Post-Processing & QC

Overview#

Raw GNSS observations are not survey results. Between the field data and the final coordinates lies post-processing -- the series of computational steps that transform carrier phase observations into precise baseline vectors, adjust those baselines into a self-consistent network, and produce coordinates with quantified uncertainties. Post-processing is where the surveyor exercises professional judgment about data quality, where bad observations are identified and excluded, and where the mathematical rigor of least-squares adjustment replaces the approximations of real-time positioning.

Even when RTK is used for production work, post-processing plays a critical quality control role. Many firms log raw data during RTK surveys and post-process selected baselines to independently verify the real-time results. For control surveys, static post-processing remains the standard of practice.

"Post-processing is not merely a computational exercise. It requires the surveyor to evaluate data quality, make informed decisions about which observations to include or reject, and verify that the final solution is consistent and reliable." -- Van Sickle, GPS for Land Surveyors (4th Ed.), Ch. 11, p. 245

Baseline Processing Workflow#

The general post-processing workflow follows a systematic sequence from raw data through final adjusted coordinates:

Step 1: Data Download and Import

Download raw observation data from all receivers in a standard format -- typically RINEX (Receiver Independent Exchange Format). RINEX files contain the observation data (pseudorange and carrier phase measurements), navigation data (broadcast ephemerides), and meteorological data (if recorded).

Verify that:

• All planned sessions are present and complete (no truncated files)
• Observation time spans match the planned session schedule
• Antenna heights and types are correctly recorded in the file headers
• Sampling rates are as planned

Step 2: Select Base Station(s)

The choice of base station is one of the most consequential decisions in post-processing. The base station provides the reference coordinates from which all baseline vectors are computed. An error in the base station coordinates propagates to every point in the survey.

CORS (Continuously Operating Reference Stations):

The preferred base station for most surveys is a nearby CORS, which provides published coordinates on a known datum realization (e.g., NAD 83(2011), epoch 2010.0) and continuously logged observation data that can be downloaded for free from NGS or other agencies.

Project Base Station:

When no CORS is sufficiently close, a project-specific base station must be established. Its coordinates should be determined by static ties to multiple CORS or other known control points. A project base with poorly determined coordinates will introduce systematic bias into all rover positions.

"The accuracy of any GNSS survey is ultimately limited by the accuracy of the base station coordinates. A 2-centimeter error in the base coordinates produces a 2-centimeter error in every point computed from that base." -- GEOG 862, GPS and GNSS for Geospatial Professionals, Penn State, Lesson 8

Step 3: Select Ephemerides

The satellite ephemeris (orbit information) directly affects the accuracy of the computed satellite positions and, consequently, the baseline solution.

For baselines shorter than approximately 10 km, the choice of ephemeris has minimal impact because orbit errors are spatially correlated and largely cancel in differential processing. For longer baselines, precise ephemerides (rapid or final) should always be used.

The improvement from broadcast to precise ephemerides on a baseline solution scales approximately with baseline length. For a 50 km baseline, using precise instead of broadcast orbits can improve accuracy by several millimeters. For a 5 km baseline, the improvement is typically negligible.

Step 4: Process Baselines

Baseline processing is the core computational step. The software takes the carrier phase (and pseudorange) observations from two receivers, forms double-difference observations, estimates the unknown parameters (baseline vector components, ambiguities, tropospheric delay), and attempts to resolve the integer ambiguities.

The processing engine typically follows this sequence:

1. Triple-difference solution. An initial position estimate derived from triple differences (which eliminate ambiguities but are noisy). This provides a starting point for the main solution.
2. Float solution. Double-difference carrier phase processing with ambiguities estimated as real-valued (floating-point) parameters. The float solution typically achieves decimeter-level accuracy.
3. Ambiguity search and validation. The software searches for the set of integer ambiguities that best fits the observations. The LAMBDA algorithm decorrelates the ambiguity search space and evaluates candidate integer sets.
4. Fixed solution. If a valid integer set is found and passes validation criteria, the ambiguities are fixed to their integer values and the baseline is recomputed. The fixed solution achieves centimeter or sub-centimeter accuracy.

