Motion Modeling and Coordinate Systems

Perform array and target trajectory modeling, coordinate transformations, and compute Doppler shift

The Phased Array System Toolbox™ lets you model the motion of radars, sonars, targets, jammers, or interference sources using the phased.Platform System object™. This System object provides constant velocity and constant acceleration motion models. These motion models can generate almost any type of trajectory. You can display a 3-D visualization of a radar scenario using the phased.ScenarioViewer System object. The toolbox contains several utility functions that let you transform between coordinates systems, transform between angular coordinates, and convert between velocity and Doppler shift.

Objects

`phased.Platform`	Model platform motion
`phased.ScenarioViewer`	Display motion of radars and targets

Blocks

Motion Platform

Motion platform

Functions

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Range and Doppler Transformations

`dop2speed`	Convert Doppler shift to speed
`speed2dop`	Convert speed to Doppler shift
`radialspeed`	Relative radial speed
`rangeangle`	Range and angle calculation

Local to Global Coordinate Transformations

`global2localcoord`	Convert global to local coordinates
`local2globalcoord`	Convert local to global coordinates

Local Coordinate Operations

`rotx`	Rotation matrix for rotations around x-axis
`roty`	Rotation matrix for rotations around y-axis
`rotz`	Rotation matrix for rotations around z-axis
`cart2sphvec`	Convert vector from Cartesian components to spherical representation
`sph2cartvec`	Convert vector from spherical basis components to Cartesian components
`azelaxes`	Spherical basis vectors in 3-by-3 matrix form

Angle Conversion

`uv2azel`	Convert u/v coordinates to azimuth/elevation angles
`azel2uv`	Convert azimuth/elevation angles to u/v coordinates
`phitheta2azel`	Convert angles from phi/theta form to azimuth/elevation form
`azel2phitheta`	Convert angles from azimuth-elevation form to phi-theta form
`uv2phitheta`	Convert u/v coordinates to phi/theta angles
`phitheta2uv`	Convert phi/theta angles to u/v coordinates

Topics

Motion Modeling

Doppler Shift and Pulse-Doppler Processing
Compute target motion using Doppler processing.
Motion Modeling in Phased Array Systems
A critical component in phased array system applications is the ability to model motion in space.
Model Motion of Circling Airplane
Start with an airplane moving along a circular track with a radius of 10 km at a horizontal speed of 100 m/s and descending at a rate of 1 m/sec.

Coordinate Systems

Global and Local Coordinate Systems
Learn about the local and global coordinate systems used in the toolbox.
Global and Local Coordinate Systems Radar Example
This example shows how several different coordinate systems come into play when modeling a typical radar scenario.
Rectangular Coordinates
Construct a rectangular, or Cartesian, coordinate system for three-dimensional space by specifying three mutually orthogonal coordinate axes.
Spherical Coordinates
Spherical coordinates describe a vector or point in space with a distance and two angles.
Standards and Conventions
This section introduces the concept of baseband signals and defines the local and global coordinate systems used in the toolbox.
Units of Measure and Physical Constants
Phased Array System Toolbox uses the International System of Units (SI).