aer

Calculate azimuth angle, elevation angle, and range of another satellite or ground station in NED frame

Since R2021a

Syntax

az = aer(asset,target)

[az,el] = aer(asset,target)

[az,el,range] = aer(asset,target)

[az,el,range,timeOut] = aer(asset,target)

[___] = aer(asset,target,timeIn)

[___] = aer(___,coordinateFrame='ned')

Description

az = aer(asset,target) returns a 2-D array of the history of azimuth angles az, between asset and target belonging to a given satelliteScenario object.

[az,el] = aer(asset,target) returns the history of elevation angles, el, between satellite or ground station asset and another satellite or ground station target.

[az,el,range] = aer(asset,target) returns row vectors of the history of the range of Satellite or GroundStation in target with respect to those in asset.

[az,el,range,timeOut] = aer(asset,target) returns the corresponding time in timeOut.

[___] = aer(asset,target,timeIn) returns the outputs at the specified datetime timeIn. az, el, and range are structured the same way as described in syntaxes with an exception that the size of the second dimension is fixed at 1, representing the values at the specified time timeIn.

[___] = aer(___,coordinateFrame='ned') returns the az, el, range, and timeOut based on the specified output arguments and the coordinate frame defined by the name-value argument.

Note

By default, the aer function uses the north-east-down (NED) system to perform all the calculations.

Examples

Determine AER of Ground Station

Create a satellite scenario object.

startTime = datetime(2021,4,25);                      % April 25, 2021, 12:00 AM UTC
stopTime = datetime(2021,4,26);                       % April 26, 2021, 12:00 AM UTC
sampleTime = 60;                                      % seconds
sc = satelliteScenario(startTime,stopTime,sampleTime);

Add a satellite to the scenario.

tleFile = "eccentricOrbitSatellite.tle";
sat = satellite(sc,tleFile);

Add a ground station to the scenario using default properties.

gs = groundStation(sc);

Determine the azimuth angle, elevation angle, and range of the ground station with respect to the satellite at April 25, 2021, 1:26 AM UTC.

time = datetime(2021,4,25,1,26,0);
[azimuth,elevation,range] = aer(sat,gs,time)

azimuth = 
12.3293

elevation = 
-68.1798

range = 
1.2784e+07

Determine AER of Platform

Create a satellite scenario object.

startTime = datetime(2023,4,25);                      % April 25, 2023, 12:00 AM UTC
stopTime = datetime(2023,4,26);                       % April 26, 2023, 12:00 AM UTC
sampleTime = 60;                                      % seconds
sc = satelliteScenario(startTime,stopTime,sampleTime);

Add a satellite to the scenario.

tleFile = "eccentricOrbitSatellite.tle";
sat = satellite(sc,tleFile);

Add a platform to the scenario.

trajectory = geoTrajectory([40.6413,-73.7781,10600;32.3634,-64.7053,10600],[0,2*3600],AutoPitch=true,AutoBank=true);
pltf = platform(sc,trajectory);

Determine the azimuth angle, elevation angle, and range of the platform with respect to the satellite at April 25, 2023, 1:26 AM UTC.

time = datetime(2023,4,25,1,26,0);
[azimuth,elevation,range] = aer(sat,pltf,time)

azimuth = 
2.6782

elevation = 
-81.3176

range = 
4.1501e+07

Input Arguments

asset — First scenario component

scalar | vector

First scenario component, specified as a Satellite, GroundStation, ConicalSensor, Gimbal, Platform, Transmitter, or a Receiver object.

target — Second scenario component

scalar | vector

Second scenario component, specified as a Satellite, GroundStation, ConicalSensor, Gimbal, Platform, Transmitter, or a Receiver object.

timeIn — Time at which output is calculated

datetime

Time at which output is calculated, specified as a datetime. If no time zone is specified in timeIn, the time zone is assumed to be UTC.

coordinateFrame — Coordinate frame

'ned' (default) | 'body'

Coordinate frame, specified as either 'ned' or 'body'.

• When coordinateFrame is 'ned' — The azimuth angle is defined in the North-East-Down (NED) frame of (and centered at) asset such that 0 degrees is North, 90 degrees is East, 180 degrees is South, and 270 degrees is West. The elevation angle is defined in the NED frame of (and centered at) asset such that 0 degrees implies target is on the North East (NE) plane, 90 degrees implies target is directly above asset, and -90 degrees implies target is directly below asset.

• When coordinateFrame is 'body' — The azimuth angle is the angle between the projection of the relative position vector of target on the x-y plane of the body frame of asset, and the x-axis of asset. The angle is positive for positive (clockwise) rotation about the z-axis of asset. The elevation angle is the angle between the relative position vector of target on the x-y plane of the body frame of asset. The angle is positive when the z component of the relative position of target defined in the body frame of asset is negative.

Output Arguments

az — Azimuth angles

vector | 2-D array | scalar

Azimuth angles of the target in the local azimuth, elevation, and range (AER) system in degrees, returned as a vector, 2-D array, or scalar in the range [0,360). Azimuths are measured clockwise from North. If the timeIn argument is not specified, the vector elements correspond to the time samples specified by the SampleTime property from the satellite scenario StartTime to StopTime.

• If both asset and target are scalars, az is a row vector where each element represents the azimuth angle of target with respect to asset in the NED frame of asset at a specified time sample.

• If asset is a scalar and target is a vector, az is a 2-D array, where each row represents the azimuth angle of each element in target with respect to asset in the NED frame of asset and the columns represent the time samples.

• If asset is a vector and target is a scalar, az is a 2-D array, where each row represents the azimuth angle of target with respect to each element in asset in the NED frame of the element in asset and the columns represent the time samples.

• If both asset and target are vectors, the length of asset must equal the length of target. The az is a 2-D array, where each row index corresponds to the index in asset and target, and represents the azimuth angle of the element at the index in target with respect to the element at the index in asset in the NED frame of that element in asset. The columns represent the time samples.

If the timeIn argument is not specified and when the AutoSimulate property of the satellite scenario is true, aer function returns the az history from StartTime to StopTime. Otherwise, it returns the az history from StartTime to SimulationTime.

el — Elevation angles

vector | 2-D array | scalar

Elevation angles of target in the local AER system in degrees, returned as a vector, 2-D array, or scalar in the range [-90 90]. Elevations are measured with respect to a plane that is perpendicular to the normal of the surface of the earth. If asset is on the surface of the Earth, then the plane is tangential to the Earth. If the timeIn argument is not specified, the vector elements correspond to the time samples specified by the SampleTime property from the satellite scenario StartTime to StopTime.

If the timeIn argument is not specified and when the AutoSimulate property of the satellite scenario is true, aer function returns the el history from StartTime to StopTime. Otherwise, it returns the el history from StartTime to SimulationTime.

range — Distances from local origin

vector | 2-D array | scalar

Distances from the local origin in meters, returned as a vector, 2-D array, or a scalar. The range array is structured the same way as the az and el, described in the above syntaxes.

If the timeIn argument is not specified and when the AutoSimulate property of the satellite scenario is true, aer function returns the range history from StartTime to StopTime. Otherwise, it returns the range history from StartTime to SimulationTime.

timeOut — Time samples between start and stop time of scenario

row vector | scalar

Time samples corresponding to az, el, and range in UTC, returned as a row vector, or a scalar.

If the timeIn argument is not specified and when the AutoSimulate property of the satellite scenario is true, aer function returns the time sample history from StartTime to StopTime. Otherwise, it returns the time sample history from StartTime to SimulationTime.

Version History

Introduced in R2021a