# Track-to-truth metrics

class stonesoup.metricgenerator.tracktotruthmetrics.SIAPMetrics(position_measure: Measure, velocity_measure: Measure)[source]

SIAP Metrics

Computes the Single Integrated Air Picture (SIAP) metrics as defined by the Systems Engineering Task Force. The implementation provided here is derived from [1] and focuses on providing the SIAP attribute measures.

The SIAP metrics provided require provision of ground truth information.

In the original paper the calculations are dependent upon $$m$$ which corresponds to the identifying number of the sense capability which is being assessed. This is not used in this implementation, with the assumption being that the fused sensor set is being assessed.

Metrics:
• Continuity (C): Fraction of true objects being tracked. The output is in the range $$0:1$$, with a target score of 1.

• Ambiguity (A): Number of tracks assigned to a true object. The output is unbounded with a range of $$0:\infty$$. The target score is 1.

• Spuriousness (S): Fraction of tracks that are unassigned to a true object. The output is in the range $$0:1$$, with a target score of 0.

• Positional Accuracy (PA): Positional error of associated tracks to their respective truths. The output is a distance measure, range $$0:\infty$$, with a target score of 0.

• Velocity Accuracy (VA): Velocity error of associated tracks to their respective truths. The output is a distance measure, range $$0:\infty$$, with a target score of 0.

• Rate of track number changes (R): SIAP continuity measure. Rate of number of track changes per truth. The output is in the range $$0:\infty$$, with a target score of 0.

• Longest track Segment (LS): SIAP continuity measure. Duration of longest associated track segment per truth. The output is a float (seconds), with a target score equal to the sum of all true object lifetimes.

Reference

[1] Single Integrated Air Picture (SIAP) Metrics Implementation, Votruba et al, 29-10-2001

Parameters
• position_measure (Measure) – Distance measure used in calculating position accuracy scores.

• velocity_measure (Measure) – Distance measure used in calculating velocity accuracy scores.

position_measure: stonesoup.measures.Measure

Distance measure used in calculating position accuracy scores.

velocity_measure: stonesoup.measures.Measure

Distance measure used in calculating velocity accuracy scores.

compute_metric(manager, **kwargs)[source]

Compute metrics:

\begin{split}\begin{alignat*}{3} \textrm{Name} &\quad \textrm{At Time} &&\quad \textrm{TimeRange}\\ C &\quad \frac{JT({t})}{J({t})} &&\quad \frac{\sum_{t_{start}}^{t_{end}}JT({t})} {\sum_{t_{start}}^{t_{end}}J({t})}\\ A &\quad \frac{N{A}({t})}{JT({t})} &&\quad \frac{\sum_{t_{start}}^{t_{end}} N{A}({t})}{\sum_{t_{start}}^{t_{end}}JT({t})}\\ S &\quad \frac{N({t}) - N{A}({t})}{N({t})} &&\quad \frac{\sum_{t_{start}}^{t_{end}} [N({t}) - N{A}({t})]}{\sum_{t_{start}}^{t_{end}}N({t})}\\ PA &\quad \frac{{\sum_{n\in tracks}PA_{n}(t)}}{NA(t)} &&\quad \frac{\sum_{t_{start}}^{t_{end}}{\sum_{n\in tracks}PA_{n}(t)}} {\sum_{t_{start}}^{t_{end}}{NA(t)}}\\ VA &\quad \frac{{\sum_{n\in tracks}VA_{n}(t)}}{NA(t)} &&\quad \frac{\sum_{t_{start}}^{t_{end}}{\sum_{n\in tracks}VA_{n}(t)}} {\sum_{t_{start}}^{t_{end}}{NA(t)}}\\ R &\quad -- &&\quad \frac{\sum_{j\in truths}NU_j-1}{\sum_{j\in truths}TT_j}\\ LS &\quad -- &&\quad \frac{\sum_{j\in truths}T{L}_{j}}{\sum_{j\in truths}T_{j}} \end{alignat*}\end{split}
Parameters

manager (MetricManager) – containing the data to be used to create the metric(s)

Returns

Generated metrics

Return type

list of Metric objects

static num_truths_at_time(manager, timestamp)[source]

$$J(t)$$. Calculate the number of true objects held by manager at timestamp.

