Selecting a Specific Navigation Accuracy | Choosing the Allowed Number of Assets | Choosing a Static Definition of Navigation Accuracy | Specifying a Time Step | Specifying One-Way Range Uncertainties | Displaying Navigation Accuracy Graphics in a Graphics Window

Measuring the Accuracy of a Navigation Solution

Navigation Accuracy measures the uncertainty of a navigation solution based on one-way range measurements from a set of transmitters. Most often, the transmitters are those on board Global Positioning System (GPS) satellites. If four or more of these satellites are in view of a ground receiver, a navigation solution consisting of the position of the receiver and the offset between the receiver clock and the GPS clock can be computed.

Our GPS equations and algorithms are based on Global Positioning System, Theory and Application Volume I (Parkinson, Spilker editors) Chapters 5 and 9.

The Navigation Accuracy Figure Of Merit considers the effect of the number of measurements (of those satellites visible at each moment in time), the geometry of the transmitters and the uncertainty in the one-way range measurements in the computation of the uncertainty in the navigation solution. The uncertainty in the one-way range measurements may be specified as a constant value or as a function of the elevation angle on a transmitter basis.

The Navigation Accuracy is related to the Dilution of Precision (DOP) in the definition of DOP through an assumption of a single value for the uncertainty in the one-way range measurements. The uncertainties in the range measurements are assumed to be uncorrelated in both Navigation Accuracy and DOP computations.

When using Navigation Accuracy to measure the quality of coverage, you need to specify:

  1. the specific Navigation Accuracy to be measured
  2. the maximum number of assets that can be used to produce navigation solutions
  3. the method for computing the static value of Navigation Accuracy over the entire coverage interval
  4. the Time Step to be used when computing the static value of Navigation Accuracy across the coverage interval
  5. the method for computing the range uncertainty for each Coverage asset

The dynamic definition of Navigation Accuracy is specified through items 1, 2, and 5, and computes the corresponding value for each grid point at the current time. The static definition of dilution of precision is specified through items 3, 4, and 5, and is computed via sampling of the dynamic definition.

Selecting a Specific Navigation Accuracy Measure

Navigation Accuracy can be calculated in a number of ways, depending on your task. The methods available to you are discussed in the following table.

Accuracy Measures

Option Description
GACC (Geometric Accuracy) Measures the accuracy of the entire navigation solution. GACC combines the accuracy of the position and clock-related components of the navigation solution.
PACC/PACC(3)* (Position Accuracy) Measures only the accuracy associated with the positional portion of the navigation solution.
HACC/HACC(3)* (Horizontal Accuracy) Measures the accuracy for the horizontal (latitude/longitude) components of the positional portion of the navigation solution.
VACC/VACC(3)* (Vertical Accuracy) Measures the accuracy for the vertical (altitude) component of the positional portion of the navigation solution.
EACC/EACC(3)* (East Accuracy) Measures the accuracy in the Eastern component of the positional portion of the navigation solution.
NACC/NACC(3)* (North Accuracy) Measures the accuracy in the Northern component of the positional portion of the navigation solution.
TACC (Time Accuracy) Measures the accuracy of the time portion of the navigation solution.

*If PACC(3), HACC(3), EACC(3), NACC(3) or VACC(3) is selected, the accuracy value is computed even if only three (3) navigation sources are available. This is done by ignoring the clock component of the navigation solution. If four (4) or more sources are available, the clock component is included.

The accuracy measure you choose affects the dynamic and static definition of the Figure Of Merit.

Choosing the Allowed Number of Assets

Although four satellites are needed for the navigation solution, additional satellites can be used to improve the accuracy of the solution. Options in the Type field are discussed in the following table.

Asset Selection

Method Value
Over Determined Computes the navigation accuracy based on all of the currently available assets. If you select this method, you need to involve a minimum of three assets in the navigation solution. If you compute a navigation accuracy based on only three assets, you will be presented with answers to a subset of main options: PDOP, HDOP, VDOP, EDOP and NDOP. Also, note that a navigation accuracy with three assets assumes no uncertainty in time.
Best Four Computes the navigation accuracy based on the set of four satellites that yields the minimum GDOP.
Best N

Computes the Navigation Accuracy based on the specified number of satellites. If you select this method, you also need to specify a value for Best N.

