###### Abstract
The earliest waveform retracking was applied to altimetry data in polar regions and the main problem is that the pulse signal reflected from the ice surface is totally different to the ocean pulse signal. Since, many algorithms are based on statistical properties of the waveform at that time, such as the \(\beta\)-parameter algorithm, OCOG, the threshold algorithm and the improved threshold algorithm [3, 4, 5, 6]. While, waveform retracking for the open ocean always considers the noise of waveform data and adopts maximum likelihood parameter estimation (MLE) with the Brown model, which is the standard processing for altimetry mission and usually improved by reducing the correlative bias between the fitted parameters of the waveform model [7,8]. The coastal areas, as the main activity area for humans, are under pressure because of climate change, population growth, expanding economic development, and meeting the risks from storm surge events and sea level rise. Altimetry data provides an irreplaceable contribution to pollutant dispersal, coastal erosion, flood risk assessment, extreme weather  
Figure 1: The diagrammatic sketch of an ideal waveform based on Brown model. forecasting, etc. In recent years, researchers have paid much attention to coastal areas and have accumulated more accurate satellite altimetry data in the range within 0-40 km offshore using new waveform retracking strategies. The main problem of coastal waveform retracking is not only the noise of data but also the 'pollution' of the waveform data, which means the standard waveform retracking process of altimetry products may lead an extra range bias and have to handle the distorted part of the waveform before fitting. For the coastal waveform, the leading edge of the waveform is usually totally fitted without any modification, and the trailing edge of the waveform is always partially fitted to avoid misinformation. In addition, under the condition of a certain performance of the waveform retracking algorithm, various types of coastal waveforms can be processed reasonably based on waveform classification. Waveform retracking based on subwaveform is an important method for coastal waveform retracking that adopts a complete leading edge and a small trailing edge to effectively fit the distorted waveform. The representative subwaveform retracking strategies are adaptive leading edge subwaveform retracking (ALES) and spatial-temporal altimeter retracking (STAR). ALES takes the adaptive subwaveform as the 'optimal' choice to yield suboptimal estimates when the coastal waveform is polluted. The adaptive subwaveform window is determined through the linear relationship between the tracking point and the SWH [9]. The coastal altimetry data of the Jason-1, Jason-2, and Envisat missions were reprocessed successfully using the ALES algorithm in the X-TRACK/ALES satellite data operational framework, and new coastal satellite altimetry data products and thematic datasets have been distributed [10; 11; 12]. However, the ALES algorithm fails when the 'pollution' is close to the leading edge of the waveform [13]. According to the spatial-temporal information of continuous waveforms integrated using random conditions, STAR separates subwaveforms from a single waveform by sparse representation. Then, the Dijkstra algorithm is used to obtain a reliable estimation from the polluted waveform [14]. The STAR algorithm shows superiority in dealing with extremely noisy waveforms, but the reliability of the derived sea surface height (SSH) data is reduced due to data smoothing and the reduction in SSH variability information in coastal areas [15]. Additionally, the subwaveform is adaptively determined by the size of the homogeneous surface, such as sea surface slick [16]. Compared with subwaveform retracking, total-waveform fitting is steadier and needs to carefully address the distortion of the waveform trailing edge.