Accurate Joint Estimation of Position and Orientation Based on Angle of Arrival and Two-Way Ranging of Ultra-Wideband Technology

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This manuscript investigates the estimation performance of the position and orientation, where the angle of arrival (AOA) and double-sided two-way ranging (DS-TWR) are both employed. Furthermore, the Cramér-Rao lower bound (CCRLB) is obtained to evaluate the efficiency of the proposed algorithm. However, there are still some comments from the reviewer to improve the work.

 

1.     The effectiveness of the proposed algorithm for the 2-D robot system should be further clarified.

2.     When the range of tags is expanding to 3-D dimension, the authors should consider the efficiency of proposed algorithms, since that AOAs include azimuth and elevation simultaneously.

3.     What are the advantages and disadvantages of self-localization?

4.     The simulation results can be further explained, such as the reason of “which are closer to the CCRLB than A VPLE and TELS”.

5.     The motivation can be significantly improved.

Author Response

This manuscript investigates the estimation performance of the position and orientation, where the angle of arrival (AOA) and double-sided two-way ranging (DS-TWR) are both employed. Furthermore, the Cramér-Rao lower bound (CCRLB) is obtained to evaluate the efficiency of the proposed algorithm. However, there are still some comments from the reviewer to improve the work.

1. The effectiveness of the proposed algorithm for the 2-D robot system should be further clarified.

Reply: Thanks for the suggestion to make the presentation better. To clarify the 2-D robot system, we have added the simulation of dynamic robot localization and orientation estimation, as shown in Subsection 6.2, Line 254, Page. 10.

2. When the range of tags is expanding to 3-D dimension, the authors should consider the efficiency of proposed algorithms, since that AOAs include azimuth and elevation simultaneously.

Reply: Thanks for letting us know what you concern. In this paper, we focus on the 2D wheel robot localization and orientation estimation system. The efficiency of proposed algorithm of computational complexity is compared in Section 5, Line 195, Page. 8. The 3D localization would be considered in future work, as stated in Page. 348, Line 15.

3. What are the advantages and disadvantages of self-localization?

Reply: Thanks for letting us know what you concern. The advantages and disadvantages of self-localization are stated in Line 62, Page. 2. As to the disadvantages of state-of-art, we proposed the SL-CWLS algorithm in this paper, and the future work would also focus on improving the performance of self-localization methods.

4. The simulation results can be further explained, such as the reason of “which are closer to the CCRLB than A VPLE and TELS”.

Reply: Thanks for the comment. The further analysis of Fig. 3 is added in Line 237, Page. 9. “In Table 1, the SL-CWLS and BCAVPLE-WIV …thus are inferior to SL-CWLS and BCAVPLE-WIV.”

5. The motivation can be significantly improved.

Reply: Thanks for your advice. The enhanced motivation is added in Line 66, Page. 2. “In practical robotic experiments for developing the mowing robot…The SL can effectively reduce the cost of equipment”

Reviewer 2 Report

Comments and Suggestions for Authors

Well structured and clearly written paper.

The paper concerns still actual problem of object localization. High accuracy positioning sets the foundation for numerous applications. like movement control of autonomous vehicles.

The contribution is clearly stated (self localization algorithm based on constrained weighted least square for AOA based UWB systems) and well supported with state of the art analysis. The theoretical background is supported with the analysis of accuracy of the method. The experimental parts involves both computer simulations and real-life tests with IEEE802.15.4 UWB compliant nodes. The performance of the proposed method is compared against reference approaches.

The paper can however be still improved (minor issues):

- the test scenario assumes line of sight visibility of the antennas - is it required for correct operation of the algorithm? What would be the impact of NLOS on the accuracy?

- the proposed algorithm outperforms reference algorithms in terms of positioning accuracy. What is the computational cost of the compared approaches? (Does the proposed algorithm also outperform the reference ones in this aspect? The cost effectiveness has not been compared against alternative/reference approaches.)

Fig. 3 and Fig. 4 - the labels are not self-explanatory. It recommended to add description of σ and M parameters in figure captions.

Author Response

Well structured and clearly written paper.

The paper concerns still actual problem of object localization. High accuracy positioning sets the foundation for numerous applications. like movement control of autonomous vehicles.