Parameters
Returns

Number of true objects held by manager at timestamp

Return type

float

static num_associated_truths_at_time(manager, timestamp)[source]

$$JT(t)$$. Calculate the number of associated true objects held by manager at timestamp.

Parameters
Returns

Number of associated true objects held by manager at timestamp

Return type

float

static num_tracks_at_time(manager, timestamp)[source]

$$N(t)$$. Calculate the number of tracks held by manager at timestamp.

Parameters
Returns

Number of tracks held by manager at timestamp

Return type

float

static num_associated_tracks_at_time(manager, timestamp)[source]

$$NA(t)$$. Calculate the number of associated tracks held by manager at timestamp.

Parameters
Returns

Number of associated tracks held by manager at timestamp.

Return type

float

accuracy_at_time(manager, timestamp, measure)[source]

$$PA(t)$$ or $$VA(t)$$ (dependent on measure). Calculate the kinematic accuracy of track-truth associations held by manager at timestamp.

Parameters
• manager (MetricManager) – Containing the data to be used

• timestamp (datetime.datetime) – Timestamp at which to compute the value

• measure (Measure) – Measure used to calculate ‘distance’ between truths and tracks

Returns

Kinematic accuracy of track-truth associations held by manager at timestamp.

Return type

float

Note

This method adds the ‘distance’ errors for each and every association. An alternative would be to consider each true object and track at most once.

static truth_track_from_association(association)[source]

Find truth and track from an association.

Parameters

association (Association) – Association that contains truth and track as its objects

Returns

True object and track that are the objects of the association

Return type
static total_time_tracked(manager, truth)[source]

$$TT$$. Calculate the total time a truth is tracked for by tracks contained by manager.

Parameters
Returns

Number of seconds that truth is tracked for

Return type

float

static min_num_tracks_needed_to_track(manager, truth)[source]

$$NU_j$$. Calculate the minimum number of tracks needed to track truth using tracks held by manager.

Parameters
Returns

Minimum number of tracks needed to track truth

Return type

int

rate_of_track_number_changes(manager)[source]

$$R$$. Calculate the average rate of track number changes for true objects held by manager.

Parameters

manager (MetricManager) – Containing the data to be used

Returns

Average rate of track number changes

Return type

float

$$T$$. Calculate how long truth exists for.

Parameters

truth (GroundTruthPath) – True object

Returns

Number of seconds that truth exists for

Return type

float

static longest_track_time_on_truth(manager, truth)[source]

$$TL_j$$. Calculate the longest time that a single track is associated to truth using associations held by manager.

Parameters
Returns

Number of seconds of longest association to truth

Return type

float

class stonesoup.metricgenerator.tracktotruthmetrics.IDSIAPMetrics(position_measure: Measure, velocity_measure: Measure, truth_id: str, track_id: str)[source]

ID-based SIAP Metrics

SIAP metric generator that additionally computes ID-based SIAP metrics.

ID-based Metrics:
• ID Completeness (CID): ID-based SIAP. Fraction of true objects with an assigned ID. The output is in the range $$0:1$$, with a target score of 1.

• ID Correctness (IDC): ID-based SIAP. Fraction of true objects with correct ID assignment. The output is in the range $$0:1$$, with a target score of 1.

• ID Ambiguity (IDA): ID-based SIAP. Fraction of true objects with ambiguous ID assignment. The output is in the range $$0:1$$, with a target score of 0.

Notes

• This implementation assumes that track and ground truth path IDs are implemented via metadata, whereby the strings track_id and truth_id are keys to track and truth metadata entries with ID data respectively.

• Track types store metadata outside of their states attribute. Therefore the ID SIAPs make metadata comparisons via the tracks’ last ID metadata values (as calling track.metadata will return a track’s metadata at the end of its life). To provide a better implementation, one might modify Track types to contain a list of state types that hold their own metadata.

