scholarly journals Polynomial Filtering Algorithm for Single-Beacon Navigation Problem

2018 ◽  
Vol 51 (32) ◽  
pp. 619-623
Author(s):  
Oleg A. Stepanov ◽  
Anton B. Toropov ◽  
Alexei V. Loparev ◽  
Vladimir A. Vasiliev ◽  
Michael V. Basin
2021 ◽  
Vol 29 (3) ◽  
pp. 3-33
Author(s):  
О.А. Stepanov ◽  
◽  
Yu.A. Litvinenko ◽  
V.A. Vasiliev ◽  
A.B. Toropov ◽  
...  

The paper considers the filtering problems solved in navigation data processing under quadratic nonlinearities both in system and measurement equations. A Kalman type recursive algorithm is proposed, where the predicted estimate and gain at each step are calculated based on the assumption on the Gaussian posterior proba-bility density function of the estimated vector at the previous step and minimization of estimation error covariance matrix using a linear procedure with respect to the current measurement. The similarities between this algorithm and other Kalman type algorithms such as extended and secondorder Kalman filters are discussed. The procedure for estimating the performance and comparing the algorithms is presented.


2020 ◽  
Vol 25 (5) ◽  
pp. 465-474
Author(s):  
V.O. Zhilinskiy ◽  
◽  
D.S. Pecheritsa ◽  
L.G. Gagarina ◽  
◽  
...  

The Global Navigation Satellite System has a huge impact on both the public and private sectors, including the social-economic development, it has many applications and is an integral part of many domains. The application of the satellite navigation systems remains the most relevant in the field of transport, including land, air and maritime transport. The GLONASS system consists of three segments and the operation of the entire system depends on functioning of each component, but primarily, the accuracy of measurements depends on the basis forming of the control segment and management, responsible for forming ephemeris-time information. In the work, the influence of ephemeris-time information on the accuracy of solving the navigation problem by the signals of the GLONASS satellite navigation system has been analyzed. The influence of both ephemeris information and the frequency information, and of the time corrections has been individually studied. The accuracy of the ephemeris-time information is especially important when solving the navigation problem by highly precise positioning method. For the analysis the following scenarios of the navigation problem solving have been formed: using high-precision and broadcast ephemeris-time information, a combination of broadcast (high-precision) ephemeris-time information, and high-precision (broadcast) satellite clock offsets and two scenarios with simulation of the calculation of the relative correction to the radio signal carrier frequency. Based on the study results it has been concluded that the contribution of the frequency-time corrections to the error of location determination is of the greatest importance and a huge impact on the error location, while the errors of the ephemeris information are insignificant


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