Dimension Definition Types

The Main page of the Advanced CAT Basic properties allows you to select among two fixed definition types, Fixed and Orbit Class, two that yield dimensions varying dynamically over time via quadratic equations, Quadratic and Quadratic Orbit Class (Quad/Orb), and two defined by positional covariance, Covariance and CovOffset. The following table describes these types:

Type	Description
Fixed	Specifies the dimensions of the threat volume ellipsoid on the basis of values you entered.
Orbit Class	Yields fixed values corresponding to ID numbers assigned via a lookup table on the basis of the object's apogee and perigee.
Quadratic	Provides coefficients based on the object's SSC number. These are used in a quadratic equation that relates each of the three dimensions to time.
Quadratic Orbit Class	A hybrid of the Orbit Class and Quadratic types. The coefficients for the quadratic equation are assigned via a lookup table based on the object's apogee and perigee.
Covariance	Use the position covariance associated with the object to size and orient the threat volume ellipsoid.
CovOffset	Computes the threat volume ellipsoid by adding together the position covariance of the object with the covariance representation of the fixed ellipsoid oriented along the tangential, crosstrack, and normal directions. Use this method to smoothly transition from a fixed size (when the covariance is very small) to the size determined by the covariance (when it has grown much bigger than the fixed size). You can get the position covariance by propagation (a satellite file using HPOP with covariance propagation turned on) or by reading from a properly formatted *.e file containing covariance information.

Fixed Definition Types

If you select the Fixed definition type, dimensions are specified in the manner described before.

The Orbit Class type employs a table lookup system, in which the object of interest is assigned a numerical ID on the basis of its apogee and perigee. The following figure represents a simplified version of a typical Orbit Class table:

For example, the above table would assign an ID of (21) to an object with an apogee of 17,000 km and a perigee of 7,000 km. Each numerical ID, in turn, is associated with a set of three indices representing the dimensions of the threat volume ellipsoid.

The lookup table takes the form of a text file with a *.foc extension. You can, if you wish, add your own propriety Orbit Class files, using the prescribed file format. To select among Orbit Class files, open the Advanced page under Basic properties for the Advanced CAT object and click the ellipsis (...) button to the right of the Fixed Orbit Class Database field.

If an Orbit Class definition fails (e.g., because there is no *.foc database, or because the satellite's apogee and/or perigee do not fall within a range for which the database provides), the default values for the Fixed definition type are used.

Quadratic Definition Types

The Quadratic and Quadratic Orbit Class (Quad/Orb) definition types define the dimensions of the threat volume ellipsoid on the basis of quadratic equations, with t = time past satellite (or TLE) epoch as the independent variable. For each dimension, the database provides the coefficients i, j, and k for an equation of the form:

where u, v, and w represent, respectively, the normal, tangential (in track), and cross track directions. Thus, each of the three dimensions defines a parabolic plot over time, such as that shown in the following graph, where i = 2, j = -3, and k = 2.

In some cases, such as the following (where i = -1.5, j = 7, and k = -3), portions of the parabola for one or more dimensions will lie at or below zero.

In such cases, the following rule is applied:

At any time when the value of the quadratic equation for any or all dimensions is equal to or less than zero, the threat volume of an object is defined as a point at the center of the object for so long as that condition holds.

In the case illustrated in the following graph, there are times at which the equation for v (normal), w (tangential), or both v and w, yields values less than or equal to zero:

Applying the above rule, the threat volume will be defined as a point rather than as an ellipsoid except when the values of both the v and w equations are greater than zero. That is, the threat volume will be treated as a point at any time before the time labeled T1 in the above graph or after the time labeled T2.

If you select the Quadratic Orbit Class (Quad/Orb) definition type, Advanced CAT uses a lookup table system like the Fixed Orbit Class type, based on the apogee and perigee of the object in question. In this case the database (with a *.qoc extension) generates nine indices, consisting of a set of three coefficients for each axis. If, instead, you select the simple Quadratic type, the database (with a *.qdb extension) assigns the nine indices on the basis of the object's SSC number.

If the Quadratic Orbit Type definition type fails, Advanced CAT tries the Fixed Orbit Class type. If that also fails, it uses the default values for the Fixed definition type. If the Quadratic type fails (e.g., because no SSC number is available for the object), Advanced CAT resorts first to the Quadratic Orbit Class type, then to the Fixed Orbit Class type. Finally, if both of those fail, it uses the default values for the Fixed type.

You can add your own propriety Quadratic (*.qdb) or Quadratic Orbit Class (*.qoc) files using the prescribed file formats. To select among database files, open the Advanced page under Basic properties for the Advanced CAT object and click the ellipsis (...) button to the right of the database field of interest.