Noise Vector Research Articles

Signal extraction approach for sparse multivariate response regression

In this paper, we consider multivariate response regression models with high dimensional predictor variables. One way to estimate the coefficient matrix is through its decomposition. Among various decomposition of the coefficient matrix, we focus on the decomposition which leads to the best approximation to the signal part in the response vector given any rank. Finding this decomposition is equivalent to performing a principal component analysis for the signal. Given any rank, this decomposition has nearly the smallest expected prediction error among all decompositions of the coefficient matrix with the same rank. To estimate the decomposition, we solve a penalized generalized eigenvalue problem followed by a least squares procedure. In the high-dimensional setting, allowing a general covariance structure for the noise vector, we establish the oracle inequalities for the estimates. Simulation studies and application to real data show that the proposed method has good prediction performance and is efficient in dimension reduction for various models.

O51. A vector based approach for fast real time orientation measurement in magnetic resonance imaging (MRI)

Introduction We aimed to make in-bore motion tracking more accessible through the use of miniature, low-cost sensors found in a large variety of consumer electronics. We identified the need for orientation estimates independent of the imaging pulse sequence that can be estimated at a temporal resolution unattainable by navigator-based methods. Materials and methods A sensor array was developed comprising a 3-axis magnetometer, 3-axis accelerometer and 3-axis angular rate sensor. Orientation estimates are obtained by comparing vector observations from the accelerometer and magnetometer in the subject frame with measurements of the a priori reference vectors (gravity [−y] and B0 [+z]) in the scanner frame. To reduce the effects of linear accelerations on the gravity vector estimate, the measurements were fused with the angular rate sensor outputs using a complementary filter. Results The magnetometer measurements of the fields within the scanner during image acquisition allow for an exceptionally high signal to noise vector reference. This and the fact that gravity and the static magnetic field are almost perfectly orthogonal result in more precise orientation estimates than are conventionally possible with similar sensor arrangements in inertial navigation applications (error Conclusion Small changes in orientation could result in substantial errors on the periphery of the image due to a ‘lever arm’ effect. These artefacts are difficult to correct retrospectively highlighting the importance of reliable orientation tracking. Angular rates of change as high as 30 degrees per second were often observed showing the importance of high temporal resolution orientation correction. With a single marker and no scanner specific calibration this method shows promise for complementing existing techniques with no extra patient discomfort.

Estimation Performance for the Bayesian Hierarchical Linear Model

Bayesian hierarchical modelling is a well-established branch of Bayesian inference. In this letter, we derive and study the estimation performance for the Bayesian hierarchical linear model (BHLM). Specifically, we consider a linear model with hierarchical priors for the involved amplitude and noise vectors. We provide closed-form expressions of the Bayesian Cramer-Rao bound (BCRB) for the following settings: (i) an arbitrary prior and hyperprior and (ii) a Gaussian- $\mathcal{Y}$ prior for the amplitudes, while the prior of noise is a Gaussian- $\mathcal{X}$ in both cases. Gaussian- $\mathcal{X}$ means that the conditional prior given the hyperparameter is Gaussian and $\mathcal{X}$ is the hyperprior. For the hierarchical distribution associated with spherical invariant random variables, the BCRB has a compact closed-form expression and enjoys several interesting properties that are discussed. Finally, we provide a theoretical analysis of the statistical efficiency of the linear minimum mean square error (MMSE) estimator in the low- and high-noise variance regimes when the hyperparameters are stochastically dominant.

Comments on “Energy-Efficient Uplink Multiuser MIMO”

In the paper “Energy-efficient Uplink Multi-user MIMO,” it was mentioned that the employed linear receiver does not change the variance of the elements of the noise vector. Then, the performance was calculated based on this proposition. In this note, we show that this proposition does not hold by providing the counter examples. In addition, we analyze how the performance will be affected by fixing this proposition.