Best Four Acc Computes the navigation accuracy based on the set of four satellites that yields the minimum geometric uncertainty.
Best N Acc Computes the Navigation Accuracy based on the specified number of satellites. If you select this method, you also need to specify a value for Best N.

The Best N value is usually greater than or equal to four satellites. However, you can specify three satellites for the Best N algorithm, when using the PDOP(3), HDOP(3), VDOP(3), EDOP(3) or NDOP(3) method AND the Best N Metric is not GDOP, TDOP, GACC, or TACC.

The asset selection strategy you choose affects the dynamic and static definition of the Figure Of Merit.

Choosing a Static Definition of Navigation Accuracy

You also need to set the method for computing the static definition for navigation accuracy using the options in the Compute field. Options are discussed in the following table.

The reported values depend on the specific number selected and the allowed number of assets.

Compute options for Navigation Accuracy

Option Description
Average The average uncertainty at each point over the entire coverage interval.
Maximum The maximum uncertainty at each point over the entire coverage interval.
Minimum The minimum uncertainty at each point over the entire coverage interval.
Percent Below The value of the uncertainty is less than the computed value X percentage of time where X is a Percent Level that you specify.

This option only affects the static definition of the Figure Of Merit.

During the generation of the selected statistic, cases may be encountered when an insufficient number of assets are available to compute a navigation solution, thus making the selected Navigation Accuracy computation impossible. The Invalid Value Action setting determines how the computation will proceed under this circumstance.

Options for Invalid Value Action

Option Description
Include Specifies that Navigation Accuracy samples lacking a sufficient number of assets are assigned the value specified by the Invalid Data Indicator and included in the computation of the selected compute option.
Ignore Specifies that Navigation Accuracy samples lacking a sufficient number of assets are ignored and not included in the computation. Effectively computes the desired metric based only on times when a navigation solution can be computed.

Specifying a Time Step

In the Time Step field, enter the value to be used during the sampling of the dynamic definition for use in the static definition.

Specifying One-way Range Uncertainties

To specify range uncertainty information, click Uncertainties to display the Navigation Accuracy Uncertainties Model window.

Two types of range measurements may be specified: Asset Range Uncertainty and Receiver Range Uncertainty.

Asset Range Uncertainty

For each asset, the uncertainty in range measurements may be specified as:

  • Constant. Constant values are specified as standard deviations in units of meters.
  • By Elevation Angle. Specify a range uncertainty file (.re) that contains range uncertainty information between a coverage asset and a grid instance, as a function of the elevation angle. For information on the file format, see Range Uncertainty Files.

    There are two ways to specify range uncertainty using an uncertainty file:

    • Elevation angles in combination with range standard deviations. See the sample file.
    • Elevation angles with range variations. See the sample file.

Receiver Range Uncertainty

The uncertainty of the range measurements due to the receiver is constant for all geometries and is independent of the transmitter. The uncertainty in the range measurements from the transmitter may be specified as constant or as a tabulated function of the elevation angle of the transmitter with respect to the receiver.

The receiver uncertainty should be interpreted as the white noise level of the pseudo-range measurements due to the receiver hardware. For example, if a pseudo-range based on a particular GPS satellite has an uncertainty of 4 m (based perhaps on the elevation angle of the satellite) and the receiver has an uncertainty of 3 m, then the resulting total uncertainty in that pseudorange will be sqrt(4^2 + 3^2) = 5 m. The inverses of the variances for each pseudorange used in the navigation solution are then inserted as the diagonal elements of the least squares weighting matrix in the construction of the information matrix. The directional uncertainties (north, east, up) are then computed as the square roots of the diagonal elements of the inverse of the information matrix.

 

Displaying Navigation Accuracy Graphics in a Graphics Window

Graphics are used to represent the static and dynamic value of Navigation Accuracy. Graphics representing the dynamic values are only displayed during animation. If Satisfaction is on, the graphics follow the general behavior for satisfaction graphics. If Satisfaction is off and no contour levels have been defined, no graphics display in the 2D Graphics window. There are no default graphics for the Navigation Accuracy Figure Of Merit. The Satisfaction Threshold value is the uncertainty in the navigation solution.

The use of Accumulation graphics options for Up to Current and Not Up to Current are not recommended for this Figure Of Merit since both options result in decreased animation performance.