The least squares algorithm, parametric system identification and bounded noise

The least squares parametric system identification algorithm is analyzed assuming that the noise is a bounded signal. A bound on the worst-case parameter estimation error is derived. This bound shows that the worst-case parameter estimation error decreases to zero as the bound on the noise is decreased to zero.     

FIR方法在维纳滤波器设计中的应用与仿真

基于最小均方误差准则,得到维纳-霍夫方程,并利用FIR(有限冲击响应)方法求解,进而得到维纳滤波器的传递函数。在MatLab环境下,基于一阶AR(自回归)模型生成原始信号,对维纳滤波器进行设计和仿真,并分析抽样点数、AR模型参数、信噪比和滤波器阶数对滤波效果的影响。仿真结果表明,增大抽样点数和信噪比以及减小AR模型参数,滤波效果增强;增大滤波器阶数,滤波效果先增强后减弱。     

On the worst-case divergence of the least-squares algorithm

In this paper, we provide a _∞-norm lower bound on the worst-case identification error of least-squares estimation when using FIR model structures. This bound increases as a logarithmic function of model complexity and is valid for a wide class of inputs characterized as being quasi-stationary with covariance function falling off sufficiently quickly.     

Worst-case/deterministic identification in H∞: the continuous-time case

Results obtained by the authors (1991) worst-case/deterministic H_∞ identification of discrete-time plants are extended to continuous-time plants. The problem involves identification of the transfer function of a stable strictly proper continuous-time plant from a finite number of noisy point samples of the plant frequency response. The assumed information consists of a lower bound on the relative stability of the plant, an upper bound on a certain gain associated with the plant, an upper bound on the roll-off rate of the plant, and an upper bound on the noise level. Concrete plans of identification algorithms are provided for this problem. Explicit worst-case/deterministic error bounds for each algorithm establish that they are robustly convergent and (essentially) asymptotically optimal. Additionally, these bounds provide an a priori computable H_∞ uncertainty specification, corresponding to the resulting identified plant transfer function, as an explicit function of the plant and noise prior information and the data cardinality     

基于2阶Renyi熵的自适应主动噪声控制

在前馈主动噪声控制中,基于均方误差准则的传统算法仅考虑了信号的2阶统计量,忽略了实际存在的非高斯信号,不能满足对非高斯噪声的控制要求.提出基于2阶Renyi熵的滤波X自适应有限脉冲响应 (finite impulse response,FIR)主动噪声控制算法,定义2阶Renyi熵作为性能指标,利用Parzen窗方法估计误差的概率密度函数,给出基于2阶Renyi熵的信息梯度下降算法,实现自适应FIR控制,同时分析了算法的收敛性和计算复杂度.对单频信号和实测宽带非高斯噪声的仿真结果表明该算法能很好地消除非高斯噪声.     

Guaranteed estimation of signals with bounded variances of derivatives

Consideration is given to the problem of signal estimation against the background of the white noise when the information about the signal is represented in the form of numerical characteristics such as constraints on the variance of the signal itself and variances of some its derivatives. We proposed a method to solve this problem using the technique of filtering in the time domain by minimizing the functional that is a combination of the H ₂-norm of the transfer function from the measurement noise to the error of estimation and the H _∞-norm of the transfer function from the generating noise to the error of estimation.     

Application of the genetic algorithm to real-time active noise control

A modified model, in the form of an FIR filter, is proposed for the modelling of the acoustic dynamics of an active noise control system. This is a low order filter formulation but consists of two independent elements—a time delay and a d.c. gain. Empirical data has shown that this model constitutes a good representation of the equivalent high order FIR filter and has the additional feature of being a high frequency noise filtering device. Because of its specific structure, the time delay and gain must be identified independently. This restricts the use of the conventional least mean squares technique for parameter optimization, as the cost function intrinsically comprises multimodal error surfaces. The use of Genetic Algorithms could be the best solution to address this issue but their unpredictable response in real-time require some special attention. A fully developed active noise control system, based on the Genetic Algorithm, to achieve the objective of noise reduction is described. To further guarantee the reliability of this approach, a supervisory scheme is incorporated for governing the real-time learning operations. A parallel hardware architecture, using two independent TMS320C30 digital signal processors, is designed for such implementation. The experimental results indicate that this approach to noise control is sound, and that noise reduction of more than 15dB(A) is consistently obtained.     

Opportunistic Encryption: A Trade-Off between Security and Throughput in Wireless Networks

Wireless network security based on encryption is widely prevalent at this time. However, encryption techniques do not take into account wireless network characteristics such as random bit errors due to noise and burst errors due to fading. We note that the avalanche effect that makes a block cipher secure also causes them to be sensitive to bit errors. This results in a fundamental trade-off between security and throughput in encryption based wireless security.1 Further, if there is an adversary with a certain attack strength present in the wireless network, we see an additional twist to the security-throughput trade-off issue. In this paper, we propose a framework called opportunistic encryption that uses channel opportunities (acceptable signal to noise ratio) to maximize the throughput subject to desired security constraints. To illustrate this framework and compare it with some current approaches, this paper presents the following: 1) mathematical models to capture the security-throughput trade-off, 2) adversary models and their effects, 3) joint optimization of encryption and modulation (single and multirate), 4) the use of forward error correcting (FEC) codes to protect encrypted packets from bit errors, and 5) simulation results for Rijndael cipher. We observe that opportunistic encryption produces significant improvement in the performance compared to traditional approaches.     

