Estimating the Position of an Image with Unknown Intensity Shape

The problem considered is to estimate the image position of a spatially extended object. It is assumed that the shape of the image intensity is a priori unknown, but it can be predicted with some error. In order to synthesize the estimate of the image position, the quasi-likelihood version of the maximum likelihood method is used. Behavior of the signal function in the neighborhood of the real image position is studied. Characteristics of the resulting estimate, such as bias and dispersion, are found by means of the local Markov approximation method. Influence of non-uniformity of the received image intensity upon the estimate accuracy is demonstrated by an example of receiving the rectangular image with linearly varying intensity.

The technology of a condition based maintenance of an overhead contact line with Markov approximation of contact wire wear

The technologies of OCL condition based maintenance were improved for providing reliable and economic current collecting on electrified railways and in traction power networks of urban electric transport. It is established that one of the most perspective methods of reducing operating costs is the transition to scientifically justified terms of repair and planning of works based on the actual state of OCL, the reliability of which is determined by the reliability, repair suitability and durability of the elements. The basic criteria of the current collecting process are proposed: the value of contacting pair wear, the detachment of the current collectors from the wires, the scope of oscillations of pantograph head and the contact pressure, coefficients of contact unreliability and cost savings of collecting a power from catenary, and, finally, a minimum of annual operating costs. Technology of maintenance according to Markov type parameter control is developed. Models of controlling actions on stagger and the contact wire gradient adjustment processes are developed. The standard linear programming algorithm was used to solve the problem. The application of such technology to determine the matrix of controlling actions based on the results of monitoring the stagger and the contact wire gradient is shown. The factors that determine the cost of staying in a state of stagger have been identified. The controlling actions matrices on the stagger and the contact wire gradient and the cost of staying in these gradient states are established. The technology of service with Markov approximation of wear of contact wires is offered. It has been investigated that the contact wires, primarily due to wear, are degraded during operation. Degradation processes cause gradual failures. The first group of failures: breakages, burnouts, local wear - require controlling actions to incut the insertion or putting into operation a shunt. The second group: a burnout, a decrease in the average cross-section of a wire less than the allowable one requires controlling actions to replace the wire of the entire tension length. After conducting the first type of controlling actions, the contact wire returns to the working state with the previous value of the determining parameter. When performing a second type of controlling actions, the defining parameter returns to its original state. If the quantification step is chosen such that the intensities of failures and transitions from one state to another with a sufficient degree of accuracy were constant, then the graph of states and transitions, as well as the Kolmogorov differential equations, can be used for the research. The readiness function, the density of time distribution of infallible operation, the total failure rate, and the average recovery rate from state S0i to Si are determined. Thus, all reliability indicators are defined and it is possible to use them in determining the condition of the contact wire of the tension length. Experience has shown that the most effective diagnostics of the condition of OCL devices combines the assessment of the state on mathematical, simulation models and measurements with the use of car laboratories for testing the contact network and devices for monitoring the parameters of the contact wire for the railcar. Key words –overhead contact line,contact wire, mainanance technology, controlling action models.

A Linear Spline Markov Approximation Method for Random Maps with Position Dependent Probabilities

We present a rigorous convergence analysis of a linear spline Markov finite approximation method for computing stationary densities of random maps with position dependent probabilities, which consist of several chaotic maps. The whole analysis is based on a new Lasota–Yorke-type inequality for the Markov operator associated with the random map, which is better than the previous one in the literature and much simpler to obtain. We also present numerical results to support our theoretical analysis.