Coordinate Frames and Transformations in GNSS Ray-Tracing for Autonomous Driving in Urban Areas
Ulf Bestmann
Round 1
Reviewer 1 Report
Dear Authors,
Nice paper with the collection of relevant transformations and there dependencies between. Also the impact on the MP Simulation is quite interesting to see. I wonder if the original models of the buildings reach the same level of accuracy and detail as the transformations made to compute in a common reference frame. Neverless it is a significant contribution to eleminate coordinate frame related errors. Model data can be improved independently.
Author Response
Dear Reviewer,
thank you very much for your review. I reviewed the manuscript and fixed some minor errors. To your knowledge, based on a suggestion from another reviewer, the presentation of the results in the “Results” section is redesigned. Additionally, I want to reply to your comment:
Nice paper with the collection of relevant transformations and their dependencies between. Also the impact on the MP Simulation is quite interesting to see. I wonder if the original models of the buildings reach the same level of accuracy and detail as the transformations made to compute in a common reference frame. Nevertheless, it is a significant contribution to eliminate coordinate frame related errors. Model data can be improved independently.
You are right. The differences between the extra path delay in the metric and in the planar system remain in the mm-range, after the correction steps, and thus are smaller than the horizontal inaccuracies of the building model, which are in the cm-range. Nevertheless, as you mentioned, building models will evolve independently and accuracy is expected to increase.
Reviewer 2 Report
In this manuscript, the authors expose how the performance of ray tracing techniques is decreased when different coordinate frames are involved and not projected to a common coordinate frame. They show the RMSE in meters for a simulation set consisting of one wall and four antenna positions.
The paper is well written and no important errors were found. Minor English spell check is required.
Nevertheless, in line 295 it is stated that "The single Root Mean Square Error (RMSE) for the different antenna reflector spacings can be seen in Table 2 and reach values up to 128 cm. Maximum values reaches up to 2 m." The meaning of "Maximum values reaches up to 2 m." is not clear to me and I suggest clarifying this. Besides, it is "reach" (plural) and not "reaches".
Author Response
Dear Reviewer,
thank you very much for your review. I reviewed the manuscript and fixed some minor errors. To your knowledge, based on a suggestion from another reviewer, the presentation of the results in the “Results” section is redesigned. Additionally, I want to reply to your comment:
Nevertheless, in line 295 it is stated that "The single Root Mean Square Error (RMSE) for the different antenna reflector spacings can be seen in Table 2 and reach values up to 128 cm. Maximum values reaches up to 2 m." The meaning of "Maximum values reaches up to 2 m." is not clear to me and I suggest clarifying this. Besides, it is "reach" (plural) and not "reaches".
“Maximum values reaches up to 2 m” should describe the magnitude of the differences, but was expressed in an inaccurate way. This has now been reformulated to “The magnitude of the differences reaches maximum values of 2.13 m.”
Reviewer 3 Report
With this manuscript, the authors have presented a study in which they have successfully conducted a conceptual model for coordinate frames' transformation in GNSS ray tracing for autonomous driving in urban areas. The core of their methodology is to establish the model to simulate, model and potentially correct multipath condition and compute delays caused by signal reflection.
The manuscript is well written, as the reviewer feels he/she is reading a good textbook. The reviewer also feels that the authors' overviews of the relevant models are adequate. The intellectual and practical aspects of the manuscript make it worthy of academic publication.
However, the reviewer would like to make some minor revisions to the current version of the manuscript. There are some suggestions as listed below for improving and clarifying certain aspects of the paper.
Question/comment #1:
In the manuscript, the authors limit themselves only to a functional model for solving the problem. Nevertheless, it would be appropriate to mention the stochastic process, because it is well known that 3D building models have their inaccuracies, which should not be neglected. How accurate should the position data be specified to be suitable for ray tracing and LOS/NLOS/multipath modelling for driving in urban areas?
Question/comment #2:
If the method is used for real-time measurements, have the authors considered or determined the differences in results when using broadcast ephemerides (or ultra-rapid ephemerides), which are of lower quality but available during positioning?
Comment #3:
In Figure 3, there is an error in two green rectangles (middle column and the bottom one) - as the physical height should be written in capital letter (H).
Author Response
Dear Reviewer,
thank you very much for your review. I reviewed the manuscript and fixed some minor errors. To your knowledge, based on a suggestion from another reviewer, the presentation of the results in the “Results” section is redesigned. Additionally, I want to reply to your comments:
In the manuscript, the authors limit themselves only to a functional model for solving the problem. Nevertheless, it would be appropriate to mention the stochastic process, because it is well known that 3D building models have their inaccuracies, which should not be neglected. How accurate should the position data be specified to be suitable for ray tracing and LOS/NLOS/multipath modelling for driving in urban areas?
