What is Trajectory Generalized Optimal Sub-Pattern Assignment Metric?
Trajectory Generalized Optimal Sub-Pattern Assignment Metric is a mathematical distance between finite sets of trajectories that combines localization, missed-target, false-target, and track-switching costs.
Quick Facts
| Specification | Official Specification |
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How It Works
Optimize assignments across time rather than frame by frame
At each time step, an assignment may pair a true object with one estimate or leave either side unassigned. Localization cost uses a base state distance capped by a cut-off. Missed and false objects receive finite penalties, while changes in assignment across adjacent times receive a switching cost.
The original trajectory-set metric paper formulates the exact distance through a multidimensional assignment and introduces a linear-programming relaxation that is itself a metric and is polynomial-time computable. Exact and relaxed values must not be mixed silently.
The Go example below enumerates complete permutations only for an equal-cardinality two-track case. It demonstrates the localization-versus-switch trade-off, not the complete T-GOSPA algorithm with missed and false trajectories.
Choose parameters from application consequences
The cut-off c sets the point beyond which a localization error is treated no better than leaving objects unmatched. The exponent p controls how strongly large component errors affect aggregation. The switching parameter controls the relative cost of changing which estimate represents a true trajectory.
A full assignment change and a transition between assigned and unassigned states are not necessarily charged identically; the latter can be represented as a half-switch in the original formulation. Parameters have units and policy meaning, so benchmark results are comparable only when the base distance, time interval, c, p, switching penalty, and solver are declared.
Use the decomposition without treating it as universal utility
The visual-tracking parameter study shows that online surveillance, offline scene understanding, and detector evaluation can justify different switch and localization preferences. T-GOSPA is not a universal business score, and changing parameters after seeing results invalidates ranking claims.
For large problems, exact multidimensional assignment can be expensive. LP relaxation or a documented approximation can be appropriate, but report solver tolerance and runtime. Pair T-GOSPA with calibration, latency, memory, first-detection delay, and scenario-specific safety measures when those properties matter.
Key Characteristics
- Measures distance between finite sets of complete trajectories
- Decomposes error into localization, missed, false, and switching costs
- Uses a cut-off, exponent, and application-dependent switch penalty
- Accounts for assignments and assignment changes across time
- Offers exact multidimensional-assignment and LP-relaxed formulations
- Requires the base state distance and evaluation interval to be declared
Common Use Cases
- Comparing Bayesian multi-object trajectory filters
- Evaluating visual trackers through occlusion and identity changes
- Diagnosing whether errors come from detection, localization, or switching
- Selecting tracking algorithms for online or offline workflows
- Running Monte Carlo studies on random finite sets of trajectories
Example
Loading code...Frequently Asked Questions
What errors does T-GOSPA measure?
T-GOSPA combines capped localization error for assigned objects, penalties for missed truth and false estimates, and penalties when trajectory assignments change over time. Its decomposition shows which source contributed to the total distance.
How is T-GOSPA different from frame-level GOSPA?
Frame-level GOSPA evaluates two object sets at one time and has no history of prior assignments. T-GOSPA evaluates sets of trajectories and couples assignments across times, so it can penalize track switches in addition to localization, misses, and false objects.
How should the T-GOSPA switching penalty be chosen?
Choose it from the operational harm of changing track continuity relative to localization and missed or false objects. Offline identity analysis may justify a larger penalty than online surveillance. Declare the value before comparing algorithms and run sensitivity analysis.
Is the LP relaxation the same as exact T-GOSPA?
No. The exact formulation solves a multidimensional assignment problem. The linear-programming relaxation is a polynomial-time lower-bound metric with its own value. Reports must identify which formulation and solver settings produced the result.
Does a lower T-GOSPA prove a tracker is production-ready?
No. It indicates a smaller declared trajectory-set error on the evaluated data and parameters. Production decisions also require uncertainty calibration, latency, memory, robustness to model shift, first-detection behavior, and application-specific safety evidence.