How the numerical lessons are prepared and checked

Primary references and explicit conventions

GPS orbit and clock terminology is connected to the GPS interface specification. Observation and precise-orbit files are connected to IGS format specifications. The ambiguity-resolution lesson cites the original LAMBDA research and implementation literature. The reference library groups these sources by the part of the algorithm they support.

A citation supports the model or definition, rather than certifying a particular numerical output. Each lesson must still specify the epoch, time scale, coordinate frame, observation order and units used in its example. In particular, GPS time and UTC are separate scales; carrier phase in cycles and code in metres require a wavelength conversion; horizontal and vertical covariance require a local coordinate frame.

Real observations, supplied examples and solver exports

The Double Difference lesson follows a real GPS RINEX epoch at 09:00:00 GPST on 14 November 2024. It uses five common satellites, G09 as reference, GPS L1 C1C/L1C observations and a stated base-minus-rover convention. Its numerical trace records the selection, differences, covariance, float estimation and candidate-fixed comparison.

The separate LAMBDA lesson uses a supplied three-ambiguity teaching input with exported solver calculations. Its input is synthetic; execution of an algorithm on that input does not make it a field-observation dataset. The Qelora companion page explains this distinction and links the available public lesson files.

Foundation lessons also contain compact supplied examples and retained teaching calculations. Such values are labeled where their interpretation matters. Conceptual satellite diagrams and low-dimensional ambiguity plots illustrate relationships; they do not reproduce orbital scale or prove acceptance of a higher-dimensional candidate.

A practical route to reproducing the numbers

First record the input files or supplied values, signal, epoch and time scale. Match the observation ordering and the reference-satellite convention before reconstructing a vector. Then reproduce a small intermediate result: one transmission time, one design row, one single difference or one propagated covariance entry.

Continue with the full matrix dimensions, weighting model and parameter order. Use the exported precision for comparisons; displayed rounding is intended for reading and may not preserve the final decimal place. Compare residuals and candidate objectives as well as final coordinates. A sign change, unit conversion or ambiguity-basis mismatch can leave some values looking plausible while changing the solution.

The relative lesson demonstrates Cholesky whitening and QR estimation, alongside numerical regression checks for the retained trace. These checks test consistency of that example. They are not a substitute for independent validation on additional receivers, epochs, baseline lengths or operating conditions.

Downloadable teaching examples

The Double Difference teaching package (v1.0.0) includes full-precision exports, a Python standard-library reproducer, a checksum manifest and citation information. Run the included script to reconstruct the frozen-LOS model, covariance, float and candidate-constrained solutions and supplied candidate objectives. Complete raw RINEX sessions and the original solver are outside this package.

The ECEF to ENU and covariance lesson supplies a separate synthetic example with downloadable inputs and code. It shows how to interpret local horizontal and vertical uncertainty before reading the positioning results.

Formal precision and integer fixing need separate evidence

A covariance matrix describes uncertainty under the assumed observation model. It does not include every possible bias, multipath effect, cycle slip or incorrect model. DOP measures geometry amplification, while actual position error needs a reference position or independent assessment.

An integer least-squares search ranks candidates within its ambiguity model. A ratio statistic describes their separation using the stated objective convention; it does not guarantee a correct fix. The Double Difference example therefore distinguishes a candidate-fixed result from an accepted operational solution and reports its diagnostics and limitations. One successful calculation does not demonstrate a complete RTK or PPP system.

Editorial responsibility, updates and corrections

OpenGNSSLab prepares the website explanations. It is an independent educational project, and some material originated in teaching assistantship work. The website does not claim institutional endorsement or independent peer review. About the project describes that context.

Visible update dates and sitemap modification dates are maintained with substantive changes to the corresponding page. They are not advanced merely because a build runs. Where a verified original publication date is unavailable, the site omits that date rather than reconstructing one from deployment timestamps.

To report a correction, include the lesson section, input or matrix entry, observed discrepancy and the reference or calculation that supports it. Distinguish a numerical rounding difference from a change in model or convention. A correction should make the affected assumption and resulting behavior clear to the next reader.