Local Markov Approximation Research Articles

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.

Detecting an Unknown Abrupt Change in the Band Center of the Fast-Fluctuating Gaussian Random Process

Abstract The generalized maximum likelihood algorithm is introduced for detecting the abrupt change in the band center of a fast-fluctuating Gaussian random process with the uniform spectral density. This algorithm has a simpler structure than the ones obtained by means of common approaches and it can be effectively implemented on the base of both modern digital signal processors and field-programmable gate arrays. By applying the multiplicative and additive local Markov approximation of the decision statistics and its increments, the analytical expressions are calculated for the false alarm and missing probabilities. And with the help of statistical simulation it is confirmed that the proposed detector is operable, while the theoretical formulas describing its quality and efficiency approximate satisfactorily the corresponding experimental data in a wide range of parameters of the observable data realization.

Measuring the Moment and the Magnitude of the Abrupt Change of the Gaussian Process Bandwidth

Abstract The maximum likelihood algorithm is introduced for measuring the unknown moment of abrupt change and bandwidth jump of a fast-fluctuating Gaussian random process. This algorithm can be technically implemented much simpler than the ones obtained by means of common approaches. The technique for calculating the characteristics of the synthesized measurer is presented and the closed analytical expressions for the conditional biases and variances of the resulting estimates are found using the additive local Markov approximation of the decision statistics. By statistical simulation methods, it is confirmed that the presented measurer is operable, while the theoretical formulas describing its performance well approximate the corresponding experimental data in a wide range of the parameter values of the analyzed random process.

Detection and Measurement of the Unknown Moment and Magnitude of the Gaussian Random Process Energy Parameter Abrupt Change

Synthesis, analysis, and simulation of the algorithms for detecting and measuring the abrupt change in the unknown mathematical expectation and dispersion of a fast fluctuating Gaussian random process at an unknown point in time are carried out in this paper. These algorithms can be technically implemented in a simpler way than the ones obtained by means of the common approaches. New asymptotic expressions are proposed for the logarithm of the functional of the likelihood ratio and its adaptive versions obtained after maximization by the unknown regular parameters under various hypotheses. By applying the joint application of the small parameter method and the local Markov approximation method, the closed asymptotically exact expressions are found for the characteristics of the performance of the synthesized detector and measurer. Both the procedure for determining the distribution law and the error moments of the estimate of the discontinuous parameter (abrupt change point) are illustrated, with an allowance of anomalous effects. By means of the statistical computer simulation, a satisfactory agreement is established between the obtained theoretical results and the corresponding experimental data.

Estimation of the stepwise random disturbance parameters with the unknown moment of appearance

We have carried out the synthesis of the joint algorithms for the estimation of the parameters of Gaussian random disturbance by the maximum likelihood method. Application of the generalization of local Markov approximation method and small parameter method makes it possible for us to find the asymptotically exact expressions for the characteristics of the specified estimates. We also establish the error range of the obtained theoretical formulas experimentally, by statistical computer simulation.

Application of the local Markov approximation method for the analysis of information processes processing algorithms with unknown discontinuous parameters under violation of the consistency property of their estimates

Application of the local Markov approximation method for the analysis of information processes processing algorithms with unknown discontinuous parameters under violation of the consistency property of their estimates

Application of the local Markov approximation method for the analysis of information processes processing algorithms with unknown discontinuous parameters

We considered the local Markov approximation method for the definition of the precision characteristics of statistical analysis algorithms of information processes with unknown discontinuous parameters in the presence of Gaussian distortions 4470 O. V. Chernoyarov et al. and illustrated the use of the stated approach in practical applications for the analysis of operating efficiency of detectors and measurers of the quasi-determined and random signals.

Characteristics of quazi-likelihood estimation of the image area in the presence of spatial noise

Asymptotic expressions for the characteristics of quasi-likelihood estimation of image area have been obtained by using the local Markov approximation method. It was shown that the accuracy of area estimation is determined by the magnitude of intensity jump over the boundary limiting the area occupied by image.

Range estimation of a fluctuating target during the probing with a sequence of rectangular optical pulses

Dispersions of the range estimates have been obtained by using the local Markov approximation method. Losses in the estimate accuracy caused by the target fluctuation were also determined.