# Real-Time DTM Generation with Sequential Estimation and OptD Method
## 1 Introduction  
Generating digital terrain models (DTMs) based on real-time data acquisition from technologies such as light detection and ranging (LiDAR), multibeam echosounder (MBES), or ground penetrating radar (GPR) for mass data acquisition is very time-consuming andlabor-intensive. The first difficulty related to filtering (p1) is the detection of outliers due to multiple reflection [1]. The second challenge (p2) involves performing the filtering process itself, which includes separating points representing the terrain from those representing detail points [2]. The third difficulty (p3) arises from the need to simultaneously generate the DTM while acquiring new data [3]. The fourth challenge (p4) pertains to the method used for generating the DTM [4]. Lastly, the fifth significant issue (p5) is the size of the output file required to store both the acquired data and the generated DTM [5]. Outlier detection, related to the p1 problem, is a technique used to identify unusual or suspicious events or datasets. Anomalies are understood as data points that differ from the norm and are rare compared to other instances in a dataset. Two commonly used methods for anomaly detection are transfer learning and local outlier factors (LOFs). Transfer learning involves using pretrained neural networks to create models more quickly and efficiently [6] while LOFs evaluate an object based on its isolation from other data points in its local environment [7; 8]. In the context of solving the second point, i.e., performing filtering, known algorithms can be used. These include progressive morphological filtering (PMF) [9], triangular irregular network (TIN)-based filtering [10], or hierarchical robust interpolation (HRI) [11]. Each of these methods has distinct advantages and limitations depending on the terrain type and data characteristics. PMF is widely applied due to its computational efficiency and ease of implementation. It classifies points based on morphological operations and elevation differences, making it effective for flat or gently sloped terrain. However, PMF struggles with steep areas and complex structures, where selecting an appropriate window size is crucial for reliable results [9]. TIN-based filtering constructs a triangulated model of the ground surface and iteratively refines it by adding points that meet slope or height criteria. This approach is particularly well-suited for steep and irregular terrain, where it preserves terrain features more effectively than PMF. However, it is more computationally demanding and sensitive to noise, often requiring additional post-processing [10]. HRI, in contrast, uses a hierarchical surface fitting approach with robust statistical measures to separate terrain from non-terrain points. This method is highly effective in areas with mixed land cover, such as forests or urban environments, as it better handles outliers and complex surface structures. Nonetheless, HRI requires more parameter tuning and is computationally intensive, making it less suitable for real-time applications [11]. The selection of an appropriate filtering method depends on the specific dataset and application requirements. Problem p3, concerning simultaneous generation and visualization of DTMs and data acquisition, requires a special approach. This approach should consider the size of the measurement dataset, the DTM generation algorithm, and efficiency. In many cases, the large amount of measurement data interferes with readability, making it difficult to determine and properly interpret the characteristics of the measured objects. For this reason, an important issue related to the management of big data is the reduction in data dimensionality in the context of analysis and visualization. This is one of the more demanding challenges of data analysis because data records are multidimensional. Taking measurements with modern technologies is often supported in real time using computers with dedicated software.