# From Target Tracking to Targeting Track -- Part III: Stochastic Process Modeling and Online Learning

arXiv: https://arxiv.org/abs/2503.05799 · HTML: https://mlsanity.com/paper/2503.05799/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 89 references that are in the map.
- First posted on arXiv 3 Mar 2025.

## Builds on (most cited first, 15 of 15)

- [Conditional Neural Processes](https://mlsanity.com/paper/1807.01613/) (2018)
- [When Gaussian Process Meets Big Data: A Review of Scalable GPs](https://mlsanity.com/paper/1807.01065/) (2018)
- [Student-t Processes as Alternatives to Gaussian Processes](https://mlsanity.com/paper/1402.4306/) (2014)
- [Maximum likelihood estimation and uncertainty quantification for Gaussian process approximation of deterministic functions](https://mlsanity.com/paper/2001.10965/) (2020)
- [Continuous-Time State Estimation Methods in Robotics: A Survey](https://mlsanity.com/paper/2411.03951/) (2024)
- [Deep State-Space Gaussian Processes](https://mlsanity.com/paper/2008.04733/) (2020)
- [Batch Nonlinear Continuous-Time Trajectory Estimation as Exactly Sparse Gaussian Process Regression](https://mlsanity.com/paper/1412.0630/) (2014)
- [Joint Smoothing, Tracking, and Forecasting Based on Continuous-Time Target Trajectory Fitting](https://mlsanity.com/paper/1708.02196/) (2017)
- [Upgrading from Gaussian Processes to Student's-T Processes](https://mlsanity.com/paper/1801.06147/) (2018)
- [From Target Tracking to Targeting Track: A Data-Driven Yet Analytical Approach to Joint Target Detection and Tracking](https://mlsanity.com/paper/2104.11122/) (2021)
- [From Target Tracking to Targeting Track -- Part I: A Metric for Spatio-Temporal Trajectory Evaluation](https://mlsanity.com/paper/2502.15842/) (2025)
- [Multi-sensor Suboptimal Fusion Student's t Filter](https://mlsanity.com/paper/2204.11098/) (2022)
- [Gaussian Process Upper Confidence Bounds in Distributed Point Target Tracking over Wireless Sensor Networks](https://mlsanity.com/paper/2409.07652/) (2024)
- [A Third-Order Gaussian Process Trajectory Representation Framework with Closed-Form Kinematics for Continuous-Time Motion Estimation](https://mlsanity.com/paper/2410.22931/) (2024)
- [From Target Tracking to Targeting Track -- Part II: Regularized Polynomial Trajectory Optimization](https://mlsanity.com/paper/2502.16121/) (2025)

## Abstract (arXiv)

This is the third part of a series of studies that model the target trajectory, which describes the target state evolution over continuous time, as a sample path of a stochastic process (SP). By adopting a deterministic-stochastic decomposition framework, we decompose the learning of the trajectory SP into two sequential stages: the first fits the deterministic trend of the trajectory using a curve function of time, while the second estimates the residual stochastic component through parametric learning of either a Gaussian process (GP) or Student's-t process (StP). This leads to a Markov-free data-driven tracking approach that produces the continuous-time trajectory with minimal prior knowledge of the target dynamics. Notably, our approach explicitly models both the temporal correlations of the state sequence and of measurement noises through the SP framework. It does not only take advantage of the smooth trend of the target but also makes use of the long-term temporal correlation of both the data noise and the model fitting error. Simulations in four maneuvering target tracking scenarios have demonstrated its effectiveness and superiority in comparison with existing approaches.