Step 5: Evaluate Solution Quality

Every processed baseline must be evaluated before being accepted into the network adjustment. The key quality indicators are:

The ratio test is particularly important. It compares the sum of squared residuals for the best integer set ($\Omega_1$) against the second-best set ($\Omega_2$):

$R = \frac{\Omega_2}{\Omega_1}$

A high ratio indicates that the best integer set is significantly better than any alternative, giving confidence that the ambiguities have been correctly resolved. A ratio below 2.0 suggests that two or more integer sets fit the data nearly equally well, and the ambiguity resolution may not be reliable.

"A fixed solution is not automatically correct. The ratio test value must be examined. A fixed solution with a ratio barely above the threshold may be less reliable than a float solution with consistent residuals." -- Van Sickle, GPS for Land Surveyors (4th Ed.), Ch. 11, p. 258

Float vs. Fixed Solutions#

The distinction between float and fixed solutions is critical for understanding GNSS accuracy:

Float solution:

• Integer ambiguities estimated as real numbers (e.g., $N = 1247832.37$)
• Accuracy: decimeter level (5--30 cm)
• Acceptable for: approximate positioning, initial processing, identifying gross errors
• Not acceptable for: survey-grade boundary or control work

Fixed solution:

• Integer ambiguities resolved to their correct integer values (e.g., $N = 1247832$)
• Accuracy: centimeter to sub-centimeter (1--3 cm typical)
• Required for: all survey-grade GNSS work
• Validation: ratio test, residual analysis, baseline repeatability

Factors that promote successful ambiguity fixing:

Network Adjustment#

Minimally Constrained Adjustment

After all baselines are processed and evaluated, they are assembled into a network and adjusted using weighted least squares. The first adjustment should be minimally constrained -- holding only one point fixed (the base station or a CORS) to prevent datum distortion from affecting the internal geometry of the network.

The minimally constrained adjustment reveals the internal consistency of the baseline observations. Large residuals indicate problematic baselines that should be investigated and potentially excluded. The adjustment statistics to examine are:

Chi-square test (global model test):

$\chi^2 = \mathbf{v}^T \mathbf{W} \mathbf{v}$

where $\mathbf{v}$ is the vector of residuals and $\mathbf{W}$ is the weight matrix. The test statistic should fall within the expected range for the given degrees of freedom and confidence level (typically 95%).

Reference variance (variance factor):

$\hat{\sigma}_0^2 = \frac{\mathbf{v}^T \mathbf{W} \mathbf{v}}{r}$

where $r$ is the number of redundant observations (degrees of freedom). A value near 1.0 indicates that the observation weights are consistent with the actual data quality. Values significantly greater than 1.0 suggest the data contain unmodeled errors; values significantly less than 1.0 suggest the weights are too pessimistic.

Fully Constrained Adjustment

After verifying internal consistency, additional control points are introduced (CORS, published control, project monuments with known coordinates). This fully constrained adjustment forces the network onto the project datum and distributes any distortion across the network.

Compare the constrained and minimally constrained solutions:

If the constrained adjustment significantly distorts the network (large shifts, inflated residuals), the control coordinates may be inconsistent. The surveyor must investigate whether the control points are on the correct datum and realization, whether one or more control coordinates are erroneous, or whether the network geometry is insufficient to absorb the constraints.

"A properly adjusted GNSS network should exhibit residuals that are small, normally distributed, and free of systematic patterns. Large residuals in the minimally constrained adjustment indicate observational problems; large residuals appearing only in the constrained adjustment indicate control problems." -- Ghilani & Wolf, Elementary Surveying (13th Ed.), Ch. 14, p. 425

Loop Closures#

Loop closures provide an independent check on baseline quality. A loop is a closed circuit of baselines -- starting and ending at the same point. The sum of the baseline vectors around the loop should theoretically be zero. The actual loop misclosure reflects the accumulated errors in the component baselines.

The loop misclosure is computed as:

$\Delta X_{\text{loop}} = \sum_{i=1}^{n} \Delta X_i, \quad \Delta Y_{\text{loop}} = \sum_{i=1}^{n} \Delta Y_i, \quad \Delta Z_{\text{loop}} = \sum_{i=1}^{n} \Delta Z_i$

$\text{Misclosure} = \sqrt{\Delta X_{\text{loop}}^2 + \Delta Y_{\text{loop}}^2 + \Delta Z_{\text{loop}}^2}$

Acceptable loop misclosures depend on the baseline lengths and the survey specifications:

If a loop misclosure exceeds the allowable value, the weakest baseline in the loop (identified by its processing statistics) should be re-examined, reprocessed, or excluded and re-observed.

