Estimation Algorithm for Vehicle Motion Parameters Based on Innovation Covariance in AC Chassis Dynamometer
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThe model and estimation mathematical frameworks should be explained more clearly and better mutually linked.
The relation of (1)-(3), if any, with (6)-(7) or with (8)-(10) is not explained.
Explain more clearly the summations in the last right-hand-side equations of (1)-(3) and reflect this concern in the equations of such equations.
The entries of the matrix D on page 5 are not explained . If they are dependent on time and the square of time, as it seems to happen, the matrix is not constant as indicated by the notation. Furthermore, it is not said where this description comes from based on the equations of the vehicle.
Explain why the noises W, V are not dependent on samples in (6)-(7) while V(k) is sample-dependent in (12)-(13).
R is constant in (9) and sample-dependent in (14).
The initialization for the samples succession with the index “k” should be initialized in the corresponding equations.
The text allocated after (17) is not clear. For instance “s” , mentioned twice, does not appear in the equation.
Why are the vehicle parameters mentioned in the second paragraph after Fig. 4 reasonable or where are they taken from using background literature or are they a particular experiment for the paper.?. Please, explain.
Please, explain more clearly how is the parameter estimation of Section 3 linked to the physical description of Section 2.
Author Response
Comments 1: The model and estimation mathematical frameworks should be explained more clearly and better mutually linked.
Response 1: Thank you for your feedback. We agree with this suggestion. Therefore, we have added section 3.3 "Determination of Kalman Filter Parameters" to provide a more detailed description of the mathematical model in the text and achieve better alignment.
Comments 2: The relation of (1)-(3), if any, with (6)-(7) or with (8)-(10) is not explained.
Response 2: Thank you for your feedback. Regarding this issue, please allow me to provide an explanation. The chassis dynamometer loading force model is obtained through equations 1-3. It can be seen from Eq.(3) that when the test vehicle is determined, α, β, γ, and M are all fixed values. The precise acquisition of the speed and acceleration of the test vehicle is crucial for enhancing the accuracy of tests conducted on the chassis dynamometer. Equations 1-3 are used to analyze the necessity of optimizing the Kalman filtering algorithm, while equations 6-10 detail the specific process of the standard Kalman filter.
Comments 3: Explain more clearly the summations in the last right-hand-side equations of (1)-(3) and reflect this concern in the equations of such equations.
Response 3: Thank you for your feedback. Equations 1-2 represent the force conditions of the experimental vehicle on the road and on the chassis dynamometer, respectively. In order to make the chassis dynamometer test more accurate, the forces acting on the vehicle in both cases should be identical, thus obtaining the loading force model of the chassis dynamometer.
Comments 4: The entries of the matrix D on page 5 are not explained . If they are dependent on time and the square of time, as it seems to happen, the matrix is not constant as indicated by the notation. Furthermore, it is not said where this description comes from based on the equations of the vehicle.
Response 4: Thank you for your feedback. We agree with this suggestion. Therefore, we have added section 3.3 "Determination of Kalman Filter Parameters" to provide a detailed explanation of the derivation process of the state transition matrix D.
Comments 5: Explain why the noises W, V are not dependent on samples in (6)-(7) while V(k) is sample-dependent in (12)-(13).
R is constant in (9) and sample-dependent in (14).
Response 5: Thank you for your feedback. Ordinary KF requires a priori statistical characteristics of noise，so noises W, V are not dependent on samples and R is constant in (9). However, the noise variance of the chassis dynamometer exhibits uncertainty during various tests. This paper employs an adaptive KF algorithm grounded in the innovation process, allowing for real-time estimation of noise variance. This is achieved through online statistical analysis of the innovation variance, ensuring that the model measured noise aligns closely with the actual noise level. In each iteration, the noise statistical estimate R(k) obtained by online statistics is used instead of R in Eq.(9) to realize adaptive filtering.
Comments 6: The initialization for the samples succession with the index “k” should be initialized in the corresponding equations.
Response 6: Thank you for your feedback. We agree with this suggestion. We have added the initialization of the sample succession with the index “k” in section 3.3. At the initial moment, the vehicle displacement and velocity are both zero, and only the acceleration is non-zero. The error in acceleration is assumed to follow a Gaussian distribution with a mean of 0 and a variance of U. the covariance matrix P(0) can be represented as Eq.(21)
Comments 7: The text allocated after (17) is not clear. For instance “s”, mentioned twice, does not appear in the equation.
