Selecting a Specific DOP | Choosing the Allowed Number of Assets | Choosing a Static Definition of DOP | Specifying a Time Step | Displaying DOP Graphics in a Graphics Window

Measuring Reduction in the Certainty of a Navigation Solution

Dilution of Precision (DOP) measures the relative degradation or reduction in the certainty 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 DOP Figure Of Merit measures the effects of the number of measurements and the geometry of the transmitters on the uncertainty in the navigation solution. The reported value can be multiplied by the uncertainty in the range measurements (assumed to be the same for all transmitters) to provide the uncertainty in the navigation solution.

When using Dilution of Precision to measure the quality of coverage, you need to specify:

the specific DOP to be measured
the maximum number of assets that can be used to produce navigation solutions
the method for computing a static DOP value over the entire coverage interval
the Time Step to be used when computing the static value of DOP across the coverage interval

The dynamic definition of dilution of precision is specified through items 1 and 2 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 and 4 and is computed via sampling of the dynamic definition.

Selecting a Specific DOP

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

DOP Methods

Option	Description
GDOP (Geometric Dilution of Precision)	Measures the dilution of precision for the entire navigation solution. GDOP combines the dilution of precision of the position and clock-related components of the navigation solution. A GDOP of less than one (1) is possible.
PDOP/PDOP(3)* (Position Dilution of Precision)	Measures only the dilution of precision associated with the positional portion of the navigation solution.
HDOP/HDOP(3)* (Horizontal Dilution of Precision)	Measures the dilution of precision for the horizontal (latitude/longitude) components of the positional portion of the navigation solution.
VDOP/VDOP(3)* (Vertical Dilution of Precision)	Measures the dilution of precision for the vertical (altitude) component of the positional portion of the navigation solution.
EDOP/EDOP(3)* (East Dilution of Precision)	Measures the dilution of precision in the Eastern component of the positional portion of the navigation solution.
NDOP/NDOP(3)* (North Dilution of Precision)	Measures the dilution of precision in the Northern component of the positional portion of the navigation solution
TDOP (Time Dilution of Precision)	Measures the dilution of precision of the time portion of the navigation solution

*If PDOP(3), HDOP(3), VDOP(3), EDOP(3) or NDOP(3) is selected, the DOP 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 DOP method you choose affects the dynamic and static DOP 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.

DOP Types

Method	Value
Over Determined	Computes the dilution of precision 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 dilution of precision 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 dilution of precision with three assets assumes no uncertainty in time.
Best Four	Computes the dilution of precision based on the set of four satellites and the Best 4 Metric.
Best N	Computes the dilution of precision 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 value, 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.

Method

Value

Over Determined

Computes the dilution of precision 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 dilution of precision 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 dilution of precision with three assets assumes no uncertainty in time.

Best Four

Computes the dilution of precision based on the set of four satellites and the Best 4 Metric.

Best N

Computes the dilution of precision 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 value, 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 DOP type you choose affects the dynamic and static DOP definition of the Figure Of Merit.

Choosing a Static Definition of DOP

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

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

Compute options for Dilution of Precision

Option	Description
Average	The average DOP at each point over the entire coverage interval
Maximum	The maximum DOP at each point over the entire coverage interval
Minimum	The minimum DOP at each point over the entire coverage interval
Percent Below	The value of the DOP 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 DOP 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 DOP 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 DOP 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.

Displaying DOP Graphics in a Graphics Window

Graphics are used to represent the static and dynamic value of Dilution of Precision. Graphics representing the dynamic values are only displayed during animation. If Satisfaction is enabled, the graphics follow the general behavior for satisfaction graphics. If Satisfaction is disabled and no contour levels have been defined, no graphics display in the 2D Graphics window. There are no default graphics for the DOP Figure Of Merit. The Satisfaction Threshold value is the dilution of precision value.

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.