Optimal Subpattern Assignment Metric
Libraries:
Sensor Fusion and Tracking Toolbox /
Track Metrics
Description
The Optimal Subpattern Assignment Metric block computes the optimal subpattern assignment metric between a set of tracks and known truths. You can enable different types of OSPA metrics by configuring these parameters:
Traditional OSPA — Specify the Metric parameter as
OSPA
and specify the Labeling error parameter, on the Properties tab, as0
. The traditional OSPA metric, which evaluates instantaneous tracking performance, contains two components:Localization error component — Accounts for state estimation errors between assigned tracks and truths.
Cardinality error component— Accounts for the number of unassigned tracks and truths.
Labeled OSPA — Specify the Metric parameter as
OSPA
and specify the Labeling error parameter, on the Properties tab, as a positive scalar. The labeled OSPA (LOSPA) metric, which evaluates instantaneous tracking performance and includes penalties for incorrect assignments, contains three components:Localization error component — Accounts for state estimation errors between assigned tracks and truths.
Cardinality error component— Accounts for the number of unassigned tracks and truths.
Labelling error component — Accounts for the error of incorrect assignments.
OSPA(2) — Specify the Metric parameter as
OSPA(2)
. The OSPA(2) metric evaluates cumulative tracking performance for a duration of time.
You can output each component individually from the block. For more details on the algorithm, see Algorithm and References.
Examples
Extended Object Tracking of Highway Vehicles with Radar and Camera in Simulink
Track highway vehicles around an ego vehicle in Simulink. In this example, you use multiple extended object tracking techniques to track highway vehicles and evaluate their tracking performance. This example closely follows the Extended Object Tracking of Highway Vehicles with Radar and Camera MATLAB® example.
- Since R2021b
- 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)
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)
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 aK-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 two IDs in a
row are assigned to each other. If a track or truth is not assigned, specify
0
as the other element in the row.
Assignments between tracks and truths must be unique. 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
OSPA Metric — OSPA metric
nonnegative real scalar
OSPA metric, returned as a nonnegative real scalar. Depending on the values of the Metric and Labeling error parameters, the block can output traditional OSPA, labeled OSPA (LOSPA), or OSPA(2).
Metric Parameter Value | Labeling error Parameter Value | Metric |
---|---|---|
OSPA | 0 | OSPA |
OSPA | Positive scalar | LOSPA |
OSPA(2) | Not applicable | OSPA(2) |
Example: 10.1
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.
Cardinality Error — Cardinality error component
nonnegative real scalar
Cardinality error component, returned as a nonnegative real scalar.
Example: 6
Dependencies
To enable this port, on the Port Setting tab, select Cardinality error.
Labeling Error — Labeling error component
nonnegative real scalar
Labeling error component, returned as a nonnegative real scalar.
Example: 7.5
Dependencies
To enable this port, on the Port Setting tab, select Labeling error.
Parameters
Metric — Metric option
OPSA
(default) | OSPA(2)
Metric option, specified as OSPA
or OSPA(2)
.
OSPA
— Computes the traditional OSPA metric by default, or computes the labeled OSPA metric after additionally specifying the Labeling error parameter as a positive value.OSPA(2)
— Computes the OSPA(2) metric, which evaluates cumulative tracking performance. Selecting this option enables these parameters for configuring the metric:Window length
Window sum order (q)
Window weights
Window weight exponent (r)
Custom window weights
Selecting this option also disables two parameters used to evaluate the labeling error component:
Assignments
Labeling error
Cutoff distance — Threshold for cutoff distance between track and truth
30
(default) | real positive scalar
Threshold for the 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 OSPA metric
2
(default) | positive integer
Order of the OSPA metric, specified as a positive integer.
Example:
3
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 positionvelnees
– NEES error of track velocityposabserr
– Absolute error of track positionvelabserr
– Absolute error of track velocitycustom
– Custom distance error
If you select custom
, you must also specify a 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)
Track
is a structure of 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.
Labeling error — Penalty for incorrect assignment
0
(default) | nonnegative scalar
Penalty for incorrect assignment of track to truth, specified as a nonnegative scalar. The function decides if an assignment is correct based on the provided known assignment input from the Assignments input port. If the assignment is not provided as an input, the last known assignment is assumed to be correct.
Example:
5
Dependencies
To enable this parameter, set the Metric parameter to
OSPA
.
Window length — Sliding window length for OSPA(2) metric
100
(default) | positive integer
Sliding window length for the OSPA(2) metric, specified as a positive integer. The window length defines the number of time steps from a previous time to the current time used to evaluate the metric. For more details, see OSPA(2) Metric.
Dependencies
To enable this parameter, set the Metric parameter to
OSPA(2)
.
Data Types: single
| double
Window sum order (q) — Order of weighted sum for track and truth history
2
(default) | positive scalar
Order of weighted sum for the track and truth history, specified as a positive scalar. For more details, see OSPA(2) Metric.
Dependencies
To enable this parameter, set the Metric parameter to
OSPA(2)
.
