Figures of Merit

STK enables you to specify the method by which the quality of coverage is measured using the options in the FigureOfMerit Definition page. The following types are available:

Dilution of Precision and Navigation Accuracy are not available for STK Attitude Coverage.

STK Attitude Coverage: The following discussion and that in the individual Figure of Merit pages linked above apply, in general, to Attitude Coverage as well as Coverage. However, in applying that information to Attitude Coverage, bear in mind that the relevant accesses and constraints are defined not for grid points as such, but for the associated object that you select on the Grid page. STK computes accesses from that object pointed via each grid point to the selected assets, and constraints on that object affect those accesses. The same thing applies to Figure Of Merit computations involving Attitude Coverage.

Satisfaction criteria

You can restrict the Figure Of Merit behavior so that STK only applies the graphical properties of the Figure Of Merit when a chosen satisfaction criterion is met.

First, you need to select Satisfaction. To do this, select the Enable check box in the Satisfaction pane of the Definition page. Once you enable Satisfaction, select an option in the Satisfied if field. The options in the Satisfied if field determine whether Satisfaction is achieved, based on the value of the Figure Of Merit.

Along with the Satisfaction criterion, enter the Threshold at which satisfaction is achieved. The Threshold value depends on the type of Figure Of Merit you select.

Criteria for satisfaction

STK applies the Satisfied if criterion to both the static and dynamic behaviors of the Figure Of Merit. The application of the Satisfaction criterion determines which grid points are graphically highlighted in the dynamic and static graphics.

If you have set contour graphics for the Figure Of Merit, STK does not display Satisfaction graphics. The Satisfaction option is not available for figures of merit that possess only yes or no values, such as simple coverage.

You can also generate several Coverage-specific reports and graphs to further analyze satisfaction-related information.

Invalid data indicator

You can set a value to indicate when contouring is invalid. In Coverage, a value of zero indicates that the contour should be level with the horizon. By default, all points without access are also set to zero for display purposes. If you wish to distinguish between zero values level with the horizon and points where coverage cannot be calculated, set the Invalid Data Indicator value to just outside the range of valid contour values.

Any point that uses the value is NOT used when calculating statistical data; the value is strictly for contouring purposes.

FOM values limits for computing statistics

You can limit the range of reported time-dependent values for figures of merit where the static value is computed as a selected statistic of the time-dependent definition. This is the Compute option selected for Access Constraint, Dilution of Precision, Navigation Accuracy, and Scalar Calculation figure of merit definitions. Time-dependent values outside the specified range are reset to be invalid. STK does not include invalid values in the computation of the statistic defined for the static value of the figure of merit. For example, you could report the average value of the Dilution of Precision for times when the Dilution of Precision lies within the range of 1 < DOP < 6 to avoid the influence of spurious peaks. In reports of the time-dependent value of the figure of merit, STK converts invalid values to the Invalid Data Indicator Value.

It is important to remember that the reported time-dependent values of the figure of merit can be altered by this option. It is also possible for the reported value time-dependent value of the figure of merit to be outside of the specified range in cases where the computed time-dependent value is outside the specified range and the Invalid Data Indicator Value is also outside the specified range.

Figures of merit and the coverage interval

When analyzing figures of merit that compute average values of a quantity over the coverage interval or on a per-day basis, it is important to use a coverage interval of sufficient duration for the result to "smooth out." Results based on intervals of short duration may be heavily biased by the conditions at the beginning or end of the interval or may not represent a sufficient variation of geometry between the assets and coverage area. This is especially true when the number of assets is small or there is a repeating ground-track pattern.

Defining a figure of merit's dynamic and static behavior

Figures of merit can exhibit two types of behavior: dynamic and static. The dynamic behavior of a Figure Of Merit enables you to compute values corresponding to a specific time. Not all figures of merit can exhibit dynamic behavior. Those which do not exhibit dynamic behavior are not able to compute time-dependent information.

The static behavior for a Figure Of Merit specifies the value of quality over the entire coverage period. Depending on the size of the coverage problem being analyzed, the computation of the static values for each grid point can be time consuming. For this reason, the static values are cached to allow for rapid generation of reports and modifications to graphical representations once the static values have been computed. STK will save and restore the computed static values with the scenario if you set the Save Mode of the parent Coverage Definition object to “Save accesses”.

STK computes the dynamic and static values for the grid points to support graphical displays, reports, and graphs for the Figure Of Merit.

Computing per-day values

Some figures of merit enable you to compute values on a per-day basis. Three quantities (minimum, maximum, and average) are possible. STK computes the average per-day selection as a value for the entire coverage interval divided by the duration of the coverage interval in days. For example, if a grid point is covered for nine hours of a 1.5-day coverage interval, the average per-day value would be 9 divided by 1.5, for an average of 6 hours a day.

STK computes the minimum and maximum per-day values in a slightly different manner. First, STK determines calendar day intervals using the coverage interval. It then determines the value of the Figure Of Merit across each interval and reports the minimum or maximum of these values. STK determines calendar days based on Coordinated Universal Time (UTC).

Per day calculations

Computing percent-level values

Some figures of merit enable you to compute a percent-level value. There are two types of percent-level values available: percent above and percent below. Both options base their derived values on a user-defined percent level between 0 and 100. The percent above option computes a value (v) for a Figure Of Merit for which the actual time-dependent value is greater than or equal to (v) x percent of the time, where x is the user-defined percent level. The percent below option computes a value (v) for a Figure Of Merit for which the actual time-dependent value is less than or equal to (v) x percent of the time, where x is the user-defined percent level.

The concept of percent level reporting is most easily demonstrated using a sampling method example. Although most of the percent value computations performed in Coverage are not performed using a sampling technique, the example should convey the concept adequately. The sampling method in this example assumes that STK has sampled the Figure Of Merit value for a grid point at 100 equally spaced intervals spanning the coverage interval. Samples would then be sorted in increasing order based on the value of the Figure Of Merit, as seen in the example below.

Example showing samples sorted into increasing order

To find the 95 Percent Above value, you would compute the value from the fifth entry in the sorted array. By doing so, you have selected a value which the Figure Of Merit is greater than 95 percent of the time. To find the 95 Percent Below value, you would compute the value from the ninety-fifth entry in the sorted array.

Figure of merit computation-sampling versus interval method

Figure of merit values are functions of the visibility times between grid points and assets or, in the case of Attitude Coverage, from the associated object pointed via the grid points to the assets. The computation of values for figures of merit are usually computed in one of two ways: using a sampling method or using direct computations based on access intervals.

A sampling method determines or accumulates a sequence of times for each grid point to be used for sampling of the Figure Of Merit. An example of this method would be to evenly distribute 100 times across the coverage interval and compute the percentage of time covered for each point as the number of times when the point is able to access an asset or, in the case of Attitude Coverage, when the associated object pointed via the point is able to access an asset. The accuracy of the answer produced by sampling is dependent on the frequency of the sampling and the duration of the accesses between grid points and assets.

STK Coverage uses algorithms based directly on the access intervals whenever possible to ensure accurate Figure Of Merit values. For example, it computes Percent Time Covered as the sum of the total time covered for each point divided by the duration of the coverage interval. This yields the same result as using a sampling method with an infinitely small sample time.

The only figures of merit that use a sampling method are Dilution of Precision, Navigation Accuracy, Pointing Accuracy, Pointing DOP and Access Constraint figures of merit, since direct solutions are not possible.