Quantized Measurements Research Articles

Efficient scrolling videotext detection with adaptive temporal differential approach

This study presents an efficient algorithm for the detection of scrolling text on continuous frames. The proposed scheme adopts both spatial and temporal computation as well as pre-processing to differentiate among noise, text and background information. Scrolling text is detected using temporal differentiation among inter-frames and then the region in which the scrolling text appears is identified as a rectangle. Simulation results demonstrate that the proposed algorithm is capable of precisely differentiating scrolling text in any direction, along any of the frame boundaries without false detection or missed text. In a comparison using quantised measurements, the proposed method outperforms all competing algorithms.

Smooth Output Reconstruction for Linear Systems with Quantized Measurements

AbstractThis paper presents a novel approach to reconstruct the output of linear systems in the case where the measured output is uniformly quantized. By fitting the quantized measurements with polynomials in a moving horizon manner, a smooth signal is reconstructed by solving a convex optimization problem with ℓ1‐norm regularization. The quantization feature and the system models are taken into account in the optimization. A numerical example is given to show the excellent reconstruction performance of the proposed method. In addition, the proposed method is implemented in a high‐precision linear stage through DSP, and its effectiveness is verified through experiments using a real positioning system.

Sparse signal recovery from one-bit quantized data: An iterative reweighted algorithm

This paper considers the problem of reconstructing sparse signals from one-bit quantized measurements. We employ a log-sum penalty function, also referred to as the Gaussian entropy, to encourage sparsity in the algorithm development. In addition, in the proposed method, the logistic function is introduced to quantify the consistency between the measured one-bit quantized data and the reconstructed signal. Since the logistic function has the tendency to increase the magnitudes of the solution, an explicit unit-norm constraint is no longer necessary to be included in our optimization formulation. An algorithm is developed by iteratively minimizing a convex surrogate function that bounds the original objective function. This leads to an iterative reweighted process that alternates between estimating the sparse signal and refining the weights of the surrogate function. Numerical results are provided to illustrate the effectiveness of the proposed algorithm.

Observability limits for networked oscillators

Inspired by the neuro-scientific problem of predicting brain dynamics from electroencephalography (EEG) measurements of the brain’s electrical activity, this paper presents limitations on the observability of networked oscillators sensed with quantised measurements. The problem of predicting highly complex brain dynamics sensed with relatively limited amounts of measurement is abstracted to a study of observability in a network of oscillators. It is argued that a low-dimensional quantised measurement is in fact, by itself, an exceptionally poor observer for a large-scale oscillator network, even for the case of a completely connected graph. The main rational is based on (i) an information-theoretic argument based on ideas of entropy in measure preserving maps, (ii) a linear deterministic observability argument, and (iii) a linear stochastic approach using Kalman filtering. For prediction of brain network activity, the findings indicate that the classic EEG signal is just not precise enough to be able to provide reliable prediction and tracking in a clinical setting in view of the complexity of underlying neural dynamics.

Networked H∞ filtering for T–S fuzzy systems with quantization and data dropouts

This paper studies the problem of H∞ filtering problem for a class of nonlinear time-varying delay systems with unideal communication links. Two defectives are concerned including measurement quantization and packet dropouts. The quantized measurements are transmitted to the filter via network, where the phenomena of packet loss are taken into account. By using Lyapunov–Krasovskii functional, a less conservative delay-dependent stability condition for the closed-loop NCSs is derived. The H∞ fuzzy controller, which is designed in terms of linear matrix inequalities (LMIs), is developed for the asymptotic stabilization of the closed-loop NCSs. Numerical examples are given to illustrate the effectiveness of the proposed method.

Energy-Efficient Target Tracking in Wireless Sensor Networks: A Quantized Measurement Fusion Framework

Optimizing the design of tracking system under energy and bandwidth constraints in wireless sensor networks (WSN) is of paramount importance. In this paper, the problem of collaborative target tracking in WSNs is considered in a framework of quantized measurement fusion. First, the measurement in each local sensor is quantized by probabilistic quantization scheme and transmitted to a fusion center (FC). Then, the quantized messages are fused and sequential importance resampling (SIR) particle filtering is employed to estimate the target state. In the FC, quantized measurement fusion via both augmented approach and weighted approach is investigated. For both approaches, the closed-form solution to the optimization problem of bandwidth scheduling is given, where the total energy consumption is minimized subject to a constraint on the fusion performance. Finally, posterior Cramer-Rao lower bounds (CRLBs) on the tracking accuracy using quantized measurement fusion are derived. Simulation results reveal that both approaches perform very closely to the posterior CRLB while obtaining average communication energy saving up to 72.8% and 45.1%, respectively.

Passification-based adaptive control with quantized measurements

We propose and analyze passification-based adaptive controller for linear uncertain systems with quantized measurements. Since the effect of the quantization error is similar to the effect of a disturbance, the adaptation law with σ-modification is used. To ensure convergence to a smaller set, the parameters of the adaptation law are being switched during the evolution of the system and a dynamic quantizer is used. It is proved that if the quantization error is small enough then the proposed controller ensures convergence of the state of a hyper-minimum-phase system to an arbitrarily small vicinity of the origin. Applicability of the proposed controller to polytopic-type uncertain systems and its efficiency is demonstrated by the example of yaw angle control of a flying vehicle.

