Reconstructing the trajectory of the object's motion on the basis of measuring the components of its velocity

Abstract

The article considers the problem of reconstructing the course of physical quantities whose measurement is not directly available, but it is possible to measure their time or spatial derivative. Since each measurement is subject to error, this error is transferred to the determined physical quantity. Therefore, the problem arises of developing methods for reproducing the signal waveform as well as assessing the quality and optimizing of this process. In addition to the measurement data, the model and parameters of the studied phenomenon, control signals and the characteristics of the occurring disturbances can be used here. The work contains an exemplary analysis and interpretation of the signals of a selected phenomenon. The two-dimensional problem of reconstructing the trajectory of the object's motion was investigated on the basis of measuring the components of its velocity relative to the fixed system of reference. The article presents a model of the tested process, taking into account disturbances in processing and measurements, and introduces an indicator of the quality of trajectory reconstruction. The qualitative and quantitative results of motion trajectory reconstruction without filtering and with the use of the Kalman filter are presented. The article in its structure contains an abstract, an introduction to the problem of reproducing a physical quantity based on the measurement of its derivative, an introduction to state estimation methods, research methodology, the course of research and its results with analysis and conclusions from the work carried out.