降秩自适应滤波算法研究

对降秩自适应滤波算法进行了系统的总结和分析,推导了其相互关系。分析表明,GSC（Generalized Sidelobe Canceller）框架降秩变换自适应滤波是各种降秩自适应滤波算法的统一模型。在此基础上导出了线性约束正交投影算法。降秩多级维纳滤波器在相关意义上进行截断降秩,其降秩性能优于基于特征子空间截断的降秩方法。酉多级维纳滤波器与共轭梯度法等效,均是基于Krylov子空间截断降秩的方法,降秩性能更优。最后通过计算机仿真试验比较了各种降秩处理算法的性能。     

一种基于广义旁瓣相消的改进降秩算法

在处理大型阵列时,阵元数较多,通常对阵列采用降秩处理可以较好地解决运算量过大的问题。基于广义旁瓣相消器(GSC)框架的降秩变换自适应滤波是各种降秩自适应滤波算法的统一模型。分析了基于GSC框架的几种降秩自适应滤波算法,针对当降秩阶数大于干扰数时方向图旁瓣过高、波形混乱和系统性能下降问题,提出了一种基于GSC框架的改进降秩算法,该算法利用特征子空间对GSC阻塞矩阵加以改进,使用改进后的阻塞矩阵进行降秩自适应处理,仿真结果证明了改进算法可以降低旁瓣电平,并形成较好的波束形状,提高了GSC性能的稳健性。     

实测数据的降秩空时自适应处理方法

本文介绍了两种在广义旁瓣相消器结构上的降秩空时自适应处理方法:主分量法和互谱法,这两种方法是利用杂波和干扰的低秩属性,应用采样数据来构造降维转换矩阵。最后对MountainTop计划进行了详细的描述,并对从MountainTop计划测得的数据,应用上述两种降秩方法对其进行了分析。仿真实验表明了这两种方法的可行性,减少了计算量,并提高了有效可测收敛性。     

GSC框架下的最小均方超声波束形成算法

针对传统超声信号幅度变迹方法中主瓣宽度较宽、空间分辨率较低的问题,提出了一种基于广义旁瓣相消器框架下的最小均方超声波束形成算法。该方法基于期望信号最小方差无失真准则,构造广义旁瓣相消器,将接收到的超声信号分解为自适应与非自适应上下两个部分:上支路保留期望信号与噪声信号,且期望信号无失真响应约束得到保证;下支路阻塞期望信号,只含有噪声。将两路信号进行维纳滤波,上下支路噪声得到抵消,期望信号被无失真输出。为了使该算法在硬件上易于实现,采用最小均方算法自适应迭代求取,并给出了FPGA的详细设计过程。仿真实验表明,采用该算法加权的得到的波束与传统幅度变迹方法相比,主瓣更窄,具有抑制干扰和噪声的能力,提高了超声成像的横向分辨率与对比度分辨率。     

基于Givens变换的广义旁瓣相消器的设计

对于传统的基于广义旁瓣相消器(Generalized Sidelobe Canceller,GSC)的降秩自适应波束形成算法,阻塞矩阵大多数需要通过特征值分解获得,而特征值分解会带来新的大运算量,大大限制了算法的工程实现.提出一种基于Givens变换的快速自适应干扰抑制方法,利用Givens变换构建的广义旁瓣相消器下支...     

一种稳健的自适应波束形成算法

一般自适应波束形成的主瓣和零陷比较尖锐,当存在指向误差,干扰信号或天线平台快速运动时,若实时处理速度跟不上,将导致干扰抑制能力下降,采用高速处理算法代价太大.本文研究了利用导数约束法来改进广义旁瓣相消器的稳健性,对信号的自相关矩阵进行改进,使主瓣和零陷展宽,仿真试验表明该方法对指向误差和当干扰或天线平台快速运动时都具有很好的稳健性.     

自适应阵列中多级维纳滤波器的有效实现算法

在分析多级维纳滤波器实现算法的基础上,证明了由相关相减算法实现的多级维纳滤波器是一种酉多级维纳滤波器,与Goldstein、Reed和Scharf提出的原始实现算法相比,酉多级维纳滤波器具有更好的降秩性能。该文对相关相减算法中的阻塞矩阵进行改进,使多级维纳滤波器前向递推中观测数据向量的维数逐步降低,且同样能应用于相关相减算法结构。新的实现算法在进一步降低计算量的同时,得到与相关相减算法几乎相同的性能。仿真结果证明了该算法的有效性。     

