# Real-Time DTM Generation with Sequential Estimation and OptD Method
## 2 Materials and Methods
### Sequential Estimation in the Context of DTM Generation  
Sequential estimation is a sequential analysis method that is part of inferential statistics and enables staged data processing. The results of calculations from the previous sequence are included in the calculations performed in the next sequence. In processing measurement results, sequential estimation is used to improve the accuracy and reliability of parameter estimates by continuously updating them as new measurement data become available. This is particularly important in contexts where measurements might be noisy. Sequential estimation helps filter out noise from measurements by updating estimates progressively. This is especially beneficial in fields like engineering and signal processing, where measurements are often affected by random noise [35; 36]. A very common approach to sequential estimation is Kalman filtering [37]. In the context of DTM generation, both sequential estimation and Kalman filtering can be used for processing and analyzing spatial data, but they differ significantly in their methodologies, applications, and assumptions. Kalman filtering is a recursive algorithm designed for estimating the state of a dynamic system over time. It updates estimates based on new measurements and the previous state, which is particularly useful for time-series data. The Kalman filter consists of two main phases: the prediction step (where it estimates the next state) and the update step (where it incorporates new measurements to refine the estimate). Sequential estimation refers to a broader approach where estimates are updated as new data become available. It is not limited to any specific algorithm and can include various techniques, including Kalman filters. Sequential estimation can handle different types of data and models, making it adaptable to various situations in DTM generation, including both static and dynamic environments. Kalman filtering is particularly effective for integrating time-series measurements, whereas sequential estimation can be employed to improve DTM generation by continuously updating terrain estimates as new data from LiDAR become available [35]. The choice of the sequential estimation method over alternative approaches, such as Kalman filtering, was driven by its adaptability to real-time DTM generation and its ability to manage LiDAR data efficiently. Unlike Kalman filtering, which is optimized for dynamic systems and requires predefined system models, sequential estimation allows flexible integration of new data segments without imposing strong assumptions about temporal dependencies. This approach ensures that each sequence of acquired data contributes to an adaptive and localized model refinement, capturing variations in terrain representation with high accuracy. Moreover, sequential estimation facilitates computational efficiency by enabling incremental updates, reducing memory and processing demands compared to batch-processing techniques. These advantages make it particularly suitable for real-time applications where rapid, high-fidelity DTM updates are required. The essence of the proposed sequential estimation method in the context of creating the DTM is to generate a 3D model based on a function. The fluctuation of height values in a certain area is approximated by a polynomial equation. The assumption of the proposed solution is to perform calculations to generate the DTM in real time during measurement. The rules during measurements are presented in Figure 2.  
Geodetic measurements providing information about the location of points (spatial coordinates) and other data are collected during measurements (e.g., reflection intensity, temperature). The technology most often used to acquire data for DTMs is LiDAR. Measurements are performed continuously with data acquired in blocks (1, 2,..., k). Within each block, following the proposed methodology, observations are acquired in measuring strips (1, 2,..., i). Each measuring strip is acquired at a specific time and has a defined width [38; 39].