# cvmeasmscjac

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

## Syntax

``jacobian = cvmeasmscjac(state)``
``jacobian = cvmeasmscjac(state,frame)``
``jacobian = cvmeasmscjac(state,frame,laxes)``
``jacobian = cvmeasmscjac(state,measurementParameters)``

## Description

````jacobian = 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.```

example

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

example

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

## Examples

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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

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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`

Measurement frame, specified as `'spherical'` or `'rectangular'`. If using the `'rectangular'` frame, the three rows present in `jacobian` 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 `jacobian` 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.

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`

Measurement parameters, specified as a struct. The structure must have the following fields (or a subset of them):

• `Frame` –– Either `'rectangular'` or `'spherical'`. Default: `'spherical'`.

• `Orientation` –– A 3-by-3 `laxes` matrix.

• `HasElevation` –– A logical scalar, `true` if elevation is measured. Default: `true` if `state` is in 3-D space, `false` if `state` is in 2-D space.

• `IsParentToChild` –– A logical scalar, `true` if the orientation is given as a parent to child frame rotation.

Data Types: `struct`

## Output Arguments

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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

### Functions

Introduced in R2018b