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dopplershift

Calculate Doppler shift at target asset in satellite scenario

Since R2023a

    Description

    shift = dopplershift(source,target) calculates the history of Doppler shifts at the target asset corresponding to the source asset. Both source and target must belong to the same satelliteScenario object. If the value of AutoSimulate property of the satelliteScenario object is true, the dopplershift function returns the Doppler shift history from the value of StartTime to the value of StopTime. Otherwise, it returns the Doppler shift history from the value of StartTime to the value of SimulationTime.

    example

    [shift,timeOut] = dopplershift(source,target) returns the sample time history timeOut.

    [shift,timeOut,info] = dopplershift(source,target) returns a structure, info, containing the Doppler rate and relative velocity information.

    [___] = dopplershift(___,timeIn) calculates Doppler shift at the specified datetime timeIn. When using this syntax, dopplershift sets the second dimension of shift, timeOut, and the fields of info to 1. In this case, the DopplerRate field of info is empty.

    [___] = dopplershift(___,Frequency=freq) additionally specifies one or more carrier frequencies at which to calculate Doppler shift.

    Note

    The dopplershift function uses the Geocentric Celestial Reference Frame (GCRF) coordinate system to perform all calculations.

    Examples

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    Determine the Doppler shift, the Doppler rate, the relative velocity, and the corresponding time history at a ground station. The source is a satellite that transmits on a carrier frequency of 14 GHz.

    Specify the start time and the stop time of the satellite scenario.

    startTime = datetime(2021,4,25);                      % April 25, 2021, 12:00 AM UTC
    stopTime = datetime(2021,4,26);                       % April 26, 2021, 12:00 AM UTC

    Set the sample time in seconds.

    sampleTime = 60; 

    Create a satelliteScenario object.

    sc = satelliteScenario(startTime,stopTime,sampleTime);

    Add a satellite to the scenario.

    semiMajorAxis = 10000000;             % In meters
    eccentricity = 0;
    inclination = 0;                      % In degrees 
    rightAscensionOfAscendingNode = 0;    % In degrees
    argumentOfPeriapsis = 0;              % In degrees
    trueAnomaly = 0;                      % In degrees
    sat = satellite(sc,semiMajorAxis,eccentricity,inclination, ...
            rightAscensionOfAscendingNode,argumentOfPeriapsis,trueAnomaly);

    Add a default ground station to the scenario.

    gs = groundStation(sc);

    Determine the Doppler shift, the Doppler rate, and the relative velocity, as well as the corresponding time history.

    carrierFrequency=14e9;
    [frequencyShift,timeOut,dopplerInfo] = dopplershift(sat,gs,Frequency=carrierFrequency);
    frequencyRate = dopplerInfo.DopplerRate;
    relativeVelocity = dopplerInfo.RelativeVelocity;

    Plot the Doppler shift at the ground station.

    plot(timeOut,frequencyShift(1,:)/1e3)       % Doppler shift in kilohertz (kHz)
    xlim([timeOut(1) timeOut(end)])
    title("Doppler Shift vs. Time")
    xlabel("Simulation Time")
    ylabel("Doppler Shift (kHz)")
    grid on

    Figure contains an axes object. The axes object with title Doppler Shift vs. Time, xlabel Simulation Time, ylabel Doppler Shift (kHz) contains an object of type line.

    Input Arguments

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    Source asset from scenario, specified as a Satellite , GroundStation , Transmitter , Platform object or an array of Satellite , GroundStation, Transmitter, Platform objects.

    Target asset from scenario, specified as a Satellite, GroundStation, Receiver, Platform object, or an array of Satellite, GroundStation, Receiver, Platform objects.

    Time at which the function calculates the Doppler shift, specified as a datetime scalar. If timeIn does not specify a time zone, the function uses Coordinated Universal Time (UTC).

    Data Types: datetime

    Carrier frequency at which to calculate Doppler shift, specified as a scalar or vector of nonnegative real numbers, in hertz or -1. Specify -1 to use the default carrier frequency value for each source asset.

