Eliezer Gai

Generalized Likelihood Test for FDI in Redundant Sensor Configurations

The Generalized Likelihood Test (GLT) approach to failure detection and isolation (FDI) in redundant sets of inertial sensors is described and its relationship to the overall FDI structure is explored. Specific formulations of both the detection and the isolation problems are presented. The performance of the resulting FDI system is analyzed by means of the second-order statistics of the detection and isolation decision functions. The equivalence of the GLT approach to several previously reported approaches for both single-degree-of-freedom (SDOF) and two-degree-of-freedom (TDOF) sensors is described. To illustrate its application, the GLT approach is used to compare the FDI performance of three different redundant sensor configurations; a conical configuration of five SDOF sensors, a dodecahedron configuration of six SDOF sensors, and an octahedron configuration of four TDOF sensors.

Star-Sensor-Based Satellite Attitude/Attitude Rate Estimator

Recent advancements in star sensor technology suggest that implementations of spacecraft on-orbit attitude determination and control systems based solely On star sensor measurements may soon become practical. This paper defines the requirements such applications impose on the star sensors and the algorithms used to estimate attitude and attitude rate. A practical filter implementation is described. Its open-loop performance is evaluated, and simulation results are presented which suggest that performance consistent with a broad class of spacecraft applications is indeed achievable.

Decision behavior with changing signal strength

Abstract The Theory of Signal Detectability (TSD) has nearly replaced classical notions of the threshold because of its ability to separate sensory and decision processes in weak-signal detection and recognition paradigms. The primary emphasis of recent work has concentrated on the sensory rather than the decision aspects and almost all work has been exclusively at one signal strength. We propose a model to describe behavior at different signal strengths based on subjective rather than objective distributions. The model predicts performance at a constant likelihood ratio (LR) criterion (even though subjective distributions are the basis for determining cutoff criteria) unless the observer adopts a Subjective Neyman-Pearson (SNP) objective. Results from an experiment in visual discrimination suggest that some observers in fact operate at constant objective LRs as signal strength is varied randomly over a wide range. The objective LRs of the other subjects changed dramatically with signal strength, but this behavior is consistent with the use of a Subjective Neyman-Pearson (SNP) decision rule and the linear relation between subjective and objective log LRs found in the studies of subjective probability.

Evaluating Sensor Orientations for Navigation Performance and Failure Detection

A study of the constraints imposed by the choice of particular orientations of redundant inertial sensors upon navigation system performance and the detection and identification of sensor failures in fault-tolerant inertial measurement units is presented. Figures of merit are derived for systematically evaluating alternative sensor orientations. The volume of the ellipsoid associated with the covariance matrix of estimation errors is used to rank sensor orientations in terms of navigation performance. Distance measures commonly used in hypothesis testing are used to rank sensor orientations in terms of the detectability of sensor failures. The application of these results is illustrated for configurations of four 2-degree-of-freedom gyroscopes.

In-Flight Parity Vector Compensation for FDI

The performance of a failure detection and isolation (FDI) algorithm applied to a redundant strapdown inertial measurement unit (IMU) is limited by sensor errors such as input axis misalignment, scale factor errors, and biases. A techique is presented for improving the performance of FDI algorithms applied to redundant strapdown IMUs. A Kalman filter provides estimates of those linear combinations of sensor errors that affect the parity vector. These estimates are used to form a compensated parity vector which does not include the effects of sensor errors. The compensated parity vector is then used in place of the uncompensated parity vector to make FDI decisions. Simulation results are presented in which the algorithm is tested in a realistic flight environment that includes vehicle maneuvers, the effects of turbulence, and sensor failures. The results show that the algorithm can significantly improve FDI performance, especially during vehicle maneuvers.

