centre of mass
R.S. Luchkin, V.V. Lavrov
Let in the observed sequence of optical images of hand-picked moments of time in which on frame images can capture (with respect to the coordinate system frame (screen)) direction of the axis orientation of the characteristic structural element of the object. It is believed that the errors of this observation image are independent.
For errors measurement moments of observation time is assumed normal distribution, then in general we can write the log likelihood function of these measurements taking into account the parameters of rotational motion, as a model which adopted the model of regular precession. The necessary parameters of orbital motion are pre-defined by the coordinate measurements.
An estimate of parameters of regular precession is constructed by minimizing the function of the logarithm of the likelihood function on these parameters.
The proposed algorithm works by using statistics (moments of time observing orientations characteristic elements of the rotating spacecraft) obtained from a single realization or their combination of the same type. Perhaps a poor quality estimates of these parameters as well as the presence of abnormal values of the measurements. Problem of determining the quality of the estimates of parameters and the possible presence of abnormal values in the original statistics arises. To solve this problem using the method of «cross-validation» (CV) («jackknife method»).
One image consistently excluded from the original statistics, consisting of a collection of images. Estimation (CV - evaluation) values of the parameters of spacecraft motion relative to the center of mass (CM), corresponding to the optimal value of the functional, are constructed in the remaining set of images (lower per unit volume).
The resulting statistics of the functional evaluations and rotation parameters used to determine the bias, variance and correlation matrix of the parameters of interest to us. In turn, these estimates are used for accepting or rejecting the hypothesis of anomalous dimensions.
The algorithm was verified by the real object on the example of rotation of satellite «Okean-1».
Comparison of the estimates with the results of a previous analysis suggests relatively well they meet each other.
Thus, this paper shows the possibility to use for estimating the parameters of spacecraft motion relative to the CM set its optical image. It is synthesized the algorithm for estimating these parameters under the assumption that the regular precession of the object. The results of the modeling and calculations using the information and images of real KO confirm performance of the proposed algorithm.