Response 7: Thank you for your feedback. Regarding this issue, please allow me to provide an explanation. Here, s represents the unit of seconds for t and t0 in the equation.
.
Comments 8: Why are the vehicle parameters mentioned in the second paragraph after Fig. 4 reasonable or where are they taken from using background literature or are they a particular experiment for the paper.? Please, explain.
Response 8: Thank you for your feedback. We agree with this suggestion. We have added relevant descriptions about the specific parameters in section 4.2. Based on the road coasting test results, the least square method is applied in Matlab to fit the test data with a polynomial, and the values of A1, B1 and C1 in Eq.(1) are obtained as 140.83, -0.40 and 0.06 respectively. By using chassis dynamometer coasting method and the vehicle coasting without load and with secondary load on the chassis dynamometer, the least square method can be applied to fit the test data to obtain that A2, B2 and C2 in Eq.(2) are 530.88, -0.96, and 0.01 respectively. Combined with the relevant parameters of the test vehicle, M is 810kg, and α, β, γ are -390.05, 0.56, and 0.05 respectively, and the loading force model of the AC chassis dynamometer is obtained.
Comments 9: Please, explain more clearly how is the parameter estimation of Section 3 linked to the physical description of Section 2.
Response 9: Thank you for your feedback. We agree with this suggestion. we have added section 3.3 "Determination of Kalman Filter Parameters" to provide a detailed introduction to the methods for determining each parameter and the relationship of the parameter estimation of Section 3 and the physical description of Section 2.
Reviewer 2 Report
Comments and Suggestions for AuthorsThe paper presents a novel adaptive Kalman Filter (KF) algorithm using innovation covariance to improve motion parameter estimation in AC chassis dynamometer systems.
The reviewer has observed what appears to be slight misalignments in the three-point lines within the legends of Figures 3 and 5, which prompts further consideration regarding the accuracy of the data.
The error reduction from 6.4% to 1.8% is presented without statistical tests (e.g., p-values or confidence intervals). Provide statistical analysis to confirm the significance of this improvement, ensuring the results are not anecdotal.(Page 9, Lines 12–16)
Author Response
Comments 1: The reviewer has observed what appears to be slight misalignments in the three-point lines within the legends of Figures 3 and 5, which prompts further consideration regarding the accuracy of the data.
Response 1: Thank you for your feedback. I must learn from your meticulous attitude. Regarding your concerns, please allow me to provide an explanation. First, I would like to clarify that both my simulation data and experimental data are real and valid，The interface of the experimental data is shown in the figure below. Figures 3 and 5 were generated using Matlab programming. When creating the legends, due to the need for translation into English, they took up a significant amount of space. No matter how I adjusted it, the legends either affected the clarity of the expression or the aesthetics, and I couldn't achieve a satisfactory result. Therefore, we copied the figures into Visio software and created the legends there, which resulted in slight misalignment. We have since made further adjustments, and I kindly ask you to review them again.
Comments 2: The error reduction from 6.4% to 1.8% is presented without statistical tests (e.g., p-values or confidence intervals). Provide statistical analysis to confirm the significance of this improvement, ensuring the results are not anecdotal.(Page 9, Lines 12–16)
Response 2: Thank you for pointing this out. We agree with this comment. Therefore, We have added the process of testing the reproducibility of the experimental data in section 4.2.
To ensure the validity of the test results, a repeatability analysis of the data from multiple trials is required. In this study, the 95th percentile distribution method is used for the repeatability assessment. Taking the road acceleration test results as an example, the test was conducted three times. Based on tabulated values, the standard deviation of the acceleration time corresponding to the vehicle speed is 0.063Q, where Q represents the arithmetic mean of the results from the three repeated tests. The computed standard deviations are 0.0693, 0.126, 0.189, 0.3087, 0.3843, 0.5103, and 0.693, while the corresponding ranges are 0, 0, 0, 0.1, 0.25, 0.15, and 0.15. These ranges are all smaller than the respective standard deviations, indicating good repeatability of the three acceleration test results. Therefore, the vehicle acceleration test data is deemed valid. Likewise, it can be concluded that the coasting test data is also valid.
