Kalman Filter-Based Integrity Monitoring Against Sensor Faults

This paper introduces a new Kalman filter-based method for detecting sensor faults in linear dynamic systems. In contrast with existing sequential fault-detection algorithms, the proposed method enables direct evaluation of the integrity risk, which is the probability that an undetected fault causes state estimate errors to exceed predefined bounds of acceptability. The new method is also computationally efficient and straightforward to implement. The algorithm’s detection test statistic is established in three steps. First, the weighted norms of current and past-time Kalman filter residuals are defined as generalized noncentrally chi-square distributed random variables. Second, these residuals are proven to be stochastically independent from the state estimate error. Third, current-time and past-time residuals are shown to be mutually independent, so that the Kalman filter-based test statistic can be recursively updated in real time by simply adding the current-time residual contribution to a previously ...

[1]  Bacem Bakhache.  A Sequential RAIM Based on the Civil Aviation Requirements , 1999 .

[2]  R. Grover Brown,et al.  GPS failure detection by autonomous means within the cockpit , 1986 .

[3]  Young C. Lee.  Analysis of Range and Position Comparison Methods as a Means to Provide GPS Integrity in the User Receiver , 1986 .

[4]  Mathieu Joerger,et al.  Sequential Residual-Based RAIM , 2010 .

[5]  Jason L. Speyer,et al.  A generalized Shiryayev sequential probability ratio test for change detection and isolation , 1999, IEEE Trans. Autom. Control..

[6]  Gary McGraw,et al.  Development of the LAAS Accuracy Models , 2000 .

[7]  P. Takis Mathiopoulos,et al.  Quadratic forms in normal RVs: theory and applications to OSTBC over hoyt fading channels , 2008, IEEE Transactions on Wireless Communications.

[8]  Mark A. Sturza,et al.  Navigation System Integrity Monitoring Using Redundant Measurements , 1988 .

[9]  Tariq S. Abuhashim,et al.  Building a robust integrity monitoring algorithm for a low cost GPS-aided-INS system , 2010 .

[10]  I. Nikiforov.  New optimal approach to Global Positioning System/Differential Global Positioning System integrity monitoring , 1996 .

[11]  Mathieu Joerger,et al.  Iridium/GPS Carrier Phase Positioning and Fault Detection Over Wide Areas , 2009 .

[12]  A. Willsky,et al.  Analytical redundancy and the design of robust failure detection systems , 1984 .

[13]  Daniel Choukroun,et al.  Mode Estimation via Conditionally Linear Filtering: Application to Gyro Failure Monitoring , 2012 .

[14]  J. Junkins,et al.  Batch State Estimation , 2004 .

[15]  Alan S. Willsky,et al.  A survey of design methods for failure detection in dynamic systems , 1976, Autom..

[16]  John E. Angus,et al.  RAIM with Multiple Faults , 2006 .

[17]  Marianne Frisén,et al.  Optimal Sequential Surveillance for Finance, Public Health, and Other Areas , 2009 .

[18]  Mathieu Joerger,et al.  Analysis of Iridium-Augmented GPS for Floating Carrier Phase Positioning , 2010 .

[19]  Steven Chan,et al.  A Sequential Probability Test for RAIM , 2004 .

[20]  E. S. Page.  CONTINUOUS INSPECTION SCHEMES , 1954 .

[21]  Hugh F. Durrant-Whyte,et al.  A high integrity IMU/GPS navigation loop for autonomous land vehicle applications , 1999, IEEE Trans. Robotics Autom..

[22]  Patrick Y. C. Hwang.  Kinematic GPS for Differential Positioning: Resolving Integer Ambiguities on the Fly , 1991 .

[23]  Rtca . Sc,et al.  Minimum operational performance standards for GPS local area augmentation system airborne equipment , 2000 .

[24]  Mathieu Joerger,et al.  Solution Separation Versus Residual-Based RAIM , 2014 .

[25]  A. Willsky,et al.  A generalized likelihood ratio approach to the detection and estimation of jumps in linear systems , 1976 .

[26]  Venugopal V. Veeravalli,et al.  Multihypothesis sequential probability ratio tests - Part II: Accurate asymptotic expansions for the expected sample size , 2000, IEEE Trans. Inf. Theory.

[27]  Dai Weiheng.  Receiver autonomous integrity monitoring in iridium-augmented GPS , 2013 .

[28]  J.J. Gertler,et al.  Survey of model-based failure detection and isolation in complex plants , 1988, IEEE Control Systems Magazine.

[29]  Tze Leung Lai.  Sequential multiple hypothesis testing and efficient fault detection-isolation in stochastic systems , 2000, IEEE Trans. Inf. Theory.

[30]  P. S. Maybeck,et al.  MMAE Detection of Interference/Jamming and Spoofing in a DGPS-Aided Inertial System , 1998 .

[31]  J. Junkins,et al.  Optimal Estimation of Dynamic Systems , 2004 .

[32]  Jason Rife,et al.  The Effect of Uncertain Covariance on a Chi-Square Integrity Monitor , 2013 .

[33]  Venugopal V. Veeravalli,et al.  Multihypothesis sequential probability ratio tests - Part I: Asymptotic optimality , 1999, IEEE Trans. Inf. Theory.

[34]  A. Wald,et al.  A Sequential Decision Procedure for Choosing One of Three Hypotheses Concerning the Unknown Mean of a Normal Distribution , 1949 .

[35]  Josef Shinar,et al.  Novel Adaptive Generalized Likelihood Ratio Detector with Application to Maneuvering Target Tracking , 2006 .

[36]  Yue Wang,et al.  Risk-Based Sensor Management for Integrated Detection and Estimation , 2011 .

[37]  Bradford W. Parkinson,et al.  Global positioning system : theory and applications , 1996 .

[38]  Bradford W. Parkinson,et al.  Autonomous GPS Integrity Monitoring Using the Pseudorange Residual , 1988 .

[39]  Christophe Macabiau,et al.  Sequential RAIM designed to detect combined step ramp pseudo-range errors , 2006 .

[40]  John Diesel,et al.  GPS/IRS AIME: Calculation of Thresholds and Protection Radius Using Chi-Square Methods , 1995 .

[41]  Mats A. Brenner,et al.  lntegrated GPS/lnertial Fault Detection Availability , 1995 .

[42]  Per Enge,et al.  An Optimized Multiple Hypothesis RAIM Algorithm for Vertical Guidance , 2007 .

[43]  G. Lorden.  PROCEDURES FOR REACTING TO A CHANGE IN DISTRIBUTION , 1971 .

[44]  Abigail L. Bristow,et al.  Map-Aided Integrity Monitoring of a Land Vehicle Navigation System , 2012, IEEE Transactions on Intelligent Transportation Systems.

[45]  J. Klobuchar.  Ionospheric Effects on GPS , 2009 .

[46]  J. V. Candy,et al.  SEQUENTIAL DETECTION ESTIMATION AND NOISE CANCELATION , 2007 .

[47]  R. Davies.  The distribution of a linear combination of 2 random variables , 1980 .

[48]  Y. Bar-Shalom,et al.  The interacting multiple model algorithm for systems with Markovian switching coefficients , 1988 .

[49]  이영재,et al.  Differential GPS와 응용 , 1994 .

[50]  Jinling Wang,et al.  Extended Receiver Autonomous Integrity Monitoring (eRAIM) for GNSS/INS Integration , 2010 .