Resampling and requantization of band-limited Gaussian stochastic signals with flat power spectrum

A theoretical analysis, aimed at characterizing the degradation induced by the resampling and requantization processes applied to band-limited Gaussian signals with flat power spectrum, available through their digitized samples, is presented. The analysis provides an efficient algorithm for computing the complete joint bivariate discrete probability distribution associated with the true quantized version of the Gaussian signal and with the quantity estimated after resampling and requantization of the input digitized sequence. The use of Fourier transform techniques allows deriving approximate analytical expressions for the quantities of interest, as well as implementing their efficient computation. Numerical experiments are found to be in good agreement with the theoretical results, and confirm the validity of the whole approach.     

Hybrid feedback stabilization of systems with quantized signals

This paper is concerned with global asymptotic stabilization of continuous-time systems subject to quantization. A hybrid control strategy originating in earlier work (Brockett and Liberzon, IEEE Trans. Automat. Control 45 (2000) 1279) relies on the possibility of making discrete on-line adjustments of quantizer parameters. We explore this method here for general nonlinear systems with general types of quantizers affecting the state of the system, the measured output, or the control input. The analysis involves merging tools from Lyapunov stability, hybrid systems, and input-to-state stability.     

Constrained and quantized Kalman filtering for an RFID robot localization problem

In this paper a global localization problem of a robot moving in a known environment is considered. The environment is equipped with a relatively sparse set of passive RFID (Radio Frequency IDentification) tags. The robot can detect the presence of the tags when traveling in their proximity and combines this information with the one given by other sensors (e.g. odometry). The RFID measurements are characterized by a highly non Gaussian noise: for this reason in the literature Particle Filter (PF) methods have often been used to fuse these data with the measurements coming from other sensors. In this paper a different approach is pursued, based on the observation that RFID readings can be considered as noisy quantized measurements of the pose of the robot or as noisy dynamic constraints on the pose itself. This allows to exploit the rich literature on Kalman quantized filtering or Kalman constrained estimation, to realize reliable methods with a satisfactory performance which require a computational time significantly lower with respect to the one needed by a PF. Simulative and experimental results will be reported to illustrate the proposed methods.     

Optimal mean-absolute-error filtering of gray-scale signals by the morphological hit-or-miss transform

The binary hit-or-miss transform is applied to filter digital gray-scale signals. This is accomplished by applying a union of hit-or-miss transforms to an observed signal's umbra and then taking the surface of the filtered umbra as the estimate of the ideal signal. The hit-or-miss union is constructed to provide the optimal mean-absolute-error filter for both the ideal signal and its umbra. The method is developed in detail for thinning hit-or-miss filters and applies at once to the dual thickening filters. It requires the output of the umbra filter to be an umbra, which in general is not true. A key aspect of the paper is the complete characterization of umbra-preserving union-of-hit-or-miss thinning and thickening filters. Taken together, the mean-absolute-error theory and the umbra-preservation characterization provide a full characterization of binary hit-or-miss filtering as applied to digital gray-scale signals. The theory is at once applicable to hit-or-miss filtering of digital gray-scale images through the three-dimensional (3-D) binary hit-or-miss transform.     

Derivation of fast algorithms via binary filtering of signals

We present a new way to derive a fast algorithm realizing the discrete Walsh transform (DWT), which can be applied both in the traditional form, i.e., to a one-dimensional numerical array, and to a multi-dimensional array, as well as for a signal of a continuous argument in the form of a function or an image. The algorithm is presented as iterated application of the primitive discrete Haar transform (DHT) over two variables. Two standard ways of arranging the results of this simplest transform lead to the fast DWT in the Hadamard or Paley enumeration in the case of splitting the signal into equal parts. Application of the algorithm to analogous shifts of the periodic source signal results in longitudinal filtering of a signal via decomposing it into a sum of simpler signals. In an incomplete version of the last algorithm, we come to an analog of the fast DHT.     

Data fusion for target tracking in wireless sensor networks using quantized innovations and Kalman filtering

A novel networked data-fusion method is developed for the target tracking in wireless sensor networks (WSNs). Specifically, this paper investigates data fusion scheme under the communication constraint between the fusion center and each sensor. Such a message constraint is motivated by the bandwidth limitation of the communication links, fusion center, and by the limited power budget of local sensors. In the proposed scheme, each sensor collects one noise-corrupted sample, performs a quantizing operation, and transmits quantized message to the fusion center. Then the fusion center combines the received quantized messages to produce a final estimate. The novel data-fusion method is based on the quantized measurement innovations and decentralized Kalman filtering (DKF) with feedback. For the proposed algorithm, the performance analysis of the estimation precision is provided. Finally, Monte Carlo simulations show the effectiveness of the proposed scheme.     

