International audienceThis paper proposes a novel quaternion-basedattitude estimator with magnetic, angular rate, and gravity (MARG) sensor arrays. A new structure of a fixed-gaincomplementary filter is designed fusing related sensors. To avoidusing iterative algorithms, the accelerometer-based attitude determination is transformed into a linear system. Stable solutionto this system is obtained via control theory. With only onematrix multiplication, the solution can be computed. Using theincrement of the solution, we design a complementary filter thatfuses gyroscope and accelerometer together. The proposed filteris fast, since it is free of iteration. We name the proposed filter thefast complementary filter (FCF). To decrease significant effectsof unknown magnetic distortion imposing on the magnetometer, a stepwise filtering architecture is designed. The magneticoutput is fused with the estimated gravity from gyroscope andaccelerometer using a second complementary filter when thereis no significant magnetic distortion. Several experiments arecarried out on real hardware to show the performance andsome comparisons. Results show that the proposed FCF canreach the accuracy of Kalman filter. It successfully finds abalance between estimation accuracy and time consumption.Compared with iterative methods, the proposed FCF has muchless convergence speed. Besides, it is shown that the magneticdistortion would not affect the estimated Euler angles

International audienceAs a key problem for multi-sensor attitudedetermination, Wahba’s problem has been studied for almost50 years. Different from existing methods, this paper presentsa novel linear approach to solving this problem. We name theproposed method the Fast Linear Attitude Estimator (FLAE)because it is faster than known representative algorithms. Theoriginal Wahba’s problem is extracted to several 1-dimensionalequations based on quaternions. They are then investigatedwith pseudo-inverse matrices establishing a linear solution to ndimensional equations, which are equivalent to the conventionalWahba’s problem. To obtain the attitude quaternion in a robustmanner, an eigenvalue-based solution is proposed. Symbolicsolutions to the corresponding characteristic polynomial isderived showing higher computation speed. Simulations aredesigned and conducted using test cases evaluated by severalclassical methods e.g. M. D. Shuster’s QUaternion ESTimator(QUEST), F. L. Markley’s SVD method, D. Mortari’s SecondEstimator of the Optimal Quaternion (ESOQ2) and some recentrepresentative methods e.g. Y. Yang’s analytical method andRiemannian manifold method. The results show that FLAEgenerates attitude estimates as accurate as that of severalexisting methods but consumes much less computation time(about 50% of the known best algorithm). Also, to verifythe feasibility in embedded application, an experiment onthe accelerometer-magnetometer combination is carried outwhere the algorithms are compared via C++ programminglanguage. An extreme case is finally studied, revealing a minorimprovement shows more effectiveness in this case inspired byY. Cheng et al

From the operational perspective, on large fingerprint data sets, a receiver operating characteristic (ROC) curve is usually measured by the true accept rate (TAR) of the genuine scores given a specified false accept rate (FAR) of the impostor scores. The ties of genuine and/or impostor scores at a threshold can often occur on large fingerprint data sets, and how to determine the TAR at an operational FAR is provided. The accuracy of the measurement of TAR at a specified FAR for an ROC curve is explored using the nonparametric two-sample bootstrap.The variability of the estimates of standard error and lower bound and upper bound of 95% confidence interval of two-sample bootstrap distribution of the statistic TARs on large fingerprint data sets is extensively studied empirically. Thereafter, the number of two-sample bootstrap replications is determined. Both high-accuracy and low-accuracy fingerprint-image matching algorithms are taken as examples.

In receiver operating characteristic (ROC) analysis, the sampling variability can result in uncertainties of performance measures. Thus, while evaluating and comparing the performances of algorithms, the measurement uncertainties must be taken into account. The key issue is how to calculate the uncertainties of performance measures in ROC analysis. Our ultimate goal is to perform the significance test in evaluation and comparison using the standard errors computed. From the operational perspective, based on fingerprint-image matching algorithms on large datasets, the measures and their uncertainties are investigated in the three scenarios: 1) the true accept rate (TAR) of genuine scores at a specified false accept rate (FAR) of impostor scores, 2) the TAR and FAR at a given threshold, and 3) the equal error rate. The uncertainties of measures are calculated using the nonparametric two-sample bootstrap based on our extensive studies of bootstrap variability on large datasets. The significance test is carried out to determine whether the difference between the performance of one algorithm and a hypothesized value, or the difference between the performances of two algorithms where the correlation is taken into account is statistically significant. Examples are provided.