An effective de-noising method for fiber optic gyroscopes （FOGs） is proposed. This method is based on second-generation Daubechies D4 （DB4） wavelet transform （WT） and level-dependent threshold estimator called S...An effective de-noising method for fiber optic gyroscopes （FOGs） is proposed. This method is based on second-generation Daubechies D4 （DB4） wavelet transform （WT） and level-dependent threshold estimator called Stein＇s unbiased risk estimator （SURE）. The whole approach consists of three critical parts： wavelet decomposition module, parameters estimation module and SURE de-noising module. First, DB4 wavelet is selected as lifting base of the second-generation wavelet in the decomposition module. Second, in the parameters estimation module, maximum likelihood estimation （MLE） is used for stochastic noise parameters estimation. Third, combined with soft threshold de-noising technique, the SURE de-noising module is designed. For comparison, both the traditional universal threshold wavelet and the second-generation Harr wavelet method are also investigated. The experiment results show that the computation cost is 40% less than that of the traditional wavelet method. The standard deviation of de-noised FOG signal is 0.012 and the three noise terms such as angle random walk, bias instability and quantization noise are reduced to 0.007 2°/√h, 0.004 1° / h, and 0.008 1°, respectively.展开更多
The objective of this paper is to quantify the complexity of rank and nuclear norm constrained methods for low rank matrix estimation problems. Specifically, we derive analytic forms of the degrees of freedom for thes...The objective of this paper is to quantify the complexity of rank and nuclear norm constrained methods for low rank matrix estimation problems. Specifically, we derive analytic forms of the degrees of freedom for these types of estimators in several common settings. These results provide efficient ways of comparing different estimators and eliciting tuning parameters. Moreover, our analyses reveal new insights on the behavior of these low rank matrix estimators. These observations are of great theoretical and practical importance. In particular, they suggest that, contrary to conventional wisdom, for rank constrained estimators the total number of free parameters underestimates the degrees of freedom, whereas for nuclear norm penalization, it overestimates the degrees of freedom. In addition, when using most model selection criteria to choose the tuning parameter for nuclear norm penalization, it oftentimes suffices to entertain a finite number of candidates as opposed to a continuum of choices. Numerical examples are also presented to illustrate the practical implications of our results.展开更多
基金Supported by the Aerospace Science and Technology Innovation Foundation of China (2006)
文摘An effective de-noising method for fiber optic gyroscopes （FOGs） is proposed. This method is based on second-generation Daubechies D4 （DB4） wavelet transform （WT） and level-dependent threshold estimator called Stein＇s unbiased risk estimator （SURE）. The whole approach consists of three critical parts： wavelet decomposition module, parameters estimation module and SURE de-noising module. First, DB4 wavelet is selected as lifting base of the second-generation wavelet in the decomposition module. Second, in the parameters estimation module, maximum likelihood estimation （MLE） is used for stochastic noise parameters estimation. Third, combined with soft threshold de-noising technique, the SURE de-noising module is designed. For comparison, both the traditional universal threshold wavelet and the second-generation Harr wavelet method are also investigated. The experiment results show that the computation cost is 40% less than that of the traditional wavelet method. The standard deviation of de-noised FOG signal is 0.012 and the three noise terms such as angle random walk, bias instability and quantization noise are reduced to 0.007 2°/√h, 0.004 1° / h, and 0.008 1°, respectively.
基金supported by National Science Foundation of USA (Grant No. DMS1265202)National Institutes of Health of USA (Grant No. 1-U54AI117924-01)
文摘The objective of this paper is to quantify the complexity of rank and nuclear norm constrained methods for low rank matrix estimation problems. Specifically, we derive analytic forms of the degrees of freedom for these types of estimators in several common settings. These results provide efficient ways of comparing different estimators and eliciting tuning parameters. Moreover, our analyses reveal new insights on the behavior of these low rank matrix estimators. These observations are of great theoretical and practical importance. In particular, they suggest that, contrary to conventional wisdom, for rank constrained estimators the total number of free parameters underestimates the degrees of freedom, whereas for nuclear norm penalization, it overestimates the degrees of freedom. In addition, when using most model selection criteria to choose the tuning parameter for nuclear norm penalization, it oftentimes suffices to entertain a finite number of candidates as opposed to a continuum of choices. Numerical examples are also presented to illustrate the practical implications of our results.
