## 1 Introduction  
Monitoring urban green space is important since the existence of green space in urban areas provides multiple biophysical, aesthetic, environment and socioeconomic benefits [1]. For pure pixels, the identification of urban vegetation is based on land use classification using different spatial resolution remote-sensing and GIS data [2; 3]. Urban areas are highly heterogeneous, however, and the radiometric data provided by space-borne sensors capture mixed pixels in most cases. The combination of the 3D structure of urban space with the spectral heterogeneity of urban objects leads to the complex spectro-directional signatures of the observed targets, even when observing pure pixels. The retrieval of a pixel signature must account for multiple scattering by surrounding urban facets. For mixed pixels, spectral unmixing is a useful method, but the spectral signatures of pure component objects must be known [4; 5; 6]. Additionally, using vegetation indices to estimate the vegetation fractional abundance has been widely investigated in remote-sensing research, especially the use of the NDVI [7; 8]. The vegetation fraction is generally written as a linear or non-linear function of the NDVI [7]. The NDVI is widely used in urban climate and environment research as an indicator of urban vegetation abundance for, e.g., emissivity estimation [9; 10; 11], or as an indicator of vegetation cooling [12]. Theoretically, an ideal vegetation index should only be sensitive to vegetative cover and insensitive to other factors, e.g., background spectral radiance, illumination and view directions, and surface geometry [13; 14]. The NDVI is sensitive to the background spectral radiance when used to characterize mixed surface targets [14]. Urban surface properties vary and the spectral signatures are very different from those of natural surfaces [15]. Additionally, urban areas have very complex geometry. The interaction between buildings and vegetation also changes the spectro-directional signal observed by remote sensing, with an impact on the retrieved vegetation indices in urban areas. The accurate quantification of urban vegetation cover is a fundamental component of urban ecosystem assessment and sustainable planning. Previous studies have concentrated on FVC estimation for land use types such as forests, agricultural lands and grasslands [16; 17; 18], and sometimes, semi-arid areas and heterogeneous ecological systems after fire were also explored [19; 20]. However, there is a paucity of knowledge and methodological development on urban FVC estimation. Air-borne remote-sensing data are useful [21], and their finer resolution facilitates the identification of urban vegetation. However, their global application is also hindered by limitations in spatial and temporal coverage, high costs, and processing complexities. Recently, the development of FVC estimation methods based on space-borne remote-sensing data predominantly employs machine learning and multi-source data fusion. [PERSON] et al. [22] proposed a generic FVC estimation process that is capable of jointly utilizing multiple satellite data. This process improves the spatio-temporal resolution of FVC products. [PERSON] et al. [23] employed radiative transfer models to simulate the GF-1 WFV canopy reflectance and FVC values and trained backpropagation neural networks with these synthetic samples. The algorithm was validated as being effective (R\({}^{2}\) = 0.790, RMSE = 0.073), but these methods are generic and have not been developed specifically for urban areas. Urban-object-based mixture analysis was performed by [PERSON] et al. [24], which differs from traditional pixel-based mixture analysis, resulting in a higher urban FVC estimation accuracy (R\({}^{2}\) = 0.92, RMSE = 0.0956).