Linear Least-squares Estimation Research Articles

A Comprehensively Improved Interval Type-2 Fuzzy Neural Network for NOx Emissions Prediction in MSWI Process

The accurate and timely prediction of nitrogen oxides (NOx) emissions ensures eco-friendly and efficient operations for municipal solid waste incineration (MSWI) plants. Due to the high nonlinearity and uncertainty in MSWI processes, constructing an efficient prediction model remains challenging. This work proposes a comprehensively improved interval type-2 fuzzy neural network (CI-IT2FNN) for NOx emissions prediction. First, the neighborhood rough set (NRS) is introduced to determine the structure of this fuzzy neural network automatically, including the number of fuzzy rules and their corresponding consequent parameters. Second, an adaptive shape factor is added to the fuzzy membership function to better cope with the uncertainty, which can help to improve the generalization ability of network. Furthermore, to reduce the computational complexity, the Begian-Melek-Mendel (BMM) method is utilized as the defuzzification method in this study. Then, by integrating the linear least square estimation (LSE) and gradient decent (GD), a hierarchical learning algorithm is applied to adjust the network parameters to further enhance the learning efficiency and accuracy. Finally, after being evaluated by a benchmark simulation, the proposed CI-IT2FNN demonstrates its effectiveness and superiority on NOx emissions prediction.

Enhanced Signal Detection and Constellation Design for Massive SIMO Communications With 1-Bit ADCs

In this paper, we investigate a transmitter and receiver design for a single-user massive SIMO (single-input multiple-output) system with 1-bit analog-to-digital converters (ADCs) at the base station (BS), where the user adopts higher-order modulation, e.g., 16-quadrature amplitude modulation (16-QAM), for the data transmission. For the channel estimation and the signal detection, linear least-squares (LS) estimation and maximum ratio combining (MRC) are respectively employed. In this context, we first introduce closed-form formulas for the mean of the estimated symbols and for the correlation matrix between their real and imaginary parts considering the effect of 1-bit quantization. The study of the distribution of the estimated symbols indicates that, in presence of 1-bit ADCs, the conventional 16-QAM detector and the typical square 16-QAM modulation are not adequate. In light of this, we propose three novel symbol detectors and re-design the 16-QAM modulation in order to improve the symbol error rate (SER). Furthermore, the upper bound on the SER is analyzed based on the pair-wise error probability and the boundary equation between two regions is also studied. Through numerical results, the proposed framework, i.e., the symbol detector and the transmit constellation design, shows a significant enhancement in the SER performance against the conventional detector and the typical square 16-QAM modulation.

Sparse Affine Sampling: Ambiguity-Free and Efficient Sparse Phase Retrieval

Conventional sparse phase retrieval schemes can recover sparse signals from the magnitude of linear measurements only up to a global phase ambiguity. This work proposes a novel approach that instead utilizes the magnitude of affine measurements to achieve ambiguity-free signal reconstruction. The proposed method relies on two-stage approach that consists of support identification followed by the exact recovery of nonzero signal entries. In the noise-free case, perfect support identification using a simple counting rule is guaranteed subject to a mild condition on the signal sparsity, and subsequent exact recovery of the nonzero signal entries can be obtained in closed-form. The proposed approach is then extended to two noisy scenarios, namely, sparse noise (or outliers) and non-sparse bounded noise. For both cases, perfect support identification is still ensured under mild conditions on the noise model, namely, the support size for sparse outliers and the power of the bounded noise. Under perfect support identification, exact signal recovery can be achieved using a simple majority rule for the sparse noise scenario, and reconstruction up to a bounded error can be achieved using linear least-squares (LS) estimation for the non-sparse bounded noise scenario. The obtained analytic performance guarantee for the latter case also sheds light on the construction of the sensing matrix and bias vector. In fact, we show that a near optimal performance can be achieved with high probability by the random generation of the nonzero entries of the sparse sensing matrix and bias vector according to the uniform distribution over a circle. Computer simulations using both synthetic and real-world data sets are provided to demonstrate the effectiveness of the proposed scheme.

