# Generalized optimal sub-pattern assignment metric

arXiv: https://arxiv.org/abs/1601.05585 · HTML: https://mlsanity.com/paper/1601.05585/

## Key facts

- Cited by 33 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jan 2016.

## Built on by (most cited first, 30 of 33)

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- [A time-weighted metric for sets of trajectories to assess multi-object tracking algorithms](https://mlsanity.com/paper/2110.13444/) (2021)
- [Can Deep Learning be Applied to Model-Based Multi-Object Tracking?](https://mlsanity.com/paper/2202.07909/) (2022)
- [Graph GOSPA metric: a metric to measure the discrepancy between graphs of different sizes](https://mlsanity.com/paper/2311.07596/) (2023)
- [Transformer-Based Multi-Object Smoothing with Decoupled Data Association and Smoothing](https://mlsanity.com/paper/2312.17261/) (2023)
- [Double Deep Q Networks for Sensor Management in Space Situational Awareness](https://mlsanity.com/paper/2205.14041/) (2022)
- [Trajectory Poisson multi-Bernoulli mixture filter for traffic monitoring using a drone](https://mlsanity.com/paper/2306.16890/) (2023)
- [TGOSPA Metric Parameters Selection and Evaluation for Visual Multi-object Tracking](https://mlsanity.com/paper/2412.08321/) (2024)
- [From Target Tracking to Targeting Track -- Part I: A Metric for Spatio-Temporal Trajectory Evaluation](https://mlsanity.com/paper/2502.15842/) (2025)
- [Decentralised Variational Inference Frameworks for Multi-object Tracking on Sensor Networks: Additional Notes](https://mlsanity.com/paper/2408.13689/) (2024)
- [Fast computation of the TGOSPA metric for multiple target tracking via unbalanced optimal transport](https://mlsanity.com/paper/2503.09449/) (2025)
- [Cell Multi-Bernoulli (Cell-MB) Sensor Control for Multi-object Search-While-Tracking (SWT)](https://mlsanity.com/paper/2108.11236/) (2021)
- [A comparison between PMBM Bayesian track initiation and labelled RFS adaptive birth](https://mlsanity.com/paper/2207.06156/) (2022)
- [Deep Fusion of Multi-Object Densities Using Transformer](https://mlsanity.com/paper/2209.08857/) (2022)
- [Set-Type Belief Propagation with Applications to Poisson Multi-Bernoulli SLAM](https://mlsanity.com/paper/2305.04797/) (2023)
- [SSP-GNN: Learning to Track via Bilevel Optimization](https://mlsanity.com/paper/2407.04308/) (2024)
- [Gaussian multi-target filtering with target dynamics driven by a stochastic differential equation](https://mlsanity.com/paper/2411.19814/) (2024)
- [Stone Soup Multi-Target Tracking Feature Extraction For Autonomous Search And Track In Deep Reinforcement Learning Environment](https://mlsanity.com/paper/2503.01293/) (2025)
- [Poisson multi-Bernoulli mixture filter for trajectory measurements](https://mlsanity.com/paper/2504.08421/) (2025)
- [Attention-Bayesian Hybrid Approach to Modular Multiple Particle Tracking](https://mlsanity.com/paper/2506.09441/) (2025)
- [A family of graph GOSPA metrics for graphs with different sizes](https://mlsanity.com/paper/2506.17316/) (2025)
- [Distributed Poisson multi-Bernoulli filtering via generalised covariance intersection](https://mlsanity.com/paper/2506.18397/) (2025)
- [Integrated Gaussian Processes for Robust and Adaptive Multi-Object Tracking](https://mlsanity.com/paper/2507.04116/) (2025)
- [GOSPA and T-GOSPA quasi-metrics for evaluation of multi-object tracking algorithms](https://mlsanity.com/paper/2507.13706/) (2025)
- [Model-based Multi-object Visual Tracking: Identification and Standard Model Limitations](https://mlsanity.com/paper/2508.13647/) (2025)
- [Compressed BC-LISTA via Low-Rank Convolutional Decomposition](https://mlsanity.com/paper/2601.23148/) (2026)
- [Context-Aware Sensor Modeling for Asynchronous Multi-Sensor Tracking in Stone Soup](https://mlsanity.com/paper/2603.15137/) (2026)
- [ModTrack: Sensor-Agnostic Multi-View Tracking via Identity-Informed PHD Filtering with Covariance Propagation](https://mlsanity.com/paper/2603.15812/) (2026)

## Abstract (arXiv)

This paper presents the generalized optimal sub-pattern assignment (GOSPA) metric on the space of finite sets of targets. Compared to the well-established optimal sub-pattern assignment (OSPA) metric, GOSPA is unnormalized as a function of the cardinality and it penalizes cardinality errors differently, which enables us to express it as an optimisation over assignments instead of permutations. An important consequence of this is that GOSPA allows us to penalize localization errors for detected targets and the errors due to missed and false targets, as indicated by traditional multiple target tracking (MTT) performance measures, in a sound manner. In addition, we extend the GOSPA metric to the space of random finite sets, which is important to evaluate MTT algorithms via simulations in a rigorous way.