triangulateLOS

Triangulate multiple line-of-sight detections

Syntax

estPos = triangulateLOS(detections)

[estPos,estCov] = triangulateLOS(detections)

Description

estPos = triangulateLOS(detections) estimates the position of a target in a global Cartesian coordinate frame by triangulating a set of angle-only detections. Angle-only detections are also known as line-of-sight (LOS) detections. For more details, see Algorithms.

[estPos,estCov] = triangulateLOS(detections) also returns estCov, the covariance of the error in target position. The function uses a Taylor-series approximation to estimate the error covariance.

Examples

Triangulate Line-of-Sight Measurements from Three Sensors

Load a MAT-file containing a set of line-of-sight detections stored in the variable detectionSet.

load angleOnlyDetectionFusion.mat

Plot the angle-only detections and the sensor positions. Specify a range of 5 km for plotting the direction vector. To specify the position of the origin, use the second measurement parameter because the sensor is located at the center of the platform. Convert the azimuth and elevation readings to Cartesian coordinates.

rPlot = 5000;

for i = 1:numel(detectionSet)
    originPos = detectionSet{i}.MeasurementParameters(2).OriginPosition;

    az = detectionSet{i}.Measurement(1);
    el = detectionSet{i}.Measurement(2);
    [xt,yt,zt] = sph2cart(deg2rad(az),deg2rad(el),rPlot);
        
    positionData(:,i) = originPos;
    plotData(:,3*i+(-2:0)) = [xt yt zt]'.*[1 0 NaN]+originPos;
end

plot3(positionData(1,:),positionData(2,:),positionData(3,:),'*')
hold on
plot3(plotData(1,:),plotData(2,:),plotData(3,:))

Triangulate the detections by using triangulateLOS. Plot the triangulated position.

[estPos,estCov] = triangulateLOS(detectionSet);

plot3(estPos(1),estPos(2),estPos(3),'pk','MarkerFaceColor','k')
hold off

legend('Sensor Positions','Angle-Only Detections','Triangulated Position', ...
    'location','southeast')
xlabel('x [m]')
ylabel('y [m]')
view(2)

Input Arguments

detections — Line-of-sight measurements

cell array of objectDetection objects

Line-of-sight measurements, specified as a cell array of objectDetection objects. Each object has the properties listed in the table.

Property	Definition
Time	Measurement time
Measurement	Object measurements
MeasurementNoise	Measurement noise covariance matrix
SensorIndex	Unique ID of the sensor
ObjectClassID	Object classification
MeasurementParameters	Parameters used by initialization functions of nonlinear Kalman tracking filters
ObjectAttributes	Additional information passed to tracker

Each detection must specify the MeasurementParameters property as a structure with the fields described in the table.

Parameter	Definition
Frame	Frame used to report measurements. Specify Frame as 'spherical' for the first structure.
OriginPosition	Position offset of the origin of the frame relative to the parent frame, represented as a 3-by-1 real vector.
OriginVelocity	Velocity offset of the origin of the frame relative to the parent frame, represented as a 3-by-1 real vector.
Orientation	A 3-by-3 real-valued orthonormal frame orientation matrix.
IsParentToChild	A logical scalar that indicates if Orientation is given as a frame rotation from the parent coordinate frame to the child coordinate frame. If false, then Orientation is given as a frame rotation from the child coordinate frame to the parent coordinate frame.
HasElevation	A logical scalar that indicates if elevation is included in the measurements. This parameter is true by default.
HasAzimuth	A logical scalar that indicates if azimuth is included in the measurements. This parameter is true by default. If specified as a field, it must be set to true.
HasRange	A logical scalar that indicates if range is included in the measurements. This parameter must be specified as a field and set to false.
HasVelocity	A logical scalar that indicates if velocity is included in the measurements. This parameter is false by default. If specified as a field, it must be set to false.

The function provides default values for fields left unspecified.

Output Arguments

estPos — Estimated position

3-by-1 vector

Estimated position of the target, returned as a 3-by-1 vector.

estCov — Estimated error covariance

3-by-3 matrix

Estimated error covariance of the target position, returned as a 3-by-3 matrix.

Algorithms

Multiple angle-only or line-of-sight measurements result in lines in space. These lines might or might not intersect because of measurement noise. triangulateLOS uses a suboptimal linear least-squares method to minimize the distance of miss between multiple detections. The formulation makes these assumptions:

• All detections report measurements with approximately the same accuracy in azimuth and elevation (if measured).

• The distances from the different sensors to the triangulated target are all of the same order.

References

[1] Blackman, Samuel, and Robert Popoli. "Design and analysis of modern tracking systems." Norwood, MA: Artech House, 1999. (1999).

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Version History

Introduced in R2018b