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This paper describes the second part of our study devoted to automated anonymization of personal data. The overview and analysis of research prospects is supplemented with a practical result. An anonymization model is proposed, which reduces anonymization of personal data to manipulation of samples of random elements of different types. The key idea of our approach to anonymization of personal data with preservation of their usefulness is the use of the synthesis method, i.e., the complete replacement of all non-anonymized data with synthetic values. In the proposed model, a set of element types is selected, for which corresponding synthesys templates are proposed. The set of templates constitutes a synthesis-based anonymization algorithm. Technically, each template is based on a well-known statistical tool: frequency estimates of probabilities, Parzen–Rosenblatt kernel density estimates, statistical means, and covariances. The proposed approach is illustrated by a simple example from civil aviation. [ABSTRACT FROM AUTHOR]

The first part of the study of the automated processing of personal data for the purpose of their anonymization and analysis is presented. This part is an overview and aims to analyze the state of research in this area and systematize the available results. Results of the analysis of a wide range of issues of anonymization are presented, which formed a systematic understanding of the state of research and substantiated the choice of direction for further study. First, definitions of the main terms and concepts used in connection with anonymization of personal data are formulated, including association with the legislation of the Russian Federation. The directions of research are grouped into four sections: anonymization methods, implementation issues, applications of anonymized data processing, and deanonymization issues. For each group of anonymization methods—randomization, grouping, data distribution and application control— descriptions of the main algorithms are given and their advantages and disadvantages are analyzed. Implementation issues concern such concepts as the usefulness of anonymized data, limitations of the applicability of universal algorithms, and the reliability in relation to maintaining the anonymity of personal data subjects. Among applications that have formed the demand for the processing anonymized data, medical, biological, and genetic research and law enforcement are discussed. In the final part, the most interesting facts of deanonymization are mentioned and a short review of mass media is given. [ABSTRACT FROM AUTHOR]

We present a model of a stochastic observation system that allows for time delays between the received observation and the actual state of the observed object that formed these observations. Such delays can occur when observing the movement of an object in a water medium using acoustic sonars and have a significant impact on the accuracy of position tracking. We present equations to solve the optimal mean square filtering problem. Since the practical use of the optimal solution is barely feasible due to its computational complexity, we pay the main attention to an alternative, suboptimal but computationally efficient approach. Specifically, we adapted a conditional minimax nonlinear filter (CMNF) to the proposed model and formulated sufficient existence conditions for its estimate. We conducted a computational experiment on a model that is close to practical needs. The results of the experiment show the effectiveness of CMNF in the model considered. However, they also show a significant decrease in the quality of estimation compared to the model without random observation delays, which can be considered as a motivation for further research into the model and related problems. [ABSTRACT FROM AUTHOR]

We study the implementation of the optimal control strategy obtained in [1] and supplemented in [2]. The algorithm for optimal stabilization of a linear stochastic differential system in a position determined by a piecewise constant Markov drift has been tested in a substantial number of model experiments. The drift value is observed indirectly; i.e., the control problem is solved in the statement with incomplete information. Practical implementation is complicated by the instability of Euler–Maruyama numerical schemes that implement the Wonham filter, which is a key element of the optimal control strategy. To perform calculations, the Wonham filter is approximated by stable schemes based on the optimal filtering of Markov chains by discretized observations [3]. These schemes have different implementation complexity and orders of accuracy. The paper presents a comparative analysis of the control performance for various stable approximations to the Wonham filter and its typical implementation using the Euler–Maruyama scheme. In addition, three versions of discretized filters are compared and final recommendations are given for their application in the problem of stabilizing a system with hopping drift. [ABSTRACT FROM AUTHOR]

For a controlled linear stochastic differential system, we consider the problem of tracking the jumping state of an additive input action determining the current stabilization direction (drift). The tracking objective, which is to stabilize the system near the varying drift, is formalized by a quadratic performance functional. The input action defines a continuous-time Markov chain. The problem is considered in the cases of complete and incomplete information. Dynamic programming is used to solve it in both cases. The solution of the Bellman equation in the first case is obtained based on the properties of a finite-dimensional chain, and in the second case, based on the principle of separation of control and state estimation problems provided by the Wonham filter estimate and the properties of the quadratic performance criterion. A numerical experiment uses an applied model describing the position of a simple mechanical drive. The results of calculations confirming the applicability of the solutions obtained, as well as ways to overcome the difficulties of their numerical implementation, are presented and discussed in detail. [ABSTRACT FROM AUTHOR]

We propose a suboptimal solution for the control problem for the Ito diffusion process and linear controlled output with a quadratic quality criterion for the case of indirect observations of the state. We use the previously obtained solution of the problem with complete information, the concept of separation between control and filtering problems, and the method of conditionally optimal filtering developed by V.S. Pugachev. We propose an alternative to the traditional practical approach for the synthesis of suboptimal control in a problem with incomplete information, which consists in a formal substitution in the solution of a state with its estimate. Instead of the problem of optimizing the output generated by the original model of the differential equation, we use as the state an estimate of a conditionally optimal filter. We develop one version of the numerical implementation of the proposed algorithm based on the Monte Carlo method and computer simulation. [ABSTRACT FROM AUTHOR]

We present the results of the analysis and comparison of the properties of two concepts in state filtering problems for nonlinear stochastic dynamic observation systems with discrete time: sigma-point Kalman filter based on a discrete approximation of continuous distributions and conditionally minimax nonlinear filter that implements the conditionally optimal filtering method based on simulation modeling. A brief discussion of the structure and properties of the estimates and justifications of the corresponding algorithms is accompanied by a significant number of model examples illustrating both positive applications and limitations of the efficiency for the estimation procedures. The simplicity and clarity of the considered examples (scalar autonomous regressions in the state equation and linear observations) allow us to objectively characterize the considered estimation methods. We propose a new modification of the nonlinear filter that combines the ideas of both considered approaches. [ABSTRACT FROM AUTHOR]

problem of estimation of states and parameters in stochastic dynamic systems of observation with discrete time containing a Markovian chain is studied. Matrices of transient probabilities and observation plans are random with unknown distribution with a given compact carrier. Observations, on the basis of which the estimation is made, are available at a fixed interval of time [0, T]. As a loss function, we have a conditional mathematical expectation with respect to the available observations of ℓ-norm of the estimation error of a signal process on [0, T]. The problem is in constructing an estimate minimizing losses correspondent to the worst distribution of the pair 'a matrix of transient probabilities-a matrix of observation plan' form a set of allowable distributions. For a correspondent minimax problem is demonstrated the existence of a saddle point and is obtained a form of the wanted minimax estimation. The applicability of the obtained results is illustrated by a numerical example of the estimation of a state of TCP under the conditions of uncertainty of communication channel parameters. [ABSTRACT FROM AUTHOR]

We consider the problems of state estimation and Bayesian parameter identification for a stochastic model of an observation system that describes the evolution of one parameter of a web portal. Based on the thread pool control process analysis, we offer a mathematical model for the oscillations of the operating parameters for the portal’s information sources as a nonlinear stochastic observation system of a special kind. We obtain solutions of the optimal estimation problem and give numerical results. [ABSTRACT FROM AUTHOR]