Modeling returned signal of a satellite laser altimeter over an urban area

Abstract

Modeling the returned signal of a satellite laser altimeter is a significant theoretical foundation for understanding the topography of the Earth. According to the lidar equation and working principle of laser altimeter, we establish the mathematical expression of the urban target response waveform (TRW) by using a definite integral formation. The characteristic parameters of the TRW, including signal energy, time delay, pulse width, and skewness are deduced in detail. Based on the specifications of the global ecosystem dynamics investigation laser altimeter and the assumption that the target is considered a rectangular plane, we simulate the influences of the geometrical parameters of the target, including the region area, the center geolocation, and the surface slope, on the TRW patterns and the characteristic parameters. The simulation results show that the TRW would present left-skewed and right-skewed patterns, with the exception that the center geolocation is nearly coincident with the laser footprint center. Such skewed distributions make the time delay derived from the TRW time centroid inaccurate for representing the range between the laser altimeter and the target center. In addition, the TRW energy is positively proportional to the region area and the proximity of the center geolocation to the laser footprint center and attenuated by the cosine of the surface slope. The root-mean-square pulse width is principally determined by the tangent of the surface slope. The simulation results contribute to a better understanding of the relationship between the TRW pattern and the geometrical parameters of the illuminated target. In particular, the characteristic parameters of the TRW can provide the detailed references for developing the waveform processing algorithm and the inversion of the surface elevation, the slope, and the reflectance. The returned signal in this paper may facilitate the application of the satellite laser altimeter over an urban area.