Broadcast Control of Multi-Agent Systems with Quantized Measurements

Broadcast Control of Multi-Agent Systems with Quantized Measurements

Joint Sampling Rate and Bit-Depth Optimization in Compressive Video Sampling

Compressed sensing is a novel technology that exploits sparsity of a signal to perform sampling below the Nyquist rate, and thus has great potential in low-complexity video sampling and compression applications, due to the significant reduction of the sampling rate ( SR) and computational complexity. However, most current work about compressive video sampling (CVS) has focused on real-valued measurements without being quantized, and thus is not applicable to engineering practices. Moreover, in many circumstances, the total number of bits is often constrained. Therefore, how to achieve a compromise between the number of measurements and the number of bits per measurement to maximize the visual quality is a great challenge for CVS, which has still not been addressed in literature. In this paper, we first present a novel distortion model that reveals the relationship between distortion, SR, and quantization bit-depth ( B). Then, using this model, we propose a joint SR - B optimization algorithm, by which we are able to easily derive the values of SR and B. Finally, we present an adaptive and unidirectional CVS framework with rate-distortion (RD) optimized rate allocation, wherein we use video characteristics extracted from partial sampling to allocate the required bits for each block, and then implement “optimized” video sampling and measurement quantization with the estimated SR and B, respectively. Simulation results show that our proposal offers comparable RD performance to the conventional method, with a 4.6 dB improvement in the average PSNR.

Weighted Measurement Fusion Quantized Filtering with Bandwidth Constraints and Missing Measurements in Sensor Networks

This paper is concerned with the estimation problem of a dynamic stochastic variable in a sensor network, where the quantization of scalar measurement, the optimization of the bandwidth scheduling, and the characteristic of transmission channels are considered. For the imperfect channels with missing measurements in sensor networks, two weighted measurement fusion (WMF) quantized Kalman filters based on the quantized measurements arriving at the fusion center are presented. One is dependent on the known message of whether a measurement is received. The other is dependent on the probability of missing measurements. They have the reduced computational cost and same accuracy as the corresponding centralized fusion filter. The approximate solution for the optimal bandwidth-scheduling problem is given under a limited bandwidth constraint. Furthermore, the vector measurement case is also discussed. The simulation research shows the effectiveness.

Variance-Constrained Robust Estimation for Discrete-Time Systems with Communication Constraints

This paper is concerned with a new filtering problem in networked control systems (NCSs) subject to limited communication capacity, which includes measurement quantization, random transmission delay, and packets loss. The measurements are first quantized via a logarithmic quantizer and then transmitted through a digital communication network with random delay and packet loss. The three communication constraints phenomena which can be seen as a class of uncertainties are formulated by a stochastic parameter uncertainty system. The purpose of the paper is to design a linear filter such that, for all the communication constraints, the error state of the filtering process is mean square bounded and the steady-state variance of the estimation error for each state is not more than the individual prescribed upper bound. It is shown that the desired filtering can effectively be solved if there are positive definite solutions to a couple of algebraic Riccati-like inequalities or linear matrix inequalities. Finally, an illustrative numerical example is presented to demonstrate the effectiveness and flexibility of the proposed design approach.

Quantization of Gaussian measures with Rényi-α-entropy constraints

We consider the optimal quantization problem with Rényi-α-entropy constraints for centered Gaussian measures on a separable Banach space. For α = ∞ we can compute the optimal quantization error by a moment on a ball. For α ∈]1,∞] and large entropy bound we derive sharp asymptotics for the optimal quantization error in terms of the small ball probability of the Gaussian measure. We apply our results to several classes of Gaussian measures. The asymptotical order of the optimal quantization error for α >1 is different from the well-known cases α = 0 and α = 1.

Compressed sensing with linear correlation between signal and measurement noise

Existing convex relaxation-based approaches to reconstruction in compressed sensing assume that noise in the measurements is independent of the signal of interest. We consider the case of noise being linearly correlated with the signal and introduce a simple technique for improving compressed sensing reconstruction from such measurements. The technique is based on a linear model of the correlation of additive noise with the signal. The modification of the reconstruction algorithm based on this model is very simple and has negligible additional computational cost compared to standard reconstruction algorithms, but is not known in existing literature. The proposed technique reduces reconstruction error considerably in the case of linearly correlated measurements and noise. Numerical experiments confirm the efficacy of the technique. The technique is demonstrated with application to low-rate quantization of compressed measurements, which is known to introduce correlated noise, and improvements in reconstruction error compared to ordinary Basis Pursuit De-Noising of up to approximately 7dB are observed for 1bit/sample quantization. Furthermore, the proposed method is compared to Binary Iterative Hard Thresholding which it is demonstrated to outperform in terms of reconstruction error for sparse signals with a number of non-zero coefficients greater than approximately 1/10th of the number of compressed measurements.