Efficient reconstruction of sampled 1-bit quantized Gaussian signals from sine wave crossings

We study the reconstruction of a Gaussian random signal, subject to extreme clipping. The reconstruction is achieved by adding a high frequency sinusoidal reference signal prior to the hard-limiter, and by low pass filtering the output. Such a scheme belongs to the area of signal reconstruction from Sine Wave Crossings (SWC). In the present paper we study in detail the effect of sampling in time domain on the reconstruction algorithm, and we carry out an analysis, valid for high sampling rates, leading to approximate analytical expressions of the cross-correlation coefficient between the signal and its reconstructed version. As a result of our analysis, the best achievable cross-correlation coefficient, together with the corresponding setting of the configuration parameters, i.e., the frequency and power of the reference signal, is obtained as a function of the sampling rate. Asymptotic closed form formulas are derived in the limit of very large sampling rates.     

Initial-value solutions for on-line smoothing and filtering of linear stationary signals

This note presents an initial-value solution for the impulse response function specifying the linear least-squares estimates of a linear scalar stationary signal with general covariance functions in the presence of a white Gaussian noise. The method employed is an invariant imbedding. The resulting initial-value solution enables us to design a new on-line filter, and fixed-point, initial-point, and fixed-lag smoothers based on covariance specification.     

Blind separation of audio signals using trigonometric transforms and Kalman filtering

This paper deals with the problem of blind separation of audio signals from noisy mixtures. It proposes the application of a blind separation algorithm on the Discrete Cosine Transform (DCT) or the Discrete Sine Transform (DST) of the mixed signals, instead of performing the separation on the mixtures in the time domain. Kalman Filtering of the noisy separated signals is recommended in this paper as a post-processing step for noise reduction. Both the DCT and the DST have an energy compaction property, which concentrates most of the signal energy in a few coefficients in the transform domain, leaving the rest of the transform-domain coefficients close to zero. As a result, the separation is performed on a few coefficients in the transform domain. Another advantage of signal separation in transform domains is that the effect of noise on the signals in the transform domains is smaller than that in the time domain due to the averaging effect of the transform equations. The simulation results confirm the effectiveness of transform-domain signal separation and the feasibility of the post-processing Kalman filtering step.     

非均匀采样信号的滑动滤波方法

针对实际采样过程中出现的采样非均匀性,提出了基于连续傅里叶变换的非均匀采样信号频谱分析方法和非均匀采样信号的滑动滤波方法。将非均匀采样信号描述为不均匀采样时刻冲激函数代数和的形式,利用连续傅里叶变换得到非均匀采样信号的频谱特性,根据不同采样间隔,得到非均匀采样信号的滑动滤波方法。通过MATLAB仿真软件验证了这种非均匀采样信号分析与处理方法的正确性,将这一研究成果应用到机械抖动激光陀螺输出信号处理中,与常规的平均滤波方法相比,激光陀螺的零偏误差减少了10.1%。     

Optimal digital filtering of continuous signals in time lag systems

The problem of the optimal estimation of continuous processes by discrete measurements in the presence of time lag (delay) is considered. On the basis of the theory of parametric transfer functions, an optimal, periodically nonstationary filter is developed, which affords a minimum of the estimation error variance at any instant of time. The comparison is performed of the obtained solution with the optimal stationary filter, which ensures a minimum of the mean (by continuous time) error variance. It is shown that in the problem of estimation of the Markov process of the first order, a simpler stationary filter with the fixer of order zero is insignificantly inferior to the optimal filter.     

Decorrelation methods of texture feature extraction

This paper presents the development and evaluation of a visual texture feature extraction method based on a stochastic field model of texture. Results of recent visual texture discrimination experiments are reviewed in order to establish necessary and sufficient conditions for texture features that are in agreement with human discrimination. A texture feature extraction technique involving autocorrelation function measurement of a texture field, combined with histogram representation of a statistically decorrelated version of the texture field, is introduced. The texture feature extraction method is evaluated in terms of a Bhattacharyya distance measure.     