基于广义旁瓣相消的机载雷达抗密集转发式干扰方法

密集转发式干扰不仅会引起雷达虚警,而且会抬高其附近单元的恒虚警率检测门限进而导致目标检测性能下降。另外,它还会污染空时自适应处理的训练样本,导致杂波抑制性能下降。针对这些问题,该文提出一种机载雷达抗密集转发式干扰算法。该算法首先估计干扰方向,然后用广义旁瓣相消技术在空域滤除干扰。广义旁瓣相消中的辅助通道为指向干扰方向的和波束,而其协方差矩阵则利用清晰区中挑选的干扰样本估计得到。该算法可以有效抑制密集转发式干扰,减少由其引起的虚警,改善雷达目标检测性能,同时该算法还具有结构简单,易于实现的优点。实验结果验证了该算法的有效性。     

实测数据的降秩空时自适应处理方法

本文介绍了两种在广义旁瓣相消器结构上的降秩空时自适应处理方法：主分量法和互谱法，这两种方法是利用杂波和干扰的低秩属性，应用采样数据来构造降维转换矩阵。最后对Mountain Top计划进行了详细的描述，并对从Mountain Top计划测得的数据，应用上述两种降秩方法对其进行了分析。仿真实验表明了这两种方法的可行性，减少了计算量，并提高了有效可测收敛性。     

一种零陷展宽稳健旁瓣相消算法

受到实际条件的限制,自适应旁瓣相消器通常不可能频繁地更新自适应权值,使得其在对抗空域非平稳干扰时,会出现权值失配现象,严重影响干扰抑制性能。该文从空域密集干扰产生宽零陷的角度出发,提出一种适用于自适应旁瓣相消器的零陷展宽算法。该算法通过对主通道的合成权值和辅助天线间的协方差矩阵同时进行锥削实现零陷展宽,锥削向量和锥削矩阵只与阵元位置和展宽宽度有关,可以离线计算,在线直接调用,实现简单,适合工程实际使用。仿真实验证明,该文方法可以有效展宽自适应零陷,增强自适应旁瓣相消器对抗空域非平稳干扰时的稳健性。     

Line search algorithms for adaptive filtering

Line search algorithms for adaptive filtering that choose the convergence parameter so that the updated filter vector minimizes the sum of squared errors on a linear manifold are described. A shift invariant property of the sample covariance matrix is exploited to produce an adaptive filter stochastic line search algorithm for exponentially weighted adaptive equalization requiring 3N+5 multiplications and divisions per iteration. This algorithm is found to have better numerical stability than fast transversal filter algorithms for an application requiring steady-state tracking capability similar to that of least-mean square (LMS) algorithms. The algorithm is shown to have faster initial convergence than the LMS algorithm and a well-known variable step size algorithm having similar computational complexity in an adaptive equalization experiment     

Improved approximate QR-LS algorithms for adaptive filtering

This paper studies a class of O(N) approximate QR-based least squares (A-QR-LS) algorithm recently proposed by Liu in 1995. It is shown that the A-QR-LS algorithm is equivalent to a normalized LMS algorithm with time-varying stepsizes and element-wise normalization of the input signal vector. It reduces to the QR-LMS algorithm proposed by Liu et al. in 1998, when all the normalization constants are chosen as the Euclidean norm of the input signal vector. An improved transform-domain approximate QR-LS (TA-QR-LS) algorithm, where the input signal vector is first approximately decorrelated by some unitary transformations before the normalization, is proposed to improve its convergence for highly correlated signals. The mean weight vectors of the algorithms are shown to converge to the optimal Wiener solution if the weighting factor w of the algorithm is chosen between 0 and 1. New Givens rotations-based algorithms for the A-QR-LS, TA-QR-LS, and the QR-LMS algorithms are proposed to reduce their arithmetic complexities. This reduces the arithmetic complexity by a factor of 2, and allows square root-free versions of the algorithms be developed. The performances of the various algorithms are evaluated through computer simulation of a system identification problem and an acoustic echo canceller.     

Analysis of conjugate gradient algorithms for adaptive filtering

The paper presents and analyzes two approaches to the implementation of the conjugate gradient (CG) algorithm for filtering where several modifications to the original CG method are proposed. The convergence rates and misadjustments for the two approaches are compared. An analysis in the z-domain is used in order to find the asymptotic performance, and stability bounds are established. The behavior of the algorithms in finite word-length computation are described, and dynamic range considerations are discussed. It is shown that in finite word-length computation and close to steady state, the algorithms' behaviors are similar to the steepest descent algorithm, where the stalling phenomenon is observed. Using 16-bit fixed-point number representation, our simulations show that the algorithms are numerically stable     