Block QIM watermarking games

While binning is a fundamental approach to blind data embedding and watermarking, an attacker may devise various strategies to reduce the effectiveness of practical binning schemes. The problem analyzed in this paper is design of worst-case noise distributions against L-dimensional lattice quantization index modulation (QIM) watermarking codes. The cost functions considered are 1) probability of error of the maximum-likelihood decoder, and 2) the more tractable Bhattacharyya upper bound on error probability, which is tight at low embedding rates. Both problems are addressed under the following constraints on the attacker's strategy: the noise is independent of the marked signal, blockwise memoryless with block length L, and may not exceed a specified quadratic-distortion level. The embedder's quadratic distortion is limited as well. Three strategies are considered for the embedder: optimization of the lattice inflation parameter (also known as Costa parameter), dithering, and randomized lattice rotation. Critical in this analysis are the symmetry properties of QIM nested lattices and convexity properties of probability of error and related functionals of the noise distribution. We derive the minmax optimal embedding and attack strategies and obtain explicit solutions as well as numerical solutions for the worst-case noise. The role of the attacker's memory is investigated; in particular, we demonstrate the remarkable effectiveness of impulsive-noise attacks as L increases. The formulation proposed in this paper is also used to evaluate the capacity of lattice QIM under worst-noise conditions.     

Robust Wiener filtering with non-parametric spectral uncertainty

In this article, robust least-squares filtering problems are considered for non-parametric multivariate spectral uncertainty defined by the so-called spectral band and generalised-moment constraints. Its major aim is to provide a basis for computing approximate solutions to worst-case, Wiener-filtering optimisation problems involving causal filters and multivariate signals. It hinges upon associating upper and lower bounds on the minimum worst-case performance achievable with causal filters with linear-cost/linear matrix inequality (LC/LMI)-constraint optimisation problems. On the basis of a Lagrangean duality formulation for the worst-case, least-squares performance of a given filter, upper bounds on it are obtained as the optimal values of LC/LMI problems. Then, for linearly parameterised classes of filter transfer functions, a causal filter which optimises such an upper bound on worst-case performance can also be obtained from an LC/LMI optimisation problem. To estimate the amount of conservatism incurred when relying on such upper bounds, optimal, nominal, least-squares performance for a given pair of power spectral densities (for the information and noise signal) is maximised over finite-dimensional, linearly parameterised classes of the latter. Again, such problems are shown to be equivalent to LC/LMI problems and the corresponding optimal values are lower bounds on the minimum worst-case, least-squares error achievable in the original robust filtering problem (say, μ_*). Finally, two simple numerical examples are presented to illustrate how causal filters can be obtained whose worst-case, least-squares performance is quite close to the optimal one (i.e. μ_*).     

Image noise induced errors in camera positioning

The problem of evaluating worst-case camera positioning error induced by unknown-but-bounded (UBB) image noise for a given object-camera configuration is considered. Specifically, it is shown that upper bounds to the rotation and translation worst-case error for a certain image noise intensity can be obtained through convex optimizations. These upper bounds, contrary to lower bounds provided by standard optimization tools, allow one to design robust visual servo systems.     

Design of RLS Wiener FIR filter using covariance information in linear discrete-time stochastic systems

This paper addresses a new design method of recursive least-squares (RLS) finite impulse response (FIR) filter, using the covariance information of the signal and observation noise, and RLS Wiener FIR filter in linear discrete-time stochastic systems. The signal is observed with additive white noise. The signal is assumed to be independent of the white observation noise. The RLS Wiener FIR filter uses the following information: (1) The observation matrix for the signal, (2) the system matrix for the state vector, (3) the variance of the state vector.     

On the time complexity of worst-case system identification

In this paper we treat a general worst-case system identification problem. This problem is worst-case with respect to both noise and system modeling uncertainty. We consider this problem under various a priori information structures. We determine bounds on the minimum duration identification experiment that must be run to identify the plant to within a specified guaranteed worst-case error bound. Our results are algorithm independent. We show that this minimum duration is prohibitively long. Based on our results, we suggest that worst-case (with respect to noise) system identification requires unrealistic amounts of experimental data     

应用对消原理辨识传递函数

本文提出了一种辨识系统传递函数的新方法.它是通过引入预滤波器对输入信号进行 预处理,调整预滤波器的参数,使其实现与系统传递函数的部分对消,并应用对消原理而得到 的一种辨识方法.这种方法可以分别辨识传递函数的分子、分母及其因子,而且不需要对噪 声进行建模.此法还可以用来辨识误差模型.     

