Towards Predicting the Measurement Noise Covariance with a Transformer and Residual Denoising Autoencoder for GNSS/INS Tightly-Coupled Integrated Navigation
Round 1
Reviewer 1 Report
The authors present a new on-line estimation algorithm of the measurement noise matrix for the extended Kalman filter that is used in the data fusion of the inertial navigation systems and the GPS navigator. The system uses a strongly coupled architecture in which the Kalman filter has as inputs the difference between the pseudoranges measured by the GPS and those estimated from the position of the inertial system. In these cases, the noise matrix of the measurement is highly variable (with the position of the satellites, the number of satellites, the geographical area...) and an online estimation mechanism of this matrix must be incorporated.
The algorithms used so far to solve the estimation of the covariance matrix are reviewed and a new one is proposed. In recent years, the current that uses artificial intelligence techniques for this type of problem has gained strength. The authors propose the use of a combination of two neural network structures (Residual Denoising Data Encoder and a Transformer NN). The algorithm is tested in a real environment with a navigation equipment installed in a car. Difficult situations that produce errors in GPS navigation (urban canyons, viaducts ...) are selected. The results are much better than with any of the previously published algorithms. In this sense, the proposal seems to have enough merit to be published.
However, in my opinion, the article is not ready for publication. I see the defects mainly in sections 2 and 3 (where the architecture and the algorithm are described). The description of the algorithm should be improved to make it more intelligible. Some examples of aspects that could be improved are:
- The models are not fully described. It remains to describe or obtain the FI, Hk matrices, the state transition matrices, the plant noise matrix... The psedorange and pseudorange rate equations are described but then they are not used to develop the extended Kalman filter matrices.
- Neural networks are explained in a very general way but it is not clearly explained how they act in this case. For example, the "Transformer" performs a mapping of the input data to a series of parameters that handle the autocorrelation matrix. What criteria is used to create the dictionary used by the neural network? How is the network trained? Eq 20 tells us about position at the output of the network, but the network gives covariance, not position …
- Make a slight revision of the article's writing.
Author Response
Dear reviewer,
We deeply appreciate your constructive comments which greatly help to improve the technical quality and the presentation of this manuscript. We took these comments and concerns seriously, and we attempted to address all these issues to reflect the advice of the reviewers in our revised manuscript. Our corresponding responses are listed point-by-point in the Word file below.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
This article aims to propose an adaptive measurement noise estimation algorithm using a Transformer based noise covariance prediction model, to dynamically estimate the covariance of measurement noise.
The English language is adequate, and the content is complete. The paper is written in an acceptable form, even if sometimes the GPS term is used and sometimes the GNSS one: please uniform that. Besides, Table 4 has been formatted in the wrong way: please fix it.
The patents section is incorrect: please verify the content and change it according to the journal’s template.
The reference section could be expanded considering more other research papers related to this topic, even if the contribution is quite new.
Starting from the previous considerations, I can affirm that the paper is not ready to be accepted for publication in the present form, but it needs a minor revision.
Author Response
Dear reviewer,
We deeply appreciate your constructive comments which greatly help to improve the technical quality and the presentation of this manuscript. We took these comments and concerns seriously, and we attempted to address all these issues to reflect the advice of the reviewers in our revised manuscript. Our corresponding responses are listed point-by-point in the Word file below.
Author Response File: Author Response.pdf
This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.