Reviewer 3 Report
Comments and Suggestions for AuthorsThis article proposes an innovative adaptive Kalman filter (KF) algorithm, which can achieve optimal estimation of vehicle motion parameters without the need for prior error statistics In my opinion, efforts should be made to improve this article.
- In section 2,some parameters in the formula, such as A1、B1 and C1, should be explained in terms of their physical meanings and the extent of their impact on the entire model,It is recommended to supplement and improve them.
- In section 3,for the calculation of innovation variance statistical estimation using the sliding window method, the impact of different values on the algorithm performance should be explained for the window width mf.
- In section 3.1,When introducing the application of Kalman filtering algorithm in AC chassis dynamometer system, the state equation and observation equation are given, but the basis for selecting these equation forms is not explained in detail.
- In section 4.2,suggest adding testing experiments on vehicles of different types and parameters, and explain in the paragraph that multi vehicle testing plans can be carried out in the future to enhance the universality of the algorithm.
- As shown in Figure 3, the specific algorithm names corresponding to each curve are not clearly labeled, which can easily cause confusion.
Author Response
Comments 1: In section 2,some parameters in the formula, such as A1 B1 and C1, should be explained in terms of their physical meanings and the extent of their impact on the entire model, It is recommended to supplement and improve them.
Response 1: Thank you for pointing this out. We agree with this comment. Therefore, We have added explanations about parameters such as A1, A2 ,B1, B2, C1, C2 in sections 2 and 4.2. A1, B1, C1 are fixed coefficients obtained by road coasting test [21], in road coasting test, the speed of the test vehicle gradually decreases to zero under the influence of air resistance and rolling resistance. The relevant coefficients can be obtained by fitting the speed and coasting time. A2, B2, C2 are the fixed coefficients obtained by relevant tests of dynamometer [21], in chassis dynamometer coasting test, the speed of the test vehicle gradually decreases to zero under the influence of rolling resistance on the chassis dynamometer and internal resistance. The least square method can be applied to fit the test data to obtain the relevant coefficients.
Comments 2: In section 3, for the calculation of innovation variance statistical estimation using the sliding window method, the impact of different values on the algorithm performance should be explained for the window width mf.
Response 2: Thank you for pointing this out. We agree with this comment. Therefore, We have added explanations about window width mf in sections 3.3. The window width directly affects the effectiveness of data processing. The choice of window width needs to be determined based on the specific application scenario and the target task. If the data changes quickly, a smaller window is usually required to quickly respond to the changes in the data. If the data changes slowly, a larger window can better smooth the noise and capture long-term trends. A smaller window reduces the computational load, making it suitable for applications with high real-time requirements. A larger window may increase computation time and storage requirements, but it can provide more accurate results.
Comments 3: In section 3.1,When introducing the application of Kalman filtering algorithm in AC chassis dynamometer system, the state equation and observation equation are given, but the basis for selecting these equation forms is not explained in detail.
Response 3: Thank you for pointing this out. We agree with this comment. Therefore, We have added section 3.3 "Determination of Kalman Filter Parameters," to provide a detailed explanation of the determination methods for parameters such as State Transition Matrix D，Observation Matrix H，Covariance Matrix P(k)，System noise Q and observation noise R Window width mf.
Comments 4: In section 4.2, suggest adding testing experiments on vehicles of different types and parameters, and explain in the paragraph that multi vehicle testing plans can be carried out in the future to enhance the universality of the algorithm.
Response 4: Thank you for pointing this out. We agree with this comment. The experimental verification in this paper shows that the algorithm developed in this study can significantly improve the testing accuracy of the chassis dynamometer. This algorithm is an enhancement to the chassis dynamometer testing system and is applicable to all vehicle models tested on the chassis dynamometer. However, due to the limited testing conditions at our university, it is not possible to complete experimental validation for different vehicle models in the short term. Once the testing conditions are met, further validation of the algorithm will be conducted as soon as possible. Thank you again for your feedback.
Comments 5: As shown in Figure 3, the specific algorithm names corresponding to each curve are not clearly labeled, which can easily cause confusion.
Response 5: Thank you for pointing this out. We agree with this comment. Therefore, we have clearly labeled the specific algorithms corresponding to each curve in Figure 3.
