БЛОЧНЫЙ ФИЛЬТР КАЛМАНА С ЛИНЕЙНОЙ ВЫЧИСЛИТЕЛЬНОЙ СЛОЖНОСТЬЮ ДЛЯ КОМПЛЕКСИРОВАННЫХ С ТЕХНИЧЕСКИМ ЗРЕНИЕМ ИНЕРЦИАЛЬНЫХ НАВИГАЦИОННЫХ СИСТЕМ

Abstract

As the use of computer vision in vehicle navigation systems increases, there is a growing need for computationally efficient optimal filtering algorithms that can jointly process measurements from inertial sensors and a large number of visual information sources. Contribution. This paper proposes a new modification of the Kalman filter (the block Kalman filter) with linear computational complexity in the number of measurement information sources. A numerically stable version of the algorithm is derived using LDL-factorization of covariance matrices. Purpose of the study. The aim is to develop an LDL-factorized block Kalman filter algorithm with linear computational complexity with respect to the number of information sources in the measurement system and demonstrate its applicability in a integrated visual-inertial navigation system. Materials and Methods. This research demonstrates the algebraic equivalence of the block Kalman filter to the standard one in a specific case. A method is proposed for approximating the estimates of the block filter to those of the standard one with desired accuracy by expanding the state vector. The computational complexity of the block Kalman filter is compared to the computational complexity of standard one within a numerical experiment. Numerical modeling of the block filter operation within a navigation system is conducted for comparison with the standard filter. Results. The equations of the block LDL-factorized Kalman filter are obtained. Its linear computational complexity with respect to the number of information sources is verified. A method for approximating the estimates of the block Kalman filter to those of the standard filter by expanding the state vector is proposed and verified within the framework of navigation system simulation. Conclusion. The main theoretical properties of the block Kalman filter were confirmed in numerical experiments. Further research will explore alternative methods of forming the extended state vector of the filter; the Kalman block filter will be tested within more complex scenarios.