Adaptive Estimation of Generalized Distance to Uniformity

Author(s):  
Yi Hao ◽  
Alon Orlitsky
Mathematics ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 17 ◽  
Author(s):  
Abdollah Alhevaz ◽  
Maryam Baghipur ◽  
Hilal A. Ganie ◽  
Yilun Shang

The generalized distance matrix D α ( G ) of a connected graph G is defined as D α ( G ) = α T r ( G ) + ( 1 − α ) D ( G ) , where 0 ≤ α ≤ 1 , D ( G ) is the distance matrix and T r ( G ) is the diagonal matrix of the node transmissions. In this paper, we extend the concept of energy to the generalized distance matrix and define the generalized distance energy E D α ( G ) . Some new upper and lower bounds for the generalized distance energy E D α ( G ) of G are established based on parameters including the Wiener index W ( G ) and the transmission degrees. Extremal graphs attaining these bounds are identified. It is found that the complete graph has the minimum generalized distance energy among all connected graphs, while the minimum is attained by the star graph among trees of order n.


Measurement ◽  
2021 ◽  
Vol 174 ◽  
pp. 109035
Author(s):  
Xuxing Zhao ◽  
Renjian Feng ◽  
Yinfeng Wu ◽  
Ning Yu ◽  
Xiaofeng Meng ◽  
...  

Inventions ◽  
2021 ◽  
Vol 6 (1) ◽  
pp. 10
Author(s):  
Sergey Sokolov ◽  
Arthur Novikov ◽  
Marianna Polyakova

In measurement systems operating under various disturbances the probabilistic characteristics of measurement noises are usually known approximately. To improve the observation accuracy, a new approach to the Kalman’s filter adaptation is proposed. In this approach, the Covariance Matrix of Measurement Noises (CMMN) is estimated by accurate measurements detected irregularly by the mobile object observation system (from radiofrequency identifiers, etalon reference, fixed points etc.). The problem of adaptive estimation of the observer’s noises covariance matrix in the Kalman filter is solved analytically for two cases: mutual noises correlation, and its absence. The numerical example for adaptive filtration of complexing navigation system parameters of a mobile object using irregular accurate measurements is given to illustrate the effectiveness of the proposed algorithm. Coordinate estimating errors have changed in comparison with the traditional scheme from 100 m to 2 m in latitude, and from 200 m to 1.5 m in longitude.


Sign in / Sign up

Export Citation Format

Share Document