An Improved Innovation Adaptive Kalman Filter for Integrated INS/GPS Navigation
Round 1
Reviewer 1 Report
Generally speaking, the article is well-organized and well-written, but there are many typos and grammar problems, such as:
1. In the last paragraph of Introduction, "Second 2", "Second 3", "Second 4", "Second 5" should be "Section 2",....;
2. Between Equation (2) and Equation (3), "of step..." should be "of step k...", "metting" should be "meeting"?;
3. On page 13, in the first line, "the article" repeated twice;
4. Under Figure 11, "the algorithm in this paper" repeated twice.
Author Response
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Author Response File: 
Author Response.pdf
Reviewer 2 Report
Dear authors,
Congratulations on an excellent job, with up-to-date references and a great effort to include both simulated and real-life validations. I have, however, a few concerns with the proposed method and the validation you chose. I broke them down into two segments. The minor comments regarding grammar, clarity, and some general required clarifications are in the attached PDF. The primary concerns and questions are the following:
1 - When the EKF implementation does not adapt the measurement noise matrix (R) values at all, I understand how a filter can either diverge or be unable to properly model the antenna dynamics (as mentioned in lines 177 to 183). However, when dealing with GPS/GNSS positioning, this is accomplished using signal-to-noise ratio metrics and other metrics derived from signal strength and the agreement between multiple signals or carriers (code-minus-carrier, for example). On a loosely-couple GNSS/INS integration, this is accomplished by modeling R based on the state covariance from the GNSS positions and velocities as well as calibration values from the INS (which won't change over time in ideal conditions). In your proposed method, my impression is that you assume that the GNSS positions will be biased - which can happen - but without any "reaction" from the covariance matrix. In integrity terms, this would be considered a misleading solution that most commercial receivers are calibrated to avoid. Am I correct in assuming that your implementation considers a completely static R matrix, regardless of the measured signal quality?
2 - There are two important factors missing from the paper: The Chi-Square test significance (90%, 95%, 99%?), and the most relevant, the window size k for the averaging window. In equation 20, the value k is undefined, even though it plays, in my opinion, the most important role in your proposed algorithm. Think about it in a practical scenario. If a vehicle has been driving through an open road for a long time, with a large k, the average value rk^ would be small. Once signal interference starts, even if it's very mild and properly modeled by the SNR, it would have a large effect when the term (rk -rk^) is calculated. In a scenario where a receiver is, for some time, in a highly challenging environment, new interferences, even if severe, would not create a significant effect since the window size hasn't been adapted as well, and the average term rk^ would be large already. What is the impact of the chi-square significance value, and, most importantly, the average window size? Don't you think the window size should be adapted, perhaps by using the antenna's velocity? Or an estimate of the environment surrounding the antenna?
3 - Your equation for the measurement noise matrix additive term along with the new matrix is:
Rk^ = (rk -rk^)(rk -rk^)^t + Rk
Considering that
rk = Zk - Hk X^k,k-1
is the innovation term, it is easy to see that the addition to the measurement noise matrix will be proportional to the innovation, or, in other words, your prediction residual. However, this innovation term is not only correlated with improper measurement statistical modeling of your filter. It also correlates with your physical model's capability of tracking the movement of the antenna. When applying a transformation from the measurement space to the state space (through the H matrix), there are assumptions in the filter that, in real life, are not perfectly realized. Do you believe the measurement noise model is the best place to correct those assumptions? In your paper, you mention several times that the R matrix is the most important place to apply those changes, but I would argue that by adapting R, you're not modeling measurement noise only but also compensating for other effects. Do you agree with this assumption? I believe this should be discussed in the paper if the answer is either yes or no. This seems to me the reason that many authors adapt R and Q simultaneously, so the proper effects can be modeled where they happen.
4 - In lines 216 to 218, you show the traditional R adaptation method that applies changes at every epoch, regardless of whether an outlier is detected. You mentioned in the paper that your method behaves better than the traditional ones by eliminating divergence problems (If I understood correctly, lines 243 to 249). I believe it would be interesting to add this traditional method as a comparison point in your paper. It makes sense to me that less interferences in the process are likely to be less damaging to convergence. However, the traditional method you mentioned also has the capability of scaling down R, while the methods proposed in the paper only scale it up. There are situations where the measurement noise is too high and needs to be adapted. Did you account for that?
