Konrad Andrzej Markowski

This paper tackles the problem of noise analysis and identification in the gyroscope of the LSM06DSO32 inertial navigation sensor based on MEMS technology, under helium exposure. This study focuses on analyzing the bias and variance of the gyroscope noise, as well as identifying its model’s order using fractional-order calculus. The order was estimated using methods based on variance and correlation analysis of data collected from the sensor at various time intervals during helium exposure. This work extends previous research on analyzing and identifying inertial sensor noise under varying temperature conditions. Considering that helium exposure may significantly influence IMU measurements, this study presents a detailed investigation into the evolution of gyroscope noise under prolonged helium exposure, followed by an analysis of the sensor’s behavior after its removal from the helium environment.

This paper deals with identifying the fractional-order noise parameters for MEMS gyroscopes under various temperature conditions. The significant contribution of the paper is to investigate the relation between the fractional noise model of MEMS devices and different ambient temperatures. In our paper, variance, correlation, and introduced estimation analysis methods have been meticulously applied to determine noise parameters with fractional-order dynamics. Experimental data were collected precisely under various ambient temperatures, while the MEMS device was located in a climate chamber. The origin of the paper is motivated by a project entitled “Family of optoelectronic heads for guided missiles—SEEKER”, where the IMU sensor is a crucial electronic device used to measure the angular velocity of the optoelectronic head. It is widely known that the IMU measurements built-in MEMS technology often come with a random walk, as well as biases and noises affecting the final results.

In the last two decades, fractional calculus has become a subject of great interest in various areas of physics, biology, economics and other sciences. The idea of such a generalization was mentioned by Leibniz and L’Hospital. Fractional calculus has been found to be a very useful tool for modeling linear systems. In this paper, a method for computation of a set of a minimal positive realization of a given transfer function of linear fractional continuous-time descriptor systems has been presented. The proposed method is based on digraph theory. Also, two cases of a possible input-output digraph structure are investigated and discussed. It should be noted that a digraph mask is introduced and used for the first time to solve a minimal positive realization problem. For the presented method, an algorithm was also constructed. The proposed solution allows minimal digraph construction for any one-dimensional fractional positive system. The proposed method is discussed and illustrated in detail with some numerical examples.

This paper presents the first proposition of a method allowing the determination of a set of (A, B, C, D) realizations of the one-dimensional single-input multi-output (SIMO) dynamic system from created digraph. The algorithm presented is the extension of previously published algorithm that finds a complete set of all possible realizations, instead of only a few realizations, as was in case of canonical form methods. The advantages of the proposed method are the possibilities of obtaining a set of state matrices directly from digraph form of the system and using fast parallel computing method. The algorithm is presented in pseudo-code and illustrated with example.

For modelling the dynamics and study of the active vibration suppression possibilities in aircraft wings, the smart beam is widely used. The advantages obtained through this approach are numerous. One of them are: aircraft stability and manoeuvrability, turbulence immunity, passenger safety and reduced fatigue damage. In this paper, the identification process has been presented, in the first step. As a result the transfer function of the continuous-time linear system was given. Then, for the obtained function the forms of minimal realizations were determined. The realization was obtained using the method based on one-dimensional digraph theory.