Can the ESA rate adapter reconstruct a maneuvering flight?

This software qualification addresses the next ESA prerequisite: complete geographic motion, rather than component integrals or a quiet trend fitted to GPS samples. It uses generated observations with known trajectories, not an ESA recording. The zero-eligible version-1 inventory and reserved confirmation groups remain unchanged.

Independent known answers

Generate trajectories directly in fixed Cartesian geometry. Define latitude, longitude, height and body attitude as analytic functions of time, and obtain their first and second derivatives analytically. Use the ellipsoid geometry for both globe candidates and the specified polar-disc geometry for the disc. Obtain gyro rates from differentiated body-frame axes. Obtain specific force from Cartesian acceleration, the declared background field and gravity.

The generator must not import the navigation predictor, its coordinate-rate or transport formulas, or lll.models. It supplies true initial position, velocity and attitude, original rate/force samples, and exact later coordinates. No fit or receiver-derived attitude enters this test. Both zero upstream removal and a declared 35% common conventional-field removal are tested.

Use two fixed maneuver patterns: a slow changing course with independently changing roll, pitch and yaw; and a faster alternating-axis attitude pattern. Both include changing speed and height. Freeze the precise analytic amplitudes, periods, phases and starting coordinates below. They define the tested capability, not a claim about every possible flight.

Use radians internally, WGS84 semi-major axis 6,378,137 m and flattening 1/298.257223563, disc scale 6,371,000 m, gravity 9.81 m/s² and the specified background magnitude 0.00007292115 rad/s. These are explicit generated inputs. Starting longitude is −40°. With a = 6378137, latitude p0 equal to ±55°, and time t in seconds, the common coordinate recipe is:

\[ \begin{aligned} \phi(t)&=p_0+\frac{8}{a k_\phi}\sin(k_\phi t),& k_\phi&=2\pi/300,\\ \lambda(t)&=-40^\circ+\frac{75}{a\cos p_0} \left(t+\frac{0.1}{k_\lambda}\sin(k_\lambda t)\right),& k_\lambda&=2\pi/180,\\ h(t)&=600+10\sin(k_h t),& k_h&=2\pi/240. \end{aligned} \]

Body-to-local attitude uses yaw–pitch–roll order Rz(yaw) Ry(pitch) Rx(roll). Each angle is its amplitude times sin(2πt/period), with π/2 added to yaw. The slow pattern's (amplitude rad, period s) values are yaw (0.12,120), pitch (0.03,90) and roll (0.06,60). The faster pattern uses yaw (0.25,25), pitch (0.08,13) and roll (0.15,9). The initial state is the generator's exact state at zero. These deliberate maneuvers exceed the old quiet-flight cutoff; they are capability tests, not inferred aircraft behavior.

Matched calculation

Use the existing streaming airquantumgrav_increments.IntervalStream under each of its three explicit hypotheses: left hold, right hold and linear points. Preserve its gap, timing, units and chunk-continuation checks. Constructed increments remain mathematical interpretations of rate samples.

Feed those increments into the unchanged native geographic navigation kernel. Do not replace the native equations with the truth generator, fit calibration, reset to later positions or score only selected axes. Use the true initial state and declared gravity and removal fraction. Antenna lever arm is zero in this first geographic check; a nonzero lever arm and uncertain initialization remain separate requirements before an observed-data study.

Test all three physical candidates, starting latitudes +55° and −55°, both removal assumptions, both maneuver patterns and all three sampling hypotheses: 72 identities. Each identity propagates 1,200 seconds at 300 Hz and again at 600 Hz. Query the same 1,200 epochs, from 0.5 to 1,199.5 seconds at one-second spacing, avoiding an unsupported final boundary.

Checks fixed before execution

Test the generator's derivatives against an independent numerical derivative at 0, 7, 31, 143 and 599 seconds. Use a five-point stencil for Cartesian derivatives at half-widths 0.5 and 0.25 seconds, with maximum velocity and acceleration disagreements of 0.00001 m/s and 0.00001 m/s². Check body-axis derivatives separately at 0.01 and 0.005 seconds, with angular-rate disagreement at most 0.00000001 rad/s. Check proper body rotations, signed gyro axes, specific-force direction and the zero-motion limit.
Compile both native translation units from the declared isolated source snapshot before the study. Missing dependencies block preparation.
Require every candidate and sampling hypothesis to reconstruct a complete, finite trajectory with all three coordinate axes and no hidden position reset.
For each hold rule, require the finer grid's maximum three-dimensional error to be at most 0.6 times the coarse-grid error plus 0.001 m. For linear points, require at most 0.4 times coarse error plus 0.001 m. These test the expected numerical refinement behavior without pretending the hold rules are identical.
For the linear-point hypothesis at 300 Hz, require horizontal RMS at most 1 m, height RMS at most 1 m, and maximum three-dimensional error at most 5 m. These are software accuracy targets, not measurement-error specifications. Preserve left/right-hold errors even when they exceed those accuracy targets.
Save per-axis and total errors, maximum errors, refinement ratios, input-array hashes and every failed result. Regenerate generated arrays from the frozen recipe; do not store 72 duplicate synthetic histories or worker trees.

Measure errors in Cartesian metres under the generating candidate's geometry, then project them onto its known true local north, east and up axes. Do not use a globe longitude-to-distance scale for a disc case. The truth generator's attitude is used only as a known answer in these software controls, never as an observation supplied by a fused navigation system.

Passing qualifies only the declared generated capability and sampling hypotheses. It does not identify the instrument's actual averaging, phase, filtering or onboard corrections, establish observational confidence, or revise selection. Failure blocks the dependent ESA adapter capability claim; do not relax targets.

Finite allowance and release gate

One worker uses four numerical threads, after the current NASA pilot releases its allocation. Freeze source/environment hashes, all analytic parameters and the generated case identities before starting. Use no original recordings, observed-data fits or protected data.

Each identity permits exactly two native propagations, at most 1,080,000 constructed intervals and at most 1,296,000,000 conservative packet/query visits. Across 72 identities the ceilings are 144 native calls, 77,760,000 constructed intervals and 93,312,000,000 packet/query visits. Also reserve the analytic sample evaluations before generation: 360,001 coarse samples, 720,001 fine samples and 1,200 answer samples per identity, totaling 1,081,202 per identity and 77,846,544 across the study. These include interval endpoints and scoring queries; they are not additional instrument observations. Charge before execution. Use a four-hour cooperative wall ceiling, no retries and no allowance expansion. Preparation must check the frozen recipe and actual counts against these limits.

This plan is not an active allowance. The final recipe, derivative and loader checks, exact definitions and environment freeze are required before launch. Additional selection, receiver-error, lever-arm, initialization and calibration qualification still precede ESA model fitting. No NASA calibration bounds or decision thresholds transfer automatically.

Motion limitation · Existing rate/body controls · ESA selection proposal · Implementation sequence · Roadmap