稳定分布环境下的时延估计新方法研究
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摘要
在传统的信号处理研究中,高斯模型占据主导的地位。许多情况下随机信号和噪声的高斯分布假定是合理的,并且这种合理性可以由中心极限定理而得到证明。另一方面,在高斯假定基础上所设计的信号处理算法易于进行理论上的解析分析。对信号和噪声的任何非高斯假定,都不可避免地会引入非线性和非最小相位问题,从而导致传统的信号处理算法、模型建立及相应分析计算的复杂化。
时间延迟作为信号处理领域中一个一直十分活跃的研究课题,在军事、工业领域和水声学、地震学、生物医学等领域都有广泛的应用。因此,本文主要考虑了时延估计问题中非高斯噪声对传统算法的挑战,依据分数低阶统计量理论提出了一些新算法;同时从信号重构的角度对多径时延估计问题进行了分析并提出了新的算法。具体包括以下几个方面:
(1)在α稳定分布噪声环境下,提出了广义的时延估计方法。在时延估计问题中,若背景噪声是脉冲性较强的α稳定分布噪声,则传统的时延估计算法都会出现性能退化甚至失效的现象。在分数低阶统计量的理论框架下,本文首先提出一种具有高分辨率的时延估计法。将FFT谱计算中的一个重要子类——线性调频Z变换(CZT)算法和共变谱同时引入时延估计问题中,将其转化为谐波信号的频率估计问题,从而得到适用于脉冲噪声环境且具有高分辨率的估计结果;然后提出两种适用于脉冲噪声环境的自适应估计非整数时延的方法,即将时延估计问题转化为FIR滤波器的参数估计问题,继而应用自适应技术得到估计结果。本文研究分析了在脉冲噪声环境下,对FIR滤波器系数分别用采样的sinc函数和拉格朗日插值滤波器进行约束时,传统的二阶代价函数失效的原因,提出了新的方法并从理论上证明了新方法有效性。
(2)考虑α稳定分布噪声对二阶循环统计量的影响,提出了分数低阶循环相关函数和p阶循环模糊函数,并将其应用到时延估计问题中。传统的循环相关函数相当于两个频移信号的互相关函数,而循环功率谱本质就是二维的功率谱,一维代表普通意义的频率,另一维代表循环频率,因此α稳定分布噪声必然对它们产生影响,本文根据分数低阶理论提出了分数低阶循环相关函数,然后在其基础上提出了一种基于p阶循环模糊函数的方法,实现了在脉冲噪声存在时有效地联合估计时延和多普勒频移,该方法比基于分数低阶模糊函数和二阶循环模糊函数的方法具有更好的准确性:同时提出α稳定分布噪声存在条件下的具有信号选择性的自适应时延估计方法。该方法可有效估计高斯噪声和脉冲噪声条件下的时变和非时变时延值,其性能优于基于二阶循环相关的自适应时延估计算法和最小平均p范数(Least Mean P-norm,LMP)自适应时延估计方法。
(3)根据Whittaker-Shannon插值定理,已知信号的多径时延问题可以归为信号重构问题,因此本文首先采用逐维求解的方法,将多维求解问题转化为多个一维问题,逐个对各径信号的幅度衰减和时间延迟进行估计;另外,将多径时延估计问题看作稀疏信号的重构,并应用Compressing Sense理论方法中的MP(Match Pursuit)和SP(SubspacePursuit)完成重构继而得到时延估计结果,同时提出一种自适应的SP方法,减少了预设参数,仿真结果验证了算法的有效性。
The Gaussian distribution plays a predominant role in signal processing. Its simple justification by the Central Limit Theorem and attractive analytic properties has made it the most important statistical distribution. However, there are many phenomena which are decidedly non-Gaussian and therefore are necessary to look beyond oversimplified Gaussian assumption and into more realistic non-Gaussian models. Any non-Gaussian assumption of signal or noise will inevitably introduce nonlinear and/or nonminimum phase problems, which result in complexity of signal processing algorithms, model construction and analytic computation.