Building models truly have their inaccuracies, in our paper we were focusing more the general case and emphasized the error sources which we can control as a user. Concerning the accuracy of positioning data, we put ourselves in the situation of highly automated vehicles or even automated vehicles that have a well defined route and trajectory so that the analysis can be performed along this well -known path. In further publications we have shown that especially in the along-track direction, a less accurate user position (few m) is sufficient to perform accurate ray tracing (https://doi.org/10.33012/2022.18171 ; https://doi.org/10.33012/2022.18510).
If the method is used for real-time measurements, have the authors considered or determined the differences in results when using broadcast ephemerides (or ultra-rapid ephemerides), which are of lower quality but available during positioning?
Azimuth and elevation of the satellite are used for the calculation of the extra path delay. The deviations in the satellite coordinates (https://igs.org/products/#about) are very small compared to the distance of the satellite and therefore lead to barely perceptible changes in the azimuth and elevation angle.
Reviewer 4 Report
This paper innovatively deals with the problem of coordinate frames and transformations in ray tracing. The correction strategy in this paper can effectively improve the estimation accuracy of multipath delay. It will help improve the positioning accuracy for autonomous driving. Before proceeding to the publication stage, I encourage the authors to address the following minor comments:
1. Line 51: “extra-path delays” should be “extra path delay”?
2. Line 118: The meaning of “δ” should be here.
3. Line 121: In equation 4 and 5, α indicates azimuth and amplitude ratio, respectively. In order not to mislead the reader, it is recommended to represent these two quantities with different characters.
4. Line 130: There should be “Blocked or Multipath” or “blocked or multipath”.
5. Line 139: CGS2000 should be CGCS2000.
6. Line 238-241: The calculation of the extra path delay in map projection system can save computational effort. But dealing with those corrections such as meridian convergence mapping distortion will increase computation burden. Compared to Cartesian 3D system, even after considering all corrections, can computational effort still be saved in map projection systems? A note is needed here, or other benefits should be given.
7. In Figure 6(a), the figure seems to be symmetrical. But for the series of 2.2m and 11.2m, there are some asymmetries. Is there a little problem here?
8. In table 2，After the corrections of meridian convergence and conformal system, the result of 11.2 m is a little better than 2.2m. An explanation is needed here.
Author Response
Dear Reviewer,
thank you very much for your review. I reviewed the manuscript and fixed some minor errors. Additionally, I want to reply to your comments:
Line 238-241: The calculation of the extra path delay in map projection system can save computational effort. But dealing with those corrections such as meridian convergence mapping distortion will increase computation burden. Compared to Cartesian 3D system, even after considering all corrections, can computational effort still be saved in map projection systems? A note is needed here, or other benefits should be given.
Admittedly, the computational effort depends on many factors and calculations in both systems can mean less/or more computational effort depending on the application. Factors that have an influence here are the resolution of the building model, the number of buildings to be transformed, the GNSS measurement rate, or the number of satellites to be expected.
Assuming a simple trajectory inside a 1 km long and straight urban canyon with 10 HZ measurement rate. Houses are 10 m wide and in the simplest case we consider only the front side with the 4 corner points. This results in 100 houses on each side, and thus 800 points need to be transformed. The transformation into the metric system requires 4 transformations, yielding in 100*2*4*4 = 3200 transformations.
At a speed of 30 km/h, we have a measuring point at about every 1 m and assuming 10 observed satellites per measurement we need to transform one user position and 10 satellite positions. However, the transformation of the satellites requires only one transformation step, because only azimuth and elevation are passed. The transformation of the user position requires four transformation steps. 1000*10*1+1000*4 = 14000 transformations.
In this example it would be less transformations to compute the extra path delay in the metric system. However, as building models are very likely to be more sophisticated (e.g., 3D houses, tilted roofs, dormers), and more buildings than the first row are incorporated, the number of building points will increase significantly.
Other reasons that could make the calculations in planar systems necessary are the integration of different sensors, like LIDAR or camera data.
In Figure 6(a), the figure seems to be symmetrical. But for the series of 2.2m and 11.2m, there are some asymmetries. Is there a little problem here?
The asymmetries occur for all 4 antenna-reflector distances, but significantly decreasing with distance. The main reason is that the distance between antenna and reflector on the x-axis is given in the metric system. The negative/positive differences are almost symmetrical for matching elevation/azimuth combination. If the distances between reflection point and antenna are chosen in the system of the mapping projection, the asymmetries are reversed.
In fact, the representation is not necessarily ideal and is replaced by figures with the azimuth on the x-axis and the incidence angle of the ray on the reflection surface for the color bar. There are still small asymmetries, which can be seen, e.g. in Figure 6 d. This is due to the fact that the azimuth is also calculated in the metric system. However, the information from which system any quantity is originating is now added in the paper.
In table 2，After the corrections of meridian convergence and conformal system, the result of 11.2 m is a little better than 2.2m. An explanation is needed here.
A zero in the decimal place was forgotten, thank you very much.
