lunar-vlbi-fim (scenario kind)

Scenario kind of the engine v0.38.0, family Lunar and cislunar. Advisory: analysis output from a research and engineering tool, not type-approved navigation equipment and not a safety-of-life service. Every label here is the engine's or the verification matrix's; a kind is MODELLED unless the matrix says otherwise (how a label is earned: the README's Evidence section).

What it does#

Lunar-VLBI station-coordinate covariance: the delay partials of the lunar-vlbi observable accumulated over an explicit SCHEDULE (baselines x epochs) into a Fisher information matrix, inverted, and reported as the station coordinate covariance and the per-coordinate station sigma — a computed engine output rather than a scalar delay precision pushed through an assumed isotropic g = 3 equipartition factor. The state carries Earth-FIXED (ITRS) station coordinates, so the Jacobian is the inertial partial rotated by each epoch's GCRS->ITRS matrix: Earth rotation is what makes those coordinates observable, and the report MEASURES the Earth-fixed line-of-sight sweep and the beacon declination rather than assuming them. One observation is one (baseline, epoch) pair with BOTH stations above the elevation mask, weighted 1/delay_sigma_s^2. Reports rank, datum defect, condition number, the full information spectrum, the covariance matrix, per-station per-axis and 3-D sigmas, and the free-network null space on every run; under a rank deficiency the headline sigma is published as NULL with a status, never read out of a near-singular inverse. The equipartition value cdelay_sigma_ssqrt(g/N) for the SAME schedule is emitted beside the computed value with the ratio, together with the isotropic trace bound sqrt(p/trace(M)) that AM-HM makes a hard floor — so the ratio is the anisotropy the assumption discarded. The delay closure tau_ik = tau_ij + tau_jk makes only n-1 of the n(n-1)/2 baselines geometrically independent; the report states both counts. MODELLED: the Moon-centre ephemeris, station clocks, troposphere and Earth-orientation parameters are held FIXED and observations are treated as independent, so the covariance is a Cramer-Rao bound for a reduced parameter set, not a predicted session result; the delay sigma, station coordinates and schedule are inputs. The partial the geometric-delay Jacobian leaves out (the differenced Shapiro term) is measured by finite difference and emitted. Not a geodetic product.

One run of scenarios/lunar-vlbi-fim.toml summarises as: lunar-vlbi-fim | 3 stations / 3 baselines x 49 epochs = 16 obs (mask 10.0 deg) | datum anchor-first-station | rank 6/6 cond 2.209e4 | station sigma 0.0926 m vs equipartition g=3 0.0013 m (ratio 71.360)

Inputs#

From the schema (kshana kinds --json):

• Required fields: none
• Optional fields: stations, beacon_lat_deg, beacon_lon_deg, beacon_alt_m, epoch_year, epoch_month, epoch_day, arc_hours, step_min, delay_sigma_s, elevation_mask_deg, datum, estimate_beacon, rel_tol, equipartition_g, planetary_kernel_path

The example scenarios/lunar-vlbi-fim.toml sets, among others:

Run it#

kshana scenarios/lunar-vlbi-fim.toml

What it gives#

The scalar results of that run, with the units the engine states:

Result label (the engine's): MODELLED lunar-VLBI station-coordinate covariance. The covariance is accumulated from the engine's own analytic delay partials over an explicit schedule of baselines and epochs and inverted; it is NOT converted from a scalar delay precision by an assumed geometry factor. The per-observation delay si

Evidence#

MODELLED 3 · VALIDATED 2: the verification matrix rows that name this kind.

• VALIDATED Delay partials accumulated over a schedule of baselines × epochs into a Fisher information matrix, inverted to the station coordinate covariance and the per-coordinate station sigma, replacing an assumed isotropic equipartition link from a
• MODELLED A third datum choice, all-stations-fixed, that holds every Earth station and estimates the BEACON's Moon-body-fixed coordinates alone — the configuration a lunar surface-point uncertainty is actually quoted for, since Earth station coordi
• VALIDATED The all-stations-fixed beacon covariance of the lunar-vlbi-fim scenario (every Earth station held, the beacon's Moon-body-fixed coordinates estimated alone) with the beacon placed on the JPL DE440 Moon read by the engine's own kernel reader
• MODELLED The seven-parameter Helmert datum propagated from a SIMULATED OBSERVING CAMPAIGN instead of recovered from an injected transform.
• and 1 more in the matrix.

