Quantized Measurements Research Articles

A Novel Algorithm for Quantized Particle Filtering With Multiple Degrading Sensors: Degradation Estimation and Target Tracking

This paper addresses the particle filtering problem for a class of nonlinear/non-Gaussian systems with quantized measurements and multiple degrading sensors. The measurement output of each sensor is quantized by a uniform quantizer before being sent to the remote filter. An augmented system is constructed which aggregates the original system state and the degradation variables. In the presence of the sensor degradation and the quantization errors, a new likelihood function at the remote filter is calculated by resorting to all the transmitted measurements. According to the mathematical characterization of the likelihood function, a novel particle filtering algorithm is developed where the parameters of both the degradation processes and the quantization functions are exploited to obtain the modified importance weights. Finally, the effectiveness of the proposed method is shown via a target tracking example with bearing measurements.

On Filtering and Smoothing Algorithms for Linear State-Space Models Having Quantized Output Data

The problem of state estimation of a linear, dynamical state-space system where the output is subject to quantization is challenging and important in different areas of research, such as control systems, communications, and power systems. There are a number of methods and algorithms to deal with this state estimation problem. However, there is no consensus in the control and estimation community on (1) which methods are more suitable for a particular application and why, and (2) how these methods compare in terms of accuracy, computational cost, and user friendliness. In this paper, we provide a comprehensive overview of the state-of-the-art algorithms to deal with state estimation subject to quantized measurements, and an exhaustive comparison among them. The comparison analysis is performed in terms of the accuracy of the state estimation, dimensionality issues, hyperparameter selection, user friendliness, and computational cost. We consider classical approaches and a new development in the literature to obtain the filtering and smoothing distributions of the state conditioned to quantized data. The classical approaches include the extended Kalman filter/smoother, the quantized Kalman filter/smoother, the unscented Kalman filter/smoother, and the sequential Monte Carlo sampling method, also called particle filter/smoother, with its most relevant variants. We also consider a new approach based on the Gaussian sum filter/smoother. Extensive numerical simulations—including a practical application—are presented in order to analyze the accuracy of the state estimation and the computational cost.

Self-Triggered Stabilization of Discrete-Time Linear Systems With Quantized State Measurements

We study the self-triggered stabilization of discrete-time linear systems with quantized state measurements. In the networked control system we consider, sensors may be spatially distributed and be connected to a self-triggering mechanism through finite data-rate channels. Each sensor independently encodes its measurements and sends them to the self-triggering mechanism. The self-triggering mechanism integrates quantized measurement data and then computes sampling times. Assuming that the closed-loop system is stable in the absence of quantization and self-triggered sampling, we propose a joint design method of an encoding scheme and a self-triggering mechanism for stabilization. To deal with data inaccuracy due to quantization, the proposed self-triggering mechanism uses not only quantized data but also an upper bound of quantization errors, which is shared with a decoder.

Outlier-resistant sequential filtering fusion for cyber-physical systems with quantized measurements under denial-of-service attacks

In this paper, an outlier-resistant sequential fusion problem is concerned for cyber-physical systems with quantized measurements under denial-of-service attacks. The multi-sensor measurements are quantized by a bank of logarithmic quantizers before entering into communication networks. The denial-of-service attack is, from the defenders' perspective, regarded to be randomly occurring and such an occurrence is governed by a Bernoulli-distributed sequence of certain probability distribution. To suppress effects from measurement outliers onto innovations, tailored saturation functions are dedicatedly introduced to filter structures at both local and fusion stages, thereby keeping satisfactory fusion performance. By finding solutions to a set of matrix difference equations, upper bounds are initially acquired on estimator error covariances, and associated estimator parameters are subsequently secured via minimizing these acquired bounds. Two examples are finally presented to showcase the applicability of this outlier-resistant sequential fusion algorithm.