FDI Performance of Two Redundant Sensor Configurations

A geometrical interpretation of the generalized likelihood test (GLT) approach to sensor failue detection and isolation (FDI) is provided, and analytical expressions are derived to evaluate FDI performance parameters of interest. These results are used to determine the FDI performance which can be achieved when various FDI decision strategies are applied to two redundant sensor configurations: a conical array of five single degree-of-freedom sensors and a dodecahedron array of six single degree-of-freedom sensors.

Reliability and Accuracy Prediction for a Redundant Strapdown Navigator

A comprehensive approach to the evaluation of the accuracy and reliability of a redundant navigation system is described. A Markov model of the redundant system is used to determine the probabilities of particular operational state time histories. Navigation system accuracies are associated with these state time histories through the use of a modified covariance analysis of the systems navigation errors. Suitable scalar figures of merit are used to assess the impact on performance of significant system parameters. The analysis is applied to a redundant navigator which is used to transfer a payload from launch to geosynchronous orbit. HE accuracy of navigation systems has traditionally been evaluated by means of conventional covariance analysis techniques,1 sensitivity analyses,2 or Monte Carlo simulations.3 These approaches are not well suited, however, to the evaluation of the accuracy of a redundant system. This is primarily due to the fact that the operational state of a redundant system changes at random points in time, resulting in a very large ensemble of operational state time histories which must be considered. An analysis approach which accounts for the effects of the random occurrence of component failures and reconfigurations of the redundant system elements is required. The operational state of a redundant system changes as system components fail and as failure detection and identification (FDI) decisions are made. A Markov model of the redundant system and its associated FDI algorithms can be used to determine the probabilities of particular operational state time histories. These probabilities can be used to identify the members of the ensemble of operational state time histories which most strongly influence system performance. A linearized stochastic sensitivity analysis4 can then be used to determine the statistics of the navigation system errors for each of the operational state time histories of interest. The many factors which influence the accuracy of a redundant navigation system also influence the systems reliability. Conventional reliability prediction methods5 must be augmented, therefore, in order to include these effects. A Markov model is well suited to this purpose. System reliability can be predicted by summing the probabilities of all operational state time histories which end in severely degraded performance. The use of Markov modeling techniques to predict system performance also provides insight into the sensitivity of this performance to significant features of the system design. These techniques thus provide a systematic method of evaluating design tradeoffs and for choosing parameters such as FDI thresholds by examining the effects of these tradeoffs and choices on system accuracy and reliability. The redundant inertial measurement unit (RIMU)6 considered in this paper consists of five gyros and five accelerometers in a conical configuration. Three power supplies

Determination of Failure Thresholds in Hybrid Navigation

A systematic approach for the determination of failure thresholds for hybrid navigation systems is described. Cost functions which reflect the importance assigned to the consequences of false and missed alarms are minimized. The false alarm probability is obtained as a function of the threshold magnitude by observing the statistical behavior of the instrument outputs in the normal operating mode. The missed alarm probability is obtained by determining the sensitivity of navigation error performance to instrument error sources. Two cost functions are considered. To illustrate this method, failure detection and identification (FDI) thresholds are determined for the Space Shuttle Approach and Landing Test flight.

Perseveration Effects in Detection Tasks with Correlated Decision Intervals

An investigation of the behavior of the human decisionmaker is described for a task related to the problem of a pilot using a traffic situation display to avoid collisions. This sequential signal detection task is characterized by highly correlated signals with time varying strength. Experimental results are presented and the behavior of the observers is analyzed using the theory of Markov processes and classical signal detection theory. Mathematical models are developed which describe the main result of the experiment: that correlation in sequential signals induced perseveration in the observer response and a strong tendency to repeat their previous decision, even when they were wrong.

Reliability analysis of a dual-redundant engine controller

A Markov model is developed to predict the reliability of a full-authority, dual-redundant aircraft engine controller. The effects of failures of any of the controllers sensors, electronic interface modules, processors and actuators, as well as the consequences of redundancy management decisions are modeled. The model is used to study parameter sensitivity and to develop quantitative data in support of design tradeoffs. The effects of scheduled maintenance of the inflight shutdown rate of the engine are determined.