The rows the run itself exercised, with the oracle the matrix gives each (the public sources are named there):

• MODELLED Deterministic, scenario-hashed, SBOM + cross-platform golden gates. Oracle (ExternalDataset): SBOM conformance to the official CycloneDX 1.5 JSON Schema (+ valid SPDX identifiers) — an external published standard, zero validation errors over the full dependency graph; the FoM-determinism / byte-reproducibility part remains a pinned self-consistency check, so the row stays MODELLED
• VALIDATED Delay partials accumulated over a schedule of baselines × epochs into a Fisher information matrix, inverted to the station coordinate covariance and the per-coo. Oracle (ExternalDataset): An independent in-repo route. Every Jacobian row is re-derived by central finite difference of lunar_vlbi::vlbi_delay_s evaluated from the state's own Earth-fixed and Moon-body-fixed coordinates rotated forward through the frame chain — a path that computes no derivative and shares no expression with the analytic partials — and the information matrices the two routes build agree to < 1e-6 of the largest diagonal. The
• MODELLED A third datum choice, all-stations-fixed, that holds every Earth station and estimates the BEACON's Moon-body-fixed coordinates alone — the configuration a lu. Oracle (ReferenceImpl): Closed-form identities, with no external oracle claimed or available. The lever arm is checked against ρ/B and the two equipartition forms against each other to 1e-15 — algebraic identities, so they catch a wiring error and nothing else, and are labelled as such. The substantive result is MEASURED rather than asserted: a delay from a fixed baseline constrains the beacon's DIRECTION, so the line-of-sight component rea

Limitations#

What the run's own report says is not modelled or not validated:

• MODELLED lunar-VLBI station-coordinate covariance. The covariance is accumulated from the engine's own analytic delay partials over an explicit schedule of baselines and epochs and inverted; it is NOT converted from a scalar delay precision by an assumed geometry factor. The per-observation delay sigma, the station coordinates, the beacon site and the schedule are inputs. The Moon-centre ephemeris, the station clocks (result label)
• Lunar-VLBI station-coordinate covariance: the delay partials of the lunar-vlbi observable accumulated over an explicit SCHEDULE (baselines x epochs) into a Fisher information matrix, inverted, and reported as the station coordinate covariance and the per-coordinate station sigma — a computed engine output rather than a scalar delay precision pushed through an assumed isotropic g = 3 equipartition factor. (kind catalogue (kshana kinds --json))
• The state carries Earth-FIXED (ITRS) station coordinates, so the Jacobian is the inertial partial rotated by each epoch's GCRS->ITRS matrix: Earth rotation is what makes those coordinates observable, and the report MEASURES the Earth-fixed line-of-sight sweep and the beacon declination rather than assuming them. (kind catalogue (kshana kinds --json))
• The equipartition value cdelay_sigma_ssqrt(g/N) for the SAME schedule is emitted beside the computed value with the ratio, together with the isotropic trace bound sqrt(p/trace(M)) that AM-HM makes a hard floor — so the ratio is the anisotropy the assumption discarded. (kind catalogue (kshana kinds --json))
• MODELLED: the Moon-centre ephemeris, station clocks, troposphere and Earth-orientation parameters are held FIXED and observations are treated as independent, so the covariance is a Cramer-Rao bound for a reduced parameter set, not a predicted session result; the delay sigma, station coordinates and schedule are inputs. (kind catalogue (kshana kinds --json))
• D3's published chain goes from a per-observation delay precision to a station coordinate uncertainty through an assumed ISOTROPIC equipartition factor g = 3. That step is the one the paper's own abstract calls modelled rather than measured. This scenario removes it: the lunar-VLBI delay partials are accumulated over a real schedule of (baseline x epoch) pairs into a Fisher information matrix, inverted, and reported a (scenario file comment, lines 3 to 8)
• The state carries Earth-FIXED (ITRS) coordinates, so the Jacobian is the inertial partial rotated by each epoch's GCRS->ITRS matrix: Earth rotation is what makes those coordinates observable at all, and the report MEASURES the Earth-fixed line-of-sight sweep and the beacon declination rather than assuming them. One observation is one (baseline, epoch) pair with BOTH stations above the elevation mask, weighted 1/delay (scenario file comment, lines 10 to 14)
• What to read in the report * per-station per-axis and 3-D sigmas — the computed answer; * the equipartition value cdelay_sigma_ssqrt(g/N) for the SAME schedule, printed beside it with the ratio. That ratio IS the anisotropy the assumption discarded, and the isotropic trace bound sqrt(p/trace(M)) makes AM-HM a hard floor, so the assumption can only ever understate; * rank, datum defect, condition number, the full sp (scenario file comment, lines 16 to 26)

See also#

• Family page: Lunar and cislunar
• All kinds: KINDS.md