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

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Filters for Object Tracking

`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

Initialization

`trackingKF`

`initcvkf`	Create constant-velocity linear Kalman filter from detection report
`initcakf`	Create constant-acceleration linear Kalman filter from detection report
`initvisionbboxkf`	Create constant-velocity linear Kalman filter for 2-D axis-aligned bounding box from detection report (Since R2024a)

`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
`initctrvekf`	Create constant turn-rate and velocity-magnitude extended Kalman filter from detection report (Since R2024b)
`initsingerekf`	Singer acceleration `trackingEKF` initialization (Since R2020b)

`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
`initctrvukf`	Create constant turn-rate and velocity-magnitude unscented Kalman filter from detection report (Since R2024b)

`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
`initcvimm`	IMM initialization with two constant velocity models (Since R2023b)

`trackingGSF`

`initapekf`	Constant velocity angle-parameterized EKF initialization
`initrpekf`	Constant velocity range-parameterized EKF initialization

`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

Motion Models

Constant Velocity Model

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

Constant Acceleration Model

`constacc`	State transition function for constant-acceleration motion model
`constaccjac`	Jacobian of state transition function based on constant-acceleration motion model
`cameas`	Measurement function for constant-acceleration motion model
`cameasjac`	Jacobian of measurement function for constant-acceleration motion model

Singer Acceleration Model

`singer`	State transition function for Singer acceleration motion model (Since R2020b)
`singerjac`	Jacobian of state transition function based on Singer acceleration motion model (Since R2020b)
`singermeas`	Measurement function for Singer acceleration motion model (Since R2020b)
`singermeasjac`	Jacobian of measurement function for Singer acceleration motion model (Since R2020b)
`singerProcessNoise`	Process noise matrix for Singer acceleration model (Since R2020b)

Constant Turn-Rate Model

`constturn`	State transition function for constant turn-rate and velocity-magnitude motion model
`constturnjac`	Jacobian of state transition function based on constant turn-rate and velocity-magnitude motion
`ctmeas`	Measurement function for constant turn-rate and velocity-magnitude motion model
`ctmeasjac`	Jacobian of measurement function for constant turn-rate and velocity- magnitude motion model
`ctrv`	State transition function for constant turn-rate and velocity-magnitude motion model (Since R2024b)
`ctrvjac`	Jacobian of state transition function based on constant turn-rate and velocity-magnitude motion model (Since R2024b)
`ctrvmeas`	Measurement function for constant turn-rate and velocity-magnitude motion model (Since R2024b)
`ctrvmeasjac`	Jacobian of measurement function for constant turn-rate and velocity-magnitude motion model (Since R2024b)

Rectangular Object Model for `gmphd`

`ctrect`	State transition function of constant turn-rate motion model for rectangular targets
`ctrectjac`	Jacobian of state transition function for constant turn-rate motion model for rectangular targets
`ctrectmeas`	Measurement function of constant turn-rate motion model for rectangular targets
`ctrectmeasjac`	Jacobian of measurement function for constant turn-rate motion model for rectangular targets
`ctrectcorners`	Corner measurements of constant turn-rate rectangular target

Switch Motion Model

switchimm Model conversion function for trackingIMM object

Tracking Filter Tuning

`trackingFilterTuner`	Tracking filter tuner (Since R2022b)
`tunableFilterProperties`	Definition of tunable properties of filter (Since R2022b)

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.
Introduction to Out-of-Sequence Measurement Handling
Definition of out-of-sequence measurement and techniques of handling OOSM.
Motion Model, State, and Process Noise
Introduce kinematic motion model, state, and process noise conventions.
Generate Code with Strict Single-Precision and Non-Dynamic Memory Allocation
Introduce functions, objects, and blocks that support strict single-precision and non-dynamic memory allocation code generation in Sensor Fusion and Tracking Toolbox.

Featured Examples

Tracking Maneuvering Targets

Track maneuvering targets using various tracking filters. The example shows the difference between filters that use a single motion model and multiple motion models.

Open Script

Tracking with Range-Only Measurements

Illustrates the use of particle filters and Gaussian-sum filters to track a single object using range-only measurements.

Open Script

Track Objects with Wrapping Azimuth Angles and Ambiguous Range and Range Rate Measurements

Track objects when measurements wrap in angle, range, or range rate.

Since R2022a
Open Live Script

Passive Ranging Using a Single Maneuvering Sensor

Illustrates how to track targets using passive angle-only measurements from a single sensor. Passive angle-only measurements contain azimuth and elevation of a target with respect to the sensor. The absence of range measurements makes the problem challenging as the targets to be tracked are fully observable only under certain conditions.

Open Script

Handle Out-of-Sequence Measurements with Filter Retrodiction

Handle out-of-sequence measurements using the retrodiction technique at the filter level.

Since R2021b
Open Live Script

Smooth Trajectory Estimation of trackingIMM Filter

Smooth state estimates of a target using the smooth object function. Smoothing is a technique to refine previous state estimates using the up-to-date measurements and the state estimate information. In this example, you will learn how to improve previously corrected estimates from an Interacting Multi-Model (IMM) filter by running a backward recursion, which produces smoothed and more accurate state estimates. In the first section, you implement a smooth algorithm to smooth the trajectory of a turning car. In the remainder of this example, you perform smoothing on several highly maneuvering aircraft trajectories, taken from the Benchmark Trajectories for Multi-Object Tracking example.