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ctmeasjac

Jacobian of measurement function for constant turn-rate motion

Syntax

measurementjac = ctmeasjac(state)
measurementjac = ctmeasjac(state,frame)
measurementjac = ctmeasjac(state,frame,sensorpos)
measurementjac = ctmeasjac(state,frame,sensorpos,sensorvel)
measurementjac = ctmeasjac(state,frame,sensorpos,sensorvel,laxes)
measurementjac = ctmeasjac(state,measurementParameters)

Description

example

measurementjac = ctmeasjac(state) returns the measurement Jacobian, measurementjac, for a constant turn-rate Kalman filter motion model in rectangular coordinates. state specifies the current state of the track.

example

measurementjac = ctmeasjac(state,frame) also specifies the measurement coordinate system, frame.

example

measurementjac = ctmeasjac(state,frame,sensorpos) also specifies the sensor position, sensorpos.

measurementjac = ctmeasjac(state,frame,sensorpos,sensorvel) also specifies the sensor velocity, sensorvel.

measurementjac = ctmeasjac(state,frame,sensorpos,sensorvel,laxes) also specifies the local sensor axes orientation, laxes.

example

measurementjac = ctmeasjac(state,measurementParameters) specifies the measurement parameters, measurementParameters.

Examples

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Define the state of an object in 2-D constant turn-rate motion. The state is the position and velocity in each dimension, and the turn rate. Construct the measurement Jacobian in rectangular coordinates.

state = [1;10;2;20;5];
jacobian = ctmeasjac(state)
jacobian = 3×5

     1     0     0     0     0
     0     0     1     0     0
     0     0     0     0     0

Define the state of an object in 2-D constant turn-rate motion. The state is the position and velocity in each dimension, and the turn rate. Compute the measurement Jacobian with respect to spherical coordinates.

state = [1;10;2;20;5];
measurementjac = ctmeasjac(state,'spherical')
measurementjac = 4×5

  -22.9183         0   11.4592         0         0
         0         0         0         0         0
    0.4472         0    0.8944         0         0
    0.0000    0.4472    0.0000    0.8944         0

Define the state of an object in 2-D constant turn-rate motion. The state is the position and velocity in each dimension, and the turn rate. Compute the measurement Jacobian with respect to spherical coordinates centered at [5;-20;0].

state = [1;10;2;20;5];
sensorpos = [5;-20;0];
measurementjac = ctmeasjac(state,'spherical',sensorpos)
measurementjac = 4×5

   -2.5210         0   -0.4584         0         0
         0         0         0         0         0
   -0.1789         0    0.9839         0         0
    0.5903   -0.1789    0.1073    0.9839         0

Define the state of an object in 2-D constant turn-rate motion. The state is the position and velocity in each dimension, and the turn rate. Compute the measurement Jacobian with respect to spherical coordinates centered at [25;-40;0].

state2d = [1;10;2;20;5];
sensorpos = [25,-40,0].';
frame = 'spherical';
sensorvel = [0;5;0];
laxes = eye(3);
measurementjac = ctmeasjac(state2d,frame,sensorpos,sensorvel,laxes)
measurementjac = 4×5

   -1.0284         0   -0.5876         0         0
         0         0         0         0         0
   -0.4961         0    0.8682         0         0
    0.2894   -0.4961    0.1654    0.8682         0

Put the measurement parameters in a structure and use the alternative syntax.

measparm = struct('Frame',frame,'OriginPosition',sensorpos,'OriginVelocity',sensorvel, ...
    'Orientation',laxes);
measurementjac = ctmeasjac(state2d,measparm)
measurementjac = 4×5

   -1.0284         0   -0.5876         0         0
         0         0         0         0         0
   -0.4961         0    0.8682         0         0
    0.2894   -0.4961    0.1654    0.8682         0

Input Arguments

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State vector for a constant turn-rate motion model in two or three spatial dimensions, specified as a real-valued vector or matrix.

