Analysis of Acoustic Signatures from Moving Vehicles Using Time-Varying Autoregressive Models

Time-varying autoregressive (TVAR) modeling approach for the analysis of acoustic signatures from moving vehicles is presented in this paper. Acoustic signatures from moving vehicles are nonstationary, and features extracted under the stationary assumption often result unsatisfactory performance. In TVAR modeling approach, the time-varying parameters are expanded as a linear combination of deterministic time functions. In this paper, the TVAR parameters are expanded by a low-order discrete cosine transform (DCT), since DCT is known to be close to the optimal Kahrunen-Loève transform when the signal is Markov. The maximum likelihood estimation and order selection in TVAR models are also discussed. Many attributes of vehicle activities, such as vehicle type, engine speed, loading, road condition, etc., may be inferred from the estimated model parameters. The performance of the TVAR modeling approach is tested with both synthetic and real acoustic signatures. A synthetic signal containing multiple time-varying sinusoids are used to compare the performances in the estimation of time-frequency distribution with other approaches. In the experiment with acoustic signatures from moving vehicles, it is shown that the TVAR models can be effectively used to determine vehicle activities and types at close range and cruising speed.     

Spectral estimation of nonstationary EEG using particle filtering with application to event-related desynchronization (ERD)

This paper proposes non-Gaussian models for parametric spectral estimation with application to event-related desynchronization (ERD) estimation of nonstationary EEG. Existing approaches for time-varying spectral estimation use time-varying autoregressive (TVAR) state-space models with Gaussian state noise. The parameter estimation is solved by a conventional Kalman filtering. This study uses non-Gaussian state noise to model autoregressive (AR) parameter variation with estimation by a Monte Carlo particle filter (PF). Use of non-Gaussian noise such as heavy-tailed distribution is motivated by its ability to track abrupt and smooth AR parameter changes, which are inadequately modeled by Gaussian models. Thus, more accurate spectral estimates and better ERD tracking can be obtained. This study further proposes a non-Gaussian state space formulation of time-varying autoregressive moving average (TVARMA) models to improve the spectral estimation. Simulation on TVAR process with abrupt parameter variation shows superior tracking performance of non-Gaussian models. Evaluation on motor-imagery EEG data shows that the non-Gaussian models provide more accurate detection of abrupt changes in alpha rhythm ERD. Among the proposed non-Gaussian models, TVARMA shows better spectral representations while maintaining reasonable good ERD tracking performance.     

基于HFM和感知后滤波器的语音增强

研究了只能获得带噪信号的情况下的语音增强问题。将语音信号看作由高斯噪声激励的自回归(AR)过程,观测噪声为加性高斯白噪声,把信号转化为状态空间模型。首先用隐马尔可夫模型(HMM)估计AR参数和噪声的方差作为卡尔曼滤波器初值,估计信号作为参数估计的中间值给出,然后将估计信号通过一个感知滤波器平滑以消除残余噪声。仿真结果表明该算法有良好的性能。     

EM-based recursive estimation of channel parameters

Recursive (online) expectation-maximization (EM) algorithm along with stochastic approximation is employed in this paper to estimate unknown time-invariant/variant parameters. The impulse response of a linear system (channel) is modeled as an unknown deterministic vector/process and as a Gaussian vector/process with unknown stochastic characteristics. Using these models which are embedded in white or colored Gaussian noise, different types of recursive least squares (RLS), Kalman filtering and smoothing and combined RLS and Kalman-type algorithms are derived directly from the recursive EM algorithm. The estimation of unknown parameters also generates new recursive algorithms for situations, such as additive colored noise modeled by an autoregressive process. The recursive EM algorithm is shown as a powerful tool which unifies the derivations of many adaptive estimation methods     

Speech Enhancement Combining Optimal Smoothing and Errors-In-Variables Identification of Noisy AR Processes

In the framework of speech enhancement, several parametric approaches based on an a priori model for a speech signal have been proposed. When using an autoregressive (AR) model, three issues must be addressed. (1) How to deal with AR parameter estimation? Indeed, due to additive noise, the standard least squares criterion leads to biased estimates of AR parameters. (2) Can an estimation of the variance of the additive noise for each speech frame be obtained? A voice activity detector is often used for its estimation. (3) Which estimation rules and techniques (filtering, smoothing, etc.) can be considered to retrieve the speech signal? Our contribution in this paper is threefold. First, we propose to view the identification of the noisy AR process as an errors-in-variables problem. This blind method has the advantage of providing accurate estimations of both the AR parameters and the variance of the additive noise. Second, we propose an alternative algorithm to standard Kalman smoothing, based on a constrained minimum variance estimation procedure with a lower computational cost. Third, the combination of these two steps is investigated. It provides better results than some existing speech enhancement approaches in terms of signal-to-noise-ratio (SNR), segmental SNR, and informal subjective tests.     

