In this study, we estimated the angular diameter distances to two high-redshift active galactic nuclei (AGNs), OJ 248 (z = 0.939) and 4C +38.41 (z = 1.814), using 43 GHz radio light curves. The aim of this work is to extend AGN variability–based distance measurement methods to the high-redshift regime. The distance estimates were analyzed under two assumptions for the maximum intrinsic brightness temperature TB, int: (1) the equipartition temperature, and (2) the sample-averaged TB, int. As a representative result, when adopting the equipartition temperature, the angular diameter distances to OJ 248 and 4C +38.41 are estimated to be 7,592.7±396.7 Mpc and 11,069.8±1,216.9 Mpc, respectively. In addition, Doppler factors were calculated using the inverse-Compton method, and additional distance estimates were obtained based on these values. Our error budget analysis shows that the most significant systematic uncertainty arises from epoch selection. These results indicate that systematic effects have a substantial impact on the derived distance estimates and limit their reliability, particularly in the high-redshift regime. Reducing these uncertainties will require improved observational cadence and reduced post-fit noise. AGN variability provides an alternative approach to distance estimation. However, our results reveal significant limitations in the current methodology and indicate that further methodological and observational improvements are required before its cosmological applicability can be reliably assessed.

Introduction
Observational Data and Analysis
Results
    Calculating Variability Time-Scale Delta t
    Estimating DA Using Maximum Intrinsic Brightness Temperature
        Case 1: Equipartition Temperature Teq
        Case 2: Average Value from Samples of Multiple Sources TCheongB,int
    Calculating Doppler Factor delta and Estimating DA Using delta
Discussion
    Optimal Parameter Sets for Distance Measurements
    Error Budget Analysis in DA Determination
    Limitations and Prospects of Distance Estimation at High Redshift
        Choice and Applicability of TB,int Assumptions
        Methodological Limitations and Future Observational Requirements
Conclusion
Acknowledgments
References
Table of the Circular Gaussian Model-Fitted Values of the Core Measurements
Estimated Distances from Each Source

• Jeffrey A. Hodgson(Department of Physics and Astronomy, Sejong University, Seoul 05006, Republic of Korea)
• Sincheol Kang(Korea Astronomy and Space Science Institute, Daejeon 34055, Republic of Korea)
• Whee Yeon Cheong(Korea Astronomy and Space Science Institute, Daejeon 34055, Republic of Korea)
• Young-Bin Shin(University of Science and Technology, Daejeon 34113, Republic of Korea, Korea Astronomy and Space Science Institute, Daejeon 34055, Republic of Korea)
• Sang-Sung Lee(University of Science and Technology, Daejeon 34113, Republic of Korea, Korea Astronomy and Space Science Institute, Daejeon 34055, Republic of Korea) Corresponding author
• Chanwoo Song(University of Science and Technology, Daejeon 34113, Republic of Korea, Korea Astronomy and Space Science Institute, Daejeon 34055, Republic of Korea)