Subsystem Geometry Considerations

Overview

Because WSF attempts to represent subsystems (sensor, weapon or comm) that operate in a variety of ways, the mechanisms it provides to define attributes, such as geometric limits, can be rather daunting. This document provides some clarity into how these mechanisms operate as well as guidance on how to define subsystem models that will behave like the real subsystems.

From a geometric standpoint, subsystems can be broadly separated into three categories:

  • Fixed pointing - the pointing angle is always in the same direction.

  • Scanning - the pointing angle is moved in a regular pattern.

  • Commanded pointing - the pointing angle is selected by command (like a track)

A subsystem may exhibit characteristics of all three depending on its operating mode. In some cases commanded pointing and scanning may be employed together (e.g., cued acquisition or cued search). In a scanning or commanded pointing subsystem, the mechanism of how the pointing angle is changed may be mechanical, electrical, optical or through some other means. Regardless, the moving of the pointing angle may be constrained in direction (e.g., only move in azimuth, only move in elevation, or move in any direction) and also in the amount that it may move in the allowed directions.

Coordinate Systems

Ultimately, subsystems interact with other platforms or subsystems (e.g., sense, send a message). When an interaction occurs, the objects are located somewhere in space and have a certain orientation. The subsystem(s) themselves have a location and orientation with respect to their host platform, and may use scanning ‘beams.’ Because the eventual success or failure of an interaction depends a great deal on the geometry, it is fundamental to understand the coordinate systems that are employed and how their key parameters are defined.

Up to seven coordinate systems are employed during the course of an interaction:

Conventional weapons, such as missiles or guns, typically only employ the first four coordinate systems (i.e., WCS, ECS, PCS, and CCS). Sensors and communications devices also use the last three (i.e., SCS, BCS, and ACS). Note that the terms ‘beam’ and ‘antenna’ are probably too reflective of the radio frequency nature of things. You could consider the ‘beam’ to be the instantaneous viewing angle and the ‘antenna’ as the aperture through which a signal is being transmitted or received.

The following section defines how the various coordinate systems are formed and the commands that are used to define the parameters that are used in the process.

World Coordinate System

The World Coordinate System (WCS) is a right-handed Cartesian system defined as follows:

  • The origin is at the center of the Earth.

  • The +X axis passes through 0N, 0E

  • The +Y axis passes through 0N, 90E

  • The +Z axis passes through 90N (the North Pole).

The Earth’s surface is modeled as an oblate ellipsoid as defined by the WGS-84 standard (NIMA TR-8350.2).

Entity Coordinate System

The Entity Coordinate System (ECS) is a coordinate frame rigidly attached to a platform (entity) and is a right-handed Cartesian system defined as follows:

  • The origin is at the center of the entity

  • The +X axis goes out the front of the entity. For an aircraft this would be forward out the nose.

  • The +Y axis goes out the right side of the entity (when looking down the +X axis). For an aircraft this would be out the right wing with respect to the pilot.

  • The +Z axis goes out the bottom of the entity.

  • Yaw is a rotation about the Z axis. Positive yaw is to the right. For an aircraft this would move the nose right with respect to the pilot.

  • Pitch is a rotation about the Y axis. Positive pitch raises the +X axis. For an aircraft this would raise the nose up.

  • Roll is a rotation about the X axis. Positive roll drops the +Y axis. For an aircraft this would drop the right wing.

Part Coordinate System

The Part Coordinate System (PCS) is a coordinate frame that is rigidly attached to the subsystem and is simply a translation and rotation of the Entity Coordinate System (ECS). The location and orientation of the part are defined with respect to the ECS. The relative location and orientation may be defined through one of two means:

The slew limits defined by azimuth_slew_limits and :command`_.articulated_part.elevation_slew_limits` are defined relative to this coordinate system and represent the absolute limits of pointing that can be achieved by the system. The sensor mode-specific cuing limit overrides (defined by azimuth_cue_limits and elevation_cue_limits) are also defined relative to this coordinate system.

One common mistake is to use the pitch command to define the tilt angle of antenna for a system that rotates about its Z axis (e.g., an airport surveillance radar, missile launcher). Unfortunately the pitch tilts the entire coordinate frame, including the Z axis! For cases where it is desirable to have the Z axis remain vertical, one of the following commands should be used:

  • tilt for platforms such as SAM launchers or tank turrets.

  • antenna_tilt for simple single aperture (beam) systems or for electronically steered systems that use body coordinates for the scan limits.

  • beam_tilt for stacked beam radar systems.

