adaptive Bayesian approach
M.E. Prokhorov, J.G. Rindyn
Today the following problems of recognition of artificial earth space objects are actual: selection of the launch elements (division of the launch elements into three groups: satellites, carrier rockets, fragments), identification of the carrier rocket type, identification of the satellite mission, identification of the satellite type. Most of these problems can be described as follows: it is necessary to make decision regarding space object belonging to one or several classes from the set of classes by its recognition indicators, received from measure means.
Besides the information about interesting space object received from measure means during process of recognition the information about other objects received earlier is also available. This information can be used as learning sample. The learning sample is unique as the amount of actual space objects is limited, and the amount of specific class objects is usually small (if compared to recognition problems in other areas). The learning sample is classified, i.e. the complete list of classes of the selected recognition problem is known, and for each object from the sample there is given a set of classes which this object belongs to.
Also a priori information about the interesting object can be used in the decision-making process.
The adaptive Bayesian approach is chosen as a mathematical basis of solving the problem. The additive function which takes into account physical and economic factors of solving the problem is taken as a loss function.
The criterion of the maximum of estimation of recognition efficiency is introduced for teaching recognition algorithms and choosing the best of them. Recognition efficiency is integral of recognition characteristic. Recognition characteristic is the dependence of probability of correct decision-making on conditional probability of correct recognition. There is developed the algorithm of restoring the recognition characteristic (calculation of estimation of recognition efficiency) by the unique leaning sample using the sliding control method. Using the sliding control method means here that the indicators of the object are not taken into account during calculating the value of decisive statistics for this object (In fact, the object is excluded from the learning sample). Recognition algorithm which has maximum estimation of recognition efficiency and the best behavior of recognition characteristic is used for decision-making regarding object belonging to the interesting class.
Various algorithms can be used as competing algorithms of decision-making. Some of them are listed here: the algorithm which approximates probability density function as a mix of unimodal distributions, the Parzen method, the nearest neighbor algorithm.
There are presented examples of recognition characteristics for some classes of space objects in the paper.