The contribution is clearly stated (self localization algorithm based on constrained weighted least square for AOA based UWB systems) and well supported with state of the art analysis. The theoretical background is supported with the analysis of accuracy of the method. The experimental parts involves both computer simulations and real-life tests with IEEE802.15.4 UWB compliant nodes. The performance of the proposed method is compared against reference approaches.

1. the test scenario assumes line of sight visibility of the antennas - is it required for correct operation of the algorithm? What would be the impact of NLOS on the accuracy?

Reply: Thanks for your so careful reading. The proposed algorithm is for the scenario of LOS, as shown in Fig.9 (a) Page 13. The NLOS is not considered in this paper, as we found out that in real-world scenarios, the NLOS has negative impact on the localization accuracies of algorithms. The SL-CWLS needs to combine with other methods for NLOS localization, which is a significant problem in our future work. In Line 348, Page. 15, we have added the related statement in future work.

2. the proposed algorithm outperforms reference algorithms in terms of positioning accuracy. What is the computational cost of the compared approaches? (Does the proposed algorithm also outperform the reference ones in this aspect? The cost effectiveness has not been compared against alternative/reference approaches.) 

Reply: Thanks for letting us know what you concern. In Line 195, Page. 8, we have added the comparison of computational complexity. As shown in Fig.3 and Fig.4, Page 10, though the SL-CWLS has higher computational complexity, it has much lower RMSEs than counterparts.

3. 3 and Fig. 4 - the labels are not self-explanatory. It recommended to add description of σ and M parameters in figure captions.

Reply: Thanks for your advice. In Fig. 3 and Fig. 4, Page. 10, we have added the caption of σ and M.

Reviewer 3 Report

Comments and Suggestions for Authors

The paper addresses the problem of self-localization (SL) in robotic systems using ultra-wideband (UWB) technology, specifically focusing on the integration of Angle of Arrival (AOA) and Time of Flight (TWR) measurements. The authors propose a novel SL algorithm called constrained weighted least squares (SL-CWLS), which aims to enhance the accuracy of position and orientation estimation while considering the noise characteristics of UWB measurements.
However, the urgency and rationale behind the proposed method are not clearly described in the Introduction.

There are some suggestions to improve this paper presentation:

1. Some technical terms and acronyms used in the article should be italicized to adhere to standard formatting conventions. For example, terms like UWB (Ultra-Wideband), AOA (Angle of Arrival), and TWR (Time of Flight) should be consistently italicized in the text. 

2. The introduction could be strengthened with a more comprehensive literature review and relevant references.

3. The methods section lacks some details that would aid in understanding the implementation and parameters of the self-localization algorithm based on the constrained weighted least squares (SL-CWLS) algorithm.

4. There may be a need for further discussion on the limitations of the proposed approach and potential areas for future research.

5. The number of references in the manuscript is relatively small; I encourage the authors to include additional related works to strengthen the research context. Additionally, it is recommended to compare the experimental results with similar studies, discussing the similarities, distinctive features, relative pros and cons, and their limitations.

6. Please ensure that all references are formatted with MDPI style correctly.

Author Response

The paper addresses the problem of self-localization (SL) in robotic systems using ultra-wideband (UWB) technology, specifically focusing on the integration of Angle of Arrival (AOA) and Time of Flight (TWR) measurements. The authors propose a novel SL algorithm called constrained weighted least squares (SL-CWLS), which aims to enhance the accuracy of position and orientation estimation while considering the noise characteristics of UWB measurements.
However, the urgency and rationale behind the proposed method are not clearly described in the Introduction.

There are some suggestions to improve this paper presentation:

1. Some technical terms and acronyms used in the article should be italicized to adhere to standard formatting conventions. For example, terms like UWB (Ultra-Wideband), AOA (Angle of Arrival), and TWR (Time of Flight) should be consistently italicized in the text. 

Reply: Thanks for your so careful reading. The technical terms and acronyms are corrected as italicized through the whole paper.

 

2. The introduction could be strengthened with a more comprehensive literature review and relevant references.

Reply: Thanks for the good suggestion. In Line 34, Page. 1, we have added more literature review and relevant references.

