Pointing Accuracy

Pointing Accuracy measures the uncertainty 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, 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 the effects of the number of vector measurements, the relative geometry of the beacons and the uncertainty of the vector measurements in determining the uncertainty of the instrument's pointing. The uncertainty in vector measurements can be specified 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 specific method for measuring Pointing Accuracy
the maximum number of assets that can be used to produce solutions
the method for computing a static Pointing Accuracy value over the entire coverage interval
the time step to be used when computing the static value of Pointing Accuracy across the coverage interval

The dynamic definition of Pointing Accuracy 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 Accuracy is specified through items 3 and 4 and is computed via sampling of the dynamic definition.

Methods

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

Pointing Accuracy Methods

Method	Description
CEP	(Circular Error Probable) Measures the pointing accuracy as the radius of the circle encompassing a probability of 50 percent as computed using a two-dimensional Gaussian probability distribution for each pointing direction based on the attitude covariance matrix.
Appx CEP	Measures the pointing accuracy as the approximate CEP computed as 3/4 of the DRMS metric.
DRMS	(Distance Root Mean Square) Measures 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	Measures the pointing accuracy as the maximum standard deviation computed for each pointing direction based on the attitude covariance matrix. This provides an upper bound (i.e. a conservative measure) for the pointing uncertainty.
Min Sigma	Measures 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.

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 Accuracy Types

Method	Value
Best Two	Computes the pointing accuracy based on the set of two assets that yields minimum pointing uncertainty as defined by the DRMS method.
Best N	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	Computes the pointing accuracy based on all of the currently available assets.

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

Compute Options

You also need to set the method for computing the static definition for pointing accuracy 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 Accuracy

Option	Description
Average	The average pointing uncertainty in each direction over the entire coverage interval.
Maximum	The maximum pointing uncertainty in each direction over the entire coverage interval.
Minimum	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.

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 a specific asset. The Figure of Merit Uncertainties Model dialog displays.

Graphics Display of Pointing Accuracy Coverage

Graphics are used to represent the static and dynamic values of Pointing Accuracy. 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 Accuracy Figure Of Merit. The satisfaction threshold value is the pointing Accuracy value.