Replacing the observed object in a dynamic measuring system

In this article the problem of an object state vector estimation is considered. This estimation is obtained by the treatment of measured parameters from several observed objects. In our case, we have two measured parameters that change their values over a certain time interval, but only one of them can be measured at each moment. The problem is to find the moment for switching the measurement from one object to another one in order to minimize the dispersion of one component of the state estimation vector. Previously, the Elfing problem was solved to repeatedly measure fixed parameters using this data in proportion to weight coefficients for processing with the least square method. Then, to change the measured values, a transfer from the discrete model to the continuous one was proposed. This made it possible to obtain an analytical expression dispersion that was dependent of the time moment on the switching. In this article, the estimation of the continuous model error is conducted and the sufficient conditions of using no more than one switching are proven. An example of this method's application is shown to estimate the sea object coordinates using navigation satellites.