3. The methods section lacks some details that would aid in understanding the implementation and parameters of the self-localization algorithm based on the constrained weighted least squares (SL-CWLS) algorithm.

Reply: Thanks for your advice. In Line 167, Page. 7, we have added the details of SL-CWLS in Algorithms.

 

4. There may be a need for further discussion on the limitations of the proposed approach and potential areas for future research.

Reply: Thanks for letting us know what you concern. In Page. 15, Line 343, we have added the limitations of the proposed approach and potential areas.

5. The number of references in the manuscript is relatively small; I encourage the authors to include additional related works to strengthen the research context. Additionally, it is recommended to compare the experimental results with similar studies, discussing the similarities, distinctive features, relative pros and cons, and their limitations.

Reply: Thanks for broadening our vision on this field. In Line 34, Page. 1, we have added more literature review and relevant references. Moreover, in Fig. 3 and Fig. 4, Page. 10, we have added the similar study of RBL algorithm to the comparison.

6. Please ensure that all references are formatted with MDPI style correctly.

Reply: Thanks for pointing out the mistake of this paper. We have corrected the reference format in Line 370, Page. 15.

Reviewer 4 Report

Comments and Suggestions for Authors

The paper presents a method for joint estimation of position and orientation in wireless sensor networks (WSNs) using ultra-wideband (UWB) technology, specifically integrating angle of arrival (AOA) and double-sided two-way ranging (DS-TWR) techniques. This topic is highly relevant for both the academic community and industry, given the increasing demand for accurate and cost-effective localization systems in robotics and IoT applications. The paper is well-written in English; however, certain sections require further clarification and improvement. My detailed comments are outlined below:

 

1) When the authors state "Simultaneously, DS-TWR measurements are conducted between the tags and the base station", nothing is said about the fact that the measurements between the tag and the various stations are not simultaneous. If the measurements are sequential, the acquisition frequency and any possible asynchrony must be specified and discussed.

2) Authors say that "The DS-TWR is assumed non-noisy as the real-life experiments confirm the high accuracy of UWB ranging". It would be appropriate to provide concrete data from a real system: for instance, what are the sensitivity, precision, and error levels observed under experimental conditions?

3) The introduction provides a good overview of UWB-based localization methods, particularly those relying on AOA and DS-TWR techniques. However, the state-of-the-art discussion could be further enriched by including relevant works on sensor fusion algorithms, which address the localization problem using heterogeneous measurements from multiple sensors. For instance, in [1], inertial measurements (IMU) are fused with distance-based information to mitigate the lack of position measurements, highlighting practical approaches to handle real-world limitations. Additionally, I suggest citing for example [2]. This work presents a robust fusion strategy for localization in GPS-denied environments, combining UWB, IMU, and odometer data. A key contribution of this paper is the theoretical analysis of observability conditions, which establishes the minimum number of anchors and the system excitation requirements for position and attitude estimation. Citing this study would provide a broader perspective on the integration of multiple sensing modalities and would strengthen the introduction by showcasing complementary techniques that enhance localization accuracy and robustness through sensor fusion approaches.

[1] F. Alonge et. al, "Hybrid Observer for Indoor Localization with Random Time-of-Arrival Measurements", 2018 IEEE 4th International Forum on Research and Technology for Society and Industry (RTSI), Palermo, Italy, 2018

[2] B. Zhou et. al "UWB-IMU-Odometer Fusion Localization Scheme: Observability Analysis and Experiments," in IEEE Sensors Journal, vol. 23, no. 3, pp. 2550-2564.

4) UWB antennas exhibit non-uniform responses depending on the angle between the transmitter and receiver. This can lead to variations in sensitivity based on the object's position, which may also be influenced by the arrangement of the fixed anchors. I suggest exploring and discussing these aspects further, as they can significantly impact the system's accuracy.

5) The experimental setup is well-described; however, it is unclear how the error is calculated in the real-world experiments. Was a ground truth device used to validate the results? If so, it would be beneficial to include a detailed description of this device.

6) The text mentions the use of a synchronization frame, but it does not clearly explain how this frame is applied to resolve synchronization issues between the station and the UWB tags. Further details on this point are needed.