Cued Coordinate System

The Cued Coordinate System (CCS) is the PCS after cueing commands have been applied. A subsystem can be ‘cued’ if it has a :command`_.articulated_part.slew_mode` or cue_mode that is not fixed. The commands that ‘cue’ the subsystem are:

If a subsystem can be cued and a cue is present, the CCS is determined as follows:

  • Compute the azimuth and elevation cue angles as the aspect of the cue point with respect to the PCS.

  • Determine the ‘active’ azimuth and elevation cue modes and cue limits.

  • Determine the final azimuth cue angle with respect to the PCS.

  • If the subsystem can cue in azimuth (active cue mode is azimuth or azimuth_and_elevation), limit the azimuth cue angle by the active azimuth cue angle limits defined in the previous step.

  • If the subsystem cannot cue in azimuth (active cue mode is fixed or elevation), the azimuth cue angle is zero.

  • Determine the final elevation cue angle with respect to the PCS.

  • If the subsystem can cue in elevation (active cue mode is elevation or azimuth_and_elevation), limit the elevation cue angle by the active elevation cue angle limits defined in the previous step.

  • If the subsystem cannot cue in elevation (active cue mode is fixed or azimuth), the elevation cue angle is zero.

  • Compute the CCS transform by rotating the PCS transform by the azimuth and elevation cue angles determined in the previous steps.

If the subsystem cannot be cued or if a cue is not defined then the CCS is just the PCS.

Scan Coordinate System

The Scan Coordinate System (SCS) defines the origin and orientation of the ‘scan pattern.’ It is the same as the CCS except when scan_stabilization is something other than none. If scan stabilization is something other than none then the SCS will be reoriented to implement the effects of scan stabilization.

The angles specified in the azimuth_scan_limits, elevation_scan_limits, azimuth_field_of_view and elevation_field_of_view commands are with respect to the SCS.

Beam Coordinate System

The Beam Coordinate System (BCS) defines the instantaneous position of a ‘beam.’ The X axis of the BCS is aligned with the center of the beam. For non-scanning systems (i.e., scan_mode is fixed), the BCS, the scan coordinate system (SCS) and cued coordinate system (CCS) should all be the same.

The BCS is formed as follows:

  • Compute the target azimuth and elevation angles with respect to the SCS.

  • Determine the beam azimuth angle with respect to the SCS:

  • If the beam can scan in azimuth (i.e., scan_mode is azimuth or azimuth_and_elevation), the beam azimuth angle is the target azimuth angle limited to the range defined by the azimuth_scan_limits.

  • If the beam cannot scan in azimuth (i.e., scan_mode is fixed or elevation), the beam azimuth angle is zero.

  • Determine the beam elevation angle with respect to the SCS:

  • If the beam can scan in elevation (i.e., scan_mode is elevation or azimuth_and_elevation), the elevation angle is the target elevation angled limited to the range defined by the elevation_scan_limits.

  • If the beam cannot scan in elevation (i.e., scan_mode is fixed or azimuth), the beam elevation angle is zero.

  • Ensure the beam position does not exceed the slew limits of the subsystem. This is done as follows:

  • Convert the beam azimuth and elevation angles from the SCS back to the cued coordinate system.

  • Adjust the converted beam azimuth and elevation angles, if necessary, so that the sum of the each angle and its respective current cue angle does not exceed the respective limit defined by the azimuth_slew_limits and elevation_slew_limits.

  • The BCS is finally formed by rotating the CCS by the converted and limited beam azimuth and elevation angles determined in the previous step.

The azimuth and elevation aspect angles of the target with respect to the BCS are used to determine the antenna gain for RF interactions.

Antenna Coordinate System

The Antenna Coordinate System (ACS) defines the orientation of an ‘antenna.’ For systems that are not electronically steered (electronic_beam_steering is none), the BCS and ACS will be the same. For systems that are electronically steered, the X axis of the ACS will be normal to the face of the array.

The angle between the X axis of the BCS and the X axis of the ACS is used to compute beam steering losses. See electronic_beam_steering, electronic_beam_steering_limit and electronic_beam_steering_loss_exponent for more information.

General Flow of Sensor and Comm Processing

This section attempts to describe the general flow of a sensor or communications attempt from a geometric point of view. It does not discuss the system-specific processing.

Beyond this the processing gets sensor specific. For something like a radar, the aspect of the target with respect to the transmitter and receiver BCS (and perhaps the ACS for electronically steered systems) will be used to derive the antenna gain.