A Sequential Student’s t-Based Robust Kalman Filter for Multi-GNSS PPP/INS Tightly Coupled Model in the Urban Environment
Round 1
Reviewer 1 Report
A well-written well-organized paper focusing on troublesome issues associated with GNSS plus INS topics. The idea to use SSTRKF to overcome gross error induced colored noises is very interesting and has been proved effective by means of field testing.
Major issues
1. The PPP model used is based on UDUC observables but the stochastic modeling of the GNSS data makes use of GF and ED observations. Why not use the variance component estimation to analyze the stochastic characteristics of UDUC observables, which I think is more straightforward.
2. I assume the PPP is not the most reasonable technique for the purpose of GNSS-based positioning in urban environment as it is always subject to the long convergence problem. Can the method used in this work be extended to the RTK+INS scenario? I think this extension is possible.
Minor issues
1. Perhaps, the references related to UDUC PPP should be properly cited
2. The experimental duration is about 750 s. I think it is little bit short to draw representative conclusions.
Author Response
Dear reviewer:
Thanks for your suggestions and questions. We have reponsed all your questions and made relevant corrections. Please see the attachment. Thanks for your time.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
The precise point positioning (PPP) and inertial navigation system (INS) tightly coupled navigation becomes a common selection for urban positioning solutions. Inteferences derived from the complex urban scenarios usually degrade localization performanc as it is hard to properly model the stochastic characteristics for urban environments. This submission has proposed the sequential Student’s t-based robust Kalman filter (SSTRKF) to deal with the obstinate multipath errors in the urban environments based on epoch-differenced and geometry-free (GF) models. Some road experiments in urban environments and simulations have tested the benefits of the suggested frame. To further validate merits for SSTRKF, authors are expected to verify the following issues: 1. in line 196, the cut-off elevation is set to 35, what is the effect if it is set lower than 35 as this may cause loss for precious satellite sources under urban conditions?. Moreover, signals below 35 degrees may suffer more NLOS influences. 2. in line 371, the sample rate is set as 1 second to for the whole test, what is different performance if it is set to another rate as stochastic features for residuals of ionosphere delays, hardware delays and NLOS from ED will challenge the predefined statistical tests.
Author Response
Dear reviewer:
Thanks for your suggestions and questions. We have reponsed all your questions and made relevant corrections. Please see the attachment. Thanks for your time.
Author Response File: Author Response.pdf
Reviewer 3 Report
This paper proposed a new robust Kalman filter (SSTRKF) to reduce the impact of blockage and multipath in urban environment on PPP/INS solution. Modeled noise was used to simulate a complex urban environment and the proposed method achieved nice results. Following are my comments:
1. line 107-109, equation (1) is GNSS-based observation equation, while the authors stated it as PPP/INS tightly coupled observation.
2. line 141-144, what’s the relations or differences among xk, xkr,and pk? And equation (2) seems to have many irrelevant un-known parameters, are they really all estimated?
3. Section 3.2 using one simple case seems to me not sufficient to support the benefits of Student’s distribution.
4. Both SSTRKF and STKF require iterations. Does SSTRKF consume less computational resources than STKF? Why is the performance of the STKF not discussed in subsequent experiments?
5. Line 397, Figure 6 alone does not show that the number of satellites has reduced, I presume that the author wants to express that the number of satellites has decreased in combination with the above data.
6. Figure 7, simulation #1 seems to suffer longer NLOS reception errors but the performance of simulation #1 is less affected compared with simulation #2 and simulation #3. Similar scenario is found in Figure 9, where the three robust methods perform very similarly in simulation #1. According to the author , this is due to the different number of AS. That is, when AS is enough, the effect of LOS and NLOS will be small. My question is how many satellites would it take to have a large error similar to the one in simulation #2 and simulation #3. Is there a threshold?
7. Figure 7&9, why the positioning error is gradually increasing after the conditions deteriorate, yet the accuracy will instantly return to normal after the environment turns better?
8. Figure 8, what these different colored dots mean?
9. Figure 8, I see multiple statistics straight beyond 13.277, why?
10. Figure 9, was the experiment done in the scheme 3 setting? Has it been mentioned somewhere?
Author Response
Dear reviewer:
Thanks for your suggestions and questions. We have reponsed all your questions and made relevant corrections. Please see the attachment. Thanks for your time.
Author Response File: Author Response.pdf
Reviewer 4 Report
This manuscript discusses navigation in an urban environment by using a combination of an inertial navigation system (INS) and GNSS data based on Precise Point Positioning (PPP).
The author states (p. 1, line 35) that PPP/INS performance depends on the quality of GNSS observations. It is not obvious to me that this is true. in gerneral A simple model would suggest that INS data is better at short averaging times, because PPP analysis is difficult in near real-time whereas PPP data is better at longer averaging times because INS devices have inherent instabilities and drift with time. This simple model would suggest that the combination of the two data sources would have some dependence on averaging time or data length. The test data of 750 seconds would seem to be much too short to be significant to address this question. It is particularly difficult to use a PPP analysis for only a few minutes of data.
Both line of sight (LOS) and non line of sight (NLOS) multipath contributions are systematic offsets. They are always greater than the direct signal, although the contribution is certainly time-dependent. Although a statistical method can attenuate and possibly remove the stochastic variation in the multipath, it is not clear from the text how the authors address the systematic portion of the contribution.
Section 2.1. It is not clear from the text whether the author is considering a static or a moving receiver. If this is a moving receiver then the author should discuss how the precise products are acquired and applied in real-time. The subsequent sections that refer to pre-processing also seem to be not compatible with a navigation solution that uses an Inertial Navigation System.
It is possible that the entire discussion is based on a post-processed analysis, and that the 750 seconds are a subset of the data that has no errors and no cycles slips so that it can be processed by using the methods that the author presents. This is certainly a possible discussion, but it significantly reduces the significance of the work.
The vector e2 and UDUC should be defined
Section 3.1 The detection and removal of cycle slips should be addressed. The author assumes that there are no cycles slips, (line 187) which is certainly possible, but not realistic. Likewise, the question of absence of gross errors (line 219). See my previous comment about this.
Author Response
Dear reviewer:
Thanks for your suggestions and questions. We have reponsed all your questions and made relevant corrections. Please see the attachment. Thanks for your time.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
Acceptable revised work, thank you.