Adaptive output feedback formation tracking for a class of multiagent systems with quantized input signals

A novel adaptive output feedback control approach is presented for formation tracking of a multiagent system with uncertainties and quantized input signals. The agents are described by nonlinear dynamics models with unknown parameters and immeasurable states. A high-gain dynamic state observer is established to estimate the immeasurable states. With a proper design parameter choice, an adaptive output feedback control method is developed employing a hysteretic quantizer and the designed dynamic state observer. Stability analysis shows that the control strategy can guarantee that the agents can maintain the formation shape while tracking the reference trajectory. In addition, all the signals in the closed-loop system are bounded. The effectiveness of the control strategy is validated by simulation.     

Automatic sleep stages classification based on iterative filtering of electroencephalogram signals

Neural Computing and Applications - Computer-aided sleep monitoring system can effectively reduce the burden of experts in analyzing the large volume of electroencephalogram (EEG) recordings...     

On-line discontinuities identification in noisy signals: Application to Kalman filtering

The problem of fault detection in a stochastic linear time invariant system is dealt with, assuming that the fault is modelled by a jump in the noisy output. An on-line identification procedure is designed based on a multiscale analysis and on the application of suitable statistical tests. Once the time and the size of the discontinuity have been identified, the state estimate evolution of a Kalman filter is adequately compensated.     

基于稀疏表示的惯性传感器信号实时滤波方法

针对惯性传感器信号处理的特点,提出了基于稀疏表示的信号滤波处理系统模型和方法。通过 K-SVD算法对信号学习训练获得字典,为了减少计算量,满足实时性,尽量降低字典的大小,仿真结果表明,在满足一定精度的条件下,字典的大小最小为3×10。在该字典下对信号进行稀疏表示和重构,改变信号的输入方式,可以实现信号的实时滤波。仿真结果表明提出的滤波方法能有效地消除噪声,改善输出信号精度,可以提高信噪比最大为4．5 dB。该滤波方法与传统的滤波方法相比有较大的优势,为惯性传感器信号处理提供了一种新的方法。     

Decorrelation of SAR data by urban damages caused by the 1995 Hyogoken-nanbu earthquake

Large part of urban area of around Kobe city were damaged by the 1995 Hyogoken-nanbu earthquake. For detecting the damaged area, the authors computed correlation coefficients from single-look complex ERS-1/SAR data. Two types of correlations, intensity correlation and coherence were computed. Decorrelation was found in the damaged urban built-up area in the data pair of which interval included the earthquake occurrence. The similarity of the decorrelation between the intensity correlation and the coherence indicated that major factor of the decorrelation is closely related to interferometric processes, which results in the change of speckle patterns in the single-look intensity images. A normalized difference was calculated from the correlation coefficients between the data pair including the earthquake occurrence and the pair before the earthquake. The distribution patterns of the pixels for which normalized difference was higher than a threshold showed good correspondence with the result of the ground survey. The result of this study indicates the possibility of detecting urban disasters using the decorrelation of SAR data.     

Clustering by scale-space filtering

In pattern recognition and image processing, the major application areas of cluster analysis, human eyes seem to possess a singular aptitude to group objects and find important structures in an efficient and effective way. Thus, a clustering algorithm simulating a visual system may solve some basic problems in these areas of research. From this point of view, we propose a new approach to data clustering by modeling the blurring effect of lateral retinal interconnections based on scale space theory. In this approach, a data set is considered as an image with each light point located at a datum position. As we blur this image, smaller light blobs merge into larger ones until the whole image becomes one light blob at a low enough level of resolution. By identifying each blob with a cluster, the blurring process generates a family of clustering along the hierarchy. The advantages of the proposed approach are: 1) The derived algorithms are computationally stable and insensitive to initialization and they are totally free from solving difficult global optimization problems. 2) It facilitates the construction of new checks on cluster validity and provides the final clustering a significant degree of robustness to noise in data and change in scale. 3) It is more robust in cases where hyperellipsoidal partitions may not be assumed. 4) it is suitable for the task of preserving the structure and integrity of the outliers in the clustering process. 5) The clustering is highly consistent with that perceived by human eyes. 6) The new approach provides a unified framework for scale-related clustering algorithms derived from many different fields such as estimation theory, recurrent signal processing on self-organization feature maps, information theory and statistical mechanics, and radial basis function neural networks     

Prediction-based event-triggered identification of quantized input FIR systems with quantized output observations

This paper addresses the identification of finite impulse response (FIR) systems with both quantized and event-triggered observations.An event-triggered communi...