Navigation Accuracy

DME Component Libraries computes two broad types of navigation accuracy: assessed and predicted. These terms refer to the type of accuracy calculation performed, rather than to the time at which the accuracy is evaluated. Assessed accuracies require performance assessment data and predicted accuracies require prediction support data. You can actually evaluate either of these accuracies at any time, past or future. The difference is that assessed accuracies provide you with signed (±) navigation errors expressed in a certain set of axes centered on the receiver's antenna location. However, predicted accuracies are statistical predictions of accuracy; providing 1-sigma navigation error results instead of signed errors. Visually, the difference is that an assessed accuracy provides you with an error vector while a predicted accuracy can only supply you with an error ellipsoid.

Setting up navigation accuracy analysis involves the following steps:

• defining the satellite constellation that provides the navigation data

• configuring the GPS receiver

Before accuracy or any other navigation quantity can be computed, the constellation of satellites providing navigation data must be identified. DME Component Libraries provides classes to load a constellation of navigation satellites from the following sources:

All of these formats and files are readily available on the internet.

The following example shows how to create a constellation of GPS satellites from a SEM almanac:

GlobalPositioningSystemDate almanacDate = new GlobalPositioningSystemDate(new GregorianDate(2007, 7, 11));
SemAlmanac almanac = SemAlmanac.ReadFrom(fileName, almanacDate.RolloverCount);
PlatformCollection constellation = almanac.CreateSatelliteCollection();

The number 1 passed to the ReadFrom method above defines the rollover count to which this almanac is referenced. Almanacs generated since August 22, 1999 will have a rollover count of 1; prior to that date, the rollover count should be 0.

The CreateSatelliteCollection method creates a Platform instance for each satellite described in the almanac. Each Platform will have a GpsSatelliteExtension attached to it. This extension describes the Pseudo-random number (PRN) associated the satellite. It also holds outage information for the satellite.

For various reasons, GPS satellites are sometimes unavailable for use by navigation users. Information about historical, current, and scheduled periods of unavailability are published in the form of Notice Advisories to Navstar Users (or NANUs). NANUs are then aggregated into a single Satellite Outage File (SOF) that contains all the historical, current, and predicted outages for all the GPS satellites as of the time the SOF is published. SOFs are available from: http://gps.afspc.af.mil/gpsoc/archive/sof/.

DME Component Libraries can read a SOF file and populate the GPS constellation with outage information. This will prevent a satellite from being used for analysis during a period when it was, or is predicted to be, unavailable. The following example shows how to read a SOF and apply it to a constellation of satellites:

SatelliteOutageFile sof = SatelliteOutageFile.ReadFrom(fileName);
sof.PopulateConstellationOutageData(constellation);

The next step, after configuring the constellation of satellites, is to configure the GPS receiver. We begin by constructing an instance of the GpsReceiver type and configuring it with the constellation of GPS satellites it can use:

GpsReceiver receiver = new GpsReceiver();
receiver.NavigationSatellites = constellation;
receiver.ReceiverConstraints.Add(new ElevationAngleConstraint(Trig.DegreesToRadians(5.0)));

The receiver has a number of properties that must be configured before it can be used in any analysis.

Channels

receiver.NumberOfChannels = 12;

Solution Type

receiver.ReceiverSolutionType = GpsReceiverSolutionType.BestN;
receiver.OptimizationCriteria = DilutionOfPrecisionOptimization.Position;

Noise Model

receiver.NoiseModel = new ConstantGpsReceiverNoiseModel(1.0);

Receiver Antenna

Cartographic receiverLocation = new Cartographic(Trig.DegreesToRadians(-75.0),
                                                 Trig.DegreesToRadians(40.0),
                                                 0.0);

Platform antenna = new Platform();

EarthCentralBody earth = CentralBodiesFacet.GetFromContext().Earth;
antenna.LocationPoint = new PointCartographic(earth, receiverLocation);
antenna.OrientationAxes = new AxesEastNorthUp(earth, antenna.LocationPoint);

receiver.Antenna = antenna;

Once the GPS satellites and receiver are configured, an assessed or predicted accuracy calculation can be performed.

