than four satellites). A clock-holdover scenario may add runs (> 1) to run a Monte Carlo ensemble — each figure of merit is then reported as a mean with a 5th–95th-percentile spread and the chart shades the error confidence band (see scenarios/clock-ensemble.toml).

A fusion scenario (same blocks as hybrid) runs two independent Kalman estimators — one for the clock state, one for the position state — disciplined by GNSS and aided by optical time transfer, and reports a combined holdover FoM. The two blocks share no cross-covariance: this is a stacked pair of error budgets, not a true coupled clock+position joint filter (cross-block covariance is a roadmap item). See scenarios/fusion-pnt.toml.

A spoof scenario injects a time-spoof — one of four [attack.shape] kinds (linear_ramp, step_jump, meaconing, replay; a bare rate_ns_per_s is still accepted as a linear ramp) — and runs each clock's spoof detector. The detector is a two-sided χ²₁ energy / Neyman–Pearson test on the clock-aided monitor statistic: the threshold is set from a target false-alarm budget target_pfa, and the missed-detection probability P_md is reported both closed-form and by Monte-Carlo (mc_runs trials per hypothesis — the two agree to a few ×1/√N). The Security figure of merit is 1 − P_md at the operationally-harmful (spec) magnitude, so a quiet clock that catches a spec-sized spoof scores ≈ 1 and a noisy one that often misses it scores lower (see scenarios/spoof-attack.toml, scenarios/spoof-meaconing.toml).

A gnss-sim scenario is a measurement-domain simulation: for each visible satellite it synthesises the pseudorange ρ = geometric range + c·δt_rx − c·δt_sv + I + T + noise + multipath and the L1 Doppler, with the Klobuchar single-frequency ionosphere ([iono], IS-GPS-200 §20.3.3.5.2.5) and the Saastamoinen zenith troposphere projected by the Niell (1996) mapping function ([tropo]). The residuals feed snapshot RAIM for per-epoch HPL/VPL, and every satellite's pseudorange, Doppler, C/N₀, and iono/tropo corrections are emitted in the JSON gnss_measurements array. It is a forward simulator (it generates measurements from a known truth), not a receiver/solver — a zero-noise run reproduces geometry plus the corrections to sub-millimetre (see scenarios/gnss-sim-raim.toml).

A jamming scenario models RF interference as a link budget: a [jammer] (ECEF position, transmit power_dbw, type) raises the jammer-to-signal ratio at a [receiver] watching a Walker [constellation]. From the geometry (free-space path loss and the per-direction receive-antenna gain) it computes each satellite's J/S, the effective C/N₀ via the standard anti-jam equation (despreading processing gain × the spectral-separation factor Q; Kaplan & Hegarty §9.4), and flags loss of lock below a configurable tracking threshold — reporting an availability_under_jamming figure of merit. A 10 W broadband jammer at 1 km denies the receiver entirely (J/S ≈ 72 dB); the same jammer at 100 km only degrades the links (see scenarios/jamming-demo.toml).

A sweep scenario runs a trade study: it varies one parameter (threshold_ns, duration_s, quantum_q_wf, or classical_q_wf) from start to stop over steps points on a lin or log scale, records a metric (e.g. holdover_s) for both clocks, and charts the two curves. The base scenario goes under [base] (see scenarios/sweep-clock-stability.toml).

A sweep-nd scenario generalises this to any pack and any number of axes: it varies dotted TOML keys of a [base] scenario (of any kind) over the Cartesian product of [[axes]], re-runs each grid node, and records metrics given as dotted JSON paths into the result (e.g. classical.fom.holdover_s). It works for every pack because it operates at the TOML/result boundary; native runs evaluate the grid in parallel (no extra dependency, wasm falls back to sequential) and the output is deterministic and row-major (see scenarios/sweep-nd-inertial.toml).

An orbit scenario derives the [gnss] timeline from geometry instead of authoring it — give a [user] orbit, a [constellation], an elevation mask_deg, and the two clock blocks. It also reports position accuracy from the satellite geometry; the optional sigma_uere_m (1-sigma user-equivalent range error, default 1 m) scales the position dilution of precision into a position sigma. The user orbit may be made eccentric with eccentricity and argp_deg, and j2 = true adds Earth-oblateness secular drift (see scenarios/orbit-molniya.toml). The constellation can instead be a real one: give [constellation] a tle block of two-line element sets and the satellites are parsed from it (see scenarios/orbit-real-tle.toml). Add one or more [[constellations]] blocks for multi-GNSS (e.g. GPS + Galileo; see scenarios/orbit-multignss.toml):

kind = "orbit"
seed = 7
threshold_ns = 5.0
mask_deg = 10.0
sigma_uere_m = 1.0           # optional; position sigma = position-DOP * this
[time]
step_s = 60.0
duration_s = 86400.0
[user]                       # spacecraft (altitude in km, angles in deg)
altitude_km = 8000.0
inclination_deg = 0.0
[constellation]              # Walker-delta GNSS (GPS-like)
altitude_km = 20180.0
inclination_deg = 55.0
planes = 6
sats_per_plane = 4
phasing_f = 1.0
[clock_quantum]  # ... as above
[clock_classical]  # ... as above

See scenarios/ for one example of every kind.

Output

The result artifact is versioned, self-describing JSON: per-step time series, the scored figures of merit, the active model specs (with provenance), the seed, a scenario hash — so any chart can be reproduced from the file — and, for each clock, an adev_curve ([{tau_s, adev, n_samples, noise, edf, ci_lo, ci_hi}]): the overlapping Allan deviation across octave-spaced averaging times — the standard way to read a clock's stability — now with a noise-type-specific 95% confidence band per point (the record's power-law type is identified from its modified-Allan slope, and the χ² interval uses the matching NIST SP 1065 effective degrees of freedom). The browser playground renders it as a log-log "Clock stability (ADEV)" chart. (MDEV, TDEV, and HDEV are available as library estimators; the exported result curve is the overlapping ADEV.) Every field, with units and a source pointer, is documented in docs/SCHEMA.md.

Every chart is self-describing. The browser playground, the CLI's *.chart.svg export, and the HTML scorecard all stamp each chart image with a footer reading Kshana v<version> · scenario <hash> · kshana.dev. The scenario <hash> is the first 12 hex characters of the run's scenario hash — a SHA-256 over the canonical scenario definition (seed, thresholds, model parameters, GNSS windows, …); the integrity and lunar reports, which carry no hash of their own, fall back to a SHA-256 of the scenario source. It is the same fingerprint shown in the one-line summary and the result JSON, so a saved or pasted chart always carries its version, the exact scenario that produced it (for bit-for-bit reproduction), and the source — change any input and the hash changes.

The figures of merit follow the standard operational PNT figures of merit:

Figure of merit	How Kshana computes it
Timing Performance (clock/orbit packs)	clock-phase error RMS + 95th-percentile over the outage, in nanoseconds (timing_rms_ns) — a timing metric, not position
Positioning Performance (inertial/hybrid packs)	1-DOF position-error RMS + 95th-percentile over the outage, in metres (pos_rms_m); single-axis. A single run is flagged monte_carlo: false; set runs = N for a Monte Carlo ensemble that reports each metric's mean, spread, and bootstrap 95% CI. Still not a 2-D CEP/2DRMS or DOP-weighted accuracy (those need the 3-axis model — roadmap)
Autonomy	holdover duration — time in-spec after GNSS loss (grid-quantised: a lower bound)
Resilience	error-growth slope during the outage
Availability	fraction of the run with an in-spec solution
Integrity	filter self-consistency — fraction of outage samples whose error stays inside the Kalman filter's own k-sigma bound. Not an aviation HPL/VPL/RAIM integrity figure (see docs/INTEGRITY.md)
Security	analytic spoof-detectability bound from clock stability — how small/slow a time-spoof a single-clock consistency monitor could flag. Meaningful only with a configured attack; not a multi-satellite RAIM detector

New to these terms? Each is defined in plain language in the glossary.

Architecture

One engine. The sensor packs plug in via a common error-model interface; alongside them sit an astrodynamics/numerical layer (analytic SGP4/SDP4 and a numerical Cowell propagator with its force model, maneuver design, and orbit determination) and a fusion / alt-PNT layer (the GNSS/INS estimators and the gravity-map matcher). See docs/ARCHITECTURE.md for the full set of diagrams.

