Practical implementation of scheduling observations of moving objects that appear at random times

. The article is devoted to practical implementation of planning of observations of the set of mobile objects appearing in the area of visibility of the measuring information system at random moments of time. A variant of the implementation of the suboptimal distribution of the measuring resources of the information system between the problems of trajectory detection and estimation is proposed. Application of the attitude proposed in the article allows to increase accuracy of measurement of paths of mobile objects up to 52% in comparison with uniform tracking plan.

MIS can be characterized by random moments of time of their appearance 12 ... tt  on the time axis t . Such a sequence of events is referred to as a random flow or a point random process [12].
In general, any one-dimensional random stream may act as an OO pattern. The selection of the model describing the patterns of OO appearance in the area of the MIS visibility is carried out in accordance with the conditions of the specific task.
This approach can also be used effectively to plan observations of a single object. At the same time, different types of distributions can be used as a model of appearance of OO in the area of visibility of MIS depending on a specific practical task and volume of a priori information on the time of appearance of the object.
In most practical problems, it is assumed that the OO state vector is described by stochastic differential equation [7] () ( ( ), ) Expression (1) is a model of a continuous Markovian process that in many cases most fully reflects the physical essence of the phenomena to be examined. As a mathematical model of process observation (1), the equation of the form is considered -is the nonlinear vector -function; () t  is the scalar function whose meaning will be refined below; () m tR   is the colored noise for which To solve the problem of estimating the information process (1), based on observation To obtain a reference trajectory, we form a set of solutions to an equation of the form Then the reference trajectory can be calculated using the approximate formula We represent the state vector y in the form Then, assuming the deviation vector () xt to be small, we obtain () The observation equation (3) for the process (9) can be transformed to the form If the composition of the measured parameters can be varied, i.e. the structure of the matrix H (t) takes into account the constraint The structure of the set () Ht , as well as the method of choosing admissible elements from it, are determined by a specific technical problem. Models (9), (10) can be provided with a Kalman filter, for which the following expressions are valid: ( ) ( ) ( ) ; forms an observation plan.
In the case of evaluating the set of information processes that appear in the visibility zone in accordance with the laws of a stochastic flow, equations (9), (10), (13) and (14) take the form respectively: where ; In this case, the restrictions on the control functions ()  It should be noted that the use of the mathematical model (19) is rather cumbersome due to its high dimension and nonlinearity [7]. Using the approach proposed in [7], we pass to the projection of the Hamiltonian system corresponding to (19) onto the space Starting from the 3rd interval of the iterative procedure, changes in program functions, and as a result, the laws of observation management, practically do not occur. Therefore, the observation plan corresponding to 3 k  it can be considered suboptimal. Figure 4 shows a suboptimal observation plan.
It should be noted that the resulting gain of 52% determines the upper potential limit. In a real situation, the observation plan may differ significantly from the a priori one, so the degree of approximation to the potential boundary depends on how significant these differences are. For example, figure 5 shows a plan of observations when the first object is detected at a time 3 t  . Observation of the second object in accordance with the a priori plan was assumed from the moment 24.2 t  , so a detection session was held in advance, during which the second object was detected at the moment 23 t  . The third object was not detected. The  value was 43% compared to the uniform plan shown in figure 2. Thus, the given example allowed us to illustrate the features of practical implementation of planning observations of mobile aerial objects that appear at random moments of time.