7) It is not clear at what speed the robot moves during the experiment. To better analyze the impact of system dynamics on position estimation, I suggest conducting tests at varying speeds. Additionally, it would be helpful to include a plot comparing the reference trajectory and the estimated position to provide a more comprehensive performance evaluation.

8) I suggest dividing the real-world experiment section into two subsections. Experimental Setup: A detailed description of the experimental configuration, including hardware specifications and anchor placement. Experimental Results: Analysis of the conducted tests, focusing on system performance and obtained results.

 

The paper is interesting and provides valuable insights for both the academic community and industry. However, the methodological aspects need further development and clarification to make the work more complete and suitable for publication.

Author Response

The paper presents a method for joint estimation of position and orientation in wireless sensor networks (WSNs) using ultra-wideband (UWB) technology, specifically integrating angle of arrival (AOA) and double-sided two-way ranging (DS-TWR) techniques. This topic is highly relevant for both the academic community and industry, given the increasing demand for accurate and cost-effective localization systems in robotics and IoT applications. The paper is well-written in English; however, certain sections require further clarification and improvement. My detailed comments are outlined below:

1. When the authors state "Simultaneously, DS-TWR measurements are conducted between the tags and the base station", nothing is said about the fact that the measurements between the tag and the various stations are not simultaneous. If the measurements are sequential, the acquisition frequency and any possible asynchrony must be specified and discussed.

Reply: Thanks for noting that we made a mistake of the measurement model in the paper. In Line 102, Page. 3, we corrected the statement as “The DS-TWR measurements are conducted between the tags and base station in numbered order, respectively.”

 

2. Authors say that "The DS-TWR is assumed non-noisy as the real-life experiments confirm the high accuracy of UWB ranging". It would be appropriate to provide concrete data from a real system: for instance, what are the sensitivity, precision, and error levels observed under experimental conditions?

Reply: Thanks for the suggestion to make the presentation better. In Table 2, Page. 14, we have added the characteristic of DS-TWR of UWB. And in Line 326, Page. 13, we have added “Moreover, the measurement error of DS-TWR has about zero mean and 5cm standard deviation, which has less impact on estimation than AOAs in practical tests.”

 

3. The introduction provides a good overview of UWB-based localization methods, particularly those relying on AOA and DS-TWR techniques. However, the state-of-the-art discussion could be further enriched by including relevant works on sensor fusion algorithms, which address the localization problem using heterogeneous measurements from multiple sensors. For instance, in [1], inertial measurements (IMU) are fused with distance-based information to mitigate the lack of position measurements, highlighting practical approaches to handle real-world limitations. Additionally, I suggest citing for example [2]. This work presents a robust fusion strategy for localization in GPS-denied environments, combining UWB, IMU, and odometer data. A key contribution of this paper is the theoretical analysis of observability conditions, which establishes the minimum number of anchors and the system excitation requirements for position and attitude estimation. Citing this study would provide a broader perspective on the integration of multiple sensing modalities and would strengthen the introduction by showcasing complementary techniques that enhance localization accuracy and robustness through sensor fusion approaches.

[1] F. Alonge et. al, "Hybrid Observer for Indoor Localization with Random Time-of-Arrival Measurements", 2018 IEEE 4th International Forum on Research and Technology for Society and Industry (RTSI), Palermo, Italy, 2018

[2] B. Zhou et. al "UWB-IMU-Odometer Fusion Localization Scheme: Observability Analysis and Experiments," in IEEE Sensors Journal, vol. 23, no. 3, pp. 2550-2564.

Reply: Thanks for broadening our vision on this field. In Line 39, Page. 2, we have added the citing in introduction.

 

4. UWB antennas exhibit non-uniform responses depending on the angle between the transmitter and receiver. This can lead to variations in sensitivity based on the object's position, which may also be influenced by the arrangement of the fixed anchors. I suggest exploring and discussing these aspects further, as they can significantly impact the system's accuracy.

Reply: Thanks for the good suggestion. Indeed we found out that the In Line 304, Page. 12, we have analyzed the impact of AOA of UWB and utilize a modified method, as shown in Fig. 10, Page. 14.

 

5. The experimental setup is well-described; however, it is unclear how the error is calculated in the real-world experiments. Was a ground truth device used to validate the results? If so, it would be beneficial to include a detailed description of this device.