5 - How was the noise created in your simulated experiments? When the higher error occurs, what is the state covariance matrix from the GPS/GNSS measurements? Does it stay the same, or is it also scaled up?
6 - In your real-life experiment, are the GPS/GNSS errors also simulated? I had the impression that those are not multipath or interference-derived errors. Are they purely Gaussian noise applied in the position output? If so, the same question above applies. What is the state covariance behavior in the GPS/GNSS solution? The behavior of real-life multipath is quite different from a Gaussian-derived noise. Actual interference from an urban canyon or overhead trees would actually show whether the proposed method is suitable for real-time applications.
Finally, I believe the paper is great in terms of cadence, references, and general idea. There's some work needed to make clear that the method is novel, since the chi-square test at the innovation term has been evaluated by a few authors:
- Y. X. Zhu, X. H. Cheng, and L. Wang, “A novel fault detection method for an integrated navigation system using Gaussian process regression,” Journal of Navigation, vol. 69, no. 4, pp. 905–919, 2016.
- C. Yang, J. Guo, L. Zhang, Q. W. Chen, and S. O. Automation, “Fuzzy adaptive unscented Kalman filter integrated navigation algorithm using chi-square test,” Control and Decision, vol. 33, no. 1, pp. 81–87, 2018.
- G. L. Gao, S. S. Gao, G. Y. Hong, X. Peng, and T. Yu, “A robust INS/SRS/CNS integrated navigation system with the chi-square test-based robust Kalman filter,” Sensors, vol. 20, no. 20, p. 5909, 2020.
- Y. T. Gao, Y. Gao, B. Y. Liu, and Y. Jiang, “Enhanced fault detection and exclusion based on Kalman filter with colored measurement noise and application to RTK,” GPS Solutions, vol. 25, no. 3, p. 82, 2021.
- C. W. Chen and S. S. Kia, “A Renyi divergence based approach to fault detection and exclusion for tightly coupled GNSS/INS system,” in Proceedings of the 2021 International Technical Meeting of the Institute of Navigation, pp. 674–687, Manassas, VA, 2021.
- J. Liu, D. Li, and Z. Xiong, “Research on an improved residual chi-square fault detection method for federated unscented Kalman filter,” Chinese Journal of Scientific Instrument, vol. 30, pp. 2568–2573, 2009.
Some work is needed to place the paper in a position where none of those previous references have been reached and assessed. Work is also needed in the real-life experiment section to ensure the proposed method is suitable for actual interference and not only simulated data.
I look forward to receiving a future paper version with those points addressed. I believe the idea has merit but needs to be more properly explored.
Comments for author File: Comments.pdf
Author Response
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Author Response File: Author Response.pdf
Reviewer 3 Report
An Improved Innovation Adaptive Kalman Filter for Integrated INS/GPS Navigation is concerned, I have following issues:
1 The contribution made is the direct application od existing techniques, since AKF has been widely and sufficiently studied in past years, and the claim can be found from the citing of design process, thus the innovation is slim.
2 The challenges and motivation as well as detailed analysis of mechanism are not given from introbuction and simulations, thus also confirming the low values of this paper.
3 How to guarantee the comparison fairness? The authors obviously miss such statement. And the existing and recent AKF should be carried out to make a comparison. Experemental outcomes seem less convincing, as videos and detailed pictures and parameter tuning are missed, which also makes a less convincing result.
4 Significant literatures on AKF are obviouly not suitably cited.
Author Response
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Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
Dear authors,
Thank you for the effort in considering and applying the suggestions from the previous review. I'll mark the paper as accepted after minor revision and recommend the following points to be addressed:
1) Mention clearly in the paper that the noise from the real-life experiment was artificially added. Show how it was added. (Gaussian noise? With which average and standard deviation? Added to the position or to the observables? Added to the R matrix as well?)
2) Make a thorough English language review. Some sentences are still difficult to read. The overall meaning can be understood, but clarity can certainly be improved.
3) Add a paragraph or two after the literature review explicitly positioning the paper and the proposed method in relation to the other papers published before. How is this method different? How is this difference relevant?
Author Response
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Author Response File: Author Response.pdf
Reviewer 3 Report
The authors have not positively answered my questions, the conribution made is still slim and is just a simple utilization of existing methods without new highlights, and the experiments are not detailed and convincing.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Round 3
Reviewer 3 Report
I am satisfied with this revison, i recommend publish in current form.