Measurement quantization

We present principles of Measurement Quantization (MQ) and approaches to measurement that support the discreteness of measure. Several claims are addressed. Notably, that measure is discrete with respect to the internal frame, non-discrete with respect to the system frame and that length is contracted due to the discreteness of measure. We address the relation of angular measure to momentum, the physical significance of count bounds and that the fundamental measures — more precise expressions for Planck’s units — are an emergent property of the internal frame. Quantum experiments by Shwartz, et. al and CODATA provide physical support. We predict and derive values for elementary charge and the gravitational, Hubble, reduced Planck, electric, magnetic, Coulomb, and fine structure constants. We then correlate gravity with electromagnetism (unification). We present expressions for galactic rotation, dark matter, dark energy, and accelerating expansion. MQ advances over Loop Quantum Gravity with two frames, the difference which leads to the physical constants and the laws of nature. We correlate the quantum and cosmological, describing an inflation free quantum epoch, why it ceases and expansion. Therein are solutions to the horizon problem and homogenous, isotropic properties of the universe. Predictions include length contraction unrelated to special or general relativity (SR/GR), 13-digit measures of the gravitational constant, the Planck momentum, and universal mass accretion. A calculation of CMB age, quantity, present-day density and temperature provides additional support. Also offered, discrete solutions to the size and age of the universe, ground state orbital, SR, GR, and equivalence.

Quantized filtering for networked Takagi–Sugeno fuzzy systems with multipath data packet dropouts

This paper concerns the mixed and passivity‐based filtering problem for networked nonlinear systems with randomly occurring parameter uncertainties, multipath data packet dropouts, time‐varying delay, and quantization effects. The discrete‐time nonlinear plant considered in this paper is modeled as a Takagi–Sugeno fuzzy system with plant rules. The data missing phenomenon is considered in both measurement and performance output signals due to the unreliable nature of communication links. Further, to reduce the network bandwidth utilization, the measurement quantization is also employed for both the outputs before transmitting through the communication channel. Also, additive filter gain fluctuation is taken into account to reflect the imprecision in filter implementation. Stochastic variables obeying the Bernoulli distribution are incorporated in the model description to characterize the random occurrence of parameter uncertainties and data packet dropouts. A set of sufficient conditions assuring the stochastic stability of the filtering error system with mixed and passivity performance is derived according to Lyapunov stability theory. Finally, three numerical examples including mass–spring–damper and tunnel diode circuit model are established to establish the validity of the developed filter design algorithm.

Direct Target Localization With Quantized Measurements in Noncoherent Distributed MIMO Radar Systems

In this paper, a direct target localization algorithm with quantized measurements for non-coherent MIMO systems is proposed. In this system, each receiver transmits a low-bit quantized version of the echo rather than the full raw data to the fusion center. We construct a joint likelihood function based on the low-bit data of each receiver, from which the unknown target position can be directly determined. The Cramer-Rao lower bound (CRLB) is derived to analyze the localization performance of our proposed algorithm. To maximize the localization performance, a CRLB-based objective function is designed to obtain the optimum quantization thresholds. The formulated problem is a high-dimensional and non-convex optimization problem that when solved, determines two types of coupled parameters for the quantization thresholds and the complex-valued scaling coefficients of the signal. We propose a batch gradient descent embedded particle swarm optimization algorithm to solve this problem effectively. Numerical results show that the proposed algorithm delivers superior performance in terms of maximizing the overall localization performance, and the 3-bit quantized algorithm is able to provide performance that is very close to the unquantized algorithm. Experimental data recorded by three small radars are also provided to demonstrate the effectiveness of the proposed algorithm.

