# Estimation Filters

Kalman and particle filters, linearization functions, and motion models

Sensor Fusion and Tracking Toolbox™ provides estimation filters that are optimized for specific scenarios, such as linear or nonlinear motion models, linear or nonlinear measurement models, or incomplete observability.

## Functions

expand all

 `trackingKF` Linear Kalman filter for object tracking `trackingEKF` Extended Kalman filter for object tracking `trackingUKF` Unscented Kalman filter for object tracking `trackingABF` Alpha-beta filter for object tracking `trackingCKF` Cubature Kalman filter for object tracking `trackingIMM` Interacting multiple model (IMM) filter for object tracking `trackingGSF` Gaussian-sum filter for object tracking `trackingPF` Particle filter for object tracking `trackingMSCEKF` Extended Kalman filter for object tracking in modified spherical coordinates (MSC) `ggiwphd` Gamma Gaussian Inverse Wishart (GGIW) PHD filter `gmphd` Gaussian mixture (GM) PHD filter

#### `trackingKF`

 `initcvkf` Create constant-velocity linear Kalman filter from detection report `initcakf` Create constant-acceleration linear Kalman filter from detection report

#### `trackingEKF`

 `initcvekf` Create constant-velocity extended Kalman filter from detection report `initcaekf` Create constant-acceleration extended Kalman filter from detection report `initctekf` Create constant turn-rate extended Kalman filter from detection report `initapekf` Constant velocity angle-parameterized EKF initialization `initrpekf` Constant velocity range-parameterized EKF initialization `initsingerekf` Singer acceleration `trackingEKF` initialization

#### `trackingUKF`

 `initcvukf` Create constant-velocity unscented Kalman filter from detection report `initcaukf` Create constant-acceleration unscented Kalman filter from detection report `initctukf` Create constant turn-rate unscented Kalman filter from detection report

#### `trackingABF`

 `initcvabf` Create constant velocity tracking alpha-beta filter from detection report `initcaabf` Create constant acceleration alpha-beta tracking filter from detection report

#### `trackingCKF`

 `initcvckf` Create constant velocity tracking cubature Kalman filter from detection report `initcackf` Create constant acceleration tracking cubature Kalman filter from detection report `initctckf` Create constant turn rate tracking cubature Kalman filter from detection report

#### `trackingIMM`

 `initekfimm` Initialize `trackingIMM` object

#### `trackingPF`

 `initcvpf` Create constant velocity tracking particle filter from detection report `initcapf` Create constant acceleration tracking particle filter from detection report `initctpf` Create constant turn rate tracking particle filter from detection report

#### `trackingMSCEKF`

 `initcvmscekf` Constant velocity `trackingMSCEKF` initialization

#### `ggiwphd`

 `initcvggiwphd` Create constant velocity `ggiwphd` filter `initcaggiwphd` Create constant acceleration `ggiwphd` filter `initctggiwphd` Create constant turn-rate `ggiwphd` filter

#### `gmphd`

 `initcvgmphd` Create constant velocity `gmphd` filter `initcagmphd` Create constant acceleration `gmphd` filter `initctgmphd` Create constant turn-rate `gmphd` filter `initctrectgmphd` Create constant turn-rate rectangular target `gmphd` filter

#### Constant Velocity Model

 `constvel` Constant velocity state update `constveljac` Jacobian for constant-velocity motion `constvelmsc` Constant velocity (CV) motion model in MSC frame `constvelmscjac` Jacobian of constant velocity (CV) motion model in MSC frame `cvmeas` Measurement function for constant velocity motion `cvmeasjac` Jacobian of measurement function for constant velocity motion `cvmeasmsc` Measurement based on constant velocity (CV) model in MSC frame `cvmeasmscjac` Jacobian of measurement using constant velocity (CV) model in MSC frame

#### Constant Acceleration Model

 `constacc` Constant-acceleration motion model `constaccjac` Jacobian for constant-acceleration motion `cameas` Measurement function for constant-acceleration motion `cameasjac` Jacobian of measurement function for constant-acceleration motion

#### Singer Acceleration Model

 `singer` Singer acceleration motion model `singerjac` Jacobian of Singer acceleration motion model `singermeas` Measurement function for Singer acceleration motion model `singermeasjac` Jacobian of measurement function for Singer acceleration motion model `singerProcessNoise` Process noise matrix for Singer acceleration model

#### Constant Turn-Rate Model

 `constturn` Constant turn-rate motion model `constturnjac` Jacobian for constant turn-rate motion `ctmeas` Measurement function for constant turn-rate motion `ctmeasjac` Jacobian of measurement function for constant turn-rate motion

#### Rectangular Object Model for `gmphd`

 `ctrect` Constant turn-rate rectangular target motion model `ctrectjac` Jacobian of constant turn-rate rectangular target motion model `ctrectmeas` Constant turn-rate rectangular target measurement model `ctrectmeasjac` Jacobian of constant turn-rate rectangular target measurement model `ctrectcorners` Corner measurements of constant turn-rate rectangular target

#### Switch Motion Model

 `switchimm` Model conversion function for `trackingIMM` object

## Topics

Introduction to Estimation Filters

General review of estimation filters provided in the toolbox.

Linear Kalman Filters

Estimate and predict object motion using a Linear Kalman filter.

Extended Kalman Filters

Estimate and predict object motion using an extended Kalman filter.
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