Selective temporal filtering and its application to hand gesture recognition

In temporal data analysis, noisy data is inevitable in both testing and training. This noise can seriously influence the performance of the temporal data analysis. To address this problem, we propose a novel method, termed Selective Temporal Filtering that builds a noise-free model for classification during training and identifies key-feature vectors that are noise-filtered data from the input sequence during testing. The use of these key-feature vectors makes the classifier robust to noise within the input space. The proposed method is validated on a synthetic-dataset and a database of American Sign Language. Using key-feature vectors results in robust performance with respect to the noise content. Futhermore, we are able to show that the proposed method not only outperforms Conditional Random Fields and Hidden Markov Models in noisy environments, but also in a well-controlled environment where we assume no significant noise vectors exist.

Recovery of Sparse Signals via Generalized Orthogonal Matching Pursuit: A New Analysis

As an extension of orthogonal matching pursuit (OMP) for improving the recovery performance of sparse signals, generalized OMP (gOMP) has recently been studied in the literature. In this paper, we present a new analysis of the gOMP algorithm using the restricted isometry property (RIP). We show that if a measurement matrix Φ ∈ ℜ m×n satisfies the RIP with isometry constant δ max{9,S+1}K ≤ 1/8, then gOMP performs stable reconstruction of all K-sparse signals x ∈ ℜ n from the noisy measurements y=Φx+v, within max{K,⌊8K/S⌋} iterations, where v is the noise vector and S is the number of indices chosen in each iteration of the gOMP algorithm. For Gaussian random measurements, our result indicates that the number of required measurements is essentially m=O(Klog n /K), which is a significant improvement over the existing result m=O(K 2 log n /K), especially for large K.

Divergence-free smoothing for volumetric PIV data

This paper proposes a divergence-free smoothing (DFS) method for the post-process of volumetric particle image velocimetry (PIV) data, which can smooth out noise and divergence error at the same time. The method is a combination of the penalized least squares regression and the divergence corrective scheme (DCS), employing the generalized cross-validation method to automatically determine the best smoothing parameter. By introducing a weight-changing algorithm similar to the all-in-one method, a robust version of DFS can simultaneously deal with vector validation, replacement of outliers and missing vectors, smoothing, and zero-divergence correction of the velocity field. Direct numerical simulation data of turbulent channel flow (Johns Hopkins Turbulence Databases) added with artificial noise, outliers and missing vectors are used to test the accuracy of DFS. The results show that DFS can smooth the velocity field to divergence-free and performs better than the all-in-one method, DCS and some other available conventional processing methods for post-process of velocity field, especially in dealing with clustered outliers and missing vectors. A block DFS is suggested to process large velocity field to save both time and memory. Tests on tomographic PIV data validate the effectiveness of DFS on improving both flow statistics and flow visualization.

Secure Beamforming for SWIPT in Multiuser MISO Broadcast Channel With Confidential Messages

In this letter, we consider simultaneous wireless information and power transfer (SWIPT) in multiuser multiple-input single-output (MISO) broadcast channel with confidential messages, where each receiver adopts the power splitting (PS) approach to decode information and harvest energy simultaneously. Our goal is to minimize the total transmit power while guaranteeing the secrecy rate and harvested energy constraints at each receiver by jointly optimizing the transmit beamforming vectors, artificial noise vector, and PS ratios. To solve this non-convex problem, a two-stage optimization approach is proposed. In addition, we also propose a low-complexity suboptimal algorithm based on the genetic algorithm to solve the original problem. Simulation results are finally presented to illustrate the effectiveness of our proposed algorithm.

