ctmeasjac

Jacobian of measurement function for constant turn-rate and velocity- magnitude motion model

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

measurementjac = ctmeasjac(state) returns the Jacobian of the measurement function, measurementjac, for a state based on the constant turn-rate and velocity-magnitude motion model. state specifies the current state of the track.

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

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.

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

Examples

Measurement Jacobian of Constant Turn-Rate Motion in Rectangular Frame

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

Measurement Jacobian of Constant Turn-Rate Motion in Spherical Frame

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

Measurement Jacobian of Constant Turn-Rate Object in Translated Spherical Frame

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

Measurement Jacobian of Constant Turn-Rate Object Using Measurement Parameters

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

state — State vector

real-valued 5-element vector | real-valued 7-element vector

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

• When specified as a 5-element vector, the state vector describes 2-D motion in the xy-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 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.

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: single | double

frame — Frame to report measurements

'rectangular' (default) | 'spherical'

Frame to report measurements, specified as 'rectangular' or 'spherical'. When you specify frame as 'rectangular', a measurement consists of x, y, and z Cartesian coordinates. When you specify frame as 'spherical', a measurement consists of azimuth, elevation, range, and range rate.

Data Types: char | string

sensorpos — Sensor position

[0;0;0] (default) | real-valued 3-by-1 column vector

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

Data Types: single | double

sensorvel — Sensor velocity

[0;0;0] (default) | real-valued 3-by-1 column vector

Sensor velocity with respect to the navigation frame, specified as a real-valued 3-by-1 column vector. Units are in m/s.

Data Types: single | double

laxes — Local sensor axes coordinates

[1,0,0;0,1,0;0,0,1] (default) | 3-by-3 orthogonal matrix

Local sensor axes coordinates, 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 navigation frame. The matrix is the rotation matrix from the global frame to the sensor frame.

Data Types: single | double

measurementParameters — Measurement parameters

structure | array of structures

Measurement parameters, specified as a structure or an array of structures. This table lists the fields in the structure.

Field	Description	Example
Frame	Frame used to report measurements, specified as one of these values: 'Rectangular' — Detections are reported in rectangular coordinates. 'Spherical' — Detections are reported in spherical coordinates. Tip In Simulink, when you create an object detection Bus, specify Frame as an enumeration object of fusionCoordinateFrameType.Rectangular or fusionCoordinateFrameType.Spherical because Simulink does not support variables such as a character vector that can vary in size.	'spherical'
OriginPosition	Position offset of the origin of the frame relative to the parent frame, specified as an [x y z] real-valued vector.	[0 0 0]
OriginVelocity	Velocity offset of the origin of the frame relative to the parent frame, specified as a [vx vy vz] real-valued vector.	[0 0 0]
Orientation	Frame rotation matrix, specified as a 3-by-3 real-valued orthonormal matrix.	[1 0 0; 0 1 0; 0 0 1]
HasAzimuth	Logical scalar indicating if azimuth is included in the measurement. This field is not relevant when the Frame field is 'Rectangular'.	1
HasElevation	Logical scalar indicating if elevation information is included in the measurement. For measurements reported in a rectangular frame, and if HasElevation is false, the reported measurements assume 0 degrees of elevation.	1
HasRange	Logical scalar indicating if range is included in the measurement. This field is not relevant when the Frame is 'Rectangular'.	1
HasVelocity	Logical scalar indicating if the reported detections include velocity measurements. For a measurement reported in the rectangular frame, if HasVelocity is false, the measurements are reported as [x y z]. If HasVelocity is true, the measurement is reported as [x y z vx vy vz]. For a measurement reported in the spherical frame, if HasVelocity is true, the measurement contains range-rate information.	1
IsParentToChild	Logical scalar indicating if Orientation performs a frame rotation from the parent coordinate frame to the child coordinate frame. When IsParentToChild is false, then Orientation performs a frame rotation from the child coordinate frame to the parent coordinate frame.	0

If you want to perform only one coordinate transformation, such as a transformation from the body frame to the sensor frame, you must specify a measurement parameter structure. If you want to perform multiple coordinate transformations, you must specify an array of measurement parameter structures. To learn how to perform multiple transformations, see the Convert Detections to objectDetection Format (Sensor Fusion and Tracking Toolbox) example.

Data Types: struct

Output Arguments

measurementjac — Jacobian of measurement function

real-valued M-by-N matrix

Jacobian of the measurement function, returned as a real-valued M-by-N matrix. The function constructs the Jacobian from the partial derivatives of the measurement vector with respect to the input state. The form of the measurement vector depends on the syntax.

• When you do not specify the measurementParameters argument and set the frame argument to 'rectangular', the function outputs measurement vectors in the format of [x;y;z].

• When you do not specify the measurementParameters argument and set the frame argument to 'spherical', the function outputs measurement vectors in the format of [az;el;r;rr].

• When you specify the measurementParameters argument and set the frame field to 'rectangular', the size of the measurement vector depends on the value of the HasVelocity field in the measurementParameters structure. The measurement vector includes the Cartesian position and velocity coordinates of the tracked object with respect to the ego vehicle coordinate system.

  Rectangular Measurements

  HasVelocity = 'false'	[x;y;z]
  HasVelocity = 'true'	[x;y;z;vx;vy;vz]

  Position units are in meters and velocity units are in m/s.

• When you specify the measurementParameters argument and set the frame field to 'spherical', the size of the measurement vector depends on the value of the HasVelocity, HasRange, and HasElevation fields in the measurementParameters structure. The measurement vector includes the azimuth angle, az, elevation angle, el, range, r, and range rate, rr, of the object with respect to the local ego vehicle coordinate system. Positive values for range rate indicate that an object is moving away from the sensor.

  Spherical Measurements

  	HasRange = 'true'		HasRange = 'false'
  	HasElevation = 'false'	HasElevation = 'true'	HasElevation = 'false'	HasElevation = 'true'
  HasVelocity = 'false'	[az;r]	[az;el;r]	[az]	[az;el]
  HasVelocity = 'true'	[az;r;rr]	[az;el;r;rr]	[az]	[az;el]

  Angle units are in degrees, range units are in meters, and range rate units are in m/s.

More About

Azimuth and Elevation Angle Definitions

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 when 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™.

Version History

Introduced in R2017a