ntn-positioning (scenario kind)

Scenario kind of the engine v0.38.0, family Low-Earth-orbit navigation. 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#

Positioning from a 5G non-terrestrial network (NTN) downlink in the mobile-satellite service (MSS) S band (3GPP band n256, downlink 2170 to 2200 MHz; default carrier 2172.5 MHz): the Cramér-Rao bound (CRB) on time of arrival, c / (2 pi beta sqrt(2 (C/N0) T)) with beta the root-mean-square (Gabor) bandwidth of the flat OFDM spectrum (B/sqrt(12)), and on the Doppler of a complex tone, sqrt(3 / (2 pi^2 (C/N0) T^3)), for each signal (default a 5 MHz New Radio channel with 4.5 MHz occupied and a 200 kHz narrowband channel with 180 kHz occupied); then, over any LEO constellation, downlink time-of-arrival fixes with an unknown receiver clock (seeded, with the bound plus a network synchronisation error as the sigma), their PDOP and formal 3D sigma, and a single-satellite Doppler fix over the longest pass with the height held. MODELLED: the bandwidth-to-bound step is the textbook closed form, checked against numerical integration of the flat and band-limited BPSK spectra (internal consistency, no published worked figure pinned), and the positioning accuracy is a bound on a multipath-free channel with a stated synchronisation error, not an achieved result.

One run of scenarios/ntn-5g-positioning.toml summarises as: 5G NTN positioning at 2172.5 MHz, C/N0 38 to 50 dB-Hz, 324 satellites (10.0 in view) NR 5 MHz: 4500 kHz, CRB range 0.26 to 1.03 m; median formal 3D 2.09 m, RMS error 2.01 m NB 200 kHz: 180 kHz, CRB range 6.49 to 25.85 m; median formal 3D 25.94 m, RMS error 26.73 m one-satellite Doppler pass: 53 samples over 520 s, horizontal error 1.9 m

Inputs#

From the schema (kshana kinds --json):

• Required fields: none
• Optional fields: seed, carrier_hz, signal, integration_s, doppler_integration_s, cn0_dbhz, sync_error_m, user, duration_s, step_s, system

The example scenarios/ntn-5g-positioning.toml sets, among others:

Run it#

kshana scenarios/ntn-5g-positioning.toml

What it gives#

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

Result label (the engine's): MODELLED positioning from Cramér-Rao bounds: the bandwidth-to-bound step is a textbook closed form (checked against numerical integration, not against a published worked figure); the accuracy is a bound on a multipath-free channel with a stated synchronisation error, not an achieved result

Evidence#

VALIDATED: the verification matrix rows that name this kind.

• VALIDATED The Cramér-Rao bound on time of arrival from the root-mean-square (Gabor) bandwidth, c/(2 pi beta sqrt(2 (C/N0) T)), for a flat OFDM spectrum (beta = B/sqrt(12)), a band-limited BPSK spectrum (closed-form numerator) or any spectrum by quadr Tests: leo_fusion_scenarios.rs.

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 The Cramér-Rao bound on time of arrival from the root-mean-square (Gabor) bandwidth, c/(2 pi beta sqrt(2 (C/N0) T)), for a flat OFDM spectrum (beta = B/sqrt(12). Oracle (ExternalDataset): Published worked values (P1): Bachl, Lei and Nabeel, arXiv:2608.10270 (2026), single-SSB bounds of NR NTN reproduced from the 3GPP TS 38.211 SSB map through Kshana own numeric functions (W_rms 1.9616 vs 1.96 MHz, sigma_t 38.755 vs 39 us, sigma_f 100.79/87.28 vs 101/87 Hz, sigma_rho 0.5970/0.5831 vs 0.60/0.58 m, each within half a unit of the printed last digit); Betz 2001 Table 1 BPSK-R RMS bandwidths (1.128/3.477 vs

Limitations#

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

• MODELLED positioning from Cramér-Rao bounds: the bandwidth-to-bound step is a textbook closed form (checked against numerical integration, not against a published worked figure); the accuracy is a bound on a multipath-free channel with a stated synchronisation error, not an achieved result (result label)
• MODELLED: the bandwidth-to-bound step is the textbook closed form, checked against numerical integration of the flat and band-limited BPSK spectra (internal consistency, no published worked figure pinned), and the positioning accuracy is a bound on a multipath-free channel with a stated synchronisation error, not an achieved result. (kind catalogue (kshana kinds --json))
• The bandwidth-to-bound step is a textbook closed form; the positioning accuracy is MODELLED (a bound on a multipath-free channel, not an achieved result). (scenario file comment, lines 12 to 13)
• Reproducibility & software assurance is MODELLED, not validated: a sub-claim is externally checked, but the whole capability composes modelled pieces, so the capability stays Modelled. (verification matrix (docs/MODELLED-RATIONALE.md))

See also#

• Family page: Low-Earth-orbit navigation
• All kinds: KINDS.md
• Topic page: LEO-PNT.md
• Topic page: LEO-PNT-FUSION.md