Reference

[1] Single Integrated Air Picture (SIAP) Metrics Implementation, Votruba et al, 29-10-2001

Parameters
• position_measure (Measure) – Distance measure used in calculating position accuracy scores.

• velocity_measure (Measure) – Distance measure used in calculating velocity accuracy scores.

• truth_id (str) – Metadata key for ID of each ground truth path in data-set

• track_id (str) – Metadata key for ID of each track in data-set

truth_id: str

Metadata key for ID of each ground truth path in data-set

track_id: str

Metadata key for ID of each track in data-set

compute_metric(manager, **kwargs)[source]

Compute metrics:

\begin{split}\begin{alignat*}{3} \textrm{Name} &\quad \textrm{At Time} &&\quad \textrm{TimeRange}\\ C &\quad \frac{JT({t})}{J({t})} &&\quad \frac{\sum_{t_{start}}^{t_{end}}JT({t})} {\sum_{t_{start}}^{t_{end}}J({t})}\\ A &\quad \frac{N{A}({t})}{JT({t})} &&\quad \frac{\sum_{t_{start}}^{t_{end}} N{A}({t})}{\sum_{t_{start}}^{t_{end}}JT({t})}\\ S &\quad \frac{N({t}) - N{A}({t})}{N({t})} &&\quad \frac{\sum_{t_{start}}^{t_{end}} [N({t}) - N{A}({t})]}{\sum_{t_{start}}^{t_{end}}N({t})}\\ PA &\quad \frac{{\sum_{n\in tracks}PA_{n}(t)}}{NA(t)} &&\quad \frac{\sum_{t_{start}}^{t_{end}}{\sum_{n\in tracks}PA_{n}(t)}} {\sum_{t_{start}}^{t_{end}}{NA(t)}}\\ VA &\quad \frac{{\sum_{n\in tracks}VA_{n}(t)}}{NA(t)} &&\quad \frac{\sum_{t_{start}}^{t_{end}}{\sum_{n\in tracks}VA_{n}(t)}} {\sum_{t_{start}}^{t_{end}}{NA(t)}}\\ R &\quad -- &&\quad \frac{\sum_{j\in truths}NU_j-1}{\sum_{j\in truths}TT_j}\\ LS &\quad -- &&\quad \frac{\sum_{j\in truths}T{L}_{j}}{\sum_{j\in truths}T_{j}}\\ CID &\quad \frac{J{T}({t}) - J{U}({t})}{JT({t})} &&\quad \frac{\sum_{t_{start}}^{t_{end}}[J{T}({t}) - J{U}({T})]} {\sum_{t_{start}}^{t_{end}}J{T}({t})}\\ IDC &\quad \frac{J{C}({t})}{JT({t})} &&\quad \frac{\sum_{t_{start}}^{t_{end}} J{C}({t})}{\sum_{t_{start}}^{t_{end}}J{T}({t})}\\ IDA &\quad \frac{J{A}({t})}{JT({t})} &&\quad \frac{\sum_{t_{start}}^{t_{end}} J{A}({t})}{\sum_{t_{start}}^{t_{end}}J{T}({t})} \end{alignat*}\end{split}
Parameters

manager (MetricManager) – containing the data to be used to create the metric(s)

Returns

Generated metrics

Return type

list of Metric objects

find_track_id(track, timestamp)[source]

Find track ID at timestamp.

Parameters
Returns

track ID at timestamp

Return type

any

num_id_truths_at_time(manager, timestamp)[source]
$$JU$$, $$JC$$, $$JI$$. Calculate the number of true objects that are:

Un-identified, correctly identified, incorrectly identified at timestamp according to associations held by manager.

Parameters
Returns

Number of true objects: Un-identified, correctly identified, incorrectly identified

Return type

Note

• A true object is considered to be un-identified if all tracks associated with it at timestamp have no ID.

• A true object is considered to be correctly identified if all tracks associated with it at timestamp have the same ID as it.

• A true object is considered to be incorrectly identified if all tracks associated with it at timestamp have a different ID to it.

• A true object is considered to have ambiguous identification if tracks associated with it have differing ID (this value is calculated in the compute_metric() method).