Estimation of Motion Parameters of Unmanned Aerial Vehicles of Wireless Sensor Networks Based on the Least Squares Method with a Fractional Taylor Series in a “Sliding Window”

Abstract

AbstractIn this paper, to improve the accuracy of estimating the motion parameters of constantly maneuvering quadrocopters as elements of flying wireless sensor networks, a mathematical approach is proposed based on the use of the capabilities of fractional Taylor series, which are still little studied and have not yet found proper practical application in describing complex dynamic processes in various technical applications. At present, for high-precision determination of the coordinates of the motion parameters of unmanned aerial vehicles, with a known motion model, algorithms based on the Kalman-Bucy filter or the least squares method are used, since the potential estimation accuracy of these methods is almost the same. However, in order to estimate the motion parameters of constantly maneuvering aircraft, it is necessary to use the method of estimating from a selection of measurements in a “sliding window”. Comparative evaluation using algebraic polynomials, Chebyshev polynomials and fractional polynomials by the method of least squares “in a sliding window” showed that the use of fractional polynomials allows us to evaluate not only changes in coordinates and velocities, but also using fractional derivatives, other parameters that occupy an intermediate position between coordinates, the first and second derivatives with respect to coordinates. The latter makes it possible to improve the accuracy of estimates of the coordinates of the motion parameters of maneuvering unmanned aerial vehicles. Moreover, the most acceptable polynomial for estimation is a polynomial with fractional degrees equal to 2.5. The use of fractional Taylor series in the problem of estimating the motion parameters of constantly maneuvering quadrocopters makes it possible not to use recurrent estimation algorithms with adaptation elements, but to achieve the same goal by changing the degree of the polynomial.KeywordsWireless sensor networkUnmanned aerial vehiclesMotion parametersLeast squares methodFractional Taylor seriesChebyshev polynomialsSliding window interval