Estimation of the error in determining the motion parameters of maneuvering objects

The study contains the definition of errors in estimating the motion parameters of maneuvering objects that arise due to the discrepancy between the real model and the model used to build the filter. In the real model, along with noise and stochastic uncertainties, non-stochastic uncertainties act. The solution to the problem of estimation errors is based on the use of convex polyhedra. The statement of the research problem is given. It is shown that since the observer uses the motion model and the measurement equation, the source of estimation errors is not only the above, but also the fact that along with the random component of the measurement noise, there is also a non-stochastic component that is not taken into account by the observer. At the same time, the statistical characteristics of the latter do not exist or are unknown. It is shown that the use of a filter, for example, Kalman, will lead to errors. The conditions that determine the average filtering error and the total standard error of the estimation are described. It is noted that the obtained calculation results allow us to estimate the maximum permissible values used in the design of the filter for the most unfavorable case of evaluation. The relationship between the filtration quality and the parameters of the effects is determined. Expressions are obtained regarding the filtration quality for the worst and the best for object maintenance. The asymptotic properties of filtering errors are considered. It is shown that the "convergence" of the filter means its final "memory", since errors at the next step do not depend on errors from all previous steps, but only on steps from a certain value. The conditions under which the potential accuracy of the filter is achieved are also determined. The solution of extreme problems is described. You can determine the maximum filtering quality by iterating over the values on a set of corner points or using extremum conditions. Numerical simulation of extreme values of filtering errors is given. The asymptotic properties of filtering errors are considered. It is shown that the "convergence" of the filter means its final "memory", since errors at the next step do not depend on errors from all previous steps, but only on steps from a certain value. The conditions under which the potential accuracy of the filter is achieved are also determined. The solution of extreme problems is described. You can determine the maximum filtering quality by iterating over the values on a set of corner points or using extremum conditions. Numerical simulation of extreme values of filtering errors is given. Expressions for the set of average values of filtering errors are found, asymptotic and extreme properties of errors and sets are considered. It is shown that the conducted analysis of the accuracy of the filtering algorithm is evaluative in nature and is designed for the worst case. If the accuracy is not satisfactory, it is necessary to either change the model or synthesize a minimax-stochastic filter.