cvmeasmscjac

Jacobian of measurement using constant velocity (CV) model in MSC frame

Syntax

measurementJac = cvmeasmscjac(state)

measurementJac = cvmeasmscjac(state,frame)

measurementJac = cvmeasmscjac(state,frame,laxes)

measurementJac = cvmeasmscjac(state,measurementParameters)

Description

measurementJac = cvmeasmscjac(state) calculates the Jacobian with respect to angular measurement (azimuth and elevation) of the state in the sensor frame. The motion can be either in 2-D or 3-D space. If motion model is in 2-D space, values corresponding to elevation are assumed to be zero.

The trackingEKF and trackingMSCEKF filters require a definition of the MeasurementJacobianFcn property. The cvmeasmscjac function can be used as the MeasurementJacobianFcn. To use this MeasurementFcn with trackerGNN and trackerTOMHT, you can use the trackingMSCEKF filter.

measurementJac = cvmeasmscjac(state,frame) provides the Jacobian measurement in the frame specified. The allowed values for frame are 'rectangular' and 'spherical'.

measurementJac = cvmeasmscjac(state,frame,laxes) specifies the axes of the sensor's coordinate system. The laxes input is a 3-by-3 matrix with each column specifying the direction of local x, y, and z axes in the sensor coordinate system. The default for laxes is [1 0 0;0 1 0;0 0 1].

measurementJac = cvmeasmscjac(state,measurementParameters) specifies the measurement parameters as a struct.

Examples

Obtain Jacobian of State Measurements in MSC Frame

Using the cvmeasmscjac function, you can obtain the jacobian of the state measurements in the spherical and the rectangular frames.

Spherical Frame

Obtain the Jacobian of the azimuth and elevation measurements from an MSC state.

mscState = [0.5;0;0.3;0;1e-3;1e-2];
cvmeasmscjac(mscState)

ans = 2×6

   57.2958         0         0         0         0         0
         0         0   57.2958         0         0         0

Rectangular Frame

Obtain the Jacobian of the position measurement from an MSC state. Specify the frame as a second input.

cvmeasmscjac(mscState,'rectangular')

ans = 3×6
105 ×

   -0.0046         0   -0.0026         0   -8.3839         0
    0.0084         0   -0.0014         0   -4.5801         0
         0         0    0.0096         0   -2.9552         0

Alternatively, you can specify the frame using measurementParameters.

cvmeasmscjac(mscState,struct('Frame','rectangular'))

ans = 3×6
105 ×

   -0.0046         0   -0.0026         0   -8.3839         0
    0.0084         0   -0.0014         0   -4.5801         0
         0         0    0.0096         0   -2.9552         0

Input Arguments

state — Relative state

vector

State that is defined relative to an observer in modified spherical coordinates, as a vector. For example, if there is a target state, xT, and an observer state, xO, the state used by the function is xT - xO.

The 2-D version of modified spherical coordinates (MSC) is also referred to as the modified polar coordinates (MPC). In the case of:

• 2-D space –– State equals [az azRate 1/r vr/r].

• 3-D space –– State equals [az omega el elRate 1/r vr/r].

The variables used in the convention are:

• az –– Azimuth angle (rad)

• el –– Elevation angle (rad)

• azRate –– Azimuth rate (rad/s)

• elRate –– Elevation rate (rad/s)

• omega –– azRate × cos(el) (rad/s)

• 1/r –– 1/range (1/m)

• vr/r –– range-rate/range or inverse time-to-go (1/s)

If the motion model is in 2-D space, values corresponding to elevation are assumed to be zero if elevation is requested as an output.

Data Types: single | double

frame — Measurement frame

'spherical' (default) | 'rectangular'

Measurement frame, specified as 'spherical' or 'rectangular'. If using the 'rectangular' frame, the three rows present in measurementJac represent the Jacobian of the measurements with respect to x, y, and z position of the target in the sensor's Cartesian frame. If using the 'spherical' frame, the two rows present in measurementJac represent the Jacobian of the azimuth and elevation measurements of the target. If not specified, the function provides the Jacobian of the measurements in the 'spherical' frame.

laxes — Direction of local axes

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

Direction of local x, y, and z axes in the scenario, specified as a 3-by-3 matrix. Each column of the matrix specifies the direction of the local x, y, and z axes in the sensor coordinate system. If not specified, the laxes is equal to [1 0 0;0 1 0;0 0 1].

Data Types: 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 example.

Data Types: struct

Output Arguments

measurementJac — Measurement from MSC state

matrix

Target measurement in MSC frame, returned as a:

• One-row matrix –– When HasElevation is set to false.

• Two-row matrix –– When the frame is set to 'spherical', the function measures the azimuth and elevation measurements from a MSC state.

• Three-row matrix –– When the frame is set to 'rectangular', the function measures the position measurement from a MSC state.

Extended Capabilities

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

Version History

Introduced in R2018b