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gpsSensor

GPS receiver simulation model

Since R2022a

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Description

The gpsSensor System object™ models data output from a Global Positioning System (GPS) receiver. The object models the position noise as a first order Gauss Markov process, in which the sigma values are specified in the HorizontalPositionAccuracy and the VerticalPositionAccuracy properties. The object models the velocity noise as Gaussian noise with its sigma value specified in the VelocityAccuracy property.

To model a GPS receiver:

  1. Create the gpsSensor object and set its properties.

  2. Call the object with arguments, as if it were a function.

To learn more about how System objects work, see What Are System Objects?

Creation

Syntax

GPS = gpsSensor
GPS = gpsSensor('ReferenceFrame',RF)
GPS = gpsSensor(___,Name=Value)

Description

GPS = gpsSensor returns a gpsSensor System object that computes a Global Positioning System receiver reading based on a local position and velocity input signal. The default reference position in geodetic coordinates is

  • latitude: 0o N

  • longitude: 0o E

  • altitude: 0 m

GPS = gpsSensor('ReferenceFrame',RF) returns a gpsSensor System object that computes a global positioning system receiver reading relative to the reference frame RF.

GPS = gpsSensor(___,Name=Value) sets one or more properties using name-value arguments in addition to any of the previous input arguments.

example

Input Arguments

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Reference frame of the sensor inputs, specified as either 'NED' (North-East-Down) or 'ENU' (East-North-Up).

Data Types: char | string

Properties

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Unless otherwise indicated, properties are nontunable, which means you cannot change their values after calling the object. Objects lock when you call them, and the release function unlocks them.

If a property is tunable, you can change its value at any time.

For more information on changing property values, see System Design in MATLAB Using System Objects.

Update rate of the receiver in Hz, specified as a positive real scalar.

Data Types: single | double

Reference location, specified as a 3-element row vector in geodetic coordinates (latitude, longitude, and altitude). Altitude is the height above the reference ellipsoid model, WGS84. The reference location is in [degrees degrees meters]. The degree format is decimal degrees (DD).

Data Types: single | double

Position coordinate input format, specified as 'Local' or 'Geodetic'.

  • If you set the property as 'Local', then you need to specify the truePosition input as Cartesian coordinates with respect to the local navigation frame whose origin is fixed and defined by the ReferenceLcation property. Additionally, when you specify the trueVelocity input, you need to specify it with respect to this local navigation frame.

  • If you set the property as 'Geodetic', then you need to specify the truePosition input as geodetic coordinates in latitude, longitude, and altitude. Additionally, when you specify the trueVelocity input, you need to specify it with respect to the navigation frame (NED or ENU) whose origin corresponds to the truePosition input. When setting the property as 'Geodetic', the gpsSensor object neglects the ReferenceLocation property.

Data Types: character vector

Horizontal position accuracy in meters, specified as a nonnegative real scalar. The horizontal position accuracy specifies the standard deviation of the noise in the horizontal position measurement.

Tunable: Yes

Data Types: single | double

Vertical position accuracy in meters, specified as a nonnegative real scalar. The vertical position accuracy specifies the standard deviation of the noise in the vertical position measurement.

Tunable: Yes

Data Types: single | double

Velocity accuracy in meters per second, specified as a nonnegative real scalar. The velocity accuracy specifies the standard deviation of the noise in the velocity measurement.

Tunable: Yes

Data Types: single | double

Global position noise decay factor, specified as a scalar in the range [0,1].

A decay factor of 0 models the global position noise as a white noise process. A decay factor of 1 models the global position noise as a random walk process.

Tunable: Yes

Data Types: single | double

Random number source, specified as a character vector or string:

  • 'Global stream' –– Random numbers are generated using the current global random number stream.

  • 'mt19937ar with seed' –– Random numbers are generated using the mt19937ar algorithm with the seed specified by the Seed property.

Data Types: char | string

Initial seed of an mt19937ar random number generator algorithm, specified as a nonnegative integer scalar.