Robust distributed maximum likelihood estimation with dependent quantized data

In this paper, we consider the distributed maximum likelihood estimation (MLE) with dependent quantized data under the assumption that the structure of the joint probability density function (pdf) is known, but it contains unknown deterministic parameters. The parameters may include different vector parameters corresponding to marginal pdfs and parameters that describe the dependence of observations across sensors. Since MLE with a single quantizer is sensitive to the choice of thresholds due to the uncertainty of pdf, we concentrate on MLE with multiple groups of quantizers (which can be determined by the use of prior information or some heuristic approaches) to fend off against the risk of a poor/outlier quantizer. The asymptotic efficiency of the MLE scheme with multiple quantizers is proved under some regularity conditions and the asymptotic variance is derived to be the inverse of a weighted linear combination of Fisher information matrices based on multiple different quantizers which can be used to show the robustness of our approach. As an illustrative example, we consider an estimation problem with a bivariate non-Gaussian pdf that has applications in distributed constant false alarm rate (CFAR) detection systems. Simulations show the robustness of the proposed MLE scheme especially when the number of quantized measurements is small.

Networked Control With State Reset and Quantized Measurements: Observer-Based Case

Quantization has been an important research area for a long time for networked control systems. This paper addresses the problem of a reset state observer (RSO)-based control (RSOC) for linear systems using quantized measurements. According to the characteristic of the logarithmic quantizer, an RSOC is presented based on the standard one to suppress sensor quantization effects. By using the Lyapunov approach, the closed-loop system is still asymptotically stable when the reset technique is introduced. The observer and controller gains of the closed-loop systems are obtained via solving linear matrix inequalities. At last, a numerical example is given to illustrate the effectiveness of the proposed results.

Scalar Quantization for Estimation: From An Asymptotic Design to a Practical Solution

In this paper, we study an asymptotic approximation of the Fisher information for the estimation of a scalar parameter using quantized measurements. We show that, as the number of quantization intervals tends to infinity, the loss of Fisher information induced by quantization decreases exponentially as a function of the number of quantization bits. A characterization of the optimal quantizer through its interval density and an analytical expression for the Fisher information are obtained. A comparison between optimal uniform and nonuniform quantization for the location and scale estimation problems shows that nonuniform quantization is only slightly better than uniform quantization. As the optimal quantization intervals are shown to depend on the unknown parameters, by applying adaptive algorithms that jointly estimate the parameter and set the thresholds in the location and scale estimation problems, we show that the asymptotic results can be approximately reached in practice using only 4 or 5 quantization bits.

Optimal Asymmetric Binary Quantization for Estimation Under Symmetrically Distributed Noise

Estimation of a location parameter based on noisy and binary quantized measurements is considered in this letter. We study the behavior of the Cramér-Rao bound as a function of the quantizer threshold for different symmetric unimodal noise distributions. We show that, in some cases, the intuitive choice of threshold position given by the symmetry of the problem, placing the threshold on the true parameter value, can lead to locally worst estimation performance.

Fixed-order FIR approximation of linear systems from quantized input and output data

The problem of identifying a fixed-order FIR approximation of linear systems with unknown structure, assuming that both input and output measurements are subjected to quantization, is dealt with in this paper. A fixed-order FIR model providing the best approximation of the input–output relationship is sought by minimizing the worst-case distance between the output of the true system and the modeled output, for all possible values of the input and output data consistent with their quantized measurements. The considered problem is firstly formulated in terms of robust optimization. Then, two different algorithms to compute the optimum of the formulated problem by means of linear programming techniques are presented. The effectiveness of the proposed approach is illustrated by means of a simulation example.

Channel-Aware Tracking in Multi-Hop Wireless Sensor Networks with Quantized Measurements

A channel-aware target tracking approach is proposed for multi-hop sensor networks based on M-bit quantized measurements. For two cases where the fusion center has the knowledge of the instantaneous fading channel gains and where only the knowledge of fading channel statistics is available, particle filtering (PF)-based channel-aware tracking algorithms are developed. Furthermore, the posterior Cramer-Rao lower bounds (PCRLBs) for the tracking filters are derived. The improved tracking accuracy and robustness of the proposed approach are demonstrated through simulations.

Quantized stabilization of discrete-time systems in a networked environment

This paper is concerned with the problem of output feedback stabilization for a class of discrete-time systems with sector nonlinearities and imperfect measurements. A unified control law model is proposed to take the network-induced delay, random packet dropout and measurement quantization into consideration simultaneously. By choosing appropriate Lyapunov functional, a new stability condition, which is dependent on multiple network status, is established for the resulting closed-loop system. Based on the result, a design criterion for the static output feedback controller is formulated in the form of nonconvex matrix inequalities, and the cone complementary linearization (CCL) procedure is exploited to solve the nonconvex feasibility problem. Incidentally, a less conservative synthesis method is also developed for the state feedback stabilization purpose. Finally, two illustrative examples are provided to illustrate the effectiveness and applicability of the proposed design method.