In modern integrated monitoring systems and systems of automated control of technological processes there are several essential algorithms and procedures for obtaining primary information about an object and its behavior. The primary information is characteristics of static and moving objects: distance, speed, position in space etc. In order to obtain such information in the present work we proposed to use photos and video detectors that could provide the system with high-quality images of the object with high resolution. In the modern systems of video monitoring and automated control there are several ways of obtaining primary data on the behaviour and state of the studied objects: a multisensor approach (stereovision), building an image perspective, the use of fixed cameras and additional lighting of the object, and a special calibration of photo or video detector.In the present paper the authors develop a method of determining the distances to objects by analyzing a series of images using depth evaluation using defocusing. This method is based on the physical effect of the dependence of the determined distance to the object on the image from the focal length or aperture of the lens. When focusing the photodetector on the object at a certain distance, the other objects both closer and farther than a focal point, form a spot of blur depending on the distance to them in terms of images. Image blur of an object can be of different nature, it may be caused by the motion of the object or the detector, by the nature of the image boundaries of the object, by the object’s aggregate state, as well as by different settings of the photo-detector (focal length, shutter speed and aperture).When calculating the diameter of the blur spot it is assumed that blur at the point occurs equally in all directions. For more precise estimates of the geometrical parameters determination of the behavior and state of the object under study a statistical approach is used to determine the individual parameters and estimate their accuracy. A statistical approach is used to evaluate the deviation of the dependence of distance from the blur from different types of standard functions (logarithmic, exponential, linear). In the statistical approach the evaluation method of least squares and the method of least modules are included, as well as the Bayesian estimation, for which it is necessary to minimize the risks under different loss functions (quadratic, rectangular, linear) with known probability density (we consider normal, lognormal, Laplace, uniform distribution). As a result of the research it was established that the error variance of a function, the parameters of which are estimated using the least squares method, will be less than the error variance of the method of least modules, that is, the evaluation method of least squares is more stable. Also the errors’ estimation when using the method of least squares is unbiased, whereas the mathematical expectation when using the method of least modules is not zero, which indicates the displacement of error estimations. Therefore it is advisable to use the least squares method in the determination of the parameters of the function.In order to smooth out the possible outliers we use the Kalman filter to process the results of the initial observations and evaluation analysis, the method of least squares and the method of least three standard modules for the functions after applying the filter with different coefficients.
Determination of parameters for Cauchy’s problem for systems of ODEs with application to biological modelling
