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• PROBABILISTIC CHARACTERISTICS OF THE THRESHOLD ALGORITHM FOR DETECTING SYNCHRONIZING PULSES IN THE QUANTUM KEY DISTRIBUTION SYSTEM BASED ON INFORMATION FROM AN ADJACENT PAIR OF TIME SEGMENTS

  K. E. Rumyantsev, Y. K. Mironov, P.D. Mironova

  2020-11-22

  Abstract ▼

  Quantum key distribution systems (QKD) provide increased security of transmitted information.
  For the stable operation of the QKD system, accurate synchronization of user stations is
  required with minimal time costs. An algorithm for detecting a sync signal with a threshold test is
  proposed. It is assumed that the sync pulse is simultaneously in two adjacent time segments. The
  probability of detecting a pair of time segments where a sync pulse is present is determined by the
  probability of exceeding the threshold level by the total number of signal and noise pulses recorded
  in two adjacent segments. The purpose of the research is aimed at a comparative analysis of the
  threshold level and probabilistic characteristics of synchronization equipment during threshold
  testing of each pair of time segments within a time frame, obtained when orienting on the Gauss
  and Poisson model for the number of photons and dark current pulses (DCP) received during the
  time segment analysis. The probabilistic characteristics of the detection algorithm for sync signals
  are studied in a quantum key distribution system based on a comparison of the number of photons
  from an adjacent pair of time segments with a threshold level. The application of the approximation
  of the statistical properties of the processes at the output of the photodetector by the Poisson
  law and the normal distribution is analyzed. The influence of the Poisson and Gaussian models on
  the choice of the threshold level and the calculation of the synchronization efficiency during the
  threshold testing of each pair of time segments within the time frame are estimated, obtained by
  orientation on the Gauss and Poisson models for the number of photons and DCP received during
  the analysis of the time segment. It was established that the choice of the threshold level based on
  the normal distribution gives an underestimated value. The approximation of the statistics of photons
  and pulses of dark current by a normal law provides a threshold level lower than the required
  one. Moreover, the difference grows with stricter requirements for the probability of false positives.
  The obtained probabilistic properties of the sync signal detection algorithm based on the
  analysis of the sum of counts from an adjacent pair of segments with a threshold level allow us to
  formulate recommendations for choosing an approximation of the signal statistics: for express
  calculations of probabilistic characteristics, it is advisable to use the Gaussian model; if a higher
  analysis accuracy is required, it is recommended to use the Poisson model.

• EVALUATION OF THE CHARACTERISTICS OF A TWO-STAGE SYNCHRONIZATION ALGORITHM BASED ON THE SELECTION OF AN ADJACENT PAIR OF SEGMENTS WITH THE MAXIMUM TOTAL COUNT IN THE QKD SYSTEM

  К. Y. Rumyantsev, Y.К. Mironov, P.D. Mironova

  2024-08-12

  Abstract ▼

  A two-stage synchronization algorithm is proposed based on the selection of an adjacent pair of
  segments with the maximum total count in the QKD system. The algorithm is based on a well–known approach
  to reducing the time of entering into synchronism - the analysis of adjacent pairs of time segments.
  A distinctive feature of the proposed algorithm is to ensure that the probability of successful search and
  testing is not worse than the required level. It should be noted that due to the testing stage, erroneous
  decisions made at the search stage are rejected, which minimizes the probability of false synchronization
  due to the registration of noise pulses. At the search stage, the equipment sequentially registers the total
  counts from all adjacent pairs of segments. Next, a pair of segments with the maximum total count is selected,
  and the count in one of the pairs of segments reliably exceeds the values of the counts from all other
  pairs of segments, and the equipment proceeds to the testing stage. Testing consists of polling the
  photodetector during the gating pulse to re-register the count. In case of positive testing, the process of
  «rough» estimation of the moment of reception of the sync pulse is considered successfully completed,
  otherwise the equipment returns to the search in the next frame. Note that the maximum allowable number
  of frames and tests correspond to the search and testing stages, respectively. Analytical expressions are
  obtained for calculating the time and probabilistic characteristics of the search and testing stages of the
  proposed detection algorithm based on the selection of an adjacent pair of segments with the maximum
  total count, including for calculating the allowable number of frames and tests while ensuring the required probabilities of successful search and testing, respectively. It has been found that with an increase in the
  average number of photons in the sync pulse, the average number of frames and tests, as well as the average
  time of successful search and testing, decrease significantly. For example, when the average number
  of photons in a sync pulse increases by 5 times, the average number of tests for successful testing and the
  average time for successful testing decrease by 1.5 times, and the permissible number of tests by 5 times.

• MATHEMATICAL METHODS OF COMPLEX PROCESSING OF RTC NAVIGATION DATA

  А. P. Zykov, P.N. Mironov

  2024-04-15

  Abstract ▼

  Nowadays, the navigation systems of robot-technical complexes (RTC) use heterogeneous sensors
  of primary information, which can provide redundancy of navigation data. This allows to increase
  the accuracy of calculation of motion parameters, as well as allows to determine them with greater
  reliability in case of failure of one or more sensors. The paper gives a review and classification of lowlevel
  mathematical methods of processing overridden state parameters of RTC navigation systems. It is
  noted that the problem of combining is a subfield of the problem of system identification and therefore
  has common approaches to the construction of the solution. In the vast majority of methods based on the
  optimization approach, the quadratic error function is used as the optimality criterion. All mathematical
  methods of combining (complex processing or fusion) any data are divided into low-, medium- and
  high-level methods. In navigation systems, low-level methods such as recursive, nonrecursive, and covariance-
  based methods are the most used. Non-recursive methods are rarely used directly. Recursive
  ones are usually constructed using a Kalman filter scheme. Recursive ones, as a rule, are constructed
  according to the Kalman filter scheme. Not all methods are robust to non-Gaussianity and correlation
  dependence of the original data, which is often encountered in navigation systems with overdetermined
  data. In addition, not all methods can be used to address the relevance of data from navigation instruments.
  It is noted that the key for combining methods is the approach of fusion data in an information
  space, understood as the inverse of covariance, since the vast majority of methods, including Bayesian
  methods, are reducible to it. In this regard, covariance-based methods are of most interest. However, for solving the problem of data relevance in navigation, the existing methods are poorly suited to the problem
  of data relevance because they require computationally intensive optimization problem solving at
  each step, and navigation systems are real-time systems. Thus, there is a problem of developing new
  approaches to solve this problem