The model of accuracy of a local radio navigation system considering unstable performance of individual elements
DOI:
https://doi.org/10.15587/1729-4061.2016.71921Keywords:
pseudo satellite, radio navigation system, state vector of the consumer, accuracy, navigation parameter, pseudo remotenessAbstract
A mathematical model of the accuracy of the local radio navigation system was considered, built on the base of a network of pseudo satellites. It was determined that the key factor influencing the accuracy of determining the vector of status of the consumer is the geometry of the structure.
However, for certain categories of consumers there is a necessity of taking into account a possibility of degradation of the structure because of malfunctioning and possible intentional damage. Existing mathematical models of accuracy do not consider a capacity of change in the topology structure.
It was defined that for the assessment of the accuracy of navigation of specific consumers it is expedient to use a geometric factor that determines the degree of deterioration of finding the location relative to the accuracy of defining the pseudo remoteness from the consumer to the radio-navigation points.
To consider the possibility of failure (destruction) of individual elements of the structure of a local radio navigation system, we introduce a probabilistic model that, on the base of registering the combinations of usable/faulty pseudo satellites and their relative geometric position, makes it possible to define the process of changing the accuracy of the system. As the main indicator of the accuracy, we use a root mean square deviation of the location definition (the state vector) of the consumer.
As a result of the research we identified and confirmed by simulation that the maximum accuracy (minimum values of geometric factor) can be achieved in the case when a consumer is located in the centre of a regular tetrahedron.
Given the sphericity of the Earth, a minimum value for a ground consumer is achieved when one pseudo satellite is in the zenith and the other three are evenly located in the horizontal plane.
The combination of the base model of accuracy with a stochastic model of reliability/survivability will allow designing spatial structure of local radio navigation systems by the criterion of stable performance.
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Copyright (c) 2016 Vitalii Savchenko, Oleh Vorobiov, Mykolaichuk Roman Mykolaichuk, Alisa Mykolaychuk, Tymur Kurtseitov
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