Proxy system models (PSMs) translate climate signals to proxy measurements and make the direct comparison between climate model simulations and proxy observations possible. They are also known as "forward data models" in contrast to "inverse models" that translate proxy measurements to climate signals. Since the forward process is natural (climate affects proxy formation; not the other direction), and the solution of an inverse process could be non-unique, PSMs have become a key component in paleoclimate data assimilation frameworks that bridges climate model simulations and proxy observations.

Existing statistical PSMs usually yield output with uncertainties, assuming the input climate signals are noiseless. This study proposes a new PSM framework that considers noises not only in the output, but also in the input. The comparison against existing PSMs may improve our understanding of the impact of the input noise on PDA reconstructions. I find the topic of this study to be important, and the proposed approach is noteworthy. The manuscript overall maintains a fine quality, although there are instances where the writing seems informal, and several places require clarification regarding the details. Furthermore, a major concern of mine is that while an application example is presented and some differences are compared, it is still unclear, at least not straightforward enough, on how the new PSM framework shows improvement compared to the traditional ones in terms of proxy data modeling accuracy. Therefore, I think a major revision is necessary. A few specific comments are listed below.

• The idea of introducing prior noises is understandable. However, the setup of the current PDA projects applies an ensemble prior that samples potential prior errors as the input for the traditional statistical PSMs, which eventually can take into account the impact of the prior noises. In this ensemble prior setting, does the proposed new PSM framework show significant advantage? More discussions are needed.
• L31: What does "a" represent here; noise? Also, the word "unobservable" requires some clarification to readers not familiar with the method, as it is used many times in the manuscript. Does it mean the real signal without noise?
• L32: "Appendix 1" --> "Appendix A".
• Code availability: "Easy to read" --> "Intuitive"
• Conclusions: While I appreciate the author's theoretical work, overall it seems to me that the manuscript lacks a convincing validation. The author states that the next step is to apply the proposed PSM to different proxy types and to incorporate it into PDA projects. However, in my opinion, more tests and validations, e.g., real-world data modeling tests on more sites, and perhaps even a pseudoproxy DA experiment if the author would like to make concrete connections to PDA applications, are actually needed for this study to clearly show that this new PSM indeed works. The analyses in Figs. 1-4 and Table 2 show only the differences, which may not necessarily be the improvements.