The paper presents an improvement to a previous work of the authors where a transition, model, an activity recognition method, a recovery method for the particle filter, and an improved density estimation.

The novelty of the paper was collected in the reading and it should be more clearly listed. At the current status of the paper it is not clear. It should be itemized in the abstract and also in the obtained results.
-> Thank you very much for this advice. We tried to clarify this within the abstract as well as at the end of the introduction (see line xxx to xxx). We further added a discussion to the results,  which addresses the contributions and their impact on the system. 

The rapid computation declaration is not proven, given that the authors do not compare the non-gridded approach timings.
-> The terminology "rapid computation scheme" only refers to the state estimation process, not the underlying graph or the complete system performance. It seems this is not clearly formulated within the paper. The weighted-average estimator yields faster estimates of the position compared to the KDE approach as we have shown in our previous work .... This previous work does also provide an extensive comparison between other state-of-the-art KDE approximations. 
However, if you refer to the comparison between gridded graph and navigation mesh, ...
Nevertheless, ...

Does the system will also work in regular buildings? A final comment on the lessons learned in this case of the 13th century building should be in the conclusions, given that the title focus on this very specific context.
-> 

From the middle of the paper the quality of the English decreases with several sentences with errors, some of them were identified.
->

Given that the authors declare that this is an update they should be more clear on what was already done. We also consider that the authors use auto citation excessively (7 in 32) and or compress the self-citation or increase the comparison with other works.
->

The paper is relevant and should be published after a clarification on the produced work and at least report two comparisons, one in the performance of the KDE and other on the initialization time.
->

Some notes follow along the lines of the paper:

 

Ln 1- "of our award-winning"  

The authors should refrain to be excessive in the connotation of the work, at least in the abstract. Should not hide but can declare the award in a more soft way.
-> We have removed the remark and have formulated the remaining text passages more modestly.

Ln 9-…

"Continuous and smooth floor changes are enabled by using a simple activity recognition. Our rapid computation scheme of the kernel density estimation allows to find an exact estimation of the pedestrian’s current position. We further tackle advanced problems like multimodal densities and sample impoverishment (system gets stuck) by introducing different countermeasures, leading to a more robust localization.  " Too many adjectives without justification: simple, rapid, advanced...
-> You are right and we have rewritten the particular text-block. 

Ln 14: Why low cost solution? Are the material less expensive compared to what alternative? If the authors do not want to defend this property we suggest it should be removed. (also in Ln 64)
-> The argument that our system is inexpensive is based on several considerations: With under 10 dollars per piece the Wi-Fi beacons are very cheap compared to conventional access points. 
They only require a power source in order to operate, which keeps the need for additional infrastructure small. Furthermore, we believe that a janitor is able to set up our system independently. This means that there is no need to pay an external contractor to utilize the system and only the hardware costs and, if applicable, the price of the software have to be calculated. Nevertheless, as you suggested correctly, these considerations could not apply to all buildings and scenarios, which is why the property "low cost" is removed. 

Ln 21: “optimization scheme enables a setup-time of under 120 min for the complete building.  ”- Should indicate the mapped area.
-> Fixed in line 26. 

Ln 38: “There is also a higher chance of detecting false or misplaced turns,”
The sentence appears incorrect
-> Fixed in line 43.

Ln 40: “presents a robust but realistic movement”
Too many adjectives not explained
-> Fixed in line 45.

Ln 52: "This leads to problems for methods..." This phrase should be reformulated since Wi-Fi fingerprinting is RSSI based and might actually benefit from the high signal attenuation between different rooms. The problem is probably coverage of the whole building, not parameter estimation. 
-> This line was written with signal strength prediction models in mind, which is wrong in terms of fingerprinting, of course. Thank you for the hint! We tried the incorporate both, coverage and parameter estimation between line xxx and xxx.

Ln 58 of simple and cheap- How simple and how cheap?
-> The price mostly depends on the reseller, ranging from 3 dollar to 10 dollar. The term "simple" is of course difficult to substantiate, which is why it was removed. 

Ln 160 “are based on the nature of particle filter.” -> “are based on the nature of a particle filter.” 
-> Fixed in line 180.

Ln 215: "Using variable shaped/sized elements instead of rigid grid-cells provide both higher accuracy for reaching every corner, and ..." Is accuracy the right word here?
-> TODO: @Frank

Ln 228: "If the destination is unreachable, e.g. due to the walls or other obstacles." This phrase is incorrect, the authors should reformulate it.
-> TODO: Echt? Haben wir in der Intro oben auch. Warum ist das falsch?