.
Reviewer 4 Report
Comments and Suggestions for AuthorsDear author,
thank you very much for allowing me to study your research and write a review of it.
The submitted article on the topic:
Estimation Algorithm for Vehicle Motion Parameters Based on
Innovation Covariance in AC Chassis Dynamometer, in my opinion, meets the set goals and has potential from a research point of view.
The article consists of 11 pages of text, 5 images, 5 main chapters and 26 publication sources.
In terms of content structure, the title of the scientific article and the abstract correspond and I have no reservations.
The individual chapters are appropriately connected and form a coherent text, which I have no reservations about.
The research itself and data validation are processed at the required level and presented in a high-quality manner.
Overall, the article, in my opinion, is acceptable for publication and I have no reservations and I do not see any shortcomings that would prevent its publication.
I recommend accepting the article in its current form.
Thank you very much
Author Response
Response：Thank you very much for your recognition of my paper. I will continue to work hard! With best regards to you!
Reviewer 5 Report
Comments and Suggestions for AuthorsEstimation Algorithm for Vehicle Motion Parameters Based on Innovation Covariance in AC Chassis Dynamometer
Brief Summary:
This article presents an estimation algorithm for vehicle motion parameters using an adaptive Kalman Filtering (KF) method based on innovation covariance in an AC chassis dynamometer system. The study aims to improve measurement accuracy by addressing noise-related issues that impact vehicle test results. The proposed approach enhances the precision of motion parameter estimation, resulting in reduced testing errors. Through simulation and experimental validation, the authors demonstrate the effectiveness of the adaptive KF algorithm in refining the loading force model, ultimately improving the accuracy of vehicle testing.
In general, the work is interesting and this study has merit for publication. However, there are some problems that should be addressed.
- Ensure that all figures have clear and descriptive captions. Some figures (e.g., Figure 5) could benefit from additional explanation regarding the presented data.
- Check the resolution of figures, particularly any graphs. Low-resolution images should be replaced with high-quality versions (Fig. 5).
- The paper describes an adaptive KF algorithm to optimize the estimation of vehicle motion parameters. Can the authors provide a comparative analysis with other state-of-the-art adaptive filtering techniques, such as particle filtering or unscented Kalman filtering, to strengthen the validation of their approach?
- The experimental validation of the algorithm primarily relies on chassis dynamometer tests. How do the authors account for real-world environmental factors such as varying road conditions and tire dynamics that may affect the performance of the algorithm in actual vehicle operations?
- Given that adaptive KF algorithms may introduce additional computational complexity, can the authors elaborate on the real-time feasibility of implementing this method in a commercial chassis dynamometer system? Have they tested the computational burden of their approach?
- The study discusses Gaussian white noise filtering, but real-world signals often contain colored noise. How does the proposed approach perform when tested with non-Gaussian noise sources commonly encountered in automotive testing environments?
- The paper discusses fixed values for certain model parameters. Can the authors clarify whether the algorithm is adaptable to different vehicle types, or if it requires re-tuning for various test scenarios?
The quality of the English language in the sent article is good. But there are some grammatical and phrasing issues that should be improved for greater clarity and readability such as:
Original: "The chassis dynamometer plays an important role in the research and development throughout the entire lifecycle of vehicle."
Correction: "The chassis dynamometer plays an important role in research and development throughout the entire lifecycle of a vehicle."
Author Response
Comments 1: Ensure that all figures have clear and descriptive captions. Some figures (e.g., Figure 5) could benefit from additional explanation regarding the presented data.
Response 1: Thank you for pointing this out. We agree with this comment. Therefore, We have presented the experimental data from Figure 5 in table format and provided a more detailed explanation of the origins of each parameter in the verification process.
Comments 2: Check the resolution of figures, particularly any graphs. Low-resolution images should be replaced with high-quality versions (Fig. 5).
Response 2: Thank you for pointing this out. We agree with this comment. Therefore, We have modified Figure 5 and presented the experimental data from Figure 5 in table format, such as Table 3 and Table 4, making it more intuitive.
Comments 3: The paper describes an adaptive KF algorithm to optimize the estimation of vehicle motion parameters. Can the authors provide a comparative analysis with other state-of-the-art adaptive filtering techniques, such as particle filtering or unscented Kalman filtering, to strengthen the validation of their approach?
