Generalized Optimal Subpattern Assignment Metric

Calculate Generalized Optimal Subpattern Assignment Metric

Since R2021a

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Libraries:
Sensor Fusion and Tracking Toolbox / Track Metrics

Description

The Generalized Optimal Subpattern Assignment Metric block evaluates the performance of a tracking algorithm by computing the generalized optimal subpattern assignment (GOSPA) metric between tracks and known truths. The metric is comprised of the switching error, localization error, missed target error, and false track error components. You can also select each individual error components as a block output.

Examples

Track-Level Fusion of Radar and Lidar Data in Simulink

Autonomous systems require precise estimation of their surroundings to support decision making, planning, and control. High-resolution sensors such as radar and lidar are frequently used in autonomous systems to assist in estimation of the surroundings. These sensors generally output tracks. Outputting tracks instead of detections and fusing the tracks together in a decentralized manner provide several benefits, including low false alarm rates, higher target estimation accuracy, a low bandwidth requirement, and low computational costs. This example shows you how to track objects from measurements of a radar and a lidar sensor and how to fuse them using a track-level fusion scheme in Simulink®. You process the radar measurements using a Gaussian Mixture Probability Hypothesis Density (GM-PHD) tracker and the lidar measurements using a Joint Probabilistic Data Association (JPDA) tracker. You further fuse these tracks using a track-level fusion scheme. The example closely follows the Track-Level Fusion of Radar and Lidar Data MATLAB® example.

• Since R2021a
• Open Model

Track Point Targets in Dense Clutter Using GM-PHD Tracker in Simulink

Radars generally receive echoes from all surfaces in the signal path. These unwanted back-scattered signals or echoes generated from physical objects are called clutter. In a densely cluttered environment, missed detections and false alarms make tracking objects a challenging task for conventional trackers such as Global Nearest-Neighbor (GNN) tracker. In such an environment a PHD tracker provides better estimation of objects as it can handle multiple detections per object per sensor without clustering them first. This example shows you how to track points targets in dense clutter using a Gaussian mixture probability hypothesis density (GM-PHD) tracker with a constant velocity model in Simulink. The example closely follows the Track Point Targets in Dense Clutter Using GM-PHD Tracker MATLAB® example.

• Since R2021a
• Open Model

Ports

Input

Tracks — Track list

Simulink^® bus containing MATLAB^® structure

Track list, specified as a Simulink bus containing a MATLAB structure.

If you specify the Track bus parameter on the Port Setting tab to objectTrack, the structure must use this form:

Field	Description
NumTracks	Number of tracks
Tracks	Array of track structures

Each track structure must contain TrackID and State fields. Additionally, if you specify an NEES-based distance (posnees or velnees) in the Distance type parameter, each structure must contain a StateCovariance field.

Field	Definition
TrackID	Unique track identifier used to distinguish multiple tracks, specified as a nonnegative integer.
State	Value of state vector at the update time, specified as an N-element vector, where N is the dimension of the state.
StateCovariance	Uncertainty covariance matrix, specified as an N-by-N matrix, where N is the dimension of the state.

If you specify an NEES-based distance (posnees or velnees) in the Distance type parameter, then the structure must contain a StateCovariance field.

If you specify the Track bus parameter to custom, then you can use your own track bus format. In this case, you must define a track extractor function using the Track extractor function parameter. The function must use this syntax:

tracks = trackExtractorFcn(trackInputFromBus)

where trackInputFromBus is the input from the track bus and tracks must return as an array of structures with TrackID and State fields.

Truths — Truth list

Simulink bus containing MATLAB structure

Truth list, specified as a Simulink bus containing a MATLAB structure.

If you specify the Truth bus parameter on the Port Setting tab to Platform, the structure must use this form:

Field	Description
NumPlatforms	Number of truth platforms
Platforms	Array of truth platform structures

Each platform structure has these fields:

Field	Definition
PlatformID	Unique identifier used to distinguish platforms, specified as a nonnegative integer.
Position	Position of the platform, specified as an M-element vector, where M is the dimension of the position state. For example, M = 3 for 3-D position.
Velocity	Velocity of the platform, specified as an M-element vector, where M is the dimension of the velocity state. For example, M = 3 for 3-D velocity.

If you specify the Truth bus parameter as Actor, the structure must use this form:

Field	Description
NumActors	Number of truth actors
Actors	Array of truth actor structures

Each actor structure has these fields:

Field	Definition
ActorID	Unique identifier used to distinguish actors, specified as a nonnegative integer.
Position	Position of the actor, specified as an M-element vector, where M is the dimension of the position state. For example, M = 3 for 3-D position.
Velocity	Velocity of the actor, specified as an M-element vector, where M is the dimension of the velocity state. For example, M = 3 for 3-D velocity.

If you specify the Truth bus parameter to custom, then you can define your own truth bus format. In this case, you must define a truth extractor function using the Truth extractor function parameter. The function must use this syntax:

 truths = truthExtractorFcn(truthInputFromBus)

where truthInputFromBus is the input from the truth bus and truths must return as an array of structures with PlatformID, Position, and Velocity fields.