Protocol-based fault detection for discrete-time memristive neural networks with quantization effect

This paper is concerned with the event-triggered fault detection filter design problem for discrete-time memristive neural networks with measurement quantization. Aiming at saving communication bandwidth and improving communication efficiency, a new component-based adjusted dynamic event-triggered protocol is proposed. The transmission status of each measurement component can be determined based on the individual prescribed triggering condition. The quantizer with variable density is introduced to meet different performance requirements, in which the quantization densities vary among a finite set of modes. By constructing an augmented Lyapunov functional, an asynchronous filter is designed to achieve the desired performance while assuring the stochastic stability of the filtering error system. Finally, a simulation example is provided to verify the effectiveness of obtained theoretical results.

Event-triggered filtering for uncertain semi-Markov jump systems with time-varying delay by using quantized measurement

This paper focuses on the extended dissipative filter design problem for a class of uncertain semi-Markov jump systems in the discrete-time context, where the parameter uncertainties are assumed to be occurred in a special probabilities way. The aim of this paper is to design a mode-dependent filter ensuring the stochastic stability of the resulting filtering error system. To reduce the burden of communication network, the event-triggered scheme and quantized measurement are employed. By constructing a new Lyapunov functional, the filter design methodology is put forward. Finally, two numerical examples are proposed to demonstrate the usefulness of the filter design methodology.

Adaptive recovery of dictionary-sparse signals using binary measurements

One-bit compressive sensing (CS) is an advanced version of sparse recovery in which the sparse signal of interest can be recovered from extremely quantized measurements. Namely, only the sign of each measure is available to us. The ground-truth signal is not sparse in many applications yet can be represented in a redundant dictionary. A strong line of research has addressed conventional CS in this signal model, including its extension to one-bit measurements. However, one-bit CS suffers from an extremely large number of required measurements to achieve a predefined reconstruction error level. A common alternative to resolve this issue is to exploit adaptive schemes. We utilize an adaptive sampling strategy to recover dictionary-sparse signals from binary measurements in this work. A multi-dimensional threshold is proposed for this task to incorporate the previous signal estimates into the current sampling procedure. This strategy substantially reduces the required number of measurements for exact recovery. We show that the proposed algorithm considerably outperforms the state-of-the-art approaches through rigorous and numerical analysis.

Granger causality from quantized measurements

An approach is proposed for inferring Granger causality between jointly stationary, Gaussian signals from quantized data. First, a necessary and sufficient rank criterion for the equality of two conditional Gaussian distributions is proved. Assuming a partial finite-order Markov property, a characterization of Granger causality in terms of the rank of a matrix involving the covariances is presented. We call this the causality matrix. The smallest singular value of the causality matrix gives a lower bound on the distance between the two conditional Gaussian distributions appearing in the definition of Granger causality and yields a new measure of causality. Then, conditions are derived under which Granger causality between jointly Gaussian processes can be reliably inferred from the second order moments of quantized measurements. A necessary and sufficient condition is proposed for Granger causality inference under binary quantization. Furthermore, sufficient conditions are introduced to infer Granger causality between jointly Gaussian signals through measurements quantized via non-uniform or high resolution quantizers. Apart from the assumed partial Markov order and joint Gaussianity, this approach does not require the parameters of a system model to be identified. No assumptions are made on the identifiability of the jointly Gaussian random processes through the quantized observations. The effectiveness of the proposed method is illustrated by simulation results.

Decentralized observer‐based controller design for large‐scale systems with quantized measurements and actuator faults

AbstractThis paper is focused on designing observer‐based decentralized memory feedback controller for ensuring the asymptotic mean square stability of the large‐scale systems with minimum H∞ performance index. Precisely, the unknown interconnection between each subsystems of a large‐scale system is assumed to satisfy quadratic bounds, and measured output is quantized by a logarithmic quantizer. Also, the signals are transmitted through the actuator component wherein the occurrence of fault is indispensable. Thus, the impact of faults in actuator is considered in control design to tolerate the fault effects and also for ensuring robust performance. A state space representation of the system is formulated to reconstruct the unmeasurable states via the available informations of input/output dynamics. Based on the designed observer, a decentralized memory feedback controller is developed. Specifically, in terms of linear matrix inequalities, the stability conditions are derived and which are sufficient to guarantee the desired result. At last, simulations are carried out for two numerical examples to validate the potential of the theoretical result.