Rejecting Bad Baselines#

Not every baseline deserves to be in the final adjustment. Baselines should be rejected when:

• The ambiguity resolution failed (float-only solution) and the baseline is critical to the network
• The ratio test value is marginal (< 2.0) and independent verification is unavailable
• The RMS residuals are abnormally large compared to other baselines of similar length
• The baseline creates a large loop misclosure
• The observation conditions were documented as poor (cycle slips, low satellite count, high multipath)

Rejection decisions should be documented. The surveyor must record which baselines were excluded, why they were excluded, and whether the remaining network has adequate redundancy and geometric strength.

Final Coordinate Comparison#

After the fully constrained adjustment, the adjusted coordinates of the network points should be compared against all available independent checks:

Quality Indicators Summary#

Documentation and Deliverables#

A complete GNSS survey record should include:

Processing Report

• Software used (name, version)
• Ephemeris type (broadcast, rapid, or final)
• Tropospheric model applied
• Ionospheric handling (dual-frequency combination, model, or differencing)
• Antenna calibration models (ANTEX source, calibration type)
• Elevation mask used
• Baseline processing results (solution type, RMS, ratio test for each baseline)

Adjustment Report

• Minimally constrained adjustment results (residuals, reference variance, chi-square test)
• Fully constrained adjustment results (same statistics, plus coordinate shifts from constrained to minimally constrained)
• Error ellipses (semi-major axis, semi-minor axis, orientation) for each adjusted point
• Relative accuracy between points (expressed as ppm or distance accuracy at 95% confidence)
• Control points used (IDs, datum, realization, epoch, source of coordinates)

Field Documentation

• Point descriptions and photographs
• Antenna types, serial numbers, and measured heights
• Observation session logs (start/stop times, operator, weather conditions, known issues)
• Obstruction diagrams for static sites
• Notes on any unusual conditions (nearby construction, high multipath, RF interference)

Coordinate Table

The final deliverable is the adjusted coordinate table, which should clearly state:

"Every GNSS survey deliverable must clearly identify the datum, realization, epoch, projection, and units. Coordinates without this metadata are ambiguous and potentially dangerous." -- Ghilani & Wolf, Elementary Surveying (13th Ed.), Ch. 14, p. 430

Key Takeaways#

• Post-processing transforms raw GNSS observations into reliable coordinates through baseline processing, quality evaluation, and network adjustment. It is not optional for survey-grade work.
• Base station selection is critical -- an error in the base coordinates propagates to every computed position. Use CORS when available; establish project bases with rigorous static ties when CORS are too distant.
• Precise ephemerides (IGS rapid or final) should be used for baselines longer than 10 km. For short baselines, broadcast ephemerides are adequate.
• Fixed solutions (integer ambiguities resolved) are required for survey-grade accuracy. Always check the ratio test -- a fixed solution with a low ratio may not be reliable.
• Network adjustment should be performed in two stages: minimally constrained (to evaluate internal consistency) and fully constrained (to fit the network to the project datum). Compare the two to detect control problems.
• Loop closures provide independent verification of baseline quality. Misclosures exceeding order-specific tolerances indicate problematic baselines.
• Document everything -- processing parameters, adjustment statistics, antenna information, and metadata. Coordinates without datum, realization, epoch, and accuracy statements are professionally incomplete.
• Quality indicators (RMS, ratio test, reference variance, loop misclosures, repeatability) are the tools for evaluating whether the survey meets its specifications. Learn to interpret them, not just read them.

References#

1. Van Sickle, J. GPS for Land Surveyors (4th Ed.). CRC Press, 2015. Chapters 11--12.
2. Ghilani, C.D. & Wolf, P.R. Elementary Surveying: An Introduction to Geomatics (13th Ed.). Pearson, 2012. Chapters 14, 16.
3. GEOG 862: GPS and GNSS for Geospatial Professionals. Penn State College of Earth and Mineral Sciences. Lessons 8--10.
4. National Geodetic Survey. "OPUS -- Online Positioning User Service." NOAA/NGS. https://geodesy.noaa.gov/OPUS/
5. National Geodetic Survey. "CORS Network." NOAA/NGS. https://geodesy.noaa.gov/CORS/
6. Ghilani, C.D. Adjustment Computations: Spatial Data Analysis (6th Ed.). Wiley, 2017. Chapters 16, 21.
7. International GNSS Service. "IGS Product Table." https://igs.org/products/