Robust Technology with Analysis of Interference in Signal Processing

"T.A. Aliev obtains important results on interference analysis of noisy signals. They offer great possibilities and prospects for solving numerous problems of statistical analysis while not fulfilling the known classical conditions. His results on interference analysis are completely unexpected and of great practical importance." (K.A. Pupkov, Moscow State Technical University)

• 1. Needs in Development of Statistical Analysis Technology.- 1.1 Opportunities of Robust Statistical Analysis Technology.- 1.2 Features of Improving Correlation Matrix Stipulation.- 1.3 Analysis of Factors of Poor Stipulation of Correlation Matrices.- 1.4 Analysis of Methods of Improving Correlation Matrix Stipulation.- 2. Robust Methods for Determining Estimates of Statistical Characteristics.- 2.1 Methods for Determining Noise Variance.- 2.2 Robust Method for Improving Estimates of Autocorrelation Functions.- 2.3 Robust Method for Improving Estimates of Cross Correlation Functions.- 3. Robust Technology of Correlation Analysis.- 3.1 Algorithms for Determining Estimates of Noise Variance.- 3.2 Algorithms for Determining Magnitude Providing Robustness of Estimates of Auto- and Cross Correlation Functions.- 3.3 Robust Algorithms for Improving Estimates of Auto- and Cross Correlation Functions.- 4. Robust Technology for Improving Correlation Matrix Stipulation and Identification Adequacy.- 4.1 Robust Technology for Improving Correlation Matrix Stipulation.- 4.2 Analysis of the Efficiency of Robust Technology for Improving Correlation Matrix Stipulation.- 4.3 Robust Technology for Improving Identification Adequacy of Statics of Technological Processes.- 4.4 Algorithms for Providing Adequacy of Mathematical Models at Expense of Compensation of Errors of Diagonal Elements of Correlation Matrices by Means of Estimates of Noise Variance.- 4.5 Robust Technology of Choice of Regularization Parameters by Statistical Identification.- 4.6 Determination of a Priori Values of Model Coefficients in Using Regularization Methods.- 5. Robust Technology of Harmonic Analysis.- 5.1 Methods of Spectral Analysis of Experimental Information.- 5.2 Practical Harmonic Analysis.- 5.3 Analysis of Features of Spectral Analysis Algorithms.- 5.4 Causes of Appearance of Difference between Positive and Negative Errors Caused by Noise.- 5.5 Algorithms for Providing Robustness of Estimates an, bn.- 5.6 Robust Technology of Determining Coefficients of Fourier Series.- 5.7 Analysis of Results of Computer Experiment.- 6. Position-Binary Technology of Statistical Analysis of Cyclic Processes and Noises.- 6.1 Special Features of Cyclic Processes.- 6.2 Position-Binary Technology of Analysis of Cyclic Signals.- 6.3 Application of Position-Binary Technology for Noisy Signal Analysis.- 6.4 Position-Selective Discretization of Analog Signals.- 6.5 Examples of Application of Position-Binary Technology for Analyzing Random Processes.- 6.6 Position-Selective Filtering of Noise.- 6.7 Position-Binary Technology of Analysis of Noise.- 7. Algorithms and Technology of Analysis of Interference as Information Carrier.- 7.1 Problem of the Analysis of Interference as an Information Carrier.- 7.2 Algorithm for Determining the Mean-Root-Square Deviation of Interference.- 7.3 Algorithm for Determining the Relative Mean-Root-Square Error of Samples Caused by Interference.- 7.4 Decomposition of Noisy Signal to Useful Signal and Interference.- 7.5 Algorithms of Correlation Analysis of Interference.- 7.6 Algorithms of Spectral Analysis of Interference.- 7.7 Informative Technology of Analysis of Interference.- 8. Application of Robust Technology for Solving Problems of Control, Diagnostics, and Forecasting.- 8.1 Alternatives of Using Robust Technology in Information Systems.- 8.2 Robust Technology of System Analysis of Seismic Signals.- 8.3 Hybrid Robust System of Control and Diagnostics of Sea Platform State.- 8.4 Robust Technology of Controlling Seismostability of Objects of Sea Oil-and-Gas Deposits.- 8.5 Robust Information System for Early Detection and Diagnostics of Failures in Drilling Oil Wells.- 8.6 Diagnostics of Oil Well State.- 8.7 Robust Technology of Diagnostics of State of Objects of Petrochemical Productions.- References.