flowchart LR
    SCN["Scenario (.toml)<br/>seed · GNSS timeline · sensor params"] --> ENG
    subgraph ENG["Engine (per step)"]
      direction TB
      M["Error model<br/>step(): evolve noise state"] --> E["Estimator<br/>GNSS-disciplined holdover"]
      E --> F["FoM scoring<br/>vs the 6 figures of merit"]
    end
    ENG --> OUT["result.json + chart.svg<br/>(reproducible: scenario+seed+version)"]

flowchart TD
    cli["CLI · Python · WebAssembly"] --> api["api — run_toml / run_scenario: typed dispatch by kind"]
    subgraph shared["Shared core"]
      types["types"]
      scenario["scenario · GNSS timeline"]
      allan["allan — Allan deviation"]
    end
    subgraph packs["Sensor packs"]
      p1["Clock — models · estimator · kalman · security · fom"]
      p2["inertial — strapdown INS + quantum-CAI"]
      p3["timetransfer (+ _adv) — optical/RF link"]
      p4["hybrid — fused PNT suite"]
    end
    subgraph astro["Astrodynamics & numerical"]
      orbit["orbit — geometry → GNSS timeline + DOP"]
      sgp4["sgp4 · tle — SGP4/SDP4"]
      prop["propagator — Cowell"]
      forces["forces — J2–J6 · 3rd-body · SRP · drag · relativity"]
      integ["integrator — RK4 · DOPRI"]
      ephem["ephem — Sun/Moon"]
      man["maneuver — burns · Lambert · porkchop"]
      od["orbit_determination — batch · sequential"]
    end
    subgraph fnav["Fusion & alt-PNT"]
      fus["fusion — EKF · UKF · 17-state · coupled"]
      grav["gravimeter · mapmatch · particle_filter"]
    end
    api --> packs
    api --> astro
    api --> fnav
    packs --> shared
    orbit --> sgp4
    prop --> forces
    prop --> integ
    forces --> ephem
    man --> integ
    od --> forces
    od --> integ
    fus --> p2
    grav --> p2
    orbit --> p1
    p4 -. composes .-> p1
    p4 -. composes .-> p2
    p4 -. composes .-> p3

Repository layout

kshana/
├── src/
│   ├── types.rs · scenario.rs · allan.rs   # shared core (time grid, GNSS timeline, Allan)
│   ├── api.rs · main.rs                     # typed dispatch + CLI
│   ├── python.rs · wasm.rs                  # optional PyO3 / wasm-bindgen bindings
│   │
│   ├── models.rs · estimator.rs · kalman.rs # Pack 1 — clock holdover + integrity
│   ├── security.rs · detection.rs · spoof.rs · spoof_monitors.rs # spoof detection
│   ├── filter_health.rs · fom.rs · report.rs · chart.rs · run.rs  # health · scoring · output
│   ├── inertial/        # Pack 2 — strapdown INS (attitude, mechanization, imu_errors, quantum_imu)
│   ├── timetransfer.rs · timetransfer_adv.rs · timegeo.rs # Pack 3 — TWSTFT/CV/PPP/optical, Sagnac
│   ├── hybrid.rs · ensemble.rs · sweep.rs   # Pack 4 — fused PNT suite, Monte-Carlo, trade sweeps
│   │
│   ├── orbit.rs · sgp4.rs · tle.rs · walker.rs   # geometry, SGP4/SDP4, TLE, Walker design
│   ├── propagator.rs · forces.rs · integrator.rs # numerical Cowell propagator + force model + RK4/DOPRI
│   ├── ephem.rs · precession.rs · frames.rs · timescales.rs · jd2.rs # ephemerides, IAU precession, time/frames
│   ├── maneuver.rs · batch_ls.rs · orbit_determination.rs # burns/Lambert/porkchop, Gauss-Newton, OD
│   │
│   ├── fusion/          # GNSS/INS — EKF, UKF, tightly_coupled, tightly_coupled17, coupled
│   ├── gravimeter.rs · mapmatch.rs · particle_filter.rs  # gravity-map / alt-PNT navigation
│   ├── raim.rs · lunar.rs        # ARAIM HPL/VPL, cislunar integrity
│   ├── gnss_sim.rs · ionex.rs · jamming.rs   # measurement domain, ionosphere maps, jamming
│   └── rinex.rs · rinex_obs.rs · glonass.rs · sp3.rs · oem.rs · omm.rs · permalink.rs # interop formats
├── scenarios/          # cited scenarios (one per kind + geometry-driven + GPS-denied)
├── scripts/            # reproducibility + repo-hygiene guards
├── docs/               # CONCEPTS, ARCHITECTURE, CAPABILITY, VALIDATION, PROVENANCE, GLOSSARY, …
├── web/                # the WebAssembly playground + kshana.dev site
├── .github/workflows/  # CI gate, release, wheels, publish, and pages pipelines
├── pyproject.toml      # Python packaging (maturin)
├── CHANGELOG.md        # Keep a Changelog + SemVer
└── CONTRIBUTING.md

