Development of an algorithm for industrial production objects continuous tracking based on recursive Kalman filter

Trilateration and triangulation methods are usually used to determine the location of an object. Their implementation requires solving a system of nonlinear equations with respect to unknown coordinates. As the number of objects being tracked increases, the number of equations grows significantly, which increases the complexity of calculations and the time it takes to update current coordinates. Under conditions of industrial production, due to reflections and noise, the calculation error also increases, which can lead to disruption of production tasks and reduce the safety of employees. The paper sets the task of developing an algorithm based on the recursive Kalman filter, which, in combination with modern noise-resistant technical means, allows increasing the accuracy of the positioning system under production conditions and reducing the time of updating coordinates. The authors have used methods of physical modeling of devices of the objects location determination system under conditions of industrial production, based on ultra-wideband transceivers. Mathematical methods, particularly the robust recursive Kalman filter with M-estimate, are used to solve equations of determination of object coordinates. The authors have developed a positioning algorithm based on a recursive Kalman filter with M-estimate of measurement and state errors using the proposed modification of the Geman–McCluer loss function. The algorithm provides a submeter accuracy to determine coordinates that updated every 2–3 seconds. Prototypes of positioning system devices based on ultra-wideband transceivers have been developed. The results of mathematical and physical experiments have shown that the maximum error of coordinate deviation is 2,3 m, and the minimum error is 0,1 m. The developed algorithm is effective for production, including energy production. It is resistant to noise measurement, providing the necessary positioning accuracy for linear and nonlinear motion trajectories. Future research is related to testing the algorithm in case of an increase in the number of tracked objects, as well as further improving the accuracy of its operation.