Research of Divergence Trajectory with a Given Risk of Ships Collisions

2021 ◽  
pp. 64-67
Author(s):  
Kostiantyn
Keyword(s):  
Mathematical Models ◽  
Normal Distribution ◽  
Control Systems ◽  
Collision Avoidance ◽  
State Vector ◽  
Measurement Errors ◽  
Local Network ◽  
Mean Square ◽  
Distribution Law ◽  
Imitation Modeling

There were considered the issues of the optimal collision avoidance in the target’s risk field. A method of optimal divergence by course maneuvering is proposed, which makes it possible to minimize the divergence trajectory for a given risk of collision and consists in organizing the movement of the vessel along the trajectory of a given risk. The risk field of the target is a normal distribution law characterized by the root-mean-square parameters of the uncertainties associated with measurement errors of the parameters of the vessel's state vector and target, errors of actuators, errors of the used mathematical models, errors of calculation, etc. The operability and efficiency of the proposed method, algorithmic and software were tested on the Imitation Modeling Stand, which is the Navi Trainer 5000 navigation simulator and a model of on-board controller included in its local network with the software of the risk divergence module. The Imitation Modeling Stand allows to work out the software of control systems, including the considered optimal divergence module, in a closed circuit with the Navi Trainer 5000 navigation simulator, using all its advantages.

Limit tolerances for sums of measurement errors

2018 ◽  
Vol 934 (4) ◽  
pp. 59-62
Author(s):  
V.I. Salnikov
Keyword(s):  
Normal Distribution ◽  
Mean Square Error ◽  
Gaussian Distribution ◽  
Measurement Errors ◽  
Theory And Practice ◽  
Mean Square ◽  
The Mean ◽  
Limiting Values ◽  
Limiting Value

The question of calculating the limiting values of residuals in geodesic constructions is considered in the case when the limiting value for measurement errors is assumed equal to 3m, ie ∆рred = 3m, where m is the mean square error of the measurement. Larger errors are rejected. At present, the limiting value for the residual is calculated by the formula 3m√n, where n is the number of measurements. The article draws attention to two contradictions between theory and practice arising from the use of this formula. First, the formula is derived from the classical law of the normal Gaussian distribution, and it is applied to the truncated law of the normal distribution. And, secondly, as shown in [1], when ∆рred = 2m, the sums of errors naturally take the value equal to ?pred, after which the number of errors in the sum starts anew. This article establishes its validity for ∆рred = 3m. A table of comparative values of the tolerances valid and recommended for more stringent ones is given. The article gives a graph of applied and recommended tolerances for ∆рred = 3m.

DETERMINATION OF THE JUICE EVAPORATION MATHEMATICAL MODELS EFFICIENCY FOR AUTOMATED PROCESS CONTROL SYSTEMS

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
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Keyword(s):  
Process Control ◽  
Mathematical Models ◽  
Control Systems ◽  
Process Control Systems ◽  
Automated Process

Mean-square Exponential Input-to-state Euler-Maruyama Method Applied to Stochastic Control Systems

2010 ◽  
Vol 36 (3) ◽  
pp. 406-411 ◽  
Author(s):  
Qiao ZHU ◽  
Guang-Da HU ◽  
Li ZENG
Keyword(s):  
Control Systems ◽  
Stochastic Control ◽  
Mean Square

Features of accumulation of amounts of measurement error

2017 ◽  
Vol 928 (10) ◽  
pp. 58-63 ◽  
Author(s):  
V.I. Salnikov
Keyword(s):  
Measurement Error ◽  
Confidence Interval ◽  
Normal Distribution ◽  
Confidence Level ◽  
Measurement Errors ◽  
Truncated Normal Distribution ◽  
Truncated Normal ◽  
The Law ◽  
Normal Law

The initial subject for study are consistent sums of the measurement errors. It is assumed that the latter are subject to the normal law, but with the limitation on the value of the marginal error Δpred = 2m. It is known that each amount ni corresponding to a confidence interval, which provides the value of the sum, is equal to zero. The paradox is that the probability of such an event is zero; therefore, it is impossible to determine the value ni of where the sum becomes zero. The article proposes to consider the event consisting in the fact that some amount of error will change value within 2m limits with a confidence level of 0,954. Within the group all the sums have a limit error. These tolerances are proposed to use for the discrepancies in geodesy instead of 2m*SQL(ni). The concept of “the law of the truncated normal distribution with Δpred = 2m” is suggested to be introduced.

scholarly journals Consistency of the Empirical Distributions of Navigation Positioning System Errors with Theoretical Distributions—Comparative Analysis of the DGPS and EGNOS Systems in the Years 2006 and 2014

Sensors ◽  
2020 ◽  
Vol 21 (1) ◽  
pp. 31
Author(s):  
Mariusz Specht
Keyword(s):  
Normal Distribution ◽  
Root Mean Square ◽  
Statistical Tests ◽  
Position Error ◽  
Positioning System ◽  
Navigation Systems ◽  
Mean Square ◽  
Positioning Systems ◽  
Position Errors ◽  
System Errors

Positioning systems are used to determine position coordinates in navigation (air, land and marine). The accuracy of an object’s position is described by the position error and a statistical analysis can determine its measures, which usually include: Root Mean Square (RMS), twice the Distance Root Mean Square (2DRMS), Circular Error Probable (CEP) and Spherical Probable Error (SEP). It is commonly assumed in navigation that position errors are random and that their distribution are consistent with the normal distribution. This assumption is based on the popularity of the Gauss distribution in science, the simplicity of calculating RMS values for 68% and 95% probabilities, as well as the intuitive perception of randomness in the statistics which this distribution reflects. It should be noted, however, that the necessary conditions for a random variable to be normally distributed include the independence of measurements and identical conditions of their realisation, which is not the case in the iterative method of determining successive positions, the filtration of coordinates or the dependence of the position error on meteorological conditions. In the preface to this publication, examples are provided which indicate that position errors in some navigation systems may not be consistent with the normal distribution. The subsequent section describes basic statistical tests for assessing the fit between the empirical and theoretical distributions (Anderson-Darling, chi-square and Kolmogorov-Smirnov). Next, statistical tests of the position error distributions of very long Differential Global Positioning System (DGPS) and European Geostationary Navigation Overlay Service (EGNOS) campaigns from different years (2006 and 2014) were performed with the number of measurements per session being 900’000 fixes. In addition, the paper discusses selected statistical distributions that fit the empirical measurement results better than the normal distribution. Research has shown that normal distribution is not the optimal statistical distribution to describe position errors of navigation systems. The distributions that describe navigation positioning system errors more accurately include: beta, gamma, logistic and lognormal distributions.

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