Estimation of autoregressive signals from noisy measurements

The paper presents an asymptotically unbiased estimator of autoregressive parameters from noisy observations. The key ingredient in the author's method is that a new and simple scheme for estimation of the variance of the white measurement noise is developed. This estimated variance is then used in conjunction with the known technique for elimination of the least-squares estimation bias when the noise statistics are known a priori. The properties of the method are illustrated by means of some simulated examples     

Recursive parameter estimation for noisy autoregressive signals (Corresp.)

The problem of recursively estimating the unknown parameters of a scalar autoregressive (AR) signal observed in additive white noise, including signal power and noise variance, is considered. A state-space model in a canonical but noninnovations form is used to represent the noisy AR signal. An algorithm based on a system identification/parameter estimation technique known as the recursive prediction error method is presented for recursive parameter estimation. Two simulation examples illustrate the effectiveness of the proposed algorithm.     

Two-dimensional noisy autoregressive estimation with application to joint frequency and direction of arrival estimation

The present study addresses the problem of two-dimensional autoregressive estimation in the presence of additive white noise. The estimation method is based on combining the low-order and high-order Yule-Walker equations. The noise-compensated YW equations are solved using an iterative algorithm. The proposed method is also applied to joint frequency and direction of arrival estimation in uniform linear arrays. Using simulation study, the performance of the proposed algorithm is evaluated and compared with other methods.     

多变量自回归信号信息融合辨识方法

近年来,为了提高系统模型和状态估计的精度,多传感器数据融合引起了广泛关注。对于带白色公共干扰噪声和有色观测噪声的多传感器多变量自回归（AR）模型,当AR模型参数和噪声方差未知时,提出了一种信息融合多段辨识方法,其中采用多维递推辅助变量（MRIV）方法得到AR模型参数的局部和融合估值器,再用相关方法得到局部和融合噪声方差估值器。这些估值器具有一致性,通过一个信号仿真例子验证了其有效性。     

Inverse filtering based method for estimation of noisy autoregressive signals

In this paper we present a new method for estimating the parameters of an autoregressive (AR) signal from observations corrupted with white noise. The least-squares (LS) estimate of the AR parameters is biased when the observation noise is added to the AR signal. This bias is related to observation noise variance. The proposed method uses inverse filtering technique and Yule-Walker equations for estimating observation noise variance to yield unbiased LS estimate of the AR parameters. The performance of the proposed unbiased algorithm is illustrated by simulation results and they show that the performance of the proposed method is better than the other estimation methods.     

Estimation of autoregressive fading channels based on two cross-coupled H ∞ filters

This paper deals with the on-line estimation of time-varying frequency-flat Rayleigh fading channels based on training sequences and using H _∞ filtering. When the fading channel is approximated by an autoregressive (AR) process, the AR model parameters must be estimated. As their direct estimations from the available noisy observations at the receiver may yield biased values, the joint estimation of both the channel and its AR parameters must be addressed. Among the existing solutions to this joint estimation issue, Expectation Maximization (EM) algorithm or cross-coupled filter based approaches can be considered. They usually require Kalman filtering which is optimal in the H ₂ sense provided that the initial state, the driving process and measurement noise are independent, white and Gaussian. However, in real cases, these assumptions may not be satisfied. In addition, the state-space matrices and the noise variances are not necessarily accurately estimated. To take into account the above problem, we propose to use two cross-coupled H _∞ filters. This method makes it possible to provide robust estimation of the fading channel and its AR parameters.     

Estimation of event-related synchronization changes by a new TVARmethod

The modeling of nonstationary electroencephalogram (EEG) with time-varying autoregressive (TVAR) models is discussed. The classical least squares TVAR approach is modified so that prior assumptions about the signal can be taken into account in an optimal way. The method is then applied to the estimation of event-related synchronization changes in the EEG. The results show that the new approach enables effective estimation of the parameter evolution of the time-varying EEG with better time resolution compared to previous methods. The new method also allows single-trial analysis of the event-related synchronization     

Cramer-Rao bounds in the parametric estimation of fadingradiotransmission channels

The context of this paper is parameter estimation for linearly modulated digital data signals observed on a frequency-flat time-selective fading channel affected by additive white Gaussian noise. The aim is the derivation of Cramer-Rao lower bounds for the joint estimation of all those channel parameters that impact signal detection, namely, carrier phase, carrier frequency offset (Doppler shift), frequency rate of change (Doppler rate), signal amplitude, fading power, and Gaussian noise power. Time-selective frequency-flat fading is modeled as a low-pass autoregressive multiplicative distortion process. In particular, the important case of “slow” fading, with the multiplicative process remaining constant over the whole data burst, is specifically discussed. Asymptotic expressions of the bounds, valid for a large observed sample or for high signal-to-noise ratio (SNR), are also derived in closed form. A few charts with numerical results are finally reported to highlight the dependence of the bounds on channel status (SNR, fading bandwidth, etc.)     