Ln 237: "...the average acceleration..." This includes both linear acceleration and gravity, use "linear acceleration".
-> TODO: @Frank?

Ln 258 -  This equation needs revision. Should it be "p(s_i|p)  ~ N(u_i,p , std²_wifi)" ? Also the wall-attenuation-factor-model only takes into account attenuation by floors, not walls.
-> TODO: Eigentlich passt das mit der NV, für Ihn tdz ändern? Und das model nimmt keine wände, weil wir keine wände nehmen :D. 

Ln 271-272: The authors mention that their WiFi fingerprinting approximation process is faster than classical fingerprinting, but they fail to provide a reference for an example of the latter or significant metrics such as the average time per square meter for fingerprinting a whole building. Furthermore, the authors should also take into account that while there are approaches where reference measurements are recorded on small grids between 1 to 2m, there are also approaches able to record reference measurements using faster methods. One example is walking by the building while registering ground truth points and using dead reckoning techniques (see Guimarães, V. et al. A motion tracking solution for indoor localization using smartphones. In Proceedings of the 2016 International Conference on Indoor Positioning and Indoor Navigation (IPIN)).
-> TODO: vielleicht den satz hier entfernen und im related work darauf hinweisen, dass es auch andere schnelle ansätze gibt? Wobei wir im related work schon [20] gecited haben, der genau das macht! vielleicht erwähnen wir seinen noch, damit er zufrieden ist? Oder wir zeigen das kleine fingerprints schneller ist als laufen? was vermutlich nicht der fall ist. 

Ln 275 - Equation 9 The d0 parameter of eq.8 shpuld also be presented in eq.9.
-> Fixed in line xxx

Ln 307 “Activity Recognition ” The threshold approach should have reports on the detection capability
-> TODO: Also die pfade nochmal berechnen und da die erkennungsrate ausspucken.

Ln 316 - Equation 10 According to these rules a user could be standing and walking at the same time. The algorithm would be better represented by a flowchart or a decision tree.
-> You are right. Standing and walking at the same time should not supposed to be happen. We exchanged the equation with a decision tree. In our opinion the algorithm is now very easy to understand, thank you for the good advice. 

Ln 316: t_baro = 0.042 m/s² ? Wrong unit, please confirm value and unit again.
-> Of course, m/s² is the wrong unit for pressure. Changed to hPa.

Ln 360 “It is obvious, that a computation of the probability density function of the posterior could solve the above, but finding such an analytical solution is clearly an intractable problem, which is the reason for applying a sample representation in the first place.” The authors should refrain to make non scientific comments like “obvious” or “clearly”. Do direct statements. 
-> The objection is valid and we will fix the appropriate text passages.

Ln 381 “Our rapid computation scheme” – As commented before. Be more concrete and remove non justified adjectives.
-> As before, the adjective "rapid computation" was removed in behalf of approximation scheme.

Ln 453 “By utilizing it to a 13th century historic building”-> “By utilizing the proposed technology in a 13th century historic building”
-> Fixed as recommended. 

Ln 469: "8 cores..." The i7-4702HQ has 4 cores and 8 threads, not 8 cores.
-> This misstatement has been fixed.

Ln 551  - “above are more moderately attenuated” revise.
-> More understandable and correctly formulated in line xxx.

Ln 524 - Figure 4 "...xz plane..." should be xy plane
-> Fixed. 

Ln 578 “This allows us to discuss everything in detail” – irrelevant or should be better expressed.
-> Removed.

Ln 711 -  “The KDE-based estimation illustrates this behavior very accurate” – Revise
-> This sentence was very daring and incomprehensible. We tried to explain the situation in greater detail. Please refer to lines xxx to xxx.

Ln 713 – “the teal square” – It is not a square.
-> Replaced throughout the whole work by rectangle, area or border depending on the use. 

Ln 720 – “In the end, it is a question of optimal harmony between transition and evaluation.” This is sentence is not providing information and lacks scientific objectivity.
-> The sentence was removed, as it was irrelevant.

Ln 726 “At the end, in the here shown examples we only searched for a global maxima” – revise english


Ln 733 – “Compared to other state-of-the-art solutions, the setup time is only a few hours and does not require any expert knowledge or hardware.” This comparision is not done in the paper. The authors should be more specific given that this property of the purposed system is declared important, and so should be given with ore detail and (m^2 per hour) and compared with the coverage time of other systems.

Ln 754 – “opens up completely new possibilities when” – revise tone of writing. 
