In order to improve the bias stability of the micro-electro mechanical system（MEMS） gyroscope and reduce the impact on the bias from environmental temperature,a digital signal processing method is described for impr...In order to improve the bias stability of the micro-electro mechanical system（MEMS） gyroscope and reduce the impact on the bias from environmental temperature,a digital signal processing method is described for improving the accuracy of the drive phase in the gyroscope drive mode.Through the principle of bias signal generation,it can be concluded that the deviation of the drive phase is the main factor affecting the bias stability.To fulfill the purpose of precise drive phase control,a digital signal processing circuit based on the field-programmable gate array（FPGA） with the phase-lock closed-loop control method is described and a demodulation method for phase error suppression is given.Compared with the analog circuit,the bias drift is largely reduced in the new digital circuit and the bias stability is improved from 60 to 19 °/h.The new digital control method can greatly increase the drive phase accuracy,and thus improve the bias stability.展开更多
Let d ≥ 1 and Z be a subordinate Brownian motion on R^d with infinitesimal generator ? + ψ(?),where ψ is the Laplace exponent of a one-dimensional non-decreasing L′evy process(called subordinator). We establish th...Let d ≥ 1 and Z be a subordinate Brownian motion on R^d with infinitesimal generator ? + ψ(?),where ψ is the Laplace exponent of a one-dimensional non-decreasing L′evy process(called subordinator). We establish the existence and uniqueness of fundamental solution(also called heat kernel) pb(t, x, y) for non-local operator L^b= ? + ψ(?) + b ?, where Rb is an Rd-valued function in Kato class K_(d,1). We show that p^b(t, x, y)is jointly continuous and derive its sharp two-sided estimates. The kernel pb(t, x, y) determines a conservative Feller process X. We further show that the law of X is the unique solution of the martingale problem for(L^b, C_c~∞(R^d)) and X is a weak solution of Xt = X0+ Zt + integral from n=0 to t(b(Xs)ds, t ≥ 0).Moreover, we prove that the above stochastic differential equation has a unique weak solution.展开更多
基金The National Natural Science Foundation of China (No.60974116)the Research Fund of Aeronautics Science (No. 20090869007)Specialized Research Fund for the Doctoral Program of Higher Education(No. 200802861063)
文摘In order to improve the bias stability of the micro-electro mechanical system（MEMS） gyroscope and reduce the impact on the bias from environmental temperature,a digital signal processing method is described for improving the accuracy of the drive phase in the gyroscope drive mode.Through the principle of bias signal generation,it can be concluded that the deviation of the drive phase is the main factor affecting the bias stability.To fulfill the purpose of precise drive phase control,a digital signal processing circuit based on the field-programmable gate array（FPGA） with the phase-lock closed-loop control method is described and a demodulation method for phase error suppression is given.Compared with the analog circuit,the bias drift is largely reduced in the new digital circuit and the bias stability is improved from 60 to 19 °/h.The new digital control method can greatly increase the drive phase accuracy,and thus improve the bias stability.
基金supported by National Science Foundation of USA(Grant No.DMS-1206276)National Natural Science Foundation of China(Grant No.11371217)
文摘Let d ≥ 1 and Z be a subordinate Brownian motion on R^d with infinitesimal generator ? + ψ(?),where ψ is the Laplace exponent of a one-dimensional non-decreasing L′evy process(called subordinator). We establish the existence and uniqueness of fundamental solution(also called heat kernel) pb(t, x, y) for non-local operator L^b= ? + ψ(?) + b ?, where Rb is an Rd-valued function in Kato class K_(d,1). We show that p^b(t, x, y)is jointly continuous and derive its sharp two-sided estimates. The kernel pb(t, x, y) determines a conservative Feller process X. We further show that the law of X is the unique solution of the martingale problem for(L^b, C_c~∞(R^d)) and X is a weak solution of Xt = X0+ Zt + integral from n=0 to t(b(Xs)ds, t ≥ 0).Moreover, we prove that the above stochastic differential equation has a unique weak solution.