  • When specified as a 5-element vector, the state vector describes 2-D motion in the x-y plane. You can specify the state vector as a row or column vector. The components of the state vector are [x;vx;y;vy;omega] where x represents the x-coordinate and vx represents the velocity in the x-direction. y represents the y-coordinate and vy represents the velocity in the y-direction. omega represents the turn rate.

    When specified as a 5-by-N matrix, each column represents a different state vector N represents the number of states.

  • When specified as a 7-element vector, the state vector describes 3-D motion. You can specify the state vector as a row or column vector. The components of the state vector are [x;vx;y;vy;omega;z;vz] where x represents the x-coordinate and vx represents the velocity in the x-direction. y represents the y-coordinate and vy represents the velocity in the y-direction. omega represents the turn rate. z represents the z-coordinate and vz represents the velocity in the z-direction.

    When specified as a 7-by-N matrix, each column represents a different state vector. N represents the number of states.

Position coordinates are in meters. Velocity coordinates are in meters/second. Turn rate is in degrees/second.

Example: [5;0.1;4;-0.2;0.01]

Data Types: double

Measurement frame, specified as 'rectangular' or 'spherical'. When the frame is 'rectangular', a measurement consists of the x, y, and z Cartesian coordinates of the tracked object. When specified as 'spherical', a measurement consists of the azimuth, elevation, range, and range rate of the tracked object.

Data Types: char

Sensor position with respect to the global coordinate system, specified as a real-valued 3-by-1 column vector. Units are in meters.

Data Types: double

Sensor velocity with respect to the global coordinate system, specified as a real-valued 3-by-1 column vector. Units are in meters/second.

Data Types: double

Local sensor coordinate axes, specified as a 3-by-3 orthogonal matrix. Each column specifies the direction of the local x-, y-, and z-axes, respectively, with respect to the global coordinate system.

Data Types: double

Measurement parameters, specified as a structure. The fields of the structure are:

measurementParameters struct

ParameterDefinitionDefault
OriginPositionSensor position with respect to the global coordinate system, specified as a real-valued 3-by-1 column vector. Units are in meters.[0;0;0]
OriginVelocitySensor velocity with respect to the global coordinate system, specified as a real-valued 3-by-1 column vector. Units are in m/s.[0;0;0]
OrientationLocal sensor coordinate axes, specified as a 3-by-3 orthogonal matrix. Each column specifies the direction of the local x-, y-, and z-axes, respectively, with respect to the global coordinate system.eye(3)
HasVelocityIndicates whether measurements contain velocity or range rate components, specified as true or false.false when frame argument is 'rectangular' and true when frame argument is 'spherical'
HasElevationIndicates whether measurements contain elevation components, specified as true or false.true

Data Types: struct

Output Arguments

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Measurement Jacobian, returned as a real-valued 3-by-5 or 4-by-5 matrix. The row dimension and interpretation depend on value of the frame argument.

FrameMeasurement Jacobian
'rectangular'Jacobian of the measurements [x;y;z] with respect to the state vector. The measurement vector is with respect to the local coordinate system. Coordinates are in meters.
'spherical'Jacobian of the measurement vector [az;el;r;rr] with respect to the state vector. Measurement vector components specify the azimuth angle, elevation angle, range, and range rate of the object with respect to the local sensor coordinate system. Angle units are in degrees. Range units are in meters and range rate units are in meters/second.

More About

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Azimuth and Elevation Angle Definitions

Define the azimuth and elevation angles used in Sensor Fusion and Tracking Toolbox™.

The azimuth angle of a vector is the angle between the x-axis and its orthogonal projection onto the xy plane. The angle is positive in going from the x axis toward the y axis. Azimuth angles lie between –180 and 180 degrees. The elevation angle is the angle between the vector and its orthogonal projection onto the xy-plane. The angle is positive when going toward the positive z-axis from the xy plane.

Extended Capabilities

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

Introduced in R2018b