Computationally Efficient Maximum Likelihood Channel Estimation for Coarsely Quantized Massive MIMO Systems

We consider computationally efficient maximum likelihood (ML) channel estimation for massive multiple-input multiple-output (MIMO) systems using coarsely quantized measurements obtained from low-resolution analog-to-digital converters (ADCs) at the receivers. We first devise a computationally efficient ML estimator (referred to as CQML) by using the cyclic optimization and majorization-minimization (MM) techniques. Then, we show the connections between CQML and the conventional unquantized ML estimator. Numerical examples are provided to demonstrate the effectiveness and computational efficiency of the proposed channel estimation algorithm.

Quantized Corrupted Sensing With Random Dithering

Corrupted sensing concerns the problem of recovering a high-dimensional structured signal from a collection of measurements that are contaminated by unknown structured corruption and unstructured noise. In the case of linear measurements, the recovery performance of different convex programming procedures (e.g., generalized Lasso and its variants) is well established in the literature. However, in practical applications of digital signal processing, the quantization process is inevitable, which often leads to non-linear measurements. This paper is devoted to studying corrupted sensing under quantized measurements. Specifically, we demonstrate that, with the aid of uniform dithering, both constrained and unconstrained Lassos are able to recover signal and corruption from the quantized samples when the measurement matrix is sub-Gaussian. Our theoretical results reveal the role of quantization resolution in the recovery performance of Lassos. Numerical experiments are provided to confirm our theoretical results.

Target Detection Using Quantized Cloud MIMO Radar Measurements

Target detection is studied for a cloud multiple-input multiple-output (MIMO) radar using quantized measurements. According to the local sensor quantization strategies and fusion strategies, this paper discusses three methods: quantize local test statistics which are linearly fused (QTLF), quantize local test statistics which are optimally fused (QTOF), and quantize local received signals which are optimally fused (QROF). We first directly analyze the detection performance of each method when the quantizer output is represented as a discrete random variable, where it is difficult to obtain a closed-form expression for the detection probability. Then, an approximate description for the quantization is analyzed for the case of a Gaussian signal and a closed-form expression for the detection probability is obtained. We prove that the QTOF method outperforms the QTLF method in general, and for small SCNR the QROF method has the best detection performance among the three methods, while for large SCNR the QROF method performs the worst. The correctness of theoretical analysis is verified by simulations.

Robust Quantized Sampled–Data Stabilization for a Class of Lipschitz Nonlinear Systems With Time–Varying Uncertainties

In this letter, a robust quantized sampled-data controller is provided for a class of nonlinear systems affected by time-varying uncertainties, actuation disturbances and measurement noises. Sufficient conditions based on linear matrix inequalities and ensuring the existence of the proposed robust quantized sampled-data controller are given. Quantization of both state measurements and input signals is simultaneously considered. Input-to-state stability redesign technique is used in order to attenuate the effects of bounded actuation disturbances and of bounded observation errors. It is proved that, under suitably fast sampling and accurate quantization of the input/output channels, the proposed controller achieves the semi-global practical stability, with arbitrarily small final target ball, of the related quantized sampled-data closed-loop system provided that the observation errors do not affect (or affect marginally) the robustification term added in the controller and, that the bounds of the actuation disturbances as well as of the observation errors are a priori known. The theory here developed includes also the cases of time-varying sampling intervals and of non-uniform quantization of the input/output channels as well as the stability analysis of the inter-sampling system behavior. The provided results are validated through an example of one-link manipulator.