Data Types: single
| double
Window weights — Options for window weights
auto
(default) | custom
Options for window weights, specified as auto
or
custom
.
auto
— Automatically generates the window weights using the algorithm given in OSPA(2) Metric.custom
— Customizes the window weights using the Custom window weights parameter.
Dependencies
To enable this parameter, set the Metric parameter to
OSPA(2)
.
Data Types: single
| double
Window weight exponent (r) — Exponent for automatic weight calculation
1
(default) | nonnegative scalar
Exponent for automatic weight calculation, specified as a nonnegative scalar. An
exponent value, r, of 0
represents equal weights
in the window. A higher value of r assigns more weights on recent
data. For more details, see OSPA(2) Metric.
Dependencies
To enable this parameter, set the Window weights parameter to
auto
.
Data Types: single
| double
Custom window weights — Custom weights in time window
N-element of vector of nonnegative values
Custom weights in the time window, specified as an N-element of vector of nonnegative values, when N is the window length, specified in the Window length parameter.
Dependencies
To enable this parameter, set the Window weights parameter to
custom
.
Data Types: single
| double
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. InInterpreted 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.
Assignments — Enable assignment input
off
(default) | on
Select this parameter to enable the input of known assignments through the Assignments input port.
Dependencies
To enable this parameter, set the Metric parameter to
OSPA
.
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.
Cardinality error — Enable cardinality error component output
off
(default) | on
Select this parameter to enable the output of the cardinality error component through the Cardinality Error output port.
Labeling error — Enable labeling error component output
off
(default) | on
Select this parameter to enable the output of the labeling error component through the Labeling Error output port.
Dependencies
To enable this parameter, set the Metric parameter to
OSPA
.
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)
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)
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
OSPA Metric
At time tk, a list of truths is:
At the same time, a tracker obtains a list of tracks:
The traditional OSPA metric is:
Assuming m ≤ n, the two components, dloc and dcard are calculated using these equations. The localization error component dloc is computed as:
where p is the order of the OSPA metric, dc is the cutoff-based distance, and yπ(i) represents the track assigned to truth xi. The cutoff-based distance dc is defined as:
where c is the cutoff distance threshold, and db(x,y) is the distance between truth x and track y calculated by the distance function. The cutoff-based distance dc takes the smaller value of db and c.
The cardinality error component dcard is:
The labeled OSPA (LOSPA) is:
Here, additionally, the labeling error component dlab is:
where α is the penalty for incorrect assignment in the
labeling error component,
L(xi)
represents the truth ID of xi,
and
L(yπ(i))
represents the track ID of
yπ(i).
The function γ = 0 if the IDs of the truth and track pair agree with the
known assignment given by the assignment
input, or agree with the
assignment in the last update if the known assignment is not given. Otherwise,
γ = 1.
If m > n, exchange m and n in the formulation to obtain the OSPA metric.
OSPA(2) Metric
Consider a time period of N time steps, from time tk-N+1 to time tk. During this time period, you have a list of m truth histories:
Each truth history xi, is composed of :
where xi(s) is the track history for xi at time step ts, and xi(s)= ∅ if xi does not exist at time ts. For the same time period, you have a list of n track histories:
Each track history yi is composed of :
where yi(s) is the track history at time step ts, and yi(s)= ∅ if yi does not exist at time ts.
Assuming m ≤ n, the OPSA(2) metric is calculated as:
where the cardinality error component dcard is:
In this equation, p is the order of the OSPA metric, and c is the cutoff distance threshold.
The localization error component dloc is computed as:
where yπ(i) represents the track assigned to truth xi, and dq is the base distance between a truth and a track, accounting for cumulative tracking errors.
You can obtain dq between a truth xi and a track yj as:
where N is the window length, w(τ) is the window weight at time step τ, and q is the window sum order. d* is defined as:
From the equation, the cutoff-based distance dc takes the smaller value of db and c, where db(xi(τ),yj(τ) ) is the distance between truth xi and track yj at time τ, calculated by the distance function.
If you do not customize the window weights, the object assigns the window weights as:
where r is the window weight component.
If m > n, exchange m and n in the formulation to obtain the OSPA(2) metric.
References
[1] Schuhmacher, B., B. -T. Vo, and B. -N. Vo. "A Consistent Metric for Performance Evaluation of Multi-Object Filters." IEEE Transactions on Signal Processing, Vol, 56, No, 8, pp. 3447–3457, 2008.
[2] Ristic, B., B. -N. Vo, D. Clark, and B. -T. Vo. "A Metric for Performance Evaluation of Multi-Target Tracking Algorithms." IEEE Transactions on Signal Processing, Vol, 59, No, 7, pp. 3452–3457, 2011.
[3] M. Beard, B. -T. Vo, and B. -N. Vo. “OSPA (2) : Using the OSPA Metric to Evaluate Multi-Target Tracking Performance.” 2017 International Conference on Control, Automation and Information Sciences, IEEE, 2017, pp. 86–91.
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.
Version History
Introduced in R2021aR2023a: Simulink buses do not show in workspace
As of R2023a, the Simulink buses created by this block no longer show in MATLAB workspace.
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