Random weighting estimation of kinematic model error for dynamic navigation

This paper presents a new random weighting method to deal with the systematic error of the kinematic model for dynamic navigation. This method incorporates random weights in the kinematic model to control the systematic error of the kinematic model for improving the navigation accuracy. A theory of random weighting estimation is established, showing that 1) the random weighting estimation of the kinematic model’s systematic error is unbiased and 2) the covariance matrix of the predicted state vector can be controlled by adjusting the covariance matrices of the predicted residual vector and estimated state vector to improve the accuracy of state prediction. Random weighting estimations are also constructed for the systematic error of the kinematic model as well as the covariance matrices of predicted residual vector, predicted state vector, and state noise vector. Experimental results demonstrate the effectiveness of the proposed random weighting method in resisting the disturbances of the kinematic model noise for improving the accuracy of dynamic navigation.

Robust One-Bit Bayesian Compressed Sensing with Sign-Flip Errors

We consider the problem of sparse signal recovery from one-bit measurements. Due to the noise present in the acquisition and transmission process, some quantized bits may be flipped to their opposite states. These bit-flip errors, also referred to as the sign-flip errors, may result in severe performance degradation. To address this issue, we introduce a robust Bayesian compressed sensing framework to account for sign flip errors. Specifically, sign-flip errors are considered as a result of a sparse noise-corrupted model in which original (unquantized) observations are corrupted by sparse (impulse) noise. A Gaussian-inverse Gamma hierarchical prior is assigned to the noise vector to promote sparsity. Based on the modified hierarchical model, we develop a variational expectation-maximization (EM) algorithm to identify the sign-flip errors and recover the sparse signal simultaneously. Numerical results are provided to illustrate the effectiveness and superiority of the proposed method.

Monitoring nonlinear profiles adaptively with a wavelet-based distribution-free CUSUM chart

A wavelet-based distribution-free tabular CUSUM chart based on adaptive thresholding, is designed for rapidly detecting shifts in the mean of a high-dimensional profile whose noise components have a continuous nonsingular multivariate distribution. First computing a discrete wavelet transform of the noise vectors for randomly sampled Phase I (in-control) profiles, uses a matrix-regularization method to estimate the covariance matrix of the wavelet-transformed noise vectors; then, those vectors are aggregated (batched) so that the non-overlapping batch means of the wavelet-transformed noise vectors have manageable covariances. Lower and upper in-control thresholds are computed for the resulting batch means of the wavelet-transformed noise vectors using the associated marginal Cornish–Fisher expansions that have been suitably adjusted for between-component correlations. From the thresholded batch means of the wavelet-transformed noise vectors, Hotelling’s -type statistics are computed to set the parameters of a CUSUM procedure. To monitor shifts in the mean profile during Phase II (regular) operation, computes a similar Hotelling’s -type statistic from successive thresholded batch means of the wavelet-transformed noise vectors using the in-control thresholds; then applies the CUSUM procedure to the resulting -type statistics. Experimentation with several normal and non-normal test processes revealed that outperformed existing non-adaptive profile-monitoring schemes.

Sage windowing and random weighting adaptive filtering method for kinematic model error

This paper presents a new method for adaptive estimation of kinematic model error in dynamic aircraft navigation. This method combines the concepts of random weighting and Sage windowing to online monitor predicted and observation residuals to control the influence of the kinematic model's systematic error on system state estimation. Based on the Sage windowing, random weighting estimations are constructed within a moving time window for the systematic error of the kinematic model as well as the covariance matrices of the observation noise vector, the predicted residual vector, and the predicted state vector. Experimental results and comparison analysis demonstrate that the proposed method not only adjusts the covariance matrices of the observation noise vector and the predicted residual vector, but also effectively controls the influence of the kinematic model error on state parameter estimation, thus improving the navigation accuracy.