The estimation or tracking of the time delay between received signals impinging on two separated sensors is important in some fields, such as sonar, radar, biomedical application and position locating in wireless networks, etc. Although the work that deals with the problem of time delay estimation has already been presented in the literature, it has always assumed a Gaussian signal and noise model. A better model for the noise is the a stable distribution which can model, in addition to the Gaussian distribution, a wider and more impulsive range of phenomena. Based on this obersation, new methods for time delay estimation in impulsive noise environments are studied using theαstable distribution theory. And multipath time delay estimation problem is thrown into signal reconstruction to arise novel alogrithms. Main research and conclusions are summarized as:
(1)New time delay estimation methods for impulsive noise environments are addressed. The impulsiveness ofαstable distributed noise can make the performance of conventional time delay estimation methods degrade even invalidate. Firstly, considering the effect of a stable distributed noises for the classical second order statistics, this dissertation combines covariation spectrum and chirp Z transformation (CZT) which is one of the most useful spectrum analysis methods, and consequently proposes a novel multi-source time delay estimation method in impulsive noise environment. Simulations show that the proposed algorithm is a high resolution method suited forαstable distributed noises condition and its performance is better than the common method named covariation method. Secondly, two roubst adaptive algorithms are proposed for fractional time delay estimation which define novel cost function and transfer the time delay estimation into the parameter estimation of FIR filter. Some conclusions are deduced in theory.
(2) Taking into consideration the influence ofαstable distributed noise on second order cyclostationary statistics, fractional lower order cyclostationary statistics are developed, and then applied to time delay estimation problems. The trational cyclic correlation is just a correlation of two frequency shift signals and in nature cyclic spectrum is just power spectrum with two dimentions which represent time lag and cyclic frequency respectively. Therefore theαstable distributed noise has impact on them. Combinig with the theory of fractional lower order statistics theory, novel function are introduced and their properties are proven. Firstly, an approach for estimating time delay with signal selectivity in the presence of impulsive noise is developed. Simulations show that the performance of proposed algorithm is not only better than that based on second order cyclic correlation, but also the covariation algorithm. Secondly, considering such circumstance that relative motions can be discribed as a fixed time delay and Doppler shift, a new algorithm based on the propesed p th order cyclic ambiguity function is investigated.It is showed that time delay and Doppler shift can be jointly estimated in the presence of impulse noise. It has better estimation accuracy than second order, fractional lower order and cyclic ambiguity function. Finally, a new adaptive time delay estimation method is proposed for highly corruptive environments, which is based on the proposed robust cyclic correlation estimator. Simulations show that the performance of the proposed algorithm is superior to the LMP (Least Mean P-norm) time delay estimation method and adaptive time delay estimation method based on second order cyclic correlation in alpha-stable distributed noises.
(3)According to Whittaker-Shannon theorem, this dissertation announces that the problem of multipath time delay estimation is equal to that of signal reconstruction problem. Firstly, the multi-dimention optimization is transfered into mulitiple one-dimention optimization, which simplize the process.Then by using the match pursuit and subspace pursuit algorithms in compressing sense theory, the amplitude and time difference of different paths are gained. At the same time, a proposed adaptive subspace pursuit algorithm is applied into multipath time delay estimation, which needs less prior knowledge with effective results.
时间延迟作为信号处理领域中一个一直十分活跃的研究课题,在军事、工业领域和水声学、地震学、生物医学等领域都有广泛的应用。因此,本文主要考虑了时延估计问题中非高斯噪声对传统算法的挑战,依据分数低阶统计量理论提出了一些新算法;同时从信号重构的角度对多径时延估计问题进行了分析并提出了新的算法。具体包括以下几个方面:
(1)在α稳定分布噪声环境下,提出了广义的时延估计方法。在时延估计问题中,若背景噪声是脉冲性较强的α稳定分布噪声,则传统的时延估计算法都会出现性能退化甚至失效的现象。在分数低阶统计量的理论框架下,本文首先提出一种具有高分辨率的时延估计法。将FFT谱计算中的一个重要子类——线性调频Z变换(CZT)算法和共变谱同时引入时延估计问题中,将其转化为谐波信号的频率估计问题,从而得到适用于脉冲噪声环境且具有高分辨率的估计结果;然后提出两种适用于脉冲噪声环境的自适应估计非整数时延的方法,即将时延估计问题转化为FIR滤波器的参数估计问题,继而应用自适应技术得到估计结果。本文研究分析了在脉冲噪声环境下,对FIR滤波器系数分别用采样的sinc函数和拉格朗日插值滤波器进行约束时,传统的二阶代价函数失效的原因,提出了新的方法并从理论上证明了新方法有效性。
(2)考虑α稳定分布噪声对二阶循环统计量的影响,提出了分数低阶循环相关函数和p阶循环模糊函数,并将其应用到时延估计问题中。传统的循环相关函数相当于两个频移信号的互相关函数,而循环功率谱本质就是二维的功率谱,一维代表普通意义的频率,另一维代表循环频率,因此α稳定分布噪声必然对它们产生影响,本文根据分数低阶理论提出了分数低阶循环相关函数,然后在其基础上提出了一种基于p阶循环模糊函数的方法,实现了在脉冲噪声存在时有效地联合估计时延和多普勒频移,该方法比基于分数低阶模糊函数和二阶循环模糊函数的方法具有更好的准确性:同时提出α稳定分布噪声存在条件下的具有信号选择性的自适应时延估计方法。该方法可有效估计高斯噪声和脉冲噪声条件下的时变和非时变时延值,其性能优于基于二阶循环相关的自适应时延估计算法和最小平均p范数(Least Mean P-norm,LMP)自适应时延估计方法。
