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A Protocol for Real-time 3D Single Particle Tracking
Published on: January 3, 2018
A comparison of error bounds for a nonlinear tracking system with detection probability Pd < 1
Huisi Tong1, Hao Zhang, Huadong Meng
1Department of Electronic Engineering, Tsinghua University, Beijing 100084, China. tonghs08@mails.tsinghua.edu.cn
Sensors (Basel, Switzerland)
|December 18, 2012
Summary
This study compares three nonlinear filtering error bounds for target tracking. The random finite set (RFS) bound is proven tighter than information reduction factor (IRF) and enumeration (ENUM) posterior Cramer-Rao lower bounds (PCRLB), especially with changing target existence.
Area of Science:
- * Probabilistic data association and target tracking.
- * Statistical signal processing and estimation theory.
Background:
- * Error bounds are crucial for evaluating nonlinear filtering performance and sensor management.
- * Existing bounds include Random Finite Set (RFS), Information Reduction Factor (IRF) Posterior Cramer-Rao Lower Bound (PCRLB), and Enumeration (ENUM) PCRLB.
- * Performance analysis is challenging when target detection probability is less than unity.
Purpose of the Study:
- * To comparatively analyze three distinct error bounds for tracking filters under partial observability.
- * To establish theoretical relationships between RFS bound and vector-based PCRLB variants (IRF and ENUM).
- * To investigate the impact of target existence uncertainty on the relative performance of these bounds.
Main Methods:
- * Deduction of two propositions to establish theoretical equivalences and inequalities between bounds.
- * Analysis within the frameworks of finite set statistics (for RFS) and finite vector statistics (for IRF and ENUM PCRLB).
- * Application and simulation in nonlinear tracking scenarios, including ballistic object and bearings-only tracking.
Main Results:
- * The RFS bound is proven equal to the ENUM PCRLB when target existence is constant.
- * The RFS bound is demonstrated to be tighter than the IRF PCRLB under constant target existence.
- * When accounting for target appearance/disappearance, the RFS bound shows improved tightness over both IRF and ENUM PCRLB over time.
Conclusions:
- * The RFS bound offers superior performance and tightness compared to IRF and ENUM PCRLB in scenarios with dynamic target existence.
- * The theoretical findings are validated through simulations in practical nonlinear tracking applications.
- * This study clarifies the relationships among key error bounds, aiding in filter selection and performance assessment for complex tracking problems.
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