## 1 Introduction
The LFDO constrains the solution since the update of adjacent atmospheric parameters in a profile are close, which is less harmful than the use of an a priori of what are significantly dynamic atmospheric parameters. Theoretically, the final RTLS solution is independent of the initial guess parameters of targeted retrievals and regularization is data-driven at all iterations. A successful implementation of a similar algorithm (termed as \"Modified Total Least Squares\" or MTLS) in the near-real time (NRT) operational environment [27; 28] for sea surface temperature (SST) retrievals has been in effect since August 2013 for three operational geostationary satellite sensors (GOES-13, GOES-14 and GOES15) at the Office of Satellite and Product Operations (OSPO), National Oceanic and Atmospheric Administration (NOAA). This is a relatively low ill-conditioned problem (typical condition number of Jacobian \(\sim\)5) and is solved by a single iteration. The paradigm shift in operational inverse method is providing NRT high-quality SST data to the community with a 50% reduction in error, as compared to the previous stochastic (regression) method. The implementation has been made after careful investigation of comparative results from various inverse methods. It is worth mentioning that OEM error is always higher than least squares(LS) error see Figure 11 [28] for such a simple problem, which is expected because additional error input into the retrieval system increases the error in OEM output. Similar algorithms employing MTLS or truncated total least squares (TTLS) on offline SST retrieval using MODIS-A L1B data [29; 30] have significantly improved the retrieval results. This provides us with strong confidence that the proposed physically deterministic method can also be successfully employed in real-time operations for hyper-spectral measurements. We have published preliminary simulated results [13; 14], where it was found that satellite hyperspectral retrieval problems can be uniquely solved using the RTLS method for simulated retrievals (IR and microwave). We demonstrated successful O\({}_{3}\) retrieval using RTLS [16] for a limited observation, where balloon-based occultation FTIR measurements were used with very high spectral resolution (0.004 cm\({}^{-1}\)). The horizontal spatial resolution of nadir-viewing atmospheric measurement is high compared to limb/occultation, which makes it attractive to understand local as well as global atmospheric processes. This study will focus on the simultaneous simulated retrieval of O\({}_{3}\) and ST from the nadir-viewing satellite-based FTIR measurements of CrIS, Cross-Track Infrared sounder, with a spectral resolution of 0.625 cm\({}^{-1}\)) and TES, Tropospheric Emission Spectrometer, with a spectral resolution 0.06 cm\({}^{-1}\). These results have also been compared against a prevalent method using OEM. We have made significant progress in this field, but we realize that more is needed to convince the scientific community of our findings, and to secure support from space agencies to make further progress through wider implementation of deterministic techniques in satellite retrieval problems. The key points of the retrieval algorithm using RTLS method for remote sensing measurement are rewritten for the convenience of readers in Section 2. Simultaneous smooth profile of O\({}_{3}\) and surface temperature using RTLS for two different infrared sounders CrIS and TES will be presented in Section 3. The information content using sub-space analysis for understanding of the noise propagation from measurement to the state space under ill-conditioned matrix will be discussed in Section 3.3. Section 4 includes the simulated retrievals from realisticozonesonde data. The retrievals from selective profiles ofozonesonde data is explained in Sections 4.1 and 4.2 for two different methods of RTLS and OEM, respectively. Sections 4.3 and 4.4 include the comparative retrievals between methods of RTLS and OEM for both CrIS and TES.