A multi-baseline PolInSAR forest height inversion method based on the Fourier-Legendre model and regularization

The Fourier-Legendre (FL) model employs Legendre polynomials to characterize radar wave propagation within vegetation. Compared to empirical functions used in conventional models, it has greater flexibility and adaptability, enabling a more accurate representation of complex scattering mechanisms. When applied to Polarimetric Interferometric Synthetic Aperture Radar (PolInSAR) forest height inversion, the FL model can significantly improve retrieval accuracy. In theory, higher polynomial orders provide more precise descriptions of radar scattering, however, increasing polynomial order introduces excessive unknown parameters, leading to ill-posed problems and reduced estimation stability. Given this, this paper proposes a multi-baseline fusion PolInSAR forest height inversion method based on the FL model and linear least squares estimation theory. Additionally, the regularization method is incorporated to mitigate ill-posed influence and enhance parameter stability. By constructing a regularization matrixforest height inversion experiments were then conducted using multi-baseline PolInSAR data. Finally, the results show that the conventional single-baseline inversion method achieves an optimal forest height estimate with an root mean square error (RMSE) of 6.73 m and an coefficient of determination (R2) of 0.84, while the new method yielded an RMSE of 5.53 m and an R2 of 0.89, representing an accuracy improvement of 18%. Therefore, the new method can effectively enhance the accuracy of forest height parameter inversion and is a practical and effective PolInSAR forest height inversion approach.