Accurate Joint Estimation of Position and Orientation Based on Angle of Arrival and Two-Way Ranging of Ultra-Wideband Technology
Abstract
:1. Introduction
2. Signal Model and Problem Formulation
3. SL Algorithm Based on Constrained Weighted Least Squares
Algorithm 1 SL-CWLS. |
Input: Measured AOAs , DS-TWRs , noise variance . Output: Estimation of , including location and rotation . Initialization from (15). for do Construct the Lagrange function of (31) Construct Karush–Kuhn–Tucker condition. ,,,,. Newton direction solution with Karush–Kuhn–Tucker condition. Update variables. , stop condition. or . end for |
4. Constrained Cramér–Rao Lower Bound
5. Computational Complexity Analysis
6. Simulation Evaluation
6.1. Static Points Tests
6.2. Dynamic Trajectory Test
7. Real-World Experiment
7.1. Experiment Settings
7.2. Analysis of Experimental Results
8. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
WSNs | Wireless sensor networks |
UWB | Ultra-wideband |
RSSI | Received signal strength indicator |
TOA | Time of arrival |
TDOA | Time difference of arrival |
AOA | Angle of arrival |
DS-TWR | Double-sided two-way ranging |
IMU | Inertial measurements |
RBL | Rigid body localization |
SDP | Semi-definite program |
SL | Self-localization |
CWLS | Constrained weighted least squares |
CCRLB | Constrained Cramér–Rao lower bound |
CRLB | Cramér–Rao lower bound |
FIM | Fisher information matrix |
RMSE | Root mean square error |
CDF | Cumulative distribution function |
NLOS | Non-line-of-sight |
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Method | Description | Complexity |
---|---|---|
AVPLE | PLE method in [21] based on AOA | |
BCAVPLE-WIV | Two-step method in [21] based on AOA and TWR | |
TELS | Two-step method in [24] based on AOA | |
BC-CWLS | RBL method in [17] based on AOA | |
SL-CWLS | Proposed method based on AOA and TWR |
Positions | Mean of AOA errors (°) | Standard deviation of AOA errors (°) | ||||||
30° | −30° | 60° | −60° | 30° | −30° | 60° | −60° | |
(80,320) | 0.0340 | 0.0480 | −0.0463 | 0.0515 | 5.0723 | 5.1210 | 5.0559 | 5.0933 |
(160,160) | 0.0453 | 0.0380 | 0.0258 | −0.0373 | 5.0935 | 5.1267 | 5.0807 | 5.1010 |
(80,80) | −0.0418 | 0.0640 | 0.0103 | 0.0473 | 5.1112 | 5.0832 | 5.1210 | 5.0318 |
(240,0) | 0.0405 | 0.0175 | 0.0193 | −0.1900 | 5.0895 | 5.0687 | 5.0909 | 5.0810 |
(320,240) | 0.0475 | 0.0293 | −0.0488 | −0.0498 | 5.1186 | 5.0357 | 5.0563 | 5.0672 |
Mean of DS-TWR errors (cm) | Standard deviation of DS-TWR errors (cm) | |||||||
30° | −30° | 60° | −60° | 30° | −30° | 60° | −60° | |
(80,320) | 0.4760 | −0.4863 | 0.5005 | 0.5110 | 5.0361 | 5.0628 | 4.9380 | 5.0356 |
(160,160) | −0.5415 | 0.4058 | 0.4768 | 0.4878 | 4.9482 | 5.0749 | 4.9644 | 5.0428 |
(80,80) | 0.4923 | −0.5203 | 0.5098 | −0.5658 | 5.0476 | 4.0733 | 5.0616 | 5.0496 |
(240,0) | 0.4440 | 0.4708 | −0.5430 | 0.4785 | 4.9528 | 5.0515 | 5.0426 | 5.0354 |
(320,240) | −0.5198 | 0.5175 | −0.5110 | 0.4883 | 5.0397 | 4.9682 | 5.0569 | 5.0419 |
Positions | RMSE (cm) | |||
---|---|---|---|---|
AVPLE | BCAVPLE-WIV | TELS | SL-CWLS | |
(80,320) | 27.9279 | 16.4774 | 20.2654 | 13.7289 |
(160,160) | 28.4858 | 16.8066 | 20.2518 | 12.6901 |
(80,80) | 29.2753 | 17.2724 | 20.8831 | 10.5079 |
(240,0) | 31.1556 | 18.3818 | 22.4452 | 8.1818 |
(320,240) | 30.4628 | 18.0705 | 22.0644 | 9.2941 |
Positions | RMSE | |||
---|---|---|---|---|
AVPLE | BCAVPLE-WIV | TELS | SL-CWLS | |
(80,320) | 0.04763 | 0.04239 | 0.04760 | 0.04330 |
(160,160) | 0.04841 | 0.04309 | 0.04818 | 0.04272 |
(80,80) | 0.04887 | 0.04350 | 0.04806 | 0.04443 |
(240,0) | 0.05410 | 0.04815 | 0.05104 | 0.04806 |
(320,240) | 0.05254 | 0.04346 | 0.04964 | 0.04335 |
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Zhang, D.; Xu, H.; Zhan, L.; Li, Y.; Yin, G.; Wang, X. Accurate Joint Estimation of Position and Orientation Based on Angle of Arrival and Two-Way Ranging of Ultra-Wideband Technology. Electronics 2025, 14, 429. https://doi.org/10.3390/electronics14030429
Zhang D, Xu H, Zhan L, Li Y, Yin G, Wang X. Accurate Joint Estimation of Position and Orientation Based on Angle of Arrival and Two-Way Ranging of Ultra-Wideband Technology. Electronics. 2025; 14(3):429. https://doi.org/10.3390/electronics14030429
Chicago/Turabian StyleZhang, Di, Hongbiao Xu, Li Zhan, Ye Li, Guangqiang Yin, and Xinzhong Wang. 2025. "Accurate Joint Estimation of Position and Orientation Based on Angle of Arrival and Two-Way Ranging of Ultra-Wideband Technology" Electronics 14, no. 3: 429. https://doi.org/10.3390/electronics14030429
APA StyleZhang, D., Xu, H., Zhan, L., Li, Y., Yin, G., & Wang, X. (2025). Accurate Joint Estimation of Position and Orientation Based on Angle of Arrival and Two-Way Ranging of Ultra-Wideband Technology. Electronics, 14(3), 429. https://doi.org/10.3390/electronics14030429