ctmeas

measurement = ctmeas(state) returns the measurement for a constant turn-rate Kalman filter motion model in rectangular coordinates. The state argument specifies the current state of the filter.

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

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

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

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

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

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

Examples

Create Measurement from Constant Turn-Rate Motion in Rectangular Frame

Create a measurement from an object undergoing constant turn-rate motion. The state is the position and velocity in each dimension and the turn-rate. The measurements are in rectangular coordinates.

state = [1;10;2;20;5];
measurement = ctmeas(state)

measurement = 3×1

     1
     2
     0

The z-component of the measurement is zero.

Create Measurement from 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. The measurements are in spherical coordinates.

state = [1;10;2;20;5];
measurement = ctmeas(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 indicating that the object is moving away from the sensor.

Create Measurement from Constant Turn-Rate Motion in Translated Spherical Frame

Define the state of an object moving in 2-D constant turn-rate motion. The state consists of position and velocity, and the turn rate. The measurements are in spherical coordinates with respect to a frame located at [20;40;0].

state = [1;10;2;20;5];
measurement = ctmeas(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 Turn-Rate Motion using Measurement Parameters

state2d = [1;10;2;20;5];
frame = 'spherical';
sensorpos = [20;40;0];
sensorvel = [0;5;0];
laxes = eye(3);
measurement = ctmeas(state2d,frame,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 indicating 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 = ctmeas(state2d,measparm)

measurement = 4×1

 -116.5651
         0
   42.4853
  -17.8885

Display Residual Wrapping Bounds for `ctmeas`

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

state = [10 1 10 1 0.5]'; % [x vx y vy omega]'
mp = struct("Frame","Spherical", ...
    "HasAzimuth",true, ...
    "HasElevation",false, ...
    "HasRange",true, ...
    "HasVelocity",false);

Output the measurement and wrapping bounds using the ctmeas function.

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

measure = 2×1

   45.0000
   14.1421

bounds = 2×2

  -180   180
  -Inf   Inf

Input Arguments

`state` — State vector
real-valued 5-element vector | real-valued 7-element vector | 5-by-N real-valued matrix | 7-by-N real-valued matrix

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

`frame` — Measurement output frame
`'rectangular'` (default) | `'spherical'`

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

Data Types: char

`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: 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: double

`laxes` — Local sensor coordinate axes
`[1,0,0;0,1,0;0,0,1]` (default) | 3-by-3 orthogonal matrix

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 navigation frame. That is, the matrix is the rotation matrix from the global frame to the sensor frame.

Data Types: double

`measurementParameters` — Measurement parameters
structure | array of structure

Measurement parameters, specified as a structure or an array of structures. The fields of the structure are:

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 variable-size variables such as a character vector.	`'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 only want to perform one coordinate transformation, such as a transformation from the body frame to the sensor frame, you only need to specify a measurement parameter structure. If you want to perform multiple coordinate transformations, you need to specify an array of measurement parameter structures. To learn how to perform multiple transformations, see the Convert Detections to objectDetection Format example.

Data Types: struct

Output Arguments

`measurement` — Measurement vector
real-valued M-by-N matrix

Measurement vector, returned as an M-by-N matrix. M is the dimension of the measurement and N, the number of measurement, is the same as the number of states. The form of each measurement depends upon which syntax you use.

When the syntax does not use the measurementParameters argument, the measurement vector is [x,y,z] when the frame input argument is set to 'rectangular' and [az;el;r;rr] when the frame is set to 'spherical'.

When the syntax uses the measurementParameters argument, the size of the measurement vector depends on the values of the frame, HasVelocity, and HasElevation fields in the measurementParameters structure.

frame measurement

'spherical'

Specifies 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

		HasElevation
		false	true
HasVelocity	false	`[az;r]`	`[az;el;r]`
HasVelocity	true	`[az;r;rr]`	`[az;el;r;rr]`

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

'rectangular'

Specifies the Cartesian position and velocity coordinates of the tracked object with respect to the ego vehicle coordinate system.

Rectangular measurements

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

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

Data Types: double

`bounds` — Measurement residual wrapping bounds
M-by-2 real-valued matrix

Measurement residual wrapping bounds, returned as an M-by-2 real-valued matrix, where M is the dimension of the measurement. Each row of the matrix corresponds to the lower and upper bounds for the specific dimension in the measurement output.

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

If the frame input is specified as 'Rectangular', each row of the matrix is [-Inf Inf], indicating the filter does not wrap the measurement residual in the filter.

If the frame input is specified as 'Spherical', the returned bounds contains the bounds for specific measurement dimension based on the following:
- When HasAzimuth = true, the matrix includes a row of [-180 180], indicating the filter wraps the azimuth residual in the range of [-180 180] in degrees.
- When HasElevation = true, the matrix includes a row of [-90 90], indicating the filter wraps the elevation residual in the range of [-90 90] in degrees.
- When HasRange = true, the matrix includes a row of [-Inf Inf], indicating the filter does not wrap the range residual.
- When HasVelocity = true, the matrix includes a row of [-Inf Inf], indicating the filter does not wrap the range rate residual.

If you specify any of the options as false, the returned bounds does not contain the corresponding row. For example, if HasAzimuth = true, HasElevation = false, HasRange = true, HasVelocity = true, then bounds is returned as

  -180   180
  -Inf   Inf
  -Inf   Inf

The filter wraps the measuring residuals based on this equation:

$x_{w r a p} = m o d (x - \frac{a - b}{2}, b - a) + \frac{a - b}{2}$

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

Data Types: single | double

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