Time-of-Arrival and Angle-of-Arrival Measurement-Assisted 3D Inter-Unmanned Aerial Vehicle Relative Localization Under Distance-Dependent Noise Model
Abstract
:1. Introduction
- The CRLB under a distance-dependent noise model for UAV relative pose estimation is derived, providing a theoretical benchmark for the achievable accuracy of TOA-AOA measurements.
- A novel joint TOA-AOA formulation for relative pose estimation is developed, combining distance and angle measurements to enhance localization accuracy in anchor-free environments.
- An efficient SDR estimator is devised to handle the nonlinearity and orthogonality constraints, and its effectiveness is demonstrated through comprehensive simulations under various noise and trajectory conditions.
2. Problem Formulation
System Model
3. SDR Method for Relative Localization
3.1. SDR Method Using TOA Only
Algorithm 1 SDR-TOA. |
Data: range measurement vector , UAV speed vector , UAV initial positions and , noise related parameters and Result: relative pose estimation and 1: Compute and using (17) and (18) respectively; 2: Initialize ; 3: Compute using (26); 4: Construct constraints equations using (25); 5: Solve by optimizing (27); 6: Extract and from ; 7: Compute using (29) and (30); 8: Update using (22); 9: Solve by optimizing (27) with updated ; 10: Repeat 6–7; |
3.2. SDR Method Using TOA and AOA Measurements
Algorithm 2 SDR-TOA-AOA. |
Data: range measurement vector , angular measurement vector , UAV speed vector , UAV initial positions and , noise related parameters and Result: relative pose estimation and 1: Compute and using (35) and (36) respectively; 2: Initialize ; 3: Compute using (39); 4:bConstruct constraints equations using (25); 5: Solve by optimizing (27); 6: Extract and from ; 7: Compute using (29) and (30); 8: Update using (37); 9: Solve by optimizing (41) with updated ; 10: Repeat 6–7; |
4. Performance Analysis
4.1. CRLB Analysis for TOA Measurements Only
4.2. CRLB Analysis for TOA-AOA Measurements
5. Numerical Experiments
5.1. Simulation Configuration
5.2. Performance Comparison of Measurement Noise Variance
5.3. Performance Comparison of TOA and AOA Measurement Noise Ratio
5.4. Performance Comparison of Number of Measurements
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Tang, J.; Chang, T.; Jiang, Q.; Ding, X.; Liu, D. Time-of-Arrival and Angle-of-Arrival Measurement-Assisted 3D Inter-Unmanned Aerial Vehicle Relative Localization Under Distance-Dependent Noise Model. Electronics 2025, 14, 90. https://doi.org/10.3390/electronics14010090
Tang J, Chang T, Jiang Q, Ding X, Liu D. Time-of-Arrival and Angle-of-Arrival Measurement-Assisted 3D Inter-Unmanned Aerial Vehicle Relative Localization Under Distance-Dependent Noise Model. Electronics. 2025; 14(1):90. https://doi.org/10.3390/electronics14010090
Chicago/Turabian StyleTang, Jiawei, Tian Chang, Qinglong Jiang, Xuhui Ding, and Dekang Liu. 2025. "Time-of-Arrival and Angle-of-Arrival Measurement-Assisted 3D Inter-Unmanned Aerial Vehicle Relative Localization Under Distance-Dependent Noise Model" Electronics 14, no. 1: 90. https://doi.org/10.3390/electronics14010090
APA StyleTang, J., Chang, T., Jiang, Q., Ding, X., & Liu, D. (2025). Time-of-Arrival and Angle-of-Arrival Measurement-Assisted 3D Inter-Unmanned Aerial Vehicle Relative Localization Under Distance-Dependent Noise Model. Electronics, 14(1), 90. https://doi.org/10.3390/electronics14010090