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Gamma Gaussian Inverse Wishart (GGIW) PHD filter

The `ggiwphd`

object is a filter that implements the probability
hypothesis density (PHD) using a mixture of Gamma Gaussian Inverse-Wishart components. GGIW
implementation of a PHD filter is typically used to track extended objects. An extended object
can produce multiple detections per sensor, and the GGIW filter uses the random matrix model
to account for the spatial distribution of these detections. The filter consists of three
distributions to represent the state of an extended object.

Gaussian distribution — represents the kinematic state of the extended object.

Gamma distribution — represents the expected number of detections on a sensor from the extended object.

Inverse-Wishart (IW) distribution — represents the spatial extent of the target. In 2-D space, the extent is represented by a 2-by-2 random positive definite matrix, which corresponds to a 2-D ellipse description. In 3-D space, the extent is represented by a 3-by-3 random matrix, which corresponds to a 3-D ellipsoid description. The probability density of these random matrices is given as an Inverse-Wishart distribution.

For details about `ggiwphd`

, see [1] and [2].

`ggiwphd`

object is not compatible with `trackerGNN`

,
`trackerJPDA`

, and `trackerTOMHT`

system objects.

`PHD = ggiwphd`

`PHD = ggiwphd(States,StateCovariances)`

`phd = ggiwphd(States,StateCovariances,Name,Value)`

creates a
`PHD`

= ggiwphd`ggiwphd`

filter with default property values.

allows you to specify the `PHD`

= ggiwphd(States,StateCovariances)`States`

and
`StateCovariances`

of the Gaussian distribution for each component in
the density. `States`

and `StateCovariances`

set the
properties of the same names.

also allows you to set properties for the filter using one or more name-value pairs.
Enclose each property name in quotes.`phd`

= ggiwphd(States,StateCovariances,`Name,Value`

)

`append` | Append two ggiwphd filter objects |

`correct` | Correct ggiwphd filter with detections |

`correctUndetected` | Correct ggiwphd filter with no detection hypothesis |

`extractState` | Extract target state estimates from the ggiwphd filter |

`labeledDensity` | Keep components with a given label ID |

`likelihood` | Log-likelihood of association between detection cells and components in the density |

`merge` | Merge components in the density of ggiwphd filter |

`predict` | Predict probability hypothesis density of ggiwphd filter |

`prune` | Prune the filter by removing selected components |

`scale` | Scale weights of components in the density |

`clone` | Create duplicate ggiwphd filter object |

[1] Granstorm, K., and O. Orguner." A
PHD filter for tracking multiple extended targets using random matrices." * IEEE
Transactions on Signal Processing.* Vol. 60, Number 11, 2012, pp.
5657-5671.

[2] Granstorm, K., and A. Natale, P.
Braca, G. Ludeno, and F. Serafino."Gamma Gaussian inverse Wishart probability hypothesis
density for extended target tracking using X-band marine radar data." * IEEE
Transactions on Geoscience and Remote Sensing.* Vol. 53, Number 12, 2015, pp.
6617-6631.

`partitionDetections`

| `trackerPHD`

| `trackingSensorConfiguration`