Reply: Thanks for your so careful reading. In Line 299, Page 12, we have added “The real positions are measured with square floor tiles,…which can guarantee the accuracy of 0.1°.”

6. The text mentions the use of a synchronization frame, but it does not clearly explain how this frame is applied to resolve synchronization issues between the station and the UWB tags. Further details on this point are needed.

Reply: Thanks for pointing out the mistake of this paper. In Fig.2 Page. 3, we have corrected the “synchronization frame” as “beacon frame”. And in Line 105, Page. 3, we have revised the statement as “In the process illustrated in Fig. 2 the base station first transmits a beacon frame to initiate communication with the tags”.

7.It is not clear at what speed the robot moves during the experiment. To better analyze the impact of system dynamics on position estimation, I suggest conducting tests at varying speeds. Additionally, it would be helpful to include a plot comparing the reference trajectory and the estimated position to provide a more comprehensive performance evaluation.

Reply: Thanks for the suggestion to make the presentation better. In Subsection 6.2, Line 254, Page. 10, we add the simulation of dynamic robot localization and orientation estimation.

8.I suggest dividing the real-world experiment section into two subsections. Experimental Setup: A detailed description of the experimental configuration, including hardware specifications and anchor placement. Experimental Results: Analysis of the conducted tests, focusing on system performance and obtained results.

Reply: Thanks for your advice. In Line 288, Page 12 and Line 328, Page 14,we have divided the real-world experiment section into two subsections.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

 

(1) Some abbreviations are not defined, such as "RSS" in Line 35 Page1.

(2) In the contribution section, emphasis should be placed on innovation and expression should be improved, preferably condensed in the form of items.

 

 

Comments on the Quality of English Language

The level of English writing still needs to be improved, for example, professional vocabulary needs to be further standardized.

Author Response

（1）Some abbreviations are not defined, such as "RSS" in Line 35 Page1.

Reply: Thanks for pointing out the mistake of this paper. In Line 35, Page. 1, we have corrected the presentation of "RSS" as "RSSI" and added it into the Abbreviations of Line 382, Page. 16.

（2）In the contribution section, emphasis should be placed on innovation and expression should be improved, preferably condensed in the form of items.

Reply: Thanks for pointing out the important information that we miss in this paper. In Line 84, Page. 2, we have added the contributions of article in the form of items. “The main contributions of this article ……benchmark the performances of algorithms”

（3）The level of English writing still needs to be improved, for example, professional vocabulary needs to be further standardized.

Reply: Thanks for the suggestion to make the presentation better. We have look through the paper and improved the writing.

Reviewer 3 Report

Comments and Suggestions for Authors

In this current version, the authors try to address most problems during the first round of reviews. However, the paper's content still lacks a detailed discussion on the limitations of the proposed approach.  Line 343 of the revised version does not explain the limitations of the proposed approach.

The number of references in the manuscript is relatively small; I encourage the authors to include additional related works to strengthen the research context. A good research paper manuscript should contain at least 25 references as the basis theory or previous works.

Please ensure that all references are formatted with MDPI style correctly. The MDPI reference format should include the DOI, check the MDPI template carefully. 

 

Author Response

（1）In this current version, the authors try to address most problems during the first round of reviews. However, the paper's content still lacks a detailed discussion on the limitations of the proposed approach.  Line 343 of the revised version does not explain the limitations of the proposed approach.

Reply: Thanks for pointing out the important information that we miss in this paper. In Line 358, Page. 16, we have added the limitations of the proposed SL-CWLS, and looked forward to the improvement. “For practical industrial and domestic robot……such as IMU and odometer”.

（2）The number of references in the manuscript is relatively small; I encourage the authors to include additional related works to strengthen the research context. A good research paper manuscript should contain at least 25 references as the basis theory or previous works.

Reply: Thanks for broadening our vision on this field. In Line 59, Page. 2, we have added more literature review and relevant references.

（3）Please ensure that all references are formatted with MDPI style correctly. The MDPI reference format should include the DOI, check the MDPI template carefully. 

Reply: Thanks for pointing out the mistake of this paper. We have further corrected the reference format in Line 384, Page. 16, the DOIs are added with the form of “Crossref”.