    If the freq value is -1 and source is a Satellite or GroundStation, the carrier frequency is 14 gigahertz (GHz). If the freq value is -1 and source is a Transmitter, the carrier frequency is the Frequency property value of the Transmitter object.

    Data Types: double

    Output Arguments

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    History of Doppler shift, in hertz, returned as a scalar, vector, matrix, or 3-D array. When the source and target cannot access each other, the corresponding shift value is NaN. These tables show how this output changes based on the different input argument sizes and combinations.

    • timeIn not specified

      sourcetargetshiftDescription
      scalarscalarrow vectorDoppler shift history, in which each element represents the Doppler shift between source and target at a specific time sample.
      scalarvectormatrixEach row represents the Doppler shift history between source and an asset in target. The row corresponds to the position of the asset in target.
      vectorscalarmatrix Each row represents the Doppler shift history between target and an asset in source. The row corresponds to the position of the asset in source.
      vectorvectormatrixEach row represents the Doppler shift history between a pair of source and target assets. The row corresponds to the position of the assets in source and target.

    • timeIn specified

      sourcetargetshiftDescription
      scalarscalarscalarDoppler shift at the specified datetime timeIn.
      scalarvectorcolumn vectorEach element represents the Doppler shift between source and the corresponding asset in target at the specified datetime timeIn.
      vectorscalarcolumn vectorEach element represents the Doppler shift from the corresponding asset in source to target at the specified datetime timeIn.
      vectorvectorcolumn vectorEach element represents the Doppler shift between the corresponding pair of source and target assets at the specified datetime timeIn.

      If you specify freq as a vector, shift has a third dimension in which each page is the output of the corresponding combination of source, target, and timeIn from the previous tables for the corresponding carrier frequency in freq.

    Data Types: double

    Time samples between the start and stop time of the scenario, returned as a scalar or vector.

    If timeIn does not specify a time zone and the AutoSimulate property the satelliteScenario object is true, the dopplershift function returns the time sample history from StartTime to StopTime. Otherwise, it returns the time sample history from the value of StartTime to the value of SimulationTime.

    Data Types: datetime

    History of Doppler rate and relative velocity, returned as a structure that contains these fields.

    • DopplerRate — The Doppler rate history, returned as a vector, matrix, or 3-D array. The format of DopplerRate is similar to shift except that the number of columns equals the number of time samples minus 1. When source and target cannot see each other, the corresponding DopplerRate value is NaN.

    • RelativeVelocity — The history of relative velocity of source and target in the direction from source to target, returned as a scalar, vector, or matrix. The number of rows in the matrix is the greater number between the source and target assets. When source and target cannot access each other, the RelativeVelocity value is NaN.

    Data Types: struct

    More About

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    Doppler Shift

    If you know the position of the source (PS¯) , the position of the target (PT¯), the velocity of the source (VS¯), the velocity of the target (VT¯), and the carrier frequency (fc), use these equations to calculate Doppler shift.

    The source and target assets, their positions and velocities, and the unit vector in the direction from the source to the target.

    1. The unit vector from the source to the target is dir^=PT¯PS¯PT¯PS¯, where indicates the Euclidean norm.

    2. The velocity of the source in the unit direction is

      VS,dir=VS¯dir^.

      If the angle between VS¯ and dir^, in degrees, is in the range [0, 90], VS,dir is positive. A positive value of VS,dir indicates the source is moving towards the target. A negative value of VS,dir indicates the source is moving away from the target.

    3. The velocity of the target in the unit direction is

      VT,dir=VT¯dir.^

      If the angle between VT¯ and dir^, in degrees, is in the range [0, 90], VT,dir is positive. A positive value of VT,dirindicates the target is moving away from the source. A negative value of VT,dir indicates the target is moving towards the source.

    4. The relative velocity of source and target in the direction from the source to the target is

      Vrel=VS,dirVT,dir.

    5. The Doppler frequency observed at the target is

      fd=(cVT,dircVS,dir)fc.

      In this equation, c is the speed of light in meters per second.

    6. The Doppler shift at the target is

      fshift=fdfc=(VrelcVS,dir)fc.

    Note

    All position and velocity vectors are in the GCRF coordinate frame.

    Version History

    Introduced in R2023a