A Redundant Measurement-Based Maximum Correntropy Extended Kalman Filter for the Noise Covariance Estimation in INS/GNSS Integration

Round 1

Reviewer 1 Report

In this paper, the authors proposed a novel algorithm, which combines the second-order mutual difference method with the maximum correntropy criteria extended Kalman filter. In general, the paper is well written. Besides, the method and the experiments are well described. However, the paper has some minor queries the reviewer suggests that the authors improve.

 

1. In Introduction, the authors mentions the heavy tailed non-Gaussian noise. However, the details about non-Gaussian noise are not discussed. At this point, the reviewer suggests that non-Gaussian noises like alpha-stable, Middleton Class A, Middleton Class B, Gaussian mixture noise are discussed. Besides, the application of these non-Gaussian noises should also be refered.

 

2. In Eq.(16) and Eq. (17), the reviewer wanders to know how to determine the kernel size and length of the sampling window. The authors should comprehensively discuss the choice method of these parameters.

 

3. Since the authors’ method is based on the iteration, the reviewer wanders to know how to guarantee the global convergence. The authors should discuss this in detail in their paper.

The English is fine to me.

Author Response

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Reviewer 2 Report

This paper presents a novel algorithm combining the second-order mutual difference with the maximum correntropy criteria extended Kalman filter. The classic problems including isolation for the GNSS measurement noise estimation from the state estimation and the auto-correlated statistic sequences issues as well as the performance of EKF would be degraded under the non-Gaussian condition. These two problems are critical for the integration of GNSS and INS and impede the development of GNSS/INS integration method. I am glad to see the authors made contributions to this field. The methodology is well-designed, and the manuscript is also organized properly. The contributions are sufficient for the publication. I don’t have major concerns about this manuscript but only have some minor comments to help the authors to improve the paper and make it more impactful.

-The method in this paper is based on the pseudo-range and pseudo-range rate to develop the fusion between the INS and GNSS, which is a tightly coupled integration between them. However, in the literature, the loosely coupled integration between the GNSS/INS is also of great interest to the readers. So, it will be great to discuss the applicability of the method in this paper on the loosely coupled integration architecture between the GNSS/INS. Please discuss this point with the most recent work in autonomous vehicle kinematics and dynamics synthesis for sideslip angle estimation based on consensus kalman filter; automated vehicle sideslip angle estimation considering signal measurement characteristic; imu-based automated vehicle body sideslip angle and attitude estimation aided by gnss using parallel adaptive kalman filters; improved vehicle localization using on-board sensors and vehicle lateral velocity; estimation on imu yaw misalignment by fusing information of automotive onboard sensors. Ideally, the discussion can be in the introduction or the results and discussion sections.

-In line 397, .5.1. should be 5.1.

-Is that possible to provide the GNSS status in GPGGA in the figure 3 and 4? Having that information will make the reader know better about the GNSS signal condition.

-In Table 1, only the imu information is provided. How about the GNSS receiver?

-From my understanding, the method in this paper is dedicated to pure GNSS/INS integration regardless of the platform where the system is on. However, as of the current stage, autonomous driving and machine learning develop fast. More sensors including cameras and LiDAR are usually mounted on the roof of autonomous vehicles. For localization, the measurement from the camera and LiDAR may also include non-Gaussian or correlated noise. So, I believe the work in this paper can be applied to the areas where the LiDAR and camera play the same role as the GNSS does for the multi-sensor fusion localization structure. I suggest authors discuss the potential of the work in the areas where LiDAR and cameras are used for perception or localization in autonomous driving. Some state-of-the-art works should be investigated in the paper: automated driving systems data acquisition and processing platform; yolov5-tassel: detecting tassels in rgb uav imagery with improved yolov5 based on transfer learning.

 

-Please elaborate more on the caption for Figure.1. 

Author Response

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Reviewer 3 Report

This paper addressed a common problem for fusing GNSS/INS modules. Specifically, it resolves the auto-correlated issue of the GNSS noise measurement by calculating the noise covariance adaptively. This is a typical issue for sensor fusion even for lidar cameras and ins integration. So, the topic will be much of interest to the readers. The paper is well-written and the contributions are solid. Also the results are convincing. I just have comments below. 

1) Please add acceleration information in the results section.

2) The measurement model is based on the pseudo-range, does the method work for the loosely coupled GNSS/INS integration? Please add some relevant literature regarding the loosely coupled architecture to emphasize the significance of the work.

Author Response

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