cameas

Measurement function for constant-acceleration motion model

Syntax

measurement = cameas(state)

measurement = cameas(state,frame)

measurement = cameas(state,frame,sensorpos)

measurement = cameas(state,frame,sensorpos,sensorvel)

measurement = cameas(state,frame,sensorpos,sensorvel,laxes)

measurement = cameas(state,measurementParameters)

[measurement,bounds] = cameas(___)

Description

measurement = cameas(state) returns the expected measurement for a state based on the constant-acceleration motion model. You can also use it as a measurement function in a Kalman filter. The state argument specifies the current state.

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

measurement = cameas(state,frame,sensorpos) also specifies the sensor position, sensorpos.

measurement = cameas(state,frame,sensorpos,sensorvel) also specifies the sensor velocity, sensorvel.

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

measurement = cameas(state,measurementParameters) specifies the measurement parameters, measurementParameters.

[measurement,bounds] = cameas(___) returns the measurement bounds, used by a tracking filter (trackingEKF or trackingUKF) in residual calculations. See the HasMeasurementWrapping of the filter object for more details.

Examples

Create Measurement from Accelerating Object in Rectangular Frame

Define the state of an object in 2-D constant-acceleration motion. The state is the position, velocity, and acceleration in both dimensions. The measurements are in rectangular coordinates.

state = [1,10,3,2,20,0.5].';
measurement = cameas(state)

measurement = 3×1

     1
     2
     0

The measurement is returned in three-dimensions with the z-component set to zero.

Create Measurement from Accelerating Object in Spherical Frame

Define the state of an object in 2-D constant-acceleration motion. The state is the position, velocity, and acceleration in both dimensions. The measurements are in spherical coordinates.

state = [1,10,3,2,20,5].';
measurement = cameas(state,'spherical')

measurement = 4×1

   63.4349
         0
    2.2361
   22.3607

The elevation of the measurement is zero and the range rate is positive. These results indicate that the object is moving away from the sensor.

Create Measurement from Accelerating Object in Translated Spherical Frame

Define the state of an object moving in 2-D constant-acceleration motion. The state consists of position, velocity, and acceleration in each dimension. The measurements are in spherical coordinates with respect to a frame located at (20;40;0) meters from the origin.

state = [1,10,3,2,20,5].';
measurement = cameas(state,'spherical',[20;40;0])

measurement = 4×1

 -116.5651
         0
   42.4853
  -22.3607

The elevation of the measurement is zero and the range rate is negative indicating that the object is moving toward the sensor.

Create Measurement from Constant-Accelerating Object Using Measurement Parameters

Define the state of an object moving in 2-D constant-acceleration motion. The state consists of position, velocity, and acceleration in each dimension. The measurements are in spherical coordinates with respect to a frame located at (20;40;0) meters from the origin.

state2d = [1,10,3,2,20,5].';

The elevation of the measurement is zero and the range rate is negative indicating that the object is moving toward the sensor.

frame = 'spherical';
sensorpos = [20;40;0];
sensorvel = [0;5;0];
laxes = eye(3);
measurement = cameas(state2d,'spherical',sensorpos,sensorvel,laxes)

measurement = 4×1

 -116.5651
         0
   42.4853
  -17.8885

The elevation of the measurement is zero and the range rate is negative. These results indicate that the object is moving toward the sensor.

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

measparm = struct('Frame',frame,'OriginPosition',sensorpos,'OriginVelocity',sensorvel, ...
    'Orientation',laxes);
measurement = cameas(state2d,measparm)

measurement = 4×1

 -116.5651
         0
   42.4853
  -17.8885

Display Residual Wrapping Bounds for cameas

Specify a 2-D state and specify a measurement structure such that the function outputs azimuth, range, and range-rate measurements.

state = [10 1 0.1 10 1 0.1]'; % [x vx ax y vy ay]'
mp = struct("Frame","Spherical", ...
    "HasAzimuth",true, ...
    "HasElevation",false, ...
    "HasRange",true, ...
    "HasVelocity",false);

Output the measurement and wrapping bounds using the cameas function.

