Methods | Number of Assets | Compute Options | Time Step | Graphics Display

Pointing Dilution of Precision (DOP)

Pointing DOP (pointing dilution of precision) measures the relative degradation or reduction in the certainty of the pointing of an instrument along a selected direction based on vector measurements to a set of known beacons, e.g. stars, ground or space objects. If two or more of these beacons are in view of the object for which attitude coverage is computed, a unitless scaled attitude covariance matrix can be constructed. This matrix can be reduced to a two dimensional metric for a specific pointing direction and then reduced further to a scalar DOP metric using one of the methods listed below.

The Pointing DOP Figure Of Merit measures the effects of the number of vector measurements and the relative geometry of the beacons on the uncertainty in the instrument's pointing. The reported value can be multiplied by the uncertainty in the vector measurements (assumed to be the same for all beacons) to provide the uncertainty in the instrument's pointing.

When using Pointing DOP to measure the quality of coverage, you need to specify:

the specific method for measuring Pointing DOP
the maximum number of assets that can be used to produce solutions
the method for computing a static Pointing DOP value over the entire coverage interval
the time step to be used when computing the static value of Pointing DOP across the coverage interval

The dynamic definition of Pointing DOP is specified through items 1 and 2 and computes the corresponding value for each grid point at the current time. The static definition of Pointing DOP is specified through items 3 and 4 and is computed via sampling of the dynamic definition.

Methods

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

Pointing DOP Methods

Method	Description
DRMS	(Distance Root Mean Square) Measures the pointing DOP as the square root of the sum of the minimum and maximum variances computed for each pointing direction based on the unitless scaled attitude covariance matrix.
Max Sigma	Measures the pointing DOP as the maximum standard deviation computed for each pointing direction based on the unitless scaled attitude covariance matrix. This provides an upper bound (i.e. a conservative measure) for the relative reduction in pointing uncertainty.
Min Sigma	Measures the pointing DOP as the minimum standard deviation computed for each pointing direction based on the unitless scaled attitude covariance matrix. This provides a lower bound for the relative reduction in pointing uncertainty.

Allowed Number of Assets

Although two beacons are needed for the attitude solution, additional beacons can be used to improve the accuracy of the solution. Options in the Type field are described in the following table.

Pointing DOP Types

Method	Value
Best Two	Computes the pointing DOP based on the set of two assets that yields minimum pointing DOP as defined by the DRMS method.
Best N	Computes the pointing DOP based on the specified number of assets that yield minimum pointing DOP as defined by the DRMS method. If you select this type, you also need to specify a value for N.
Over Determined	Computes the pointing DOP based on all of the currently available assets.

The pointing DOP type that you choose affects the dynamic and static DOP definition of the Figure Of Merit.

Compute Options

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

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

Compute Options for Pointing DOP

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

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.

Graphics Display of Pointing DOP Coverage

Graphics are used to represent the static and dynamic values of Pointing DOP. Graphics representing the dynamic values are displayed only 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 on the Attitude Sphere. There are no default graphics for the Pointing DOP Figure Of Merit. The satisfaction threshold value is the pointing DOP value.