Correlation-weighted least squares residual algorithm for RAIM

The Least Squares Residual(LSR)algorithm,one of the classical Receiver Autonomous Integrity Monitoring(RAIM)algorithms for Global Navigation Satellite System(GNSS),presents a high Missed Detection Risk(MDR)for a large-slope faulty satellite and a high False Alarm Risk(FAR)for a small-slope faulty satellite.From the theoretical analysis of the high MDR and FAR cause,the optimal slope is determined,and thereby the optimal test statistic for fault detection is conceived,which can minimize the FAR with the MDR not exceeding its allowable value.To construct a test statistic approximate to the optimal one,the CorrelationWeighted LSR(CW-LSR)algorithm is proposed.The CW-LSR test statistic remains the sum of pseudorange residual squares,but the square for the most potentially faulty satellite,judged by correlation analysis between the pseudorange residual and observation error,is weighted with an optimal-slope-based factor.It does not obey the same distribution but has the same noncentral parameter with the optimal test statistic.The superior performance of the CW-LSR algorithm is verified via simulation,both reducing the FAR for a small-slope faulty satellite with the MDR not exceeding its allowable value and reducing the MDR for a large-slope faulty satellite at the expense of FAR addition.

An enhanced least squares residual RAIM algorithm based on optimal decentralized factor

The Least Squares Residual(LSR)algorithm is commonly used in the Receiver Autonomous Integrity Monitoring(RAIM).However,LSR algorithm presents high Missed Detection Risk(MDR)caused by a large-slope faulty satellite and high False Alert Risk(FAR)caused by a small-slope faulty satellite.In this paper,the LSR algorithm is improved to reduce the MDR for a large-slope faulty satellite and the FAR for a small-slope faulty satellite.Based on the analysis of the vertical critical slope,the optimal decentralized factor is defined and the optimal test statistic is conceived,which can minimize the FAR with the premise that the MDR does not exceed its allowable value of all three directions.To construct a new test statistic approximating to the optimal test statistic,the Optimal Decentralized Factor weighted LSR(ODF-LSR)algorithm is proposed.The new test statistic maintains the sum of pseudo-range residual squares,but the specific pseudo-range residual is weighted with a parameter related to the optimal decentralized factor.The new test statistic has the same decentralized parameter with the optimal test statistic when single faulty satellite exists,and the difference between the expectation of the new test statistic and the optimal test statistic is the minimum when no faulty satellite exists.The performance of the ODFLSR algorithm is demonstrated by simulation experiments.

A Deep Residual PLS for Data-Driven Quality Prediction Modeling in Industrial Process

Partial least squares(PLS)model is the most typical data-driven method for quality-related industrial tasks like soft sensor.However,only linear relations are captured between the input and output data in the PLS.It is difficult to obtain the remaining nonlinear information in the residual subspaces,which may deteriorate the prediction performance in complex industrial processes.To fully utilize data information in PLS residual subspaces,a deep residual PLS(DRPLS)framework is proposed for quality prediction in this paper.Inspired by deep learning,DRPLS is designed by stacking a number of PLSs successively,in which the input residuals of the previous PLS are used as the layer connection.To enhance representation,nonlinear function is applied to the input residuals before using them for stacking highlevel PLS.For each PLS,the output parts are just the output residuals from its previous PLS.Finally,the output prediction is obtained by adding the results of each PLS.The effectiveness of the proposed DRPLS is validated on an industrial hydrocracking process.