Documentation

Document	For whom	What's in it
Concepts primer	everyone, start here	what Kshana does and why, from zero to the physics
Playground	everyone	run the engine in your browser (WebAssembly); build & deploy notes
Glossary	everyone	plain-language definitions of every term
Architecture	developers / reviewers	module map, engine pipeline, dispatch, and diagrams
Validation status	reviewers / citers	what is validated vs not modeled, with evidence
Provenance	reviewers / citers	every sensor parameter, model, and dataset traced to its published source, in one citable table
Reproducibility & provenance	reviewers / packagers	determinism guarantees, golden-pinning, SBOM, build provenance
Positioning	evaluators	where Kshana sits vs RTKLIB/gLAB (complementary), and the zero-install browser tier
SGP4 validation	reviewers / citers	agreement with the AIAA 2006-6753 reference (666 states, ~4 mm) and a head-to-head against the independent sgp4 crate (agree to sub-micron / 4.12 mm)
Changelog	everyone	released history (Keep a Changelog + SemVer)
Contributing	contributors	build, guards, test/citation discipline, DCO
Code of Conduct	community	expected conduct (Contributor Covenant)
Security policy	reporters	how to report a vulnerability; dual-use note

Validation, reproducibility & honesty

• Every noise term is calibrated to a published, cited figure and validated against the standard relation (Allan deviation for clocks; Groves' dead-reckoning error growth for inertial; the timing→ranging conversion for time transfer). Status per term is tracked in docs/VALIDATION.md as validated or not modeled — nothing is presented as validated that is not.
• Reproducible by construction: scenario + seed + engine version → identical bits. scripts/check-reproducible.sh enforces it; quantum and classical runs use independent seeds so their noise is uncorrelated.
• Maturity is stated honestly: optical-clock and optical-link figures are targets / ground-demonstrator results, not flown.

FAQ

Do I need to understand quantum physics to use this? No. If you can run a command line you can run Kshana. Start with the plain-language primer; look terms up in the glossary.

Is this a quantum-hardware design or flight software? No. It is a performance simulator. Quantum-hardware fidelity comes from published error models, not from this tool. See What it is / is not.

Are the quantum results realistic, or marketing? Every parameter is cited to a datasheet or paper, every model is validated against a textbook relation, and maturity is labelled honestly in VALIDATION.md — including that no strontium optical clock has flown. The engine is neutral: quantum and classical are the same code with different published numbers.

Can I trust two runs to agree? Yes — runs are deterministic: scenario + seed + engine version → bit-identical output, enforced by scripts/check-reproducible.sh.

Can I use it from Python or in a browser? Yes — see Python and WebAssembly. Both call the same engine.

How do I model my own sensor? Write a scenario .toml with your sensor's published figures in the provenance fields. See Scenario format and the examples in scenarios/.

Is it free for commercial use? Yes, under Apache-2.0. Optional commercial support and proprietary extensions are available — see Support.

Troubleshooting

cargo build fails on an old toolchain. Kshana needs Rust ≥ 1.75. Update with rustup update.

Building the Python extension fails to link on macOS (Undefined symbols … _Py…). A Python extension resolves its symbols at load time. maturin sets the right linker flag automatically — use maturin develop --features python rather than a bare cargo build.

The Python build complains the interpreter is newer than PyO3 knows. Set PYO3_USE_ABI3_FORWARD_COMPATIBILITY=1 (abi3 wheels are forward-compatible across CPython versions).

WebAssembly build can't find the target. Install it once with rustup target add wasm32-unknown-unknown, then wasm-pack build --target web -- --features wasm.

Where did my output go? Each run writes <scenario>.result.json and <scenario>.chart.svg next to the input .toml. These are git-ignored by design.

