Estimating motion from IMU readings and GPS

The bounded motion estimator is implemented. Five short, deterministic software controls completed with no failures, and fifteen focused tests pass. The controls recover sensor bias, effective orientation, gain and timing when the other relevant quantities are known. They also expose an ambiguity when orientation and acceleration bias are both unknown. No measured Earth-model fit ran, no scientific acceptance rule changed, and all 232 stored originals remain preserved.

What the estimator does

An IMU measures rotation and specific force. Its acceleration channels include the effect of gravity as well as aircraft motion. The estimator follows those readings through time and predicts the position that the GPS antenna would occupy. It compares that prediction with the actual receiver coordinates at their original timestamps.

Initial orientation and velocity, position offsets, gyro and accelerometer bias, gain, gravity, antenna location and timing can be bounded nuisance parameters. Each bound must be supplied explicitly. These controls do not establish appropriate bounds for any archival instrument. An unknown constant mounting rotation and unknown initial orientation cannot be separated from these observations alone; the estimator uses one effective orientation.

GPS uncertainty is supplied in the receiver's coordinate units, including correlations between epochs when available. The same covariance applies to every candidate model; changing the Earth-model distance metric must not change the observation weights. GPS latitude, longitude and height retain their receiver conventions and are conditional inputs, not independent raw satellite ranges or proof of a geometry.

The predictor can evaluate a position partway through a packet under its explicit constant-rate/specific-force assumption. This does not interpolate or replace GPS/IMU measurements. Receiver epochs must have IMU support throughout the entire allowed timing offset. Unsupported gaps, duplicate epochs and invalid covariance are rejected.

What the controls establish

These are two-second analytic translation controls at 100 Hz, with independently calculated GPS positions. The assumed one-millimetre coordinate uncertainty is a software fixture, not measured receiver performance. Other quantities are fixed when testing one parameter. Varying acceleration tests gain and timing; it is not a flight campaign.

The small gain/timing differences are within the declared control tolerances; midpoint integration has finite-step error for changing acceleration. These tests establish software recovery under stated assumptions, not archive-wide calibration accuracy. The ambiguity control converges numerically but cannot identify all three parameters. Convergence alone does not establish identifiability.

Numerical derivatives use steps scaled to the declared bounds. The diagnostic rank cutoff also exceeds three times the discrepancy between two derivative step sizes. This prevents roundoff in latitude/longitude from being treated as a newly identified parameter. It is a local numerical diagnostic, not a calibrated statistical gate or formal error bound.

Every residual evaluation counts, including derivatives and the final rank diagnostic. The five controls used 23, 21, 22, 18 and 64 evaluations respectively; each allowance was 160. The empirical entry point rejects missing independent evidence before charging a start. Its append-only, locked and fsynced journal counts interrupted starts toward the separate six-file, 24-start, 200-evaluation-per-start allowance. No empirical start was consumed here.

Pairwise questions

The code supports a separate nuisance profile for each model pair, including globe versus disc. Bounded calibration changes cannot automatically erase a contrast just because an unbounded mathematical projection can. A test demonstrates the difference, and another preserves one pair's information when a different pair has none.

A through-model calculation on the two-second software control evaluates all three candidate anchors with common receiver weighting. This exercises the implementation; it does not establish separation for an actual flight. The bounded tangent calculation is local and varies one anchor at a time. It does not certify the separation of two independently fitted nonlinear model families. Nonlinear pair profiles and numerical stability checks are still needed before a scientific claim. Every present pairwise decision is abstention.

These flights are not uniformly low and slow

NASA describes LVIS as typically operating about ten kilometres above the ground. Its 2010 Antarctic campaign used dedicated high-altitude DC-8 flights. Low-altitude survey flying is only part of this archive's range.

The six prepared recordings have the following median values from embedded GPS. Heights are above mean sea level, not terrain. Speeds are ground speeds from adjacent actual fixes, using a conditional globe coordinate metric with altitude; they are not true airspeeds.

These summarize previously prepared stretches, not whole flights or confirmed lidar-on intervals. The earlier 108 candidate windows span roughly 0.3–12.3 km altitude and 502–923 km/h. Their median window medians are 11.7 km and 806 km/h; this is not a duration-weighted population median. Those broader summaries use fused navigation only as labeled motion context. Simultaneous instrument recordings can overlap.

The predicted horizontal globe transport rate in those windows is 4.5–8.3 degrees/hour. Slower travel reduces that curvature-related rate roughly in proportion to speed. Earth rotation does not decrease with aircraft speed. Altitude affects the transport radius too, but actual motion, sensor errors and processing still determine usable model separation. The nominal scale failure in the 26 October 2010 recording remains explicitly recorded.

What remains

The estimator now supplies the next tool, but its archive inputs still need independently supported processing, clock, calibration and receiver-uncertainty evidence. Group-1 fused navigation cannot supply the missing independent Earth observation. A plausible Earth-rate residual would not itself establish which onboard corrections were applied. There is no automatic transfer of passenger-protocol calibration to this permanently mounted IMU.

Work first on the six frozen representatives, then extend supported decoding and motion checks by configuration to the other useful recordings. Empirical Earth fitting stays limited to its separately authorized scope and requires the evidence gate before any start. Once the archival analysis is ready, the intended project direction is to make it primary and present the passenger IMU experiment as a secondary extension. Instrument-specific quality and fast flight are promising inputs; neither substitutes for the remaining checks.

Implementation: analysis/lll/ilvis0_estimator.py and ilvis0_estimator_controls.py. Launcher: analysis/tests/ilvis0_estimator_worker.py. Completed output: data/ilvis0-estimator-20261007/. This evidence directory preserves the manifest, source snapshots, complete compressed results, completion and the control-start journal. The completed run must not be resumed or combined with a revised implementation.