[measure,bounds] = cameas(state,mp)

measure = 2×1

   45.0000
   14.1421

bounds = 2×2

  -180   180
  -Inf   Inf

Input Arguments

state — Current state

real-valued 3D-byN matrix

Current state for constant-acceleration motion, specified as a real-valued 3D-byN matrix. D is the number of spatial degrees of freedom of motion and N is the number states. For each spatial degree of motion, the state vector, as a column of the state matrix, takes the form shown in this table.

Spatial Dimensions	State Vector Structure
1-D	[x;vx;ax]
2-D	[x;vx;ax;y;vy;ay]
3-D	[x;vx;ax;y;vy;ay;z;vz;az]

For example, x represents the x-coordinate, vx represents the velocity in the x-direction, and ax represents the acceleration in the x-direction. If the motion model is in one-dimensional space, the y- and z-axes are assumed to be zero. If the motion model is in two-dimensional space, values along the z-axis are assumed to be zero. Position coordinates are in meters. Velocity coordinates are in meters/second. Acceleration coordinates are in meters/second².

Example: [5;0.1;0.01;0;-0.2;-0.01;-3;0.05;0]

Data Types: 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. This matrix serves as the rotation matrix that transforms coordinates from the sensor frame to the global 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. By default, the Orientation matrix describes the rotation from the sensor frame to the navigation (global) frame. If you want to specify the rotation matrix that transforms coordinates from the navigation frame to the sensor frame, set the IsParentToChild parameter to true.	[1 0 0; 0 1 0; 0 0 1]
IsParentToChild	Logical scalar indicating if Orientation performs a frame rotation from the parent coordinate frame to the child coordinate frame. By default, the IsParentToChild parameter is set to false, meaning the Orientation performs a frame rotation from the child coordinate frame to the parent coordinate frame.	0
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

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

measurement — Measurement of state

real-valued N-element row vector | real-valued M-by-N matrix

Measurement vector, returned as an N-element real-valued row vector or an M-by-N real-valued matrix. M, the size of each measurement, can vary depending on the syntax. For more information, see the following table. N, the number of measurements, is the same as the number of states. The format 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.

Data Types: double

bounds — Measurement residual wrapping bounds

real-valued two-element row vector | M-by-2 real-valued matrix

Measurement residual wrapping bounds, returned as a two-element real-valued row vector or an M-by-2 real-valued matrix, where M is the size of each measurement. Each row of the matrix corresponds to the lower and upper bounds, respectively, of each measurement in the measurement output.

The function returns different bound values based on the frame input.

• If you specify frame as 'Rectangular', each row of the matrix is [-Inf Inf], indicating that the filter did not wrap the measurement residual.

• If you specify frame as 'Spherical', the function returns bounds for each measurement based on the following:

  • When HasAzimuth = true, the matrix includes a row of [-180 180], indicating that the filter wrapped the azimuth residual in the range of [-180 180] in degrees.

  • When HasElevation = true, the matrix includes a row of [-90 90], indicating that the filter wrapped the elevation residual in the range of [-90 90] in degrees.

  • When HasRange = true, the matrix includes a row of [-Inf Inf], indicating that the filter did not wrap the range residual.

  • When HasVelocity = true, the matrix includes a row of [-Inf Inf], indicating that the filter did not wrap the range rate residual.

If you set any of the fields to false, the returned bounds do not contain the corresponding row. For example, if HasAzimuth = true, HasElevation = false, HasRange = true, HasVelocity = true, then the function returns the bounds as:

  -180   180
  -Inf   Inf
  -Inf   Inf

The filter wraps the measuring residuals based on this equation:

$$x_{wrap}=mod(x-\frac{a-b}{2},b-a)+\frac{a-b}{2}$$

where x is the residual to wrap, a is the lower bound, b is the upper bound, mod is the remainder after division, and x_wrap is the wrapped residual.

Data Types: single | double

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