Analysis and synthesis of speech using least <Emphasis Type="Italic">P</Emphasis>th norm filter design

In this paper we analyze the combination of speech and FIR filter design aspect to achieve good results in speech quality. A new approach in the time domain based on the least Pth norm is presented to extract maximum information that represents speech. The aim of this paper is to improve the perceived quality of speech through the introduction of least Pth norm algorithm that attenuates speech contaminated with noise. This approach relates to a filter bank structure and a method for filtering and separating an information signal into different bands, particularly for filtering and separation of speech signals. Then the desired signal is reconstructed from the independent components representing every band. This approach differs from the traditional approaches since no priori knowledge of the noise statistics is required, instead the noise signals are only assumed to have finite energy. Since the estimation criterion for the filter design is to minimize the worst possible amplification of the estimation error signal in terms of modeling errors and additive noise, this approach is highly robust and appropriate in practical speech analysis and synthesis. This paper presents a least Pth approach to the optimal design of FIR digital filter banks in the minimax sense for speech analysis and synthesis. The signal to noise ratio (SNR) of around 50–60 dB is achieved with various speech samples.     

宽带雷达信号的低杂散采样系统研究

为了实现宽带雷达系统中雷达信 号的低失真采集与处理,研究并设计了具有幅相误差校正功能的宽带低杂散采样系统。该系统采用宽带模数转换（Analog to digital converter, ADC）器件和高性能可编程逻辑阵列（Field programmable gate array, FPGA）的实现方案,并从低抖动采样时钟、低噪声电源和防串扰等方面进行了低杂散最优方案研究。为了改善系统的带内传输特性,利用优化算 法设计了有限长冲激响（Finite impulse response,FIR）数字校准滤波器。最后对设计 的系统进行实验测试,结果表明系统瞬时带宽达到800 MHz以上,采样率1.8GS/s,量化位数8位、杂散电平-50 dBc,性能指标满足系统在宽带雷达信号获取、宽带雷达目标成像和宽带雷达目标回波重构等领域的应用。     

基于谱减和LMS的自适应语音增强

针对宽带噪声背景下的语音增强问题,将短时语音视为非平稳或宽平稳信号,基于谱减法和自适应滤波的最小均方（LMS）算法,提出了一种FIR型自适应滤波算法（SSLMS）：用减谱法由短时噪声观测语音估计期望信号,作为滤波器输出信号的参考信号;用滤波器的输出与参考信号的差值为误差信号,用LMS算法求得滤波器权系数修正量,并修正滤波器。权系数最速下降调整中,采用了归一化LMS、符号LMS、块LMS技术,以简化保证权系数收敛的步长选择、减少权系数修正的运算量,从而提高自适应速度。对不同的语音在各种信噪比下仿真实验,并与改进的谱减法比较,结果表明,该法增强效果优于谱减法;在信噪比为3 dB时该法的增强效果仍然令人满意。     

H∞ identification of “soft” uncertainty models

The paper investigates the problem of identifying uncertainty models of causal, SISO, LTI, discrete-time, BIBO stable, unknown systems, using frequency domain measurements corrupted by Gaussian noise of known covariance. Additive uncertainty models are looked for, consisting of a nominal model and an additive dynamic perturbation accounting for the modeling error. The nominal model is chosen within a class of affinely parametrized models with transfer function of given (possibly low) order. An estimate of the parameters minimizing the H_∞ modeling error is obtained by minimizing an upper bound of the worst-case (with respect to the modeling error) second moment of the estimation error. Then, a bound in the frequency domain guaranteeing to include, with probability α, the frequency response error between the estimated nominal model and the unknown system is derived.     

Robust steady-state tracking

This paper addresses the robust performance problem when the performance measure is the “steady-state” value of an error signal. Necessary and sufficient conditions are derived for robust steady-state tracking of fixed inputs in the presence of structured time-varying uncertainty are derived. These conditions are easily computable and fit well with existing conditions on stability robustness and performance robustness when the performance measure is the level of disturbance rejection. Using these conditions, it is shown that time-varying perturbations of a nominal linear time-invariant plant can result in large steady-state tracking errors to fixed inputs even if the nominal plant and controller give zero steady-state tracking errors. The derived expressions for the worst-case steady-state tracking error give insight into how the time variation in the plant affects tracking errors and suggest that certain transfer function norms should be minimized to reduce the effect of these perturbations on the steady-state value of error signals     

基于应变式传感器的压电陶瓷定位系统设计

基于压电陶瓷驱动的纳米扫描和定位系统,是原子力显微镜系统的关键部件。本文设计了基于电阻式应变传感器(SGS）的压电陶瓷微纳米位移定位系统。该系统在硬件上采用仪表放大器对SGS应变信号进行RF滤波、放大、模拟滤波处理得到与压电陶瓷位移变化线性相关的电压信号,该信号由高精度AD采集,并通过控制器输出到上位机软件MATLAB中进行噪声分析、FIR数字滤波去噪、线性度分析。实验结果表明,该位移检测系统输出电压噪声峰峰值小于0.5mV,输出非线性误差小于0.06%,可实现2nm的位移分辨率。该定位系统可以应用于原子力显微镜的开发中。