Using the Kalman Filter to Smooth the Shocks of a Dynamic Stochastic General Equilibrium Model

Abstract: This paper shows how to use the Kalman filter (Kalman 1960) to back out the shocks of a dynamic stochastic general equilibrium model. In particular, we use the smoothing algorithm as described in Hamilton (1994) to estimate the shocks of a sticky-prices and sticky-wages model using all the information up to the end of the sample. JEL classification: C63, C68, E37 Key words: dynamic equilibrium economies, the Kalman filter, smoothing 1. Introduction This paper shows how to use the Kalman Filter (Kalman, 1960) to back out the shocks of a dynamic stochastic general equilibrium model. The idea is as follows: First, we write the model in what is called the State-Space Representation. Second, we use the Kalman Filter to write the likelihood function of the observed data and estimated the structural parameters of the model. (1) Third, using the estimate parameters, we estimated the values of the model perturbations during the sample period conditional on all the observed data. (2) This procedure is very useful because it allows us to use a general equilibrium model to make inference about which shocks the economy was facing during any period in the sample based on the full set of collected data. In the first part of the paper we describe how to implement the Kalman filter to estimate structural parameters and smooth the shocks to an abstract linear system. In the second part, we use a sticky price model to show how to use the procedure in practice. 2. The State-Space Representation The first step is to write the model in State-Space form. Let [[eta].sub.t] be a (nx1) vector the observed variables at date t and let [[xi].sub.t] be a (rx1) vector of unobserved variables at date t (this vector is also called the state vector). The State-Space Representation of the system is (3) [[xi].sub.t+1] = F[[xi].sub.t] + [v.sub.t+1] (1) [[eta].sub.t] = H'[[xi].sub.t] + [w.sub.t] (2) where F and H' are matrices of the needed dimensions. Equation (1) is called State Equation, and (2) is the Observed Equation. [v.sub.t] and [w.sub.t] are uncorrelated normally distributed white noise vectors, therefore: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and E ([w.sub.t][v'.sub.[tau]]) = 0 for all t, [tau] 3. Using the Kalman Filter to Write the Likelihood Function of the Model Once the model has be written in State-Space form, the second step is to estimate the structural parameters that define the model. In order to do that, we will need to write the likelihood function of the observed data, [[eta].sup.T] = {[[eta].sub.1], [[eta].sub.2], ..., [[eta].sub.t]}. We will use the Kalman Filter to write the likelihood function l ([[eta].sup.T] |F, H', Q, R) = [[PI].sup.T.sub.t=1] l ([[eta].sub.t]|[[eta].sub.t-1]F, H', Q, R). First, we need to introduce some notation. Let [[xi].sub.t+1|t] = E ([[xi].sub.t+1]|[[eta.sup.t]), be the linear projection of [[xi].sub.t+1] on [[eta].sup.t] and a constant, and let [[eta].sub.t+1|t] = E ([[eta].sub.t+1]|[[eta].sup.t])= H'[[xi].sub.t+1|t] be the linear projection of [[eta].sub.t+1] on [[eta].sup.t] and a constant. Also let [P.sub.t+1|t] = E ([[xi].sub.t+1] - [[xi].sub.t+1|t])([[xi].sub.t+1] - [[xi].sub.t+1|t])', be the mean squared forecasting error when projecting [[xi].sub.t+1], and let [[SIGMA].sub.t+1|t] = E ([[eta].sub.t+1] - [[eta].sub.t+1|t])([[eta].sub.t+1] - [[eta].sub.t+1|t])' = = E (H'[[xi].sub.t+1] + [w.sub.t+1] - H'[[xi].sub.t+1|t])(H'[[xi].sub.t+1] + [w.sub.t+1] - H'[[xi].sub.t+1|t])' = H'[P.sub.t+1|t]H + R be the mean squared forecasting error when projecting [[eta].sub.t+1]. Finally notice that E ([[eta].sub.t+1] - [[eta].sub.t+1|t])([[xi].sub.t+1] - [[xi].sub.t+1|t])' = = E (H'[[xi].sub.t+1] + [w.sub.t+1] - H'[[xi].sub.t+1|t])([[xi]. …

Parametric Study of HEMP-Thruster Downscaling to <inline-formula> <tex-math notation="LaTeX">$ {\mu }$ </tex-math></inline-formula>N Thrust Levels

