一种快速产生1/f^γ分形信号的新方法  

A method of rapidly generating 1/f^γ fractal signal

作　　者：华春红[1] 任章[1] 张敏虎[1] 

机构地区：[1]北京航空航天大学自动化科学与电气工程学院,北京100191

出　　处：《中国惯性技术学报》2010年第3期355-358,共4页Journal of Chinese Inertial Technology

基　　金：航空科学基金项目(20070851011)

摘　　要：分形噪声是光纤陀螺的主要噪声源。为了能快速仿真产生常用谱指数范围的分形信号,提出了一种分数阶差分方法。该方法首先基于分数布朗运动模型,推导出其分数微分形式;接着用分数差分算子替代微分算子将其转换到离散域,那么分形信号就可以表示为高斯白噪声分数阶差分形式。这样只要指定谱指数γ,就可以构造分数差分矩阵,与高斯白噪声序列做卷积,结果就是所求的分形序列。最后与小波变换和FFT组合法生成的分形序列进行仿真性能对比,结果表明了本方法的可行性和优越性,而且分数阶差分本质上是序列的卷积运算,计算简单,能够满足分形信号快速仿真生成需求。Fractal noise is the main stochastic noise of Fiber Optic Gyroscope （FOG）.For the common spectral exponent γ,a Fractional Differencing （FD） method is put forward for rapidly generating fractal signal in simulation.First,its fractional differential expression based on Fractional Brownian Motion （FBM） model is derived.Then the derived expression is transformed into a discrete domain by substituting FD operator,thus fractal signal can be expressed as the FD form of Gaussian White Noise （GWN）.Once a spectral exponent γ is specified,the FD matrix can be constructed,and by convoluting with GWN series,the obtained result is the desired fractal series.In the end,by comparing the simulation performances with those of the fractal series generated by the integration method of Fast Fourier Transform （FFT） and wavelet transform respectively,the feasibility and the superiority of the proposed method is demonstrated.The FD mainly involves convolution operation,therefore its computation is simple,and can meet the requirement for rapidly generating fractal signal in simulation.

关 键 词：光纤陀螺 分形信号 分数阶差分 谱指数 

分 类 号：U666.1[交通运输工程—船舶及航道工程]