Pointing Dilution of Precision (DOP)

Pointing DOP (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 such as stars and ground and 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:

1. the method for calculating Pointing DOP
2. the number of assets used to produce solutions
3. the method for computing a static Pointing DOP value over the entire coverage interval
4. the time step to be used when computing the static value of Pointing DOP across the coverage interval

Items 1 and 2 specify the dynamic definition of Pointing DOP. STK uses this dynamic definition to compute the Pointing DOP value for each grid point at the current time. Specifying items 3 and 4 then enables STK to calculate a static value of Pointing DOP by sampling the dynamic values.

Method

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 computes the pointing DOP as the square root of the sum of the minimum and maximum variances computed for each pointing direction, based on an attitude covariance matrix that is unitless and scaled.
Max Sigma	This method assigns the pointing DOP value as the maximum standard deviation computed for each pointing direction, based on an attitude covariance matrix that is unitless and scaled. This provides an upper bound (i.e., a conservative measure) for the relative reduction in pointing uncertainty.
Min Sigma	This method assigns the pointing DOP value as the minimum standard deviation computed for each pointing direction, based on an attitude covariance matrix that is unitless and scaled. This provides a lower bound for the relative reduction in pointing uncertainty.

Compute options

You also need to set the method for computing the static definition for pointing DOP from the options in the Compute field, which are described in the following table. The reported values depend on the pointing accuracy you have selected and the allowed number of assets.

Compute Options for Pointing DOP

Option	Description
Average	This option applies the average pointing DOP in each direction over the entire coverage interval.
Maximum	This option applies the maximum pointing DOP in each direction over the entire coverage interval.
Minimum	This option applies 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.

Number of assets for computation (Type)

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

Pointing DOP Types

Method	Value
Best 2	This option computes the pointing DOP based on the set of two assets that yields minimum pointing DOP as defined by the DRMS method.
Best N	This option computes the pointing DOP based on the specified number of assets that yield the 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	This options computes the pointing DOP using all the currently available assets.

The pointing DOP type that you choose affects the dynamic and static DOP definition of the figure of merit.

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

STK uses graphics to represent the static and dynamic values of Pointing DOP. Graphics representing the dynamic values are displayed only during animation. Select Enable under Satisfaction if you want the graphics to follow the general behavior for satisfaction graphics. If Satisfaction is not selected and no contour levels have been defined, then no graphics will display on the Attitude Sphere. See the Satisfaction help topic for details on settings. There are no default graphics for the Pointing DOP figure of merit. The satisfaction threshold value is the pointing DOP value.