Fast adaptive algorithms for multichannel filtering and systemidentification

Fast transversal and lattice least squares algorithms for adaptive multichannel filtering and system identification are developed. Models with different orders for input and output channels are allowed. Four topics are considered: multichannel FIR filtering, rational IIR filtering, ARX multichannel system identification, and general linear system identification possessing a certain shift invariance structure. The resulting algorithms can be viewed as fast realizations of the recursive prediction error algorithm. Computational complexity is then reduced by an order of magnitude as compared to standard recursive least squares and stochastic Gauss-Newton methods. The proposed transversal and lattice algorithms rely on suitable order step-up-step-down updating procedures for the computation of the Kalman gain. Stabilizing feedback for the control of numerical errors together with long run simulations are included     

Modified partial update EDS algorithms for adaptive filtering

Partial update (PU) Euclidean direction search (EDS) algorithms have been developed to reduce the computational complexity of the full update EDS. In this paper, the PU EDS is modified to achieve better performance. The performance is analyzed for a time-invariant system and for a time-varying system. Theoretical steady-state mean and mean squared error results of the modified PU EDS are derived for both time-invariant system and time-varying system. Computer simulations are presented to support the theoretical analyses. The modified PU EDS can achieve similar performance to the full update EDS while reducing the computational complexity significantly. The performance of the modified PU EDS is also compared with the PU recursive least squares (RLS) algorithm and the PU conjugate gradient in computer simulations. The performance of modified PU EDS is comparable to PU RLS, and it needs less computational cost.     

Analysis of momentum adaptive filtering algorithms

This article analyzes the momentum LMS algorithm and other momentum algorithms using asymptotic techniques that provide information regarding the almost sure behavior of the parameter estimates and their asymptotic distribution. The analysis does not make any assumptions on the autocorrelation function of the input process     

Stable and efficient lattice algorithms for adaptive IIR filtering

Previous attempts at applying lattice structures to adaptive infinite-impulse-response (IIR) filtering have met with gradient computations of O(N²) complexity. To overcome this computational burden, two new lattice-based algorithms are proposed for adaptive IIR filtering and system identification, with both algorithms of O(N) complexity. The first algorithm is a reinterpretation of the Steiglitz-McBride method (1965), while the second is a variation on the output error method. State space models are employed to make the derivations transparent, and the methods can be extended to other parameterizations if desired. The set of possible stationary points of the algorithms is shown to be consistent with the convergent points obtained from the direct-form versions of the Steiglitz-McBride and output error methods, whose properties are well studied. The derived algorithms are as computationally efficient as existing direct-form based algorithms, while overcoming the stability problems associated with time-varying direct-form filters     

Constrained adaptive filtering algorithms: asymptotic convergenceproperties for dependent data

The convergence properties of constrained adaptive filtering algorithms are established. The constraint is in the form of a bounded set in which the filter's coefficients must lie. A recursive procedure that converges to the deterministic solution of the constrained linear mean-square estimation problem is obtained, using an appropriate contraction mapping. The recursion is used to derive the adaptive algorithm for the filter coefficients. Bounds on the mean-square error of the coefficients. Bounds on the mean-square error of the estimates of the filter coefficients and on the excess error of the input signal estimate are derived for processes that are either strong mixing or asymptotically uncorrelated. The algorithms use a moving window of size n on the data from one adaptation step to the next. However, tighter bounds can be obtained when a skipped sampling mechanism is used     

Error whitening criterion for adaptive filtering: theory and algorithms

Mean squared error (MSE) has been the dominant criterion in adaptive filter theory. A major drawback of the MSE criterion in linear filter adaptation is the parameter bias in the Wiener solution when the input data are contaminated with noise. We propose and analyze a new augmented MSE criterion called the Error Whitening Criterion (EWC). EWC is able to eliminate this bias when the noise is white. We will determine the analytical solution of the EWC, discuss some interesting properties, and develop stochastic gradient and other fast algorithms to calculate the EWC solution in an online fashion. The stochastic algorithms are locally computable and have structures and complexities similar to their MSE-based counterparts (LMS and NLMS). Convergence of the stochastic gradient algorithm is established with mild assumptions, and upper bounds on the step sizes are deduced for guaranteed convergence. We will briefly discuss an RLS-like Recursive Error Whitening (REW) algorithm and a minor components analysis (MCA) based EWC-total least squares (TLS) algorithm and further draw parallels between the REW algorithm and the Instrumental Variables (IV) method for system identification. Finally, we will demonstrate the noise-rejection capability of the EWC by comparing the performance with MSE criterion and TLS.     

基于自适应滤波技术的NQR信号处理

研究了炸药探测中微弱核四极矩共振信号的处理方法.针对核四极矩共振信号极其微弱且存在严重的振铃拖尾干扰,设计了自适应抵消器,利用干扰信号间的相关性,有效抑制了振铃拖尾,把核四极矩共振信号从干扰中提取出来.提高了核四极矩共振信号的信噪比,提升了系统检测指标.