Roadmap

See ROADMAP.md for the phased roadmap, CHANGELOG.md for released history, and docs/CAPABILITY.md for the per-capability roadmap. Near-term items include ITRF-precise frame reduction (polar motion and sub-arcsecond nutation on top of the shipped GMST-based TEME↔ECEF), two-part Julian dates, tightly-coupled carrier-phase fusion, and surfacing the loosely-/tightly-coupled GNSS/INS navigator across more packs. The quantum physics layer is a P2 item: the CAI accelerometer is now simulated from first principles (Mach–Zehnder phase, projection noise, contrast decay, vibration coupling), while the clock/time-transfer sensors are still driven by published Allan/noise-budget coefficients. GMST-based TEME↔ECEF, the IERS leap-second time systems (UTC/TAI/TT/UT1), SGP4/SDP4 orbit propagation (v0.7.0, validated against the AIAA 2006-6753 vectors), and the runnable gnss-ins fusion pack have all shipped, and the inertial velocity is exposed downstream. An active stochastic time-spoof detector (Neyman–Pearson / χ²₁ energy test with Monte-Carlo P_fa/P_md and a Security FoM of 1−P_md), a link-budget jamming model (J/S → effective C/N₀ → loss of lock), multi-constellation availability, a single-axis (1-DOF) IMU error budget, two independent (clock + position) Kalman estimators reported as a combined FoM, real constellation geometry from TLEs, an HTML scorecard report, geometry-derived GNSS availability and dilution of precision from Keplerian orbits with eccentricity and J2 drift, Monte Carlo confidence bands, trade-study parameter sweeps, an in-browser WebAssembly playground, and optional Python (PyO3) and WebAssembly (wasm-bindgen) bindings have landed on main.

Contributing

See CONTRIBUTING.md. In short: tests pass (cargo test), the two guard scripts pass, Conventional Commits, and a CHANGELOG.md [Unreleased] entry for every user-visible change. Participation is governed by our Code of Conduct. To report a security issue, see the Security policy — please do not open a public issue for vulnerabilities.

Citing

If you use Kshana in academic or technical work, please cite it. Machine-readable metadata is in CITATION.cff (GitHub renders a "Cite this repository" button from it); cite the version you used (e.g. v0.14.0) together with the scenario and seed for full reproducibility. Every release is archived on Zenodo with a citable DOI — the concept DOI 10.5281/zenodo.20528627 always resolves to the latest version.

Baweja, C. (2026). Kshana — a PNT-resilience simulator with quantum-sensor performance models. Ashforde OÜ. https://doi.org/10.5281/zenodo.20528627

Versioning & releases

Kshana follows Semantic Versioning. While pre-1.0 the public scenario/result schema may still change; breaking changes are called out explicitly in the CHANGELOG.md. Tagged releases are published to crates.io, PyPI, and npm, and listed under GitHub Releases. Every result is reproducible from scenario + seed + engine version.

License

Apache-2.0 — see LICENSE. Contributions are accepted under the same license (inbound = outbound); sign commits off per the Developer Certificate of Origin with git commit -s.

Trademark. "Kshana" and its marks are trademarks of Ashforde OÜ. The license covers the code, not the name — please rename forks and derivative distributions.

Support & professional services

Kshana is free and open source under Apache-2.0 and professionally developed and maintained by Ashforde OÜ (Estonia). The open engine is complete and usable on its own. For organisations that need more, Ashforde OÜ offers:

• Commercial support & integration — embedding Kshana in your toolchain, custom scenarios, and priority fixes.
• Custom sensor models — calibrated to your hardware, including export-sensitive resilience models maintained in a private overlay.
• Kshana Pro — proprietary model-based systems-engineering and programme tooling that plugs into the open engine to complete the workflow.
• Training & consulting on quantum/classical PNT performance analysis.

This is the open-core model: the engine is, and stays, openly licensed; the sustaining business is expertise, support, and the proprietary extensions — not license fees. Contact [e-mail].

Key references

• Riley, Handbook of Frequency Stability Analysis — NIST SP 1065 (Allan-deviation relations).
• Origlia, Schiller, Bongs et al. — arXiv:1503.08457 (strontium optical lattice clock, space-oriented goal).
• Oelker et al., Nature Photonics (2019) — JILA PDF (laboratory Sr clock, 4.8×10⁻¹⁷).
• Templier et al., Science Advances (2022) — arXiv:2209.13209 (hybrid quantum accelerometer triad).
• Groves, Principles of GNSS, Inertial, and Multisensor Integrated Navigation — IEEE AESS tutorial (UCL Discovery) (dead-reckoning error growth).
• Giorgetta et al., Nature Photonics 7, 434 (2013) — arXiv:1211.4902; Deschênes et al., Phys. Rev. X 6, 021016 (2016) — APS (optical two-way time-frequency transfer).
• Optical inter-satellite time-transfer concept — see Giorgetta and Deschênes above.