Response 3: Thank you for pointing this out. Particle Filtering (PF) typically requires a large number of particles to maintain accuracy, leading to significant computational demands, especially in real-time applications. Unscented Kalman Filtering (UKF) may not perform as well in highly non-Gaussian or highly nonlinear situations as PF. While the adaptive KF algorithm proposed in our study is well-suited for optimizing vehicle motion parameters in real-time, each filtering technique has its strengths and weaknesses. The adaptive KF is ideal for linear or mildly nonlinear systems with computational efficiency being its key advantage. For future work, integrating adaptive techniques from both KF and PF (for example, a hybrid approach) could offer a promising direction, taking advantage of the strengths of both methods while mitigating their individual limitations.
Comments 4: The experimental validation of the algorithm primarily relies on chassis dynamometer tests. How do the authors account for real-world environmental factors such as varying road conditions and tire dynamics that may affect the performance of the algorithm in actual vehicle operations?
Response 4: Thank you for pointing this out. Regarding your question, please allow me to provide an explanation. The chassis dynamometer is an important component of indoor vehicle testing equipment. The ultimate goal of the chassis dynamometer test is to make it more closely resemble outdoor road tests. To obtain more accurate experimental data, it is necessary to ensure as much consistency as possible between the vehicle conditions in indoor and outdoor tests. As noted in Chapter 2, the precise acquisition of the speed and acceleration of the test vehicle is crucial for enhancing the accuracy of tests conducted on the chassis dynamometer. Therefore, the algorithm developed in this paper is designed to make the chassis dynamometer test more closely resemble outdoor road tests.
Comments 5: Given that adaptive KF algorithms may introduce additional computational complexity, can the authors elaborate on the real-time feasibility of implementing this method in a commercial chassis dynamometer system? Have they tested the computational burden of their approach?
Response 5: Thank you for pointing this out. Regarding your question, please allow me to provide an explanation. As mentioned in Chapter 2, Compared with other filtering algorithms，The computational burden and the number of processing steps of the adaptive KF algorithm based on innovation covariance are considerably reduced, thereby enhancing real-time performance. It can avoid the phase error caused by signal output delay. The validation can be obtained from the simulation and experimental results.
Comments 6: The study discusses Gaussian white noise filtering, but real-world signals often contain colored noise. How does the proposed approach perform when tested with non-Gaussian noise sources commonly encountered in automotive testing environments?
Response 6: Thank you very much for your valuable suggestions, which have provided inspiration for my future research. As for this paper, the road test and chassis dynamometer test results show that the adaptive KF algorithm based on innovation covariance is also effective for real-world colored noise. However, the modeling methods for colored noise, non-Gaussian white noise, and the impact of chassis dynamometer tests are indeed a promising research direction, which is worth further investigation in my future work.
Comments 7: The paper discusses fixed values for certain model parameters. Can the authors clarify whether the algorithm is adaptable to different vehicle types, or if it requires re-tuning for various test scenarios?
Response 7: Thank you for pointing this out. Regarding your question, please allow me to provide an explanation. Generally, when the same model of vehicle is tested on the same chassis dynamometer, its motion parameters A1, A2, B1, B2, C1, C2 are the same. However, the specific usage conditions of different vehicles of the same model vary. To ensure the accuracy of experimental data, it is necessary to perform road coast-down tests and chassis dynamometer coast-down tests on each individual vehicle to determine the precise motion parameters.
Comments 8: The quality of the English language in the sent article is good. But there are some grammatical and phrasing issues that should be improved for greater clarity and readability such as:
Original: "The chassis dynamometer plays an important role in the research and development throughout the entire lifecycle of vehicle."
Correction: "The chassis dynamometer plays an important role in research and development throughout the entire lifecycle of a vehicle."
Response 8: Thank you for pointing this out. We agree with this comment. Therefore, We have made the modifications according to your suggestions.
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsWe do not have any further comments on this revised version.
Reviewer 2 Report
Comments and Suggestions for AuthorsThe author provided effective responses to the relevant ambiguous issues.
Reviewer 5 Report
Comments and Suggestions for AuthorsNo more comments