Assignments — Known assignment

K-by-2 matrix of nonnegative integers

Known assignment, specified as an K-by-2 matrix of nonnegative integers. K is the number of assignment pairs. The first column elements are track IDs, and the second column elements are truth IDs. The IDs in the same row are assigned to each other. If a track or truth is not assigned, specify 0 as the same row element.

The assignment must be a unique assignment between tracks and truths. Redundant or false tracks should be treated as unassigned tracks by assigning them to the "0" TruthID.

Dependencies

To enable this port, on the Port Setting tab, select Assignments.

Output

GOSPA Metric — GOSPA metric including switching error component

nonnegative real scalar

GOSPA metric including switching error component, returned as a nonnegative real scalar.

GOSPA Metric Without Switching — GOSPA metric without switching error component

nonnegative real scalar

GOSPA metric without switching error component, returned as a nonnegative real scalar.

Example: 8.5

Dependencies

To enable this port, on the Port Setting tab, select GOSPA metric without switching error component.

Switching Error — Switching error component

nonnegative real scalar

Switching error component, returned as a nonnegative real scalar.

Example: 8.5

Dependencies

To enable this port, on the Port Setting tab, select Switching error.

Localization Error — Localization error component

nonnegative real scalar

Localization error component, returned as a nonnegative real scalar.

Example: 8.5

Dependencies

To enable this port, on the Port Setting tab, select Localization error.

Missed Target Error — Missed target error component

nonnegative real scalar

Missed target error component, returned as a nonnegative real scalar.

Example: 8.5

Dependencies

To enable this port, on the Port Setting tab, select Missed target error.

False Track Error — False track error component

nonnegative real scalar

False track error component, returned as a nonnegative real scalar.

Example: 8.5

Dependencies

To enable this port, on the Port Setting tab, select False track error.

Parameters

Properties

Cutoff distance — Threshold for cutoff distance between track and truth

30 (default) | real positive scalar

Threshold for cutoff distance between track and truth, specified as a real positive scalar. If the computed distance between a track and the assigned truth is higher than the threshold, the actual distance incorporated in the metric is reduced to the threshold.

Example: 40

Order — Order of GOSPA metric

2 (default) | positive integer

Order of GOSPA metric, specified as a positive integer.

Example: 10

Alpha — Alpha parameter of GOSPA metric

2 (default) | positive scalar in range [0, 2]

Alpha parameter of the GOSPA metric, specified as a positive scalar in the range [0, 2].

Example: 1

Distance type — Distance type

posnees (default) | velnees | posabserr | velabserr | custom

Distance type, specified as posnees, velnees, posabserr, or velabserr. The distance type specifies the physical quantity used for distance calculations:

• posnees – Normalized estimation error squared (NEES) of track position

• velnees – NEES error of track velocity

• posabserr – Absolute error of track position

• velabserr – Absolute error of track velocity

• custom – Custom distance error

If you specify it as custom, you must also specify the distance function in the Custom distance function parameter.

Custom distance function — Custom distance function

function handle

Custom distance function, specified as a function handle. The function must support the following syntax:

d = myCustomFcn(Track,Truth)

where Track is a structure for track information, Truth is a structure of truth information, and d is the distance between the truth and the track. See objectTrack for an example on how to organize track information.

Example: @myCustomFcn

Dependencies

To enable this property, set the Distance type parameter to custom.

Motion model — Desired platform motion model

constvel (default) | constacc | constturn | singer

Desired platform motion model, specified as constvel, constacc, constturn, or singer. This property selects the motion model used by the Tracks input port.

The motion models expect the State field of the track structure to have a column vector containing these values:

• constvel — Position is in elements [1 3 5], and velocity is in elements [2 4 6].

• constacc — Position is in elements [1 4 7], velocity is in elements [2 5 8], and acceleration is in elements [3 6 9].

• constturn — Position is in elements [1 3 6], velocity is in elements [2 4 7], and yaw rate is in element 5.

• singer — Position is in elements [1 4 7], velocity is in elements [2 5 8], and acceleration is in elements [3 6 9].

The StateCovariance field of the track structure input must have position, velocity, and turn-rate covariances in the rows and columns corresponding to the position, velocity, and turn-rate of the State field of the track structure.

Switching penalty — Penalty for assignment switching

0 (default) | nonnegative real scalar

Penalty for assignment switching, specified as a nonnegative real scalar.

Example: 2

Simulate using — Type of simulation to run

Interpreted execution (default) | Code Generation

Select a simulation type from these options:

• Interpreted execution — Simulate the model using the MATLAB interpreter. This option shortens startup time. In Interpreted execution mode, you can debug the source code of the block.

• Code generation — Simulate the model using generated C code. The first time you run a simulation, Simulink generates C code for the block. The C code is reused for subsequent simulations as long as the model does not change. This option requires additional startup time.