A Self-Tuning Adaptive Control Scheme for a Grid-Connected Three-Phase PV System

This article presents a new self-tuning sinusoidal recursive controller (STSRC) for handling the uncertainties and disturbances in a three-phase grid-connected photovoltaic system (GCPVS). The performance of a GCPVS is greatly influenced by the uncertainties, such as intermittency in solar irradiation, change in capacitance and equivalent series resistance (ESR) of dc-link capacitor, and variation of impedance between the inverter and the grid. This STSRC comprises improved linear sinusoidal tracer-based recursive least-square estimation (IRLS) to achieve robust performances, despite the parametric uncertainties through real-time estimation of its parameters, and updation of its gains. The efficacy of the proposed STSRC is verified through simulation using MATLAB/Simulink and experimental studies pursued on a 2.5-kW prototype. It is observed that STSRC exhibits superior tracking of PV voltage with reduced ripple and improved grid current with reduced total harmonic distortion (THD) of 1.66%. The estimation accuracy is found above 92%.

Response time correction of slow-response sensor data by deconvolution of the growth-law equation

Abstract. Accurate high-resolution measurements are essential to improve our understanding of environmental processes. Several chemical sensors relying on membrane separation extraction techniques have slow response times due to a dependence on equilibrium partitioning across the membrane separating the measured medium (i.e., a measuring chamber) and the medium of interest (i.e., a solvent). We present a new technique for deconvolving slow-sensor-response signals using statistical inverse theory; applying a weighted linear least-squares estimator with the growth law as a measurement model. The solution is regularized using model sparsity, assuming changes in the measured quantity occur with a certain time step, which can be selected based on domain-specific knowledge or L-curve analysis. The advantage of this method is that it (1) models error propagation, providing an explicit uncertainty estimate of the response-time-corrected signal; (2) enables evaluation of the solution self consistency; and (3) only requires instrument accuracy, response time, and data as input parameters. Functionality of the technique is demonstrated using simulated, laboratory, and field measurements. In the field experiment, the coefficient of determination (R2) of a slow-response methane sensor in comparison with an alternative fast-response sensor significantly improved from 0.18 to 0.91 after signal deconvolution. This shows how the proposed method can open up a considerably wider set of applications for sensors and methods suffering from slow response times due to a reliance on the efficacy of diffusion processes.

Correlation dispersion as a measure to better estimate uncertainty in remotely sensed glacier displacements

Abstract. In recent years a vast amount of glacier surface velocity data from satellite imagery has emerged based on correlation between repeat images. Thereby, much emphasis has been put on the fast processing of large data volumes and products with complete spatial coverage. The metadata of such measurements are often highly simplified when the measurement precision is lumped into a single number for the whole dataset, although the error budget of image matching is in reality neither isotropic nor constant over the whole velocity field. The spread of the correlation peak of individual image offset measurements is dependent on the image structure and the non-uniform flow of the ice and is used here to extract a proxy for measurement uncertainty. A quantification of estimation error or dispersion for each individual velocity measurement can be important for the inversion of, for instance, rheology, ice thickness and/or bedrock friction. Errors in the velocity data can propagate into derived results in a complex and exaggerating way, making the outcomes very sensitive to velocity noise and outliers. Here, we present a computationally fast method to estimate the matching precision of individual displacement measurements from repeat imaging data, focusing on satellite data. The approach is based upon Gaussian fitting directly on the correlation peak and is formulated as a linear least-squares estimation, making its implementation into current pipelines straightforward. The methodology is demonstrated for Sermeq Kujalleq (Jakobshavn Isbræ), Greenland, a glacier with regions of strong shear flow and with clearly oriented crevasses, and Malaspina Glacier, Alaska. Directionality within an image seems to be the dominant factor influencing the correlation dispersion. In our cases these are crevasses and moraine bands, while a relation to differential flow, such as shear, is less pronounced on the correlation spread.

Augmented Nonlinear Least Squares Estimation With Applications to Localization

Least squares (LS) estimation is simple yet effective for parameter estimation. Most real-world problems are nonlinear. In practice, nonlinear LS problems are linearized first and then solved by a linear LS estimator. However, since these methods solve a nonlinear LS problem by a linear way, there is room for improvement only if estimators being nonlinear in the original measurement. In this article, an LS approach is proposed for nonlinear LS problems, along with theoretical analysis and justification. First, for a general nonlinear measurement model with any form of noise, a unified linearization (UL) approach is proposed under certain assumptions and a linearized least squares (LLS) estimator is defined based on the UL model. Second, an augmented nonlinear least squares (ANLS) estimator is proposed based on LLS estimation. In the ANLS estimator, the original measurement is augmented by its nonlinear conversion intended to further utilize the nonlinear measurement. Moreover, we prove that the ANLS estimator outperforms LLS estimation-based estimators. Finally, the UL and the ANLS estimator are applied to source localization with time difference of arrival and/or frequency difference of arrival measurement, and a two-step ANLS localization algorithm is developed. The performance of the proposed algorithm is evaluated via simulation of some typical localization scenarios.

Data-Selective Least Squares Methods for Elliptic Localization With NLOS Mitigation

In this letter, we consider the problem of 2-D elliptic localization, where multiple spatially separated sensors, including the transmitters and receivers, are exploited to locate the signal reflecting/relaying target in the mixed line-of-sight/nonline-of-sight (NLOS) environments. We begin by revisiting a plain closed-form linear least squares (LS) solution. As it is vulnerable to the existence of erroneous time-sum-of-arrival (TSOA) measurements under the NLOS conditions, we then devise two new data-selective LS methods, by which the outliers can be identified and mitigated and a higher level of resistance to the NLOS bias errors can be provided. To conduct data selection, the first algorithm combines the use of the traditional linear LS estimator and an additional cost function, whereas the second relies on the parameterization of the TSOA-defined ellipses and follows a nonlinear LS estimation criterion. Based on the simulations, we demonstrate the effectiveness of the proposed methods in NLOS error mitigation at acceptable computational costs.

Localisation of wireless nodes with partial connectivity in wireless sensor systems

Owing to their short communication range, wireless nodes in wireless sensor networks (WSNs) can exchange information with devices in their vicinity only. Thus, in sparse networks, the full connectivity of the network is rarely achieved. This renders a centralised approach towards localisation in WSNs useless. Moreover, the exploitation of a centralised algorithm for localisation compromises the scalability in dense networks. Thus, a decentralised, location-aware network with partial connectivity and hybrid (range and direction) measurements obtained between known sensors (reference sensors) and sensors at unknown locations (target sensors) is under focus. The decentralised location estimation is obtained using a linear least squares (LLS) approach and performance enhancements are achieved by introducing a weighing strategy to produce weighted least squares (WLS) estimates. This distributed estimation is made possible by designing a map stitching technique that forms the global map of the network from individual local maps of the wireless nodes without compromising the distributed nature of the network. In the analytical section of the study, theoretical mean squares error expression is derived for LLS estimation, and a Cramer–Rao lower bound is derived to bind the performance of the WLS solution. The algorithm's performance validation is conducted both theoretically and via simulations.

Efficient Sensing for Compressive Estimation of Frequency of a Real Sinusoid

Linear least squares (LS) frequency estimators are popular because they are closed form and easy to implement. However, they are applicable to compressive frequency estimation only after reconstruction. This is because compressive sensing (CS) breaks up the temporal order of the original sinusoidal samples. This correspondence proposes an efficient sensing scheme to obtain CS samples. They are sums of the Nyquist rate samples of the signal. There is no need for matrix multiplications and the random modulator preintegrator. A modified LS estimator is able to estimate frequency directly from the CS samples without reconstruction. This estimator has accuracy that matches the theoretical lower bound, as shown by two examples.

Least-squares estimators for systems with stochastic sensor gain degradation, correlated measurement noises and delays in transmission modelled by Markov chains

ABSTRACTThis paper addresses the linear least-squares estimation of a signal from measurements subject to stochastic sensor gain degradation and random delays during the transmission. These uncertainty phenomena, common in network systems, have traditionally been described by independent Bernoulli random variables. We propose a model that is more general and therefore has greater applicability to real-life situations. The model has two particular characteristics: firstly, the sensor gain degradation is represented by a white sequence of random variables with values in [0,1]; in addition, the absence or presence of delays in the transmission is described by a homogeneous three-state Markov chain, which reflects a possible correlation of delays at different sampling times. Furthermore, assuming that the measurement noise is one-step correlated, we obtain recursive prediction, filtering and fixed-point smoothing algorithms using the first and second-order moments of the signal and the processes present in the observation model. Simulation results for a scalar signal are provided to illustrate the feasibility of the proposed algorithms, using the estimation error variances as a measure of the quality of the estimators.

Video Multicast: Integrating Scalability of Soft Video Delivery Systems Into NOMA

Non-orthogonal Multiple Access (NOMA) has aroused research interest for its potential use in future wireless video multicast. By exploring the power domain, multiple video layers are superposed to achieve video delivery scalability and efficiency in NOMA. However, the scalability of this approach is still limited despite adopting medium-grain quality scalable (MGS) video coding. In this letter, we propose a scalable multicast design inspired by soft video delivery systems. Soft video delivery systems cannot be directly applied in NOMA networks to improve the scalability because they cannot achieve errorless decoding when utilizing linear least square estimation (LLSE) at the decoder. If there is decoding error in the former layers, the successive interference cancellation (SIC) in NOMA will give rise to error propagation and huge performance loss. To solve this problem, we propose a design with digitalized base layer and soft encoded enhanced layer. The power allocation is formulated as a distortion minimization problem. The experimental results demonstrate that the proposed design has significant performance gain over SoftCast, SupCast and the traditional digital system.

Plug in estimation in high dimensional linear inverse problems a rigorous analysis**This article is an updated version of: Fletcher A K, Pandit P, Rangan S, Sarkar S and Schniter P 2018 Plug-in estimation in high-dimensional linear inverse problems: a rigorous analysis Advances in Neural Information Processing Systems 31 ed S Bengio, H Wallach, H Larochelle, K Grauman, N Cesa-Bianchi and

Estimating a vector from noisy linear measurements often requires use of prior knowledge or structural constraints on for accurate reconstruction. Several recent works have considered combining linear least-squares estimation with a generic or ‘plug-in’ denoiser function that can be designed in a modular manner based on the prior knowledge about . While these methods have shown excellent performance, it has been difficult to obtain rigorous performance guarantees. This work considers plug-in denoising combined with the recently-developed vector approximate message passing (VAMP) algorithm, which is itself derived via expectation propagation techniques. It shown that the mean squared error of this ‘plug-and-play’ VAMP can be exactly predicted for high-dimensional right-rotationally invariant random and Lipschitz denoisers. The method is demonstrated on applications in image recovery and parametric bilinear estimation.

Investigating Impaired Aircraft's Flight Envelope Variation Predictability Using Least-Squares Regression Analysis

Aircraft failures alter the aircraft dynamics and cause the maneuvering flight envelope to change. Such envelope variations are nonlinear and generally unpredictable by the pilot, as they are governed by the aircraft’s complex dynamics. Hence, to prevent in-flight loss of control, it is crucial to practically predict the impaired aircraft’s flight envelope variation due to any a priori unknown failure degree. This Paper investigates the predictability of the number of trim points within the maneuvering flight envelope and its centroid using both linear and nonlinear least-squares estimation methods. To do so, various polynomial models and nonlinear models based on the hyperbolic tangent function, which incorporate the influencing factors on the envelope variations as the inputs and estimate the centroid and the number of trim points of the maneuvering flight envelope at any intended failure degree, are developed and compared. Results indicate that both the polynomial and hyperbolic tangent function-based models are capable of predicting the impaired fight envelope variation with good precision. Furthermore, it is shown that the regression equation of the best polynomial fit enables direct assessment of the impaired aircraft’s flight envelope contraction and displacement sensitivity to the specific parameters characterizing aircraft failure and flight condition.

Determination of source parameters of simple-shaped geologic subsurface structures from self-potential anomalies using enhanced local wavenumber method

Simple geometry model structures can be useful in quantitative evaluation of self-potential data. In this paper, we solve local wavenumber equation to estimate the horizontal position, the depth and the type of the causative source geometry by using a linear least-squares approximation. The advantages of the algorithm in determining the horizontal position and depth measure are its independency to shape factor of the sources and also its simple computations. The algorithm is built in Matlab environment. The validity of the algorithm is illustrated on variable noise-free and random noise included synthetic data from two-dimensional (2-D) models where the achieved parametric quantities coincide well with the actual ones. The algorithm is also utilized to real self-potential data from Ergani Copper district, Turkey. The results from the actual data application are in good agreement with the published literature for the study area. The source code of the algorithm is available from the authors on request.

Centralized filtering and smoothing algorithms from outputs with random parameter matrices transmitted through uncertain communication channels

The least-squares linear centralized estimation problem is addressed for discrete-time signals from measured outputs whose disturbances are modeled by random parameter matrices and correlated noises. These measurements, coming from different sensors, are sent to a processing center to obtain the estimators and, due to random transmission failures, some of the data packet processed for the estimation may either contain only noise (uncertain observations), be delayed (sensor delays) or even be definitely lost (packet dropouts). Different sequences of Bernoulli random variables with known probabilities are employed to describe the multiple random transmission uncertainties of the different sensors. Using the last observation that successfully arrived when a packet is lost, the optimal linear centralized fusion estimators, including filter, multi-step predictors and fixed-point smoothers, are obtained via an innovation approach; this approach is a general and useful tool to find easily implementable recursive algorithms for the optimal linear estimators under the least-squares optimality criterion. The proposed algorithms are obtained without requiring the evolution model of the signal process, but using only the first and second-order moments of the processes involved in the measurement model.

On the Characterization of Intermediate‐Scale Ionospheric Structure

AbstractCharacterization of ionospheric structure starts with spectral analysis of one‐dimensional time series. Unknown spectral density function (SDF) parameters are estimated by model‐fitting procedures, which will be referred to in this paper collectively as irregularity parameter estimation. If the diagnostic SDF has a power law form, linear least squares estimation (LLE) can be used to estimate the power law parameters. In this paper simulations are used to investigate LLE estimates of diagnostic single‐component and two‐component power law SDFs. There is a known turbulent strength bias and a more troublesome correlation between the turbulent strength and the spectral index. We found that this intrinsic property of LLE estimators completely explains a similar correlation long observed in both in situ and radio propagation ionospheric diagnostic measurements. Maximum likelihood estimation (MLE) is superior to LLE but requires knowledge of the probability distribution function of the SDF estimator. To this end one can exploit the fact that the probability distribution function of a periodogram about the its true mean is well approximated by a χD distribution. With an hypothesized true mean SDF defined by a small set of parameters, the parameters can be adjusted to maximize the likelihood that the periodogram was generated by the parameterized SDF. Furthermore, algorithms that adjust parameters to maximize likelihood can use functions of the defining parameters being adjusted to improve performance. Recognizing that correlation between turbulent strength and spectral index estimates is an intrinsic measurement property, error minimization is particularly important. A modified MLE procedure is presented that provides robust initiation and good two‐component power law parameter estimates.

Networked distributed fusion estimation under uncertain outputs with random transmission delays, packet losses and multi-packet processing

Abstract This paper investigates the distributed fusion estimation problem for networked systems whose multisensor measured outputs involve uncertainties modelled by random parameter matrices. Each sensor transmits its measured outputs to a local processor over different communication channels and random failures –one-step delays and packet dropouts– are assumed to occur during the transmission. White sequences of Bernoulli random variables with different probabilities are introduced to describe the observations that are used to update the estimators at each sampling time. Due to the transmission failures, each local processor may receive either one or two data packets, or even nothing and, when the current measurement does not arrive on time, its predictor is used in the design of the estimators to compensate the lack of updated information. By using an innovation approach, local least-squares linear estimators (filter and fixed-point smoother) are obtained at the individual local processors, without requiring the signal evolution model. From these local estimators, distributed fusion filtering and smoothing estimators weighted by matrices are obtained in a unified way, by applying the least-squares criterion. A simulation study is presented to examine the performance of the estimators and the influence that both sensor uncertainties and transmission failures have on the estimation accuracy.

A Robust Regression by Using Huber Estimator and Tukey Bisquare Estimator for Predicting Availability of Corn in Karanganyar Regency, Indonesia

Linear least-squares estimates can behave badly when the error distribution is not normal, particularly when the errors are heavy-tailed. One remedy is to remove influential observations from the least-squares fit. Another approach, robust regression, is to use a fitting criterion that is not as vulnerable as least squares to unusual data. The most common general method of robust regression is M-estimation. This class of estimators can be regarded as a generalization of maximum-likelihood estimation. In this paper we discuss robust regression model for corn production by using two popular estimators; i.e. Huber estimator and Tukey bisquare estimator.<br />Keywords : robust regression, M-estimation, Huber estimator, Tukey bisquare estimator

Centralized Fusion Approach to the Estimation Problem with Multi-Packet Processing under Uncertainty in Outputs and Transmissions.

This paper is concerned with the least-squares linear centralized estimation problem in multi-sensor network systems from measured outputs with uncertainties modeled by random parameter matrices. These measurements are transmitted to a central processor over different communication channels, and owing to the unreliability of the network, random one-step delays and packet dropouts are assumed to occur during the transmissions. In order to avoid network congestion, at each sampling time, each sensor’s data packet is transmitted just once, but due to the uncertainty of the transmissions, the processing center may receive either one packet, two packets, or nothing. Different white sequences of Bernoulli random variables are introduced to describe the observations used to update the estimators at each sampling time. To address the centralized estimation problem, augmented observation vectors are defined by accumulating the raw measurements from the different sensors, and when the current measurement of a sensor does not arrive on time, the corresponding component of the augmented measured output predictor is used as compensation in the estimator design. Through an innovation approach, centralized fusion estimators, including predictors, filters, and smoothers are obtained by recursive algorithms without requiring the signal evolution model. A numerical example is presented to show how uncertain systems with state-dependent multiplicative noise can be covered by the proposed model and how the estimation accuracy is influenced by both sensor uncertainties and transmission failures.