[Paper Review] From Target Tracking to Targeting Track: A Data-Driven Yet Analytical Approach to Joint Target Detection and Tracking

Tiancheng Li, Hongqi Fan+1 more|arXiv (Cornell University)|Apr 20, 2021

Target Tracking and Data Fusion in Sensor Networks74 references4 citations

TL;DR

This paper proposes a data-driven yet analytical approach for joint target detection and continuous-time trajectory estimation using a polynomial trajectory function of time (T-FoT), enabling real-time tracking under minimal prior knowledge. It outperforms model-based filters in accuracy and speed, even with unknown dynamics, clutter, and detection probabilities.

ABSTRACT

This paper addresses the problem of real-time detection and tracking of a non-cooperative target in the challenging scenario with almost no a-priori information about target birth, death, dynamics and detection probability. Furthermore, there are false and missing data at an unknown yet low rate in the measurements. The only information given in advance is about the target-measurement model and the constraint that there is no more than one target in the scenario. To solve these challenges, we model the movement of the target by using a polynomial trajectory function of time (T-FoT), which aims to estimate the continuous-time trajectory of the target rather than a series of discrete-time point estimates as is done in most existing filters/trackers. Data-driven T-FoT initiation and termination strategies are proposed for identifying the (re-)appearance and disappearance of the target. During the existence of the target, real target measurements are distinguished from clutter if the target indeed exists and is detected, in order to update the T-FoT at each scan for which we design a least-squares estimator. Overall, our approach is Markov-free, data-driven yet analytical. Simulations using either linear or nonlinear systems are conducted to demonstrate the effectiveness of our approach in comparison with the Bayes optimal Bernoulli filters. The results show that our approach is comparable to the perfectly modeled filters, even outperforms them in some cases while requiring much less a-priori information and computing much faster.

Motivation & Objective

• Address real-time target detection and tracking in scenarios with minimal a-priori information about target dynamics, birth/death, and detection probability.
• Overcome limitations of traditional Markovian state-space models that require precise noise and dynamics modeling, especially for non-cooperative targets.
• Develop a continuous-time trajectory estimation method that enables inference of position, velocity, and acceleration directly from fitted curves.
• Design data-driven initiation and termination strategies for target appearance and disappearance without relying on probabilistic Markov models.
• Achieve high accuracy and computational efficiency comparable to or exceeding model-based filters, even when those filters have perfect model knowledge.

Proposed method

• Model target motion using a polynomial trajectory function of time (T-FoT), representing continuous-time trajectories instead of discrete state estimates.
• Use a least-squares estimator to update the T-FoT at each scan, distinguishing real measurements from clutter based on trajectory consistency.
• Implement data-driven T-FoT initiation and termination strategies to detect target appearance and disappearance without prior knowledge of birth/death events.
• Apply a probabilistic distance bound using Chebyshev-type inequalities to assess measurement consistency and reduce false alarms.
• Avoid Markovian assumptions by eliminating state transition noise and relying on deterministic trajectory fitting, enhancing robustness to maneuvering.
• Leverage the trajectory’s smoothness and continuity to infer motion features such as velocity and acceleration from derivatives of the fitted polynomial.

Experimental results

Research questions

• RQ1 Can a data-driven approach achieve comparable or better performance than model-based filters when minimal prior knowledge about target dynamics and detection is available?
• RQ2 How can target initiation and termination be effectively modeled without relying on Markovian state transitions or probabilistic birth/death models?
• RQ3 To what extent can continuous-time trajectory fitting via T-FoT outperform discrete-time state estimation in terms of accuracy and computational efficiency?
• RQ4 How does the method handle unknown clutter rates and detection probabilities while maintaining low false alarm rates?
• RQ5 Can trajectory fitting with least-squares estimation provide robustness to target maneuvering and unknown inputs without requiring noise statistics?

Key findings

• The proposed T-FoT approach achieves performance comparable to the Bayes optimal Bernoulli filter, even when the latter has full model knowledge.
• In some simulation scenarios, the T-FoT method outperforms the perfectly modeled Bernoulli filter, particularly in terms of robustness to model mismatch.
• The method computes significantly faster than traditional filters due to its Markov-free, analytical structure, avoiding recursive Bayesian updates.
• The data-driven T-FoT initiation and termination strategies successfully detect target appearance and disappearance without prior knowledge of target birth or death events.
• The least-squares estimator effectively distinguishes real measurements from clutter, maintaining low false alarm rates even under unknown clutter distributions.
• The approach enables direct inference of motion features such as velocity and acceleration from the trajectory’s derivatives, offering richer insight than discrete point estimates.