Adaptive Stochastic Filtration Based on the Estimation of the Covariance Matrix of Measurement Noises Using Irregular Accurate Observations

Abstract

In measurement systems operating under various disturbances the probabilistic characteristics of measurement noises are usually known approximately. To improve the observation accuracy, a new approach to the Kalman’s filter adaptation is proposed. In this approach, the Covariance Matrix of Measurement Noises (CMMN) is estimated by accurate measurements detected irregularly by the mobile object observation system (from radiofrequency identifiers, etalon reference, fixed points etc.). The problem of adaptive estimation of the observer’s noises covariance matrix in the Kalman filter is solved analytically for two cases: mutual noises correlation, and its absence. The numerical example for adaptive filtration of complexing navigation system parameters of a mobile object using irregular accurate measurements is given to illustrate the effectiveness of the proposed algorithm. Coordinate estimating errors have changed in comparison with the traditional scheme from 100 m to 2 m in latitude, and from 200 m to 1.5 m in longitude.

Kalman Filter Adaptation to Disturbances of the Observer’s Parameters

“…For the "object-observer" system (Equations ( 1) and ( 2)), the estimation of the state vector is performed by an optimal discrete Kalman filter [3,32,34]…”

“…Previously, the idea of using accurate observations entering the measuring system at irregular (including random) points of time was considered during adaptive estimation of the a posteriori covariance matrix [32,33], as well as measurement noise covariance matrix in the Kalman filter [34], which, compared with the traditional scheme, significantly reduced estimation errors. Unfortunately, the approach described in Sokolov et al (2018Sokolov et al ( , 2021, Sokolov and Novikov (2021) [32][33][34], cannot be applied to solving the problem of estimating the matrix of itself observer's parameters, since the right part of the filter equation depends on the matrix significantly nonlinearly. In this regard, a different approach to solving this problem is considered below, based on a mathematical apparatus that is fundamentally different from the one used in [32][33][34]-on the mathematical apparatus for studying disturbed multidimensional linear systems [35].…”

“…Unfortunately, the approach described in Sokolov et al (2018Sokolov et al ( , 2021, Sokolov and Novikov (2021) [32][33][34], cannot be applied to solving the problem of estimating the matrix of itself observer's parameters, since the right part of the filter equation depends on the matrix significantly nonlinearly. In this regard, a different approach to solving this problem is considered below, based on a mathematical apparatus that is fundamentally different from the one used in [32][33][34]-on the mathematical apparatus for studying disturbed multidimensional linear systems [35]. As shown below, the use of this mathematical apparatus can significantly improve the accuracy and stability of the Kalman filtering process under the conditions of the observer's parametric disturbances.…”

The Choice of a Set of Operations for Forest Landscape Restoration Technology

“…Information exchange [25] to be conducted between scientists from various fields, providing impetus to interdisciplinary research in the FLR-technology field [5]. This has resulted in new technical means [26][27][28][29][30] and new methods [22,31] in various scientific fields, including: study of heat and mass transfer during oscillating drying [32], immersion freezing [33] and polyacrylamide encapsulation [34] of seeds, study of biophysical methods [35] of non-destructive seed quality control [36] by autofluorescence spectral imaging [37], magnetic resonance imaging [38], study of navigation characteristics [39][40][41][42][43] of unmanned dynamical objects under disturbance conditions [44] (for example, when working under a forest canopy);…”