Parametric message passing-based relative navigation in joint tactical information distribution system

Relative navigation is a key feature in the joint tactical information distribution system（JTIDS）.A parametric message passing algorithm based on factor graph is proposed to perform relative navigation in JTIDS.First of all,the joint posterior distribution of all the terminals＇ positions is represented by factor graph.Because of the nonlinearity between the positions and time-of-arrival（TOA） measurement,messages cannot be obtained in closed forms by directly using the sum-product algorithm on factor graph.To this end,the Euclidean norm is approximated by Taylor expansion.Then,all the messages on the factor graph can be derived in Gaussian forms,which enables the terminals to transmit means and covariances.Finally,the impact of major error sources on the navigation performance are evaluated by Monte Carlo simulations,e.g.,range measurement noise,priors of position uncertainty and velocity noise.Results show that the proposed algorithm outperforms the extended Kalman filter and cooperative extended Kalman filter in both static and mobile scenarios of the JTIDS.

Estimating Loss Given Default Based on Beta Regression

Loss given default(LGD)is a key parameter in credit risk management to calculate the required regulatory minimum capital.The internal ratings-based(IRB)approach under the Basel II allows institutions to determine the loss given default(LGD)on their own.In this study,we have estimated LGD for a credit portfolio data by using beta regression with precision parameter(∅)and mean parameter(μ).The credit portfolio data was obtained from a banking institution in Jordan;for the period of January 2010 untilDecember 2014.In the first stage,we have used the“outstandingamount”and“amount of borrowing”to find LGD of each default borrower(494 out of 4393 borrower).In the second stage,we fit univariate parametric distributions to the LGD data to obtain the beta distribution.After that,we have estimated the values of∅based on microeconomic variables(SPP,OE and LR).Moreover,we have estimated the values ofμbased on macroeconomic variables(GDP and Inflation rate).Finally,we have compared between six different link functions(Logit,loglog,probit,cloglog,cauchit,and log),which have used with∅andμ.The results show that Beta regression with probit link function has the highest R-squared with accepted measurements for logL,AIC and BIC.