(3)根据Whittaker-Shannon插值定理,已知信号的多径时延问题可以归为信号重构问题,因此本文首先采用逐维求解的方法,将多维求解问题转化为多个一维问题,逐个对各径信号的幅度衰减和时间延迟进行估计;另外,将多径时延估计问题看作稀疏信号的重构,并应用Compressing Sense理论方法中的MP(Match Pursuit)和SP(SubspacePursuit)完成重构继而得到时延估计结果,同时提出一种自适应的SP方法,减少了预设参数,仿真结果验证了算法的有效性。
The Gaussian distribution plays a predominant role in signal processing. Its simple justification by the Central Limit Theorem and attractive analytic properties has made it the most important statistical distribution. However, there are many phenomena which are decidedly non-Gaussian and therefore are necessary to look beyond oversimplified Gaussian assumption and into more realistic non-Gaussian models. Any non-Gaussian assumption of signal or noise will inevitably introduce nonlinear and/or nonminimum phase problems, which result in complexity of signal processing algorithms, model construction and analytic computation.
The estimation or tracking of the time delay between received signals impinging on two separated sensors is important in some fields, such as sonar, radar, biomedical application and position locating in wireless networks, etc. Although the work that deals with the problem of time delay estimation has already been presented in the literature, it has always assumed a Gaussian signal and noise model. A better model for the noise is the a stable distribution which can model, in addition to the Gaussian distribution, a wider and more impulsive range of phenomena. Based on this obersation, new methods for time delay estimation in impulsive noise environments are studied using theαstable distribution theory. And multipath time delay estimation problem is thrown into signal reconstruction to arise novel alogrithms. Main research and conclusions are summarized as:
(1)New time delay estimation methods for impulsive noise environments are addressed. The impulsiveness ofαstable distributed noise can make the performance of conventional time delay estimation methods degrade even invalidate. Firstly, considering the effect of a stable distributed noises for the classical second order statistics, this dissertation combines covariation spectrum and chirp Z transformation (CZT) which is one of the most useful spectrum analysis methods, and consequently proposes a novel multi-source time delay estimation method in impulsive noise environment. Simulations show that the proposed algorithm is a high resolution method suited forαstable distributed noises condition and its performance is better than the common method named covariation method. Secondly, two roubst adaptive algorithms are proposed for fractional time delay estimation which define novel cost function and transfer the time delay estimation into the parameter estimation of FIR filter. Some conclusions are deduced in theory.
(2) Taking into consideration the influence ofαstable distributed noise on second order cyclostationary statistics, fractional lower order cyclostationary statistics are developed, and then applied to time delay estimation problems. The trational cyclic correlation is just a correlation of two frequency shift signals and in nature cyclic spectrum is just power spectrum with two dimentions which represent time lag and cyclic frequency respectively. Therefore theαstable distributed noise has impact on them. Combinig with the theory of fractional lower order statistics theory, novel function are introduced and their properties are proven. Firstly, an approach for estimating time delay with signal selectivity in the presence of impulsive noise is developed. Simulations show that the performance of proposed algorithm is not only better than that based on second order cyclic correlation, but also the covariation algorithm. Secondly, considering such circumstance that relative motions can be discribed as a fixed time delay and Doppler shift, a new algorithm based on the propesed p th order cyclic ambiguity function is investigated.It is showed that time delay and Doppler shift can be jointly estimated in the presence of impulse noise. It has better estimation accuracy than second order, fractional lower order and cyclic ambiguity function. Finally, a new adaptive time delay estimation method is proposed for highly corruptive environments, which is based on the proposed robust cyclic correlation estimator. Simulations show that the performance of the proposed algorithm is superior to the LMP (Least Mean P-norm) time delay estimation method and adaptive time delay estimation method based on second order cyclic correlation in alpha-stable distributed noises.
(3)According to Whittaker-Shannon theorem, this dissertation announces that the problem of multipath time delay estimation is equal to that of signal reconstruction problem. Firstly, the multi-dimention optimization is transfered into mulitiple one-dimention optimization, which simplize the process.Then by using the match pursuit and subspace pursuit algorithms in compressing sense theory, the amplitude and time difference of different paths are gained. At the same time, a proposed adaptive subspace pursuit algorithm is applied into multipath time delay estimation, which needs less prior knowledge with effective results.
引文
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