Adaptive Algorithm of Filtration with Integrated Residuals

This paper proposes a filtering algorithm based on the use of not only the residuals between the measured and estimated coordinates, as in classical filtering algorithms, but also multiple integrals of these residuals. Classical filtering algorithms use reliable information about both the motion and measurement models and the statistical characteristics of the input random disturbances and measurement noise. The real control objects operate under conditions of action not only of highfrequency random disturbances, but also under the influence of low-frequency forces and moments from an aggressive environment, the characteristics of which are known with huge approximations. In this regard, the efficiency of using classical filtering algorithms for real systems is extremely low due to large errors. The algorithm proposed in the paper allows to eliminate these drawbacks by restoring external low-frequency disturbances in real time. Under external disturbances are understood not only external influences from the environment, but inaccurate knowledge about the motion model itself. For integral residuals, an algorithm is proposed for calculating the gains in the feedback in an analytical form. This algorithm is based on the processing of residuals, as well as estimates of external disturbances and their derivatives in the current time. A control algorithm is proposed that includes estimates of both phase coordinates, which are responsible for the quality of transients, and estimates of unknown disturbances, which is responsible for the compensation of external disturbances. Knowing the estimates of external disturbances in real time will, on the one hand, improve the quality of control, and, on the other hand, reduce the time and material costs associated with the study of the control object’s movement dynamics and the external environment. Using the example of an underwater vehicle model described by a linear system of differential equations under conditions of external disturbances (wave and hydrological forces and moments), the simulation was performed and the efficiency of the proposed algorithms for various numbers of integral residuals was shown.