Stabilization of Subba Rao-Liporace models

The stability of time-varying autoregressive (TVAR) models is an important issue in many applications such as time-varying spectral estimation, EEG simulation and analysis, and time-varying linear prediction coding (TVLPC). For stationary AR models there are methods that guarantee stability, but the for nonadaptive time-varying approaches there are no such methods. On the other hand, in some situations, such as in EEG analysis, the models that temporarily exhibit roots with almost unit moduli are difficult to use. Thus we may need a tighter stability condition such as stability with margin 1–. In this paper we propose a method for the estimation of TVAR models that guarantees stability with margin 1–, that is, the moduli of the roots of the time-varying characteristic polynomial are less than or equal to some arbitrary positive number for every time instant. The model class is the Subba Rao-Liporace class, in which the time-varying coefficients are constrained to a subspace of the coefficient time evolutions. The method is based on sequential linearization of the associated nonlinear constraints and the subsequent use of a Gauss-Newton-type algorithm. The method is also applied to a simulated autoregressive process.     

高阶累积量在谱估计中的应用

本文提出了两种利用高阶累积量估计MA参数的新算法。当信号可以看作一个非高斯白噪声通过一个线性时不变系统的输出时,新算法运算简单、估计准确。本文还通过模拟实验分析了两种算法的性能。     

Continuous-time AR process parameter estimation in presence ofadditive white noise

Must existing work so far on continuous-time AR (CAR) parameter estimation concentrates on the noiseless measurement case. When measurement noise is present, our previous results on CAR parameter estimation need to be revised accordingly. Here we model the additive measurement noise as continuous-time white noise, and consider some approaches including average sampling and the direct LS method which we developed previously. Their advantages and disadvantages in this application are discussed     

Cramer-Rao Bounds for parameter estimation of phase-coding signals

In this paper, Cramer-Rao Bound (CRB) is derived from phase-coding signal with additive white noise, where three important parameters are focused on: carrier frequency, chip width and amplitude. Simplified and close form expressions of CRB are obtained through complicated derivation, and then are applied to evaluate the performance of the cyclic estimator. The results are accurate enough and serve well as benchmark for evaluating the performance of parameter estimation method. Numerical simulations illustrate the accuracy and applicability of the derived CRB.     

Spectrum estimation of short-time stationary signals in additivenoise and channel distortion

In this work, spectrum estimation of a short-time stationary signal that is degraded by both channel distortion and additive noise is addressed. A maximum likelihood estimation (MLE) algorithm is developed to jointly identify the degradation system and estimate short-time signal spectra. The source signal is assumed to be generated by a hidden Markov model (HMM) with state-dependent short-time spectral distributions described by mixtures of Gaussian densities. The distortion channel is linear time-invariant, and the noise is Gaussian. The algorithm is derived by using the principle of expectation-maximization (EM), where the unknown parameters of channel and noise are estimated iteratively, and the short-time signal power spectra are obtained from the posterior sufficient statistics of the source signal. Other spectral representation parameters, such as autoregressive model parameters or cepstral parameters, are obtained by minimum mean-squared error (MMSE) estimation from the power spectral estimates. The estimation algorithm was evaluated on simulated signals at the signal-to-noise ratios (SNRs) of 20 dB down to 0 dB, where it produced convergent estimation and significantly reduced spectral distortion     

Self-tuning distributed measurement fusion Kalman estimator for the multi-channel ARMA signal

For the multisensor multi-channel autoregressive moving average (ARMA) signal with white measurement noises and a common disturbance measurement white noise, when the model parameters and the noise variances are all unknown, a multi-stage information fusion identification method is presented, where the consistent fused estimates of the model parameters and noise variances are obtained by the multi-dimension recursive instrumental variable (RIV) algorithm, correlation method and Gevers-Wouters algorithm with a dead band. Substituting these estimates into the optimal distributed measurement fusion Kalman signal estimator, a self-tuning distributed measurement fusion Kalman signal estimator is presented. Its convergence is proved by the dynamic error system analysis (DESA) method, so that it has asymptotical global optimality. In order to reduce computational load, a fast recursive inversion algorithm for a high-dimension matrix is presented by the inversion formula of partitioned matrix. Especially, when the process and measurement noise variance matrices are all diagonal matrices, the inversion formula of a high-dimension matrix is presented, which extends the formula of the inverse of Pei-Radman matrix. Applying the proposed inversion algorithm, the computation of the fused measurement and fused noise variance is simplified and their computational burden is reduced. A simulation example shows effectiveness of the proposed method.     

Two-dimensional Bayesian estimate of images

A dynamic model for pictorial data that can be represented by a random field of an exponential autocorrelation function is developed. A partial difference equation describes the dynamic model and is used to realize a two-dimensional recursive filter that gives a Bayesian-estimate of the pictorial data from a noisy observation of the data. It is assumed that the noise is additive, white, and uncorrelated with the signal. Practical application of the estimation technique is illustrated by applying the results to enhance several pictures. A comparison of this technique and its one-dimensional counterpart (Kalman filter) is made, and generalization of the estimation technique to other autoregressive sources is considered.