Pointing Accuracy

Pointing Accuracy measures the uncertainty of the pointing of an instrument along a 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, an 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 uncertainty metric using one of the methods listed below.

The Pointing Accuracy figure of merit considers a set of effects in determining the uncertainty of the instrument's pointing. These effects are the number of vector measurements, the relative geometry of the beacons, and the uncertainty of the vector measurements. You can specify the uncertainty in vector measurements for each measurement as a constant value.

The Pointing Accuracy is related to the Pointing DOP in the definition of pointing DOP through an assumption of a single value of the uncertainty in vector measurements. The uncertainties in vector measurements are assumed to be uncorrelated in both Pointing Accuracy and Pointing DOP computations.

The value reported by the Pointing Accuracy and the uncertainty of vector measurements have angular units.

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

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

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

Method

STK provides several methods to calculate Pointing Accuracy, which are described in the following table.

Pointing Accuracy Methods

Method Description
CEP Circular Error Probable computes the pointing accuracy as the radius of the circle encompassing a probability of 50 percent. This is computed using a two-dimensional Gaussian probability distribution for each pointing direction, based on the attitude covariance matrix.
Appx CEP This method computes the pointing accuracy as the approximate CEP computed as three-fourths of the Distance Root Mean Square (DRMS) metric.
DRMS Distance Root Mean Square computes the pointing accuracy as the square root of the sum of the minimum and maximum variances computed for each pointing direction, based on the attitude covariance matrix.
Max Sigma This method computes the pointing accuracy as the maximum standard deviation computed for each pointing direction, based on the attitude covariance matrix. It provides an upper bound (i.e., a conservative measure) for the pointing uncertainty.
Min Sigma This method computes the pointing accuracy as the minimum standard deviation computed for each pointing direction, based on the attitude covariance matrix. This provides a lower bound for the pointing uncertainty.

Compute options

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

Compute Options for Pointing Accuracy

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

Number of assets for computations (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 Accuracy Types

Method Value
Best 2 This option computes the pointing accuracy based on the set of two assets that yields minimum pointing uncertainty as defined by the DRMS method.
Best N This option computes the pointing accuracy based on the specified number of assets that yield minimum pointing uncertainty as defined by the DRMS method. If you select this type, you also need to specify a value for N.
Over Determined This option computes the pointing accuracy using all the currently available assets.

The pointing accuracy type that you choose affects the dynamic and static pointing accuracy 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.

Direction to asset uncertainties

Click Uncertainties... to assign a direction to asset uncertainty value to an asset. The Figure of Merit Uncertainties Model dialog box will appear. The Direction to Asset Uncertainty Value is a constant value that represents angular standard deviation of measurements away from the direction between the object on which the coverage is defined and a particular asset. Constant values are specified in units of degrees.

Graphics display of pointing accuracy coverage

STK uses graphics to represent the static and dynamic values of Pointing Accuracy. 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 Accuracy figure of merit. The satisfaction threshold value is the pointing Accuracy value.