The estimation and correction of antenna patterns are essential for ensuring the relative radiometric quality of SAR images. Traditional methods for antenna pattern estimation rely on artificial calibrators or specific stable natural scenes like the Amazon rainforest, which are limited by cost, complexity, and geographic constraints, making them unsuitable for frequent imaging demands. Meanwhile, general natural scenes are imaged frequently using SAR systems, but their true scattering characteristics are unknown, posing a challenge for direct antenna pattern estimation. Therefore, it is considered to use the calibrated SAR to obtain the scattering characteristics of these general scenarios; that is, introducing the concept of cross-calibration. Accordingly, this paper proposes a novel method for estimating the SAR range antenna pattern based on cross-calibration. The method addresses three key challenges: (1) Identifying pseudo-invariant natural scenes suitable as reference targets through spatial uniformity and temporal stability assessments using standard deviation and amplitude correlation analyses; (2) Achieving pixel-level registration of heterogeneous SAR images with an iterative method despite radiometric imbalances; (3) Extracting stable power values by segmenting images and applying differential screening to minimize outlier effects. The proposed method is validated using Gaofen-3 SAR data and shows robust performance in bare soil, grassland, and forest scenarios. Comparing the results of the proposed method with the tropical forest-based calibration method, the maximum shape deviation between the range antenna patterns of the two methods is less than 0.2 dB.