A Performance Assessment File (PAF) is required in order to compute assessed navigation accuracy. It contains GPS satellite ephemeris and clock errors for each GPS satellite at 15 minute intervals.

PAF data is available from:

https://ftp.agi.com/pub/Catalog/PAF

Once PAF data has been loaded, an evaluator can be obtained from the GPS receiver to evaluate assessed accuracy at a given time. The following example shows how to load PAF data, obtain the evaluator, and evaluate it at specific times:

PerformanceAssessmentFile paf = PerformanceAssessmentFile.ReadFrom(fileName);
Evaluator<NavigationAccuracyAssessed> assessedEvaluator = receiver.GetNavigationAccuracyAssessedEvaluator(paf);

JulianDate date = new GregorianDate(2007, 6, 10, 12, 0, 0).ToJulianDate();
NavigationAccuracyAssessed assessed = assessedEvaluator.Evaluate(date);

The errors in NavigationAccuracyAssessed are divided into two groups: SignalInSpace and Total. The SignalInSpace errors are those errors that result from the PAF data alone. No receiver errors are added to those values. The total errors include the receiver noise values specified in the receiver definition and are a root sum square (RSS) of the SignalInSpace errors and the receiver noise values.

Usually the PAF data files are complete and no adjustments are necessary. However, sometimes data is missing from the PAFs. DME Component Libraries will handle the missing data, but you can change the default interpolation and extrapolation behaviors. The next section discusses the capabilities available to deal with missing data.

Interpolation and Extrapolation

Predicted accuracy is somewhat of a misnomer, as it implies you can only obtain accuracy results in the future. In fact, you can obtain it at any time. As stated above, the evaluator returned by GetNavigationAccuracyPredictedEvaluator will provide statistical information regarding the navigation errors at a given time. This statistical accuracy information output from the NavigationAccuracyPredicted class is the 1-sigma value of the navigation error. This is also known as the square root of the navigation error covariance or RMS error.

Statistical errors are a little different to deal with than error vectors. The RMS error output is a 1-sigma value for the given metric within its distribution. For example, if the output was of vertical error, the distribution represented is a single variable normal (Gaussian) distribution. Here, the 1-sigma value represents a 68% confidence in the vertical navigation error - a familiar result. On the other hand, if the horizontal error is produced, this value is from a two-dimensional distribution. In this case, the confidence in the 1-sigma value is approximately 39.3%. Similarly, the position error confidence for the 1-sigma value produced is only 19.9%, since position errors are derived from a three-dimensional distribution.

Computing predicted navigation accuracy requires the use of a Prediction Support File (PSF). The following example shows how to load PSF data, obtain an evaluator for predicted accuracy, and evaluate the accuracy at a particular date:

PredictionSupportFile psf = PredictionSupportFile.ReadFrom(fileName);
Evaluator<NavigationAccuracyPredicted> predictedEvaluator = receiver.GetNavigationAccuracyPredictedEvaluator(psf);

JulianDate date = new GregorianDate(2007, 4, 25, 12, 0, 0).ToJulianDate();
NavigationAccuracyPredicted predicted = predictedEvaluator.Evaluate(date);

Like assessed accuracy, the errors in NavigationAccuracyPredicted are divided into two groups: SignalInSpace and Total. The SignalInSpace errors are those errors that result from the PSF data alone. No receiver errors are added to those values. The total errors include the receiver noise values specified in the receiver definition and are a root sum square (RSS) of the SignalInSpace errors and the receiver noise values.

Confidence Intervals

ConfidenceInterval confidenceInterval = new ConfidenceInterval();
double standardConfidence = confidenceInterval.ConvertToGlobalPositioningSystemConfidence(predicted.PositionTotal, 95, ConfidenceIntervalVariableDimension.Three);

Standard Predictions

Custom Predictions

GpsReceiver can be used to compute a number of other navigation-related values, in addition to the assessed and predicted accuracy described here: