Quantized Measurements Research Articles

Event-Triggered Mixed Non-Fragile and Measurement Quantization Filtering Design for Interval Type-2 Fuzzy Systems

This paper is concerned with the problem of event-triggered non-fragile $H_{\infty }$ filter design for interval type-2 (IT2) fuzzy systems subject to output quantization. The nonlinear plant is efficiently described by an IT2 fuzzy model, and the lower and upper membership functions with weighting coefficients are employed to characterize parameter uncertainties in the plant. To enhance filter adaptability, an IT2 non-fragile fuzzy filter method is proposed to acquire available information for the unknown state of the plant, where the multiplicative gain variations is taken into account in the filter analysis design process. In order to avoid continuous communications and save limited bandwidth, a dynamic event-based mechanism is employed to adopt the limited communications links. Then, based on the Lyapunov theory together with the inequality technique, a filtering system with event-based mechanism and measurement quantization is analyzed and constructed. Moreover, the obtained sufficient conditions for system analysis are given in the form of linear matrix inequalities (LMIs). Finally, a numerical simulation is provided to verify the effectiveness of the proposed filter design strategy.

Dissipative Asynchronous T-S Fuzzy Control For Singular Semi-Markovian Jump Systems.

This article addresses the problems of the dissipative asynchronous Takagi-Sugeno-Kong fuzzy control for a kind of singular semi-Markov jump system. An adjustable quantized approach is presented to deal with the uncertainties, nonlinear disturbance, actuator faults, and time-varying delay of the system. To deal with the problem of the nonsynchronous between system modes and controller modes, an asynchronous method is utilized. Then, a novel asynchronous sliding-mode controller is designed with an output measurement quantizer that is adaptive to the actuator faults and has good performance in practical applications. By solving the linear matrix inequalities, the sufficient conditions are obtained to guarantee the closed system stochastically admissible and strictly (Q,R,S)-α- dissipative and ensure the reachability of the sliding-mode surface. Finally, two numerical examples and comparisons are provided to illustrate the effectiveness and the priority of the proposed technique.

Reset Moving Horizon Estimation for Quantized Discrete Time Systems

This article addresses reset moving horizon estimation for multiple output discrete-time systems with quantized measurements. A new state reset estimator is designed based on a one-dimensional noisy measurement to overcome underestimation or overestimation of the system state, and an iterative algorithm is proposed to deal with multiple output systems. It is shown that with the proposed reset algorithm, the state estimation error is improved in the presence of over or under estimation, and the boundedness of the estimation error is established. The proposed algorithm also achieves a better estimate than the existing one for systems with a scalar measurement in the static case. A simulation of a moving vehicle is provided to demonstrate the advantage of the developed approach.

Hybrid boundary stabilization of linear first-order hyperbolic PDEs despite almost quantized measurements and control input

Abstract We develop a hybrid boundary feedback law for a class of scalar, linear, first-order hyperbolic PDEs, for which the state measurements or the control input are subject to quantization. The quantizers considered are Lipschitz functions, which can approximate arbitrarily closely typical piecewise constant, taking finitely many values, quantizers. The control design procedure relies on the combination of two ingredients—A nominal backstepping controller, for stabilization of the PDE system in the absence of quantization, and a switching strategy, which updates the parameters of the quantizer, for compensation of the quantization effect. Global asymptotic stability of the closed-loop system is established through utilization of Lyapunov-like arguments and derivation of solutions’ estimates, providing explicit estimates for the supremum norm of the PDE state, capitalizing on the relation of the resulting, nonlinear PDE system (in closed loop) to a certain, integral delay equation. A numerical example is also provided to illustrate, in simulation, the effectiveness of the developed design.

Quantitative Data-Driven Adaptive Iterative Learning Control: From Trajectory Tracking to Point-to-Point Tracking.

This article reconsiders the data quantization problem in iterative learning control (ILC) for nonlinear nonaffine systems from four aspects: 1) use of available additional control knowledge; 2) different tracking tasks; 3) adaptation to uncertainties; and 4) data-driven design and analysis framework. An iterative linear data model (iLDM) is established first to represent the nonlinear nonaffine system for subsequent control algorithm design and analysis under a data-driven framework. A quantitative data-driven adaptive ILC (QDDAILC) is then developed using quantized tracking errors based on the nonlifted iLDM and, thus, additional available input information from previous time instants can be utilized to improve control performance. The parameter estimation derived from an adaptive updating law makes the learning gain of the QDDAILC adjustable, therefore improving the robustness to uncertainties. Due to the coupled dynamics among inputs and tracking errors, a new double-dynamics analysis method is introduced besides the contraction mapping principle to show error convergence. A quantized data-driven adaptive point-to-point ILC (QDDAPTPILC) is further presented using partial quantized measurements at the specified instants for multi-intermediate-point tracking. Simulation examples verify theoretical results and illustrate that the QDDAPTPILC outperforms the QDDAILC for multi-intermediate-point tracking tasks because it removes the unnecessary constraints.

Robust recovery in 1-bit compressive sensing via ℓq-constrained least squares

In this paper, we propose using ℓq-constrained least-squares to decode n dimensional signals with sparsity level s from m noisy and sign flipped 1-bit quantized measurements. We prove that the solution of the proposed decoder approximates the target signals with the precision δ up to a positive constant with high probability as long as m≥O(s2/q−1lognδ2). A weighted primal-dual active set algorithm with continuation is utilized for computing the proposed estimator by combining the data driven majority vote tuning parameter selection rule. Comprehensive numerical simulations indicate that our proposed decoder is robust to noise and sign flips and performs better than state-of-the-art methods.

Improved non-fragile feedback control for stochastic jump system based on observer and quantized measurement

This paper elaborates the topic of observer-based non-fragile mixed passivity and H∞ control for stochastic Markovian jump system with mode-dependent time-varying delays and uncertain parameters via quantized measurements. Improved sufficient conditions are acquired via constructing a mode-dependent Lyapunov–Krasovskii (L–K) functional and using the free-weight matrix technique. A suitable observer-based non-fragile feedback controller is provided to guarantee stochastic stability of the closed-loop system. Two examples including an electrical RLC circuit are presented to illustrate the correctness of the proposed approach in this paper.

Tensor recovery from noisy and multi-level quantized measurements

Higher-order tensors can represent scores in a rating system, frames in a video, and images of the same subject. In practice, the measurements are often highly quantized due to the sampling strategies or the quality of devices. Existing works on tensor recovery have focused on data losses and random noises. Only a few works consider tensor recovery from quantized measurements but are restricted to binary measurements. This paper, for the first time, addresses the problem of tensor recovery from multi-level quantized measurements by leveraging the low CANDECOMP/PARAFAC (CP) rank property. We study the recovery of both general low-rank tensors and tensors that have tensor singular value decomposition (TSVD) by solving nonconvex optimization problems. We provide the theoretical upper bounds of the recovery error, which diminish to zero when the sizes of dimensions increase to infinity. We further characterize the fundamental limit of any recovery algorithm and show that our recovery error is nearly order-wise optimal. A tensor-based alternating proximal gradient descent algorithm with a convergence guarantee and a TSVD-based projected gradient descent algorithm are proposed to solve the nonconvex problems. Our recovery methods can also handle data losses and do not necessarily need the information of the quantization rule. The methods are validated on synthetic data, image datasets, and music recommender datasets.

Set-membership filtering for time-varying complex networks with uniform quantisations over randomly delayed redundant channels

This paper investigates the set-membership filtering problem for a class of nonlinear time-varying complex networks with uniformly quantised measurements over redundant channels. The network output is subject to uniform quantisation and then the quantised signal is sent to the filter through redundant channels with random delays. The aim of the proposed problem is to design a set-membership filter such that, at each time instant, the filtering error dynamics is confined within a closed domain whose boundary is a hyper-ellipsoid. Sufficient conditions are proposed to guarantee the existence of addressed set-membership filter in terms of certain recursive matrix inequality. Subsequently, an optimisation problem is proposed to minimise the hyper-ellipsoid (containing the true network state) in the sense of trace and a computational algorithm is then provided. Finally, a simulation example is provided to demonstrate the effectiveness of our proposed method.

Distributed moving horizon estimation under constraints of quantized measurements and packet dropouts

Distributed moving horizon estimation under constraints of quantized measurements and packet dropouts

Quantized feedback particle filter for unmanned aerial vehicles tracking with quantized measurements

Many existing state estimation approaches assume that the measurement noise of sensors is Gaussian. However, in unmanned aerial vehicles tracking applications with distributed passive radar array, the measurements suffer from quantization noise due to limited communication bandwidth. In this paper, a novel state estimation algorithm referred to as the quantized feedback particle filter is proposed to solve unmanned aerial vehicles tracking with quantized measurements, which is an improvement of the feedback particle filter (FPF) for the case of quantization noise. First, a bearing-only quantized measurement model is presented based on the midriser quantizer. The relationship between quantized measurements and original measurements is analyzed. By assuming that the quantization satisfies [Formula: see text], Sheppard’s correction is used for calculating the variances of the measurement noise. Then, a set of controlled particles is used to approximate the posterior distribution. To cope with the quantization noise of passive radars, a new formula of the gain matrix is derived by modifying the measurement noise covariance. Finally, a typical two-passive radar unmanned aerial vehicles tracking scenario is performed by QFPF and compared with the three other algorithms. Simulation results verify the superiority of the proposed algorithm.

Quantization-aware phase retrieval

We address the problem of phase retrieval (PR) from quantized measurements. The goal is to reconstruct a signal from quadratic measurements encoded with a finite precision, which is indeed the case in practical applications. We develop an iterative projected-gradient-type algorithm that recovers the signal subject to ensuring consistency with the measurement, meaning that the recovered signal, when encoded, must yield the same set of measurements that one started with. The algorithm involves rank-1 projection, which stems from the idea of lifting, originally proposed in the context of PhaseLift. The consistency criterion is enforced using a one-sided quadratic cost. We also determine the probability with which different vectors lead to the same set of quantized measurements, which makes it impossible to resolve them. Naturally, this probability depends on how correlated such vectors are, and how coarsely/finely the measurements are quantized. The proposed algorithm is also capable of incorporating a sparsity constraint on the signal. An analysis of the cost function reveals that it is bounded probabilistically, both above and below, by functions that are dependent on how well-correlated the estimate is with the ground-truth. We also derive the Cramér-Rao lower bound (CRB) on the achievable reconstruction accuracy. A comparison with the state-of-the-art algorithms shows that the proposed algorithm has a higher reconstruction accuracy and is about 2 to 3 dB away from the CRB. The edge, in terms of the reconstruction signal-to-noise ratio, over the competing algorithms is higher (about 5 to 6 dB) when the quantization is coarse, thereby making the proposed scheme particularly attractive in such scenarios. We also demonstrate a concrete application of the proposed method to frequency-domain optical-coherence tomography (FDOCT).

DeepFPC: A deep unfolded network for sparse signal recovery from 1-Bit measurements with application to DOA estimation

In this paper, we introduce a novel deep neural network, coined DeepFPC, and investigate its application to tackling the problem of direction-of-arrival (DOA) estimation. DeepFPC is designed by unfolding the iterations of the fixed-point continuation algorithm with one-sided ℓ1-norm (FPC-ℓ1), which has been proposed for solving the 1-bit compressed sensing problem. The network architecture resembles that of deep residual learning and incorporates prior knowledge about the signal structure (i.e., sparsity), thereby offering interpretability by design. Once DeepFPC is properly trained, a sparse signal can be recovered fast and accurately from quantized measurements. The proposed model is then applied in DOA estimation and is shown to outperform state-of-the-art solutions; namely, the iterative FPC-ℓ1 algorithm and the deep convolution network (DCN) model.

Quantized genetic resampling particle filtering for vision-based ground moving target tracking

This paper concentrates on the quantized measurements fusion problem. Because of the non-Gaussian property of quantized measurements, classical nonlinear filters become not applicable, especially when the quantization noise is large. Motivated by the above problem, we propose a novel particle-based filtering named quantized genetic resampling particle filtering (QGRPF) in order to fuse quantized measurements optimally and improve estimation accuracy. Unlike the Gaussian assumption in traditional filers, the probability density function (PDF) of sensor measurement is modeled here as a discrete PDF that consists of a series of Dirac impulses. The particle filtering is employed to estimate the state, where the posterior of the state based on quantized measurements is approximated and updated by a set of weighted particles. As the likelihood function is a multi-dimensional integral of Gaussian density, which has no analytical solution, Genz's transformation and quasi-Monte Carlo method are combined to calculate the integral numerically. By integrating genetic resampling method into the particle filtering method, the proposed method can avoid particle degeneracy, in the meantime, guarantee particle diversity. The proposed QGRPF is demonstrated with an illustrative vision-based ground moving target (GMT) tracking example. Simulation results show the proposed approach is effective in fusing quantized measurements.

Optimal Estimation for Discrete-Time Linear System with Communication Constraints and Measurement Quantization

This paper focuses on the linear minimum mean square estimator for a networked discrete time-varying linear system subject to data quantification and communication constraints. The communication limitation is that only one transmission node can get access to the shared communication channel at each time step, and that different transmission nodes in the networked systems are scheduled to transmit information according to a Markov protocol. Then the remote estimator completes the estimation with only partially available observations, which are quantified. Suppose that the Markov chain is unknown to the remote estimator. By using orthogonal projection principle and innovation analysis method, a Kalman type filter is designed in a recurrence form. It is shown that estimation performance depends on the transition probability matrix of the Markov chain, quantization error, and the shared channel weighting parameter. Finally, an illustrative example is given to show the effectiveness of the proposed method.

The Generalized Lasso for Sub-Gaussian Measurements With Dithered Quantization

In the problem of structured signal recovery from high-dimensional linear observations, it is commonly assumed that full-precision measurements are available. Under this assumption, the recovery performance of the popular Generalized Lasso (G-Lasso) is by now well-established. In this paper, we extend these types of results to the practically relevant settings with quantized measurements. We study two extremes of the quantization schemes, namely, uniform and one-bit quantization; the former imposes no limit on the number of quantization bits, while the second only allows for one bit. In the presence of a uniform dithering signal and when measurement vectors are sub-gaussian, we show that the same algorithm (i.e., the G-Lasso) has favorable recovery guarantees for both uniform and one-bit quantization schemes. Our theoretical results, shed light on the appropriate choice of the range of values of the dithering signal and accurately capture the error dependence on the problem parameters. For example, our error analysis shows that the G-Lasso with one-bit uniformly dithered measurements leads to only a logarithmic rate loss compared to the full-precision measurements.

Phase-Based 3-D Source Localization Using 1-b Quantized Measurements Under Uniform Circular Array

1-b quantization has become an important topic in modern signal processing. In this letter, we consider the problem of 3-D source localization by combining 1-b quantized measurements and the phase-based algorithm under a uniform circular array. With analysis, unquantized and 1-b quantized cross-correlation coefficient can be approximated by the arcsine law and Taylor series approximation under sufficiently low signal-to-noise ratio (SNR). Even at high SNR levels, the approximated error only slightly affects source localization. Therefore, under 1-b quantized measurements, the phase-based algorithm can be straightforwardly applied to source's 3-D localization without extra preprocessing. Numerical examples demonstrate the theoretical analysis.

Set-Based State Estimation in Quantized State Feedback Control Systems With Quantized Measurements

Recently, with rapid advancements in communication technologies, networked control systems (NCSs) have attracted significant attention. In an NCS, data to be transmitted are quantized to match the communication channel capacity. When only the quantized state is available as the feedback signal in an NCS and the actual state is unavailable, the control performance may be degraded because of the intrinsic quantization error of the quantized state. Therefore, a state estimator has to be designed to avoid the performance degradation. In this brief, we propose a synthesis for set-based state estimation in a discrete-time quantized feedback control system in which only the quantized measurement is available. The effectiveness of the proposed estimation approach is verified via both simulations and experiments.

Quantization in Compressive Sensing: A Signal Processing Approach

The influence of finite-length registers and the corresponding quantization effects on the reconstruction of sparse and approximately sparse signals from a reduced set of measurements is analyzed in this paper. For the nonquantized measurements, the compressive sensing (CS) framework provides highly accurate reconstruction algorithms that produce negligible errors when the reconstruction conditions are met. However, hardware implementations of signal processing algorithms inevitably involve finite-length registers and quantization of the measurements. A detailed analysis of the effects related to the measurement quantization, with an arbitrary number of bits, is provided in this paper. A unified novel mathematical model to characterize the influence of the quantization noise and the signal nonsparsity on the CS reconstruction is introduced. Using this model, an exact formula for the expected error energy in the CS-based reconstructed signal is derived, while in the literature its bounds have been reported only. The theory is validated through various numerical examples with quantized measurements, involving scenarios with approximately sparse signals, noise folding effect, and floating-point arithmetics.

Adaptive stabilization of minimum-phase systems under quantized measurements

Abstract We construct an adaptive controller for a linear minimum-phase system of an arbitrary relative degree with an unknown bounded disturbance and dynamically quantized measurements. The key novelty is the extension of the shunting method (parallel feedforward compensator) to plants with bounded disturbances. This method leads to an augmented system of relative degree one that is stabilized by a passification-based adaptive controller. Moreover, we design a switching procedure for the controller parameters and the quantizer’s zoom that ensures the state convergence from an arbitrary set to an ellipsoid whose size depends on the disturbance bound. The results are demonstrated by an example of an aircraft flight control.