Dependencies

To enable this property, set RandomStream to 'mt19937ar with seed'.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Usage

Syntax

[position,velocity,groundspeed,course] = GPS(truePosition,trueVelocity)

Description

[position,velocity,groundspeed,course] = GPS(truePosition,trueVelocity) computes global navigation satellite system receiver readings from the position and velocity inputs.

example

Input Arguments

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Position of the GPS receiver in the navigation coordinate system, specified as a real finite N-by-3 matrix. N is the number of samples in the current frame.

  • When the PositionInputFormat property is specified as 'Local', specify truePosition as Cartesian coordinates with respect to the local navigation frame whose origin is fixed at ReferenceLocation.

  • When the PositionInputFormat property is specified as 'Geodetic', specify truePosition as geodetic coordinates in [latitude longitude altitude]. latitude and longitude are in degrees. altitude is the height above the WGS84 ellipsoid model in meters.

Data Types: single | double

Velocity of GPS receiver in the navigation coordinate system in meters per second, specified as a real finite N-by-3 matrix. N is the number of samples in the current frame.

  • When the PositionInputFormat property is specified as 'Local', specify trueVelocity with respect to the local navigation frame (NED or ENU) whose origin is fixed at ReferenceLocation.

  • When the PositionInputFormat property is specified as 'Geodetic', specify trueVelocity with respect to the navigation frame (NED or ENU) whose origin corresponds to the truePosition input.

Data Types: single | double

Output Arguments

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Position of the GPS receiver in the geodetic latitude, longitude, and altitude (LLA) coordinate system, returned as a real finite N-by-3 array. Latitude and longitude are in degrees with North and East being positive. Altitude is in meters.

N is the number of samples in the current frame.

Data Types: single | double

Velocity of the GPS receiver in the local navigation coordinate system in meters per second, returned as a real finite N-by-3 array. N is the number of samples in the current frame.

  • When the PositionInputFormat property is specified as 'Local', the returned velocity is with respect to the local navigation frame whose origin is fixed at ReferenceLocation.

  • When the PositionInputFormat property is specified as 'Geodetic', the returned velocity is with respect to the navigation frame (NED or ENU) whose origin corresponds to the position output.

Data Types: single | double

Magnitude of the horizontal velocity of the GPS receiver in the local navigation coordinate system in meters per second, returned as a real finite N-by-1 column vector.

N is the number of samples in the current frame.

Data Types: single | double

Direction of the horizontal velocity of the GPS receiver in the local navigation coordinate system in degrees, returned as a real finite N-by-1 column vector of values between 0 and 360. North corresponds to 360 degrees and East corresponds to 90 degrees.

N is the number of samples in the current frame.

Data Types: single | double

Object Functions

To use an object function, specify the System object as the first input argument. For example, to release system resources of a System object named obj, use this syntax:

release(obj)

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stepRun System object algorithm
releaseRelease resources and allow changes to System object property values and input characteristics
resetReset internal states of System object

Examples

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Open Live Script

Create a gpsSensor System object™ to model GPS receiver data. Assume a typical one Hz sample rate and a 1000-second simulation time. Define the reference location in terms of latitude, longitude, and altitude (LLA) of Natick, MA (USA). Define the sensor as stationary by specifying the true position and velocity with zeros.

fs = 1;
duration = 1000;
numSamples = duration*fs;

refLoc = [42.2825 -71.343 53.0352];

truePosition = zeros(numSamples,3);
trueVelocity = zeros(numSamples,3);

gps = gpsSensor('SampleRate',fs,'ReferenceLocation',refLoc);

Call gps with the specified truePosition and trueVelocity to simulate receiving GPS data for a stationary platform.

position = gps(truePosition,trueVelocity);

Plot the true position and the GPS sensor readings for position.

t = (0:(numSamples-1))/fs;

subplot(3, 1, 1)
plot(t, position(:,1), ...
     t, ones(numSamples)*refLoc(1))
title('GPS Sensor Readings')
ylabel('Latitude (degrees)')

subplot(3, 1, 2)
plot(t, position(:,2), ...
     t, ones(numSamples)*refLoc(2))
ylabel('Longitude (degrees)')

subplot(3, 1, 3)
plot(t, position(:,3), ...
     t, ones(numSamples)*refLoc(3))
ylabel('Altitude (m)')
xlabel('Time (s)')

Figure contains 3 axes objects. Axes object 1 with title GPS Sensor Readings, ylabel Latitude (degrees) contains 1001 objects of type line. Axes object 2 with ylabel Longitude (degrees) contains 1001 objects of type line. Axes object 3 with xlabel Time (s), ylabel Altitude (m) contains 1001 objects of type line.

The position readings have noise controlled by HorizontalPositionAccuracy, VerticalPositionAccuracy, VelocityAccuracy, and DecayFactor. The DecayFactor property controls the drift in the noise model. By default, DecayFactor is set to 0.999, which approaches a random walk process. To observe the effect of the DecayFactor property:

  1. Reset the gps object.

  2. Set DecayFactor to 0.5.

  3. Call gps with variables specifying a stationary position.

  4. Plot the results.

The GPS position readings now oscillate around the true position.

reset(gps)
gps.DecayFactor = 0.5;
position = gps(truePosition,trueVelocity);

subplot(3, 1, 1)
plot(t, position(:,1), ...
     t, ones(numSamples)*refLoc(1))
title('GPS Sensor Readings - Decay Factor = 0.5')
ylabel('Latitude (degrees)')

subplot(3, 1, 2)
plot(t, position(:,2), ...
     t, ones(numSamples)*refLoc(2))
ylabel('Longitude (degrees)')

subplot(3, 1, 3)
plot(t, position(:,3), ...
     t, ones(numSamples)*refLoc(3))
ylabel('Altitude (m)')
xlabel('Time (s)')

Figure contains 3 axes objects. Axes object 1 with title GPS Sensor Readings - Decay Factor = 0.5, ylabel Latitude (degrees) contains 1001 objects of type line. Axes object 2 with ylabel Longitude (degrees) contains 1001 objects of type line. Axes object 3 with xlabel Time (s), ylabel Altitude (m) contains 1001 objects of type line.

Open Live Script

GPS receivers achieve greater course accuracy as groundspeed increases. In this example, you create a GPS receiver simulation object and simulate the data received from a platform that is accelerating from a stationary position.

Create a default gpsSensor System object™ to model data returned by a GPS receiver.

GPS = gpsSensor
GPS = 
  gpsSensor with properties:

                    SampleRate: 1                  Hz         
           PositionInputFormat: 'Local'                       
             ReferenceLocation: [0 0 0]            [deg deg m]
    HorizontalPositionAccuracy: 1.6                m          
      VerticalPositionAccuracy: 3                  m          
              VelocityAccuracy: 0.1                m/s        
                  RandomStream: 'Global stream'               
                   DecayFactor: 0.999

Create matrices to describe the position and velocity of a platform in the NED coordinate system. The platform begins from a stationary position and accelerates to 60 m/s North-East over 60 seconds, then has a vertical acceleration to 2 m/s over 2 seconds, followed by a 2 m/s rate of climb for another 8 seconds. Assume a constant velocity, such that the velocity is the simple derivative of the position.

duration = 70;
numSamples = duration*GPS.SampleRate;

course = 45*ones(duration,1);
groundspeed = [(1:60)';60*ones(10,1)];

Nvelocity   = groundspeed.*sind(course);
Evelocity   = groundspeed.*cosd(course);
Dvelocity   = [zeros(60,1);-1;-2*ones(9,1)];
NEDvelocity = [Nvelocity,Evelocity,Dvelocity];

Ndistance   = cumsum(Nvelocity);
Edistance   = cumsum(Evelocity);
Ddistance   = cumsum(Dvelocity);
NEDposition = [Ndistance,Edistance,Ddistance];

Model GPS measurement data by calling the GPS object with your velocity and position matrices.