Approximate Message Passing With Parameter Estimation for Heavily Quantized Measurements

Designing efficient sparse recovery algorithms that could handle noisy quantized measurements is important in a variety of applications -- from radar to source localization, spectrum sensing and wireless networking. We take advantage of the approximate message passing (AMP) framework to achieve this goal given its high computational efficiency and state-of-the-art performance. In AMP, the signal of interest is assumed to follow certain prior distribution with unknown parameters. Previous works focused on finding the parameters that maximize the measurement likelihood via expectation maximization -- an increasingly difficult problem to solve in cases involving complicated probability models. In this paper, we treat the parameters as unknown variables and compute their posteriors via AMP. The parameters and signal of interest can then be jointly recovered. Compared to previous methods, the proposed approach leads to a simple and elegant parameter estimation scheme, allowing us to directly work with 1-bit quantization noise model. We then further extend our approach to general multi-bit quantization noise model. Experimental results show that the proposed framework provides significant improvement over state-of-the-art methods across a wide range of sparsity and noise levels.

Distributed Fusion of Optimally Quantized Local Tracker Estimates for Underwater Wireless Sensor Networks

Multi-sensor underwater surveillance has been a significant research problem for civilian and naval applications. Due to limited bandwidth considerations, the underwater wireless sensor networks (UWSNs) use measurement quantization to transmit information from individual sensors to the fusion center to perform centralized tracking/fusion. However, at the measurement level, quantization of azimuth information is complex due to its non-linear behavior. To address this problem, this paper proposes to perform the distributed tracking and quantizing the local estimates (state and covariance) to provide improved bandwidth and reduce computational load. The local tracker estimates the updated state and covariance of a target’s time-varying dynamics in the given surveillance from the obtained measurements using extended Kalman filter (EKF) and global nearest neighbor (GNN) data association. The measurement model contains both detections of target and false alarms. This paper uses optimal quantization rather than linear quantization owing to its minimal bandwidth requirement. Once the quantized local tracks are obtained at the fusion center, these tracks are quantified using track-to-track association (T2TA) in the S-D assignment framework. The associated tracks are fused using correlation-free fusion algorithms like covariance intersect (CI), sampling covariance intersects (SCI), ellipsoidal intersect (EI), and arithmetic average (AA) algorithms to achieve the global track. The position root mean square error (PRMSE), bandwidth, and error ellipses are used to quantify the performance of the proposed framework. The simulation results show that the PRMSE of the optimally quantized fusion estimates yields good agreement with the unquantized method. Simulation results further reveals that, optimal quantization utilizes lower bandwidth compared to linear quantization. In addition, optimally quantized local estimates accomplishes promising covariance regions at the fusion center.

Secure Image Authentication Scheme Using Double Random-Phase Encoding and Compressive Sensing

Double random-phase encoding- (DRPE-) based compressive sensing (CS) systems support image authentication for noisy images. When extending such systems to resource-constrained applications, how to ensure the authentication strength for noisy images becomes challenging. To tackle the issue, an efficient and secure image authentication scheme is presented. The phase information of the plain image is generated using DRPE and quantized into a binary image as the authentication information. Meanwhile, a sparser error matrix generated by the same plain image and vector quantization (VQ) image works as the input of CS. The authentication information and VQ indexes are self-hidden into the quantized measurements to construct the combined image. Then, it is permutated and diffused with the chaotic sequences generated from a modified Henon map. After decryption at the receiver side, the verifier can implement the blind authentication between the noisy decoded image and the reconstructed image. Supported by the detailed numerical simulations and theoretical analyses, the DRPE-CSVQ exhibits more powerful compression and authentication capability than its counterpart.

Inductive limits of compact quantum groups and their unitary representations

We introduce inductive limits of compact quantum groups and their unitary representation theories. Those give a more explicit representation-theoretic meaning to our previous study of quantization of characters and central probability measures in the asymptotic representation theory. We also study tensor product representations of the infinite-dimensional quantum unitary group. As a by-product, we give an explicit representation-theoretic interpretation to certain transformations that play an important role in analyzing q-central probability measures on the paths in the q-Gelfand–Tsetlin graph.