Abstract
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.
Highlights
Systems for estimating the position of a spatially extended object by its own image are widely used for security purposes, traffic monitoring and management, in railway transport and in other sectors [1,2,3,4]
In view of the above, one can conclude that the decision statistics in Equation (15) of the QL estimation algorithm in Equation (9) is the Gaussian random process, for which the mathematical expectation and the correlation function, under conditions of high a posteriori accuracy, allow the representations in Equations (22) and (31), respectively
The expansion is found of the signal function of the decision statistics in the neighborhood of the image position real value
Summary
Systems for estimating (predicting) the position of a spatially extended object by its own image are widely used for security purposes, traffic monitoring and management, in railway transport and in other sectors [1,2,3,4]. The information processing algorithms, applied in the specified systems, can often provide the simplest operations only, such as detection of a moving object against a relatively simple background with a subsequent measurement of its speed. A more complicated task is when realization of the two-dimensional random field p^x,yh is processed, which, in general case, includes the image of an object with unknown coordinates to be measured, the background and the spatial noise [2,3,4,5]. Algorithms for detecting the quasi-deterministic image in the presence of a background are studied in [8], while in [9,10] algorithms for processing the image with unknown position, observed in the presence of the additive Gaussian spatial white noise, are developed. Is necessary to estimate the unknown position m0 of the image s^x, y,m0h with the unknown intensity distribution f^x, yh
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