[~,~,groundspeedMeasurement,courseMeasurement] = GPS(NEDposition,NEDvelocity);

Plot the groundspeed and the difference between the true course and the course returned by the GPS simulator.

As groundspeed increases, the accuracy of the course increases. Note that the velocity increase during the last ten seconds has no effect, because the additional velocity is not in the ground plane.

t = (0:numSamples-1)/GPS.SampleRate;

subplot(2,1,1)
plot(t,groundspeed);
ylabel('Speed (m/s)')
title('Relationship Between Groundspeed and Course Accuracy')

subplot(2,1,2)
courseAccuracy = courseMeasurement - course;
plot(t,courseAccuracy)
xlabel('Time (s)');
ylabel('Course Accuracy (degrees)')

Figure contains 2 axes objects. Axes object 1 with title Relationship Between Groundspeed and Course Accuracy, ylabel Speed (m/s) contains an object of type line. Axes object 2 with xlabel Time (s), ylabel Course Accuracy (degrees) contains an object of type line.

Open Live Script

Simulate GPS data received during a trajectory from the city of Natick, MA, to Boston, MA.

Define the decimal degree latitude and longitude for the city of Natick, MA USA, and Boston, MA USA. For simplicity, set the altitude for both locations to zero.

NatickLLA = [42.27752809999999, -71.34680909999997, 0];
BostonLLA = [42.3600825, -71.05888010000001, 0];

Define a motion that can take a platform from Natick to Boston in 20 minutes. Set the origin of the local NED coordinate system as Natick. Create a waypointTrajectory object to output the trajectory 10 samples at a time.

fs = 1;
duration = 60*20;

bearing = 68; % degrees
distance = 25.39e3; % meters
distanceEast = distance*sind(bearing);
distanceNorth = distance*cosd(bearing);

NatickNED = [0,0,0];
BostonNED = [distanceNorth,distanceEast,0];

trajectory = waypointTrajectory( ...
    'Waypoints', [NatickNED;BostonNED], ...
    'TimeOfArrival',[0;duration], ...
    'SamplesPerFrame',10, ...
    'SampleRate',fs);

Create a gpsSensor object to model receiving GPS data for the platform. Set the HorizontalPositionalAccuracy to 25 and the DecayFactor to 0.25 to emphasize the noise. Set the ReferenceLocation to the Natick coordinates in LLA.

GPS = gpsSensor( ...
    'HorizontalPositionAccuracy',25, ...
    'DecayFactor',0.25, ...
    'SampleRate',fs, ...
    'ReferenceLocation',NatickLLA);

Open a figure and plot the position of Natick and Boston in LLA. Ignore altitude for simplicity.

In a loop, call the gpsSensor object with the ground-truth trajectory to simulate the received GPS data. Plot the ground-truth trajectory and the model of received GPS data.

figure(1)
plot(NatickLLA(1),NatickLLA(2),'ko', ...
     BostonLLA(1),BostonLLA(2),'kx')
xlabel('Latitude (degrees)')
ylabel('Longitude (degrees)')
title('GPS Sensor Data for Natick to Boston Trajectory')
hold on

while ~isDone(trajectory)
    [truePositionNED,~,trueVelocityNED] = trajectory();
    reportedPositionLLA = GPS(truePositionNED,trueVelocityNED);

    figure(1)
    plot(reportedPositionLLA(:,1),reportedPositionLLA(:,2),'r.')
end

Figure contains an axes object. The axes object with title GPS Sensor Data for Natick to Boston Trajectory, xlabel Latitude (degrees), ylabel Longitude (degrees) contains 122 objects of type line.

As a best practice, release System objects when complete.

release(GPS)
release(trajectory)

Extended Capabilities

Version History

Introduced in R2022a

See Also

Objects