Port Setting

Assignments — Enable assignment input

off (default) | on

Select this parameter to enable the input of know assignments through the Assignments input port.

GOSPA metric without switching error — Enable GOSPA metric without switching error output

off (default) | on

Select this parameter to enable the output of the GOSPA metric without the switching error component through the GOSPA Metric Without Switching output port.

Switching error — Enable switching error component output

off (default) | on

Select this parameter to enable the output of the switching error component through the Switching Error output port.

Localization error — Enable localization error component output

off (default) | on

Select this parameter to enable the output of the localization error component through the Localization Error output port.

Missed target error — Enable missed target error component output

off (default) | on

Select this parameter to enable the output of the missed target error component through the Missed Target Error output port.

False track error — Enable false track error component output

off (default) | on

Select this parameter to enable the output of the false track error component through the False Track Error output port.

Track bus — Track bus selection

objectTrack (default) | custom

Track bus selection, specified as objectTrack or custom. See the description of the Tracks input port for more details about each selection.

Truth bus — Truth bus selection

Platform (default) | Actor | custom

Truth bus selection, specified as Platform, Actor, or custom. See the description of the Truths input port for more details about each selection.

Track extractor function — Track extractor function

function handle

Track extractor function, specified as a function handle. The function must support this syntax:

tracks = trackExtractorFcn(trackInputFromBus)

where trackInputFromBus is the input from the track bus and tracks must return as an array of structures with TrackID and State fields. If you specify an NEES-based distance (posnees or velnees) in the Distance type parameter, then the structure must contain a StateCovariance field.

Example: @myCustomFcn

Dependencies

To enable this property, set the Track bus parameter to custom.

Truth extractor function — Truth extractor function

function handle

Truth extractor function, specified as a function handle. The function must support this syntax:

 truths = truthExtractorFcn(truthInputFromBus)

where truthInputFromBus is the input from the track bus and truths must return as an array of structures with PlatformID, Position, and Velocity as field names.

Example: @myCustomFcn

Dependencies

To enable this property, set the Truth bus parameter to custom.

Algorithms

GOSPA Metric

At time t_k, a list of truths is:

$$X=[x_1,x_2,\dots ,x_m]$$

At time t_k, a tracker obtains a list of tracks:

$$Y=[y_1,y_2,\dots ,y_n]$$

In general, the GOSPA metric including the switching component (SGOSPA) is:

$$SGOSPA={\left(GOSP{A}^p+S{C}^p\right)}^{1/p}$$

where p is the order of the metric, SC is the switching component, and GOSPA is the basic GOSPA metric.

Assuming m ≤ n, GOSPA is:

$$GOSPA={\left[{\displaystyle \sum _{i=1}^m{d}_c^p(x_i,y_{\pi (i)})+\frac{c^p}{\alpha }}(n-m)\right]}^{1/p}$$

where d_c is the cutoff-based distance and y_π(i) represents the track assigned to truth x_i. The cutoff-based distance d_c is defined as:

$$d_c(x,y)=\min \left\{d_b(x,y),c\right\}$$

where c is the cutoff distance threshold, and d_b(x,y) is the base distance between track x and truth y calculated by the distance function. The cutoff based distance d_c is the smaller value of d_b and c. α is the alpha parameter.

The switching component SC is:

$$SC=SP\times n_s^{1/p}$$

where SP is the switching penalty and n_s is the number of switches. When a track switches assignment from one truth to another truth, the number of switching is counted as 1. When a track switches from assigned to unassigned or switches from unassigned to assigned, the number of switching is counted as 0.5. For example, as shown in the table, Tracks 1 and 2 both switched to different truths, whereas Track 3 switched from assigned to unassigned. Therefore, the total number of switching is 2.5.

Track Switching Scenario

Previous		Current
Tracks	Truths	Tracks	Truths
1	3	1	7
2	5	2	3
3	7	3	0

When α = 2, the GOSPA metric can reduce to three components:

$$GOSPA={\left[lo{c}^p+mis{s}^p+fals{e}^p\right]}^{1/p}$$

The localization component (loc) is calculated as:

$$loc={\left[{\displaystyle \sum _{i=1}^h{d}_b^p(x_i,y_{\pi (i)})}\right]}^{1/p}$$

where h is the number of nontrivial assignments. A trivial assignment is when a track is assigned to no truth. The missed target component is calculated as:

$$miss=\frac{c}{2^{1/p}}{(n_{miss})}^{1/p}$$

where n_miss is the number of missed targets. The false track component is calculated as:

$$false=\frac{c}{2^{1/p}}{(n_{false})}^{1/p}$$

where n_false is the number of false tracks.

If m > n, simply exchange m and n in the formulation to obtain the GOSPA metric.

Extended Capabilities

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

Version History

Introduced in R2021a

R2023a: Simulink buses do not show in workspace

As of R2023a, the Simulink buses created by this block no longer show in MATLAB workspace.