## 1 Introduction  
Altimeters play a vital role in the effective operation of onboard platforms. The altitude data they provide supports critical functions such as maintaining stable flight levels, and plays an integral role in implementing advanced automated features. This includes the execution of autonomous return to launch points and automatic takeoff and landing processes. For instance, state-of-the-art consumer unmanned aerial vehicles (UAVs) utilize the Internal Measurement Unit (IMU) and Global Positioning System (GPS) to measure height. However, both sensors can only estimate the flight altitude relative to their starting position, and not the actual altitude over current terrain or vegetation [1]. Using radar sensors is advantageous, as they can directly sense range and velocity and are not affected by lighting conditions or contrast [2]. By integrating high-accuracy radar altimeters, the altitude measurement capabilities of onboard platforms can be significantly enhanced,enabling them to adapt more proficiently to dynamic flight conditions. This integration allows for the execution of intricate navigational tasks with heightened precision and dependability. Consequently, the importance of airborne altimeters is irrefutable in UAV operations [1; 3] and aircraft takeoff and landing [4; 5; 6; 7]. Radar altimeters can determine the distance between the radar and the ground surface. Pulse radar altimeters function by emitting a series of short pulses towards the ground and then measuring the time it takes for these pulses to be reflected back to the altimeter. The distance from the surface is determined by the round-trip delay of radar signals. The issue of high-accuracy altimetry has been extensively explored. The rough estimation of height can be obtained through tracking processing. Re-tracking is a crucial procedure applied in processing radar altimeter data to get more accurate height parameters [8]. It is an algorithm used to refine the estimated parameters of a radar echo, such as the time delay, power, and shape, which have been distorted by various factors during the signal's round-trip travel from the altimeter to the ground surface and back. Re-tracking methods mitigate these distortions to obtain more accurate and reliable measurements. This is achieved by adjusting the parameters of the waveform model, which is representative of the idealized or expected shape of the radar echo. The re-tracking of altimeter echoes is commonly performed using statistical inference-based algorithms such as the Least Squares (LS) method [9; 10; 11; 12], Maximum Likelihood Estimation (MLE) algorithm [13], and Bayesian inference [14; 15]. The accuracy of altitude measurements from radar altimeters can be significantly improved through re-tracking. To improve the estimation accuracy of waveform re-tracking, a series of average echo power models for SAR altimetry have been proposed. [PERSON] made a series of assumptions about the scattering scenario of a flat sea surface in the 1970s, suggesting the seminal threefold convolution form of the radar altimeter echo model. This model states that the echo power equals the convolution of the FSIR, point target response (PTR), and scatterer height density function (PDF) [16]. Based on the [PERSON] model, a series of semi-analytical and analytical models have been developed to accommodate different scenarios [13; 17; 18]. SAR altimetry harnesses the Doppler properties of high pulse repetition frequency-transmitted pulses to enable a higher spatial resolution through along-track aperture synthesis [19]. SAR altimetry can mitigate speckle noise compared to conventional altimetry (CA) by permitting multiple observations of the same scatterers through synthetic aperture processing. The resulting shape of the multilook echo diverges from that of the CA echo, necessitating a new altimetric signal model. Numerous studies have introduced numerical models suited to SAR altimeters [20].