# Real-Time DTM Generation with Sequential Estimation and OptD Method
## 1 Introduction
Visualization of such large datasets is often impossible, and they are usually unreadable to the user. Additionally, traditional computer systems and technologies limit the ability to act quickly while creating visualizations. Therefore, corporations and scientists around the world are working on improving both data dimension reduction algorithms and innovative approaches to hierarchical data management, as well as the scalability of data structures to visualize data in 2D or 3D, enabling their graphic interpretation. The aspect that affects the p4 problem is the method of generating the DTM. To generate DTMs, methods based on the TIN or grid structures (also known as raster models) can be used [4]. The TIN model is generally more computationally efficient when dealing with irregularly distributed data, as it only uses points where necessary to define the surface. Grid models can be computationally intensive when the grid resolution is high, leading to large datasets that require significant processing power and memory. Besides using grid or TIN models, mathematical functions can represent terrain, but their applicability and accuracy depend on the context and the complexity of the terrain [12]. Terrain as a regular grid of elevation points is easy to process mathematically but may not capture sharp features like cliffs well. A TIN represents terrain using irregularly spaced points connected by triangles. It adapts to terrain variability better than a grid but is computationally more complex. Mathematical functions provide a concise way to describe terrain features compared to large datasets like grids or TINs. For example, a single equation can represent an entire surface. Calculating elevations using equations is often faster than querying large datasets, especially for analytical tasks like slope, aspect, or contour generation. Moreover, functions can represent terrain at different scales without requiring massive storage. Another important advantage is that mathematical functions can smooth out small-scale noise in terrain data, focusing on general trends and eliminating unnecessary details, and they are ideal for creating synthetic or idealized terrains for testing, modeling, or simulations where real-world data are not available or required [13]. In real-time scenarios, generating or updating large grid models may introduce latency since the model is created by interpolating points on the grid nodes. Consequently, the resulting DTM contains interpolated points rather than actual measurements, which can cause difficulties in the subsequent use of the model and the dataset of points representing this model [5]. The choice of DTM generation method and reduction techniques affects the processing efficiency, which depends on the computing power of the computer and the capabilities of the software used. This can be analyzed by considering the time needed for processing, taking into account the computer's specifications. The fifth of the mentioned problems (p5) focuses on achieving the smallest possible size of the result file to store the acquired data and the generated DTM. The generated models are stored in raster files or as objects that are part of the software. Both models and files containing measurement data (often from several measurement epochs) can occupy a substantial amount of disk memory. The aim of this paper is to develop a new concept of DTM generation that takes into account:  
* using the OptD reduction algorithm to address the p3 problem;
* adapting sequential estimation to DTM generation to improve existing methods for solving the p4 problem;
* and storing models in the form a characteristics file (a new concept in the literature on the subject), which contains all the necessary information about the model and requires a small amount of disk space (solution to p5). By using this approach, it is possible to determine the real height of any point on the object.