Main Content

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.


phased.PlatformModel platform motion
phased.ScenarioViewerDisplay motion of radars and targets


Motion PlatformMotion platform


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dop2speedConvert Doppler shift to speed
speed2dopConvert speed to Doppler shift
radialspeedRelative radial speed
rangeangleRange and angle calculation
global2localcoordConvert global to local coordinates
local2globalcoordConvert local to global coordinates
rotxRotation matrix for rotations around x-axis
rotyRotation matrix for rotations around y-axis
rotzRotation matrix for rotations around z-axis
cart2sphvecConvert vector from Cartesian components to spherical representation
sph2cartvecConvert vector from spherical basis components to Cartesian components
azelaxesSpherical basis vectors in 3-by-3 matrix form
uv2azelConvert u/v coordinates to azimuth/elevation angles
azel2uvConvert azimuth/elevation angles to u/v coordinates
phitheta2azelConvert angles from phi/theta form to azimuth/elevation form
azel2phithetaConvert angles from azimuth-elevation form to phi-theta form
uv2phithetaConvert u/v coordinates to phi/theta angles
phitheta2uvConvert phi/theta angles to u/v coordinates


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 at 150 kmph in a circle of radius 10 km and descending at the same time at a rate of 20 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).