Many on-going European Space Agency (ESA) science and earth observation missions are based on precision attitude control and formation flying. All these missions impose strong requirements on propulsion system which should provide low thrust, low noise, and high-precision thrust vectors in up to 16 directions. Also as most of these missions have a platform with limited solar cell arrays, the power consumption of the propulsion system should be as low as possible. The idea of using a small high-efficiency multistage plasma thruster (HEMPT) system for such missions is very attractive because of its relatively low complexity and low system mass. Thus, the ability of downscaling a HEMPT to the μN range is investigated experimentally. A measurement campaign studying systematically the influence of the geometrical dimensions of main thruster parameters on operation, beam profile, and ion acceleration is presented. Additionally the anode material was varied and showed relevance to ion acceleration distribution. The minimum achieved thrust was 50 μN at an anode voltage of 600 V, corresponding to a specific impulse of 230 s. Operation points with thrusts of 180 and 360 μN demonstrate a specific impulse of 610 and 860 s, respectively.

A PAPR Reduction Method Based on Differential Evolution

High peak-to-average ratio power (PAPR) is a critical practical problem for an OFDM system. Many techniques, such as clipping and filtering (ICF), cognitive clipping, have been proposed to deal with the issue. However, it needs to determine the relationship between error vector magnitude (EVM) and clipping ratio (CR). In this paper, we formulate a universal PAPR optimization model with EVM constraint, and propose a differential evolution (DE) algorithm with a time complexity of 2 ( log ) O N N . The optimization parameter of the new approach is clipping noise. The EVM constraint guarantees proper receiver operation that is specified by most modern communication standards. The proposed DE algorithm employs the noise vector as the population. It adjusts three crucial control parameters to minimize cost function which is the amount of PAPR reduction. Simulation results show that our proposed method can offer good performance in PAPR and bit error rate (BER).

Discrete EKF with pairwise Time Correlated Measurement Noise for Image-Aided Inertial Integrated Navigation

Abstract. An image-aided inertial navigation implies that the errors of an inertial navigator are estimated via the Kalman filter using the aiding measurements derived from images. The standard Kalman filter runs under the assumption that the process noise vector and measurement noise vector are white, i.e. independent and normally distributed with zero means. However, this does not hold in the image-aided inertial navigation. In the image-aided inertial integrated navigation, the relative positions from optic-flow egomotion estimation or visual odometry are pairwise correlated in terms of time. It is well-known that the solution of the standard Kalman filter becomes suboptimal if the measurements are colored or time-correlated. Usually, a shaping filter is used to model timecorrelated errors. However, the commonly used shaping filter assume that the measurement noise vector at epoch k is not only correlated with the one from epoch k – 1 but also with the ones before epoch k – 1 . The shaping filter presented in this paper uses Cholesky factors under the assumption that the measurement noise vector is pairwise time-correlated i.e. the measurement noise are only correlated with the ones from previous epoch. Simulation results show that the new algorithm performs better than the existing algorithms and is optimal.

Windowing-based random weighting fitting of systematic model errors for dynamic vehicle navigation

The Kalman filter is a commonly used computational method for dynamic vehicle navigation and positioning. However, it requires kinematic and observation models not contain any systematic error; otherwise, the resultant navigation solution will be biased or even divergent. In order to overcome this limitation, this paper presents a new windowing-based random weighting method to fit the systematic errors of kinematic and observation models within a moving time window for dynamic vehicle navigation. This method compensates the systematic model errors by correcting observation residual vector and state noise vector during the filtering process. Random weighting theories are established to fit the systematic model errors and the covariance matrices of observation vector and predicted state vector within a moving time window. Experiments and comparison analysis with the existing methods demonstrate that the proposed method can effectively resist the disturbances on system state estimation due to the systematic errors of kinematic and observation models, thus significantly improving the accuracy of dynamic vehicle navigation.

Propeller Synchrophase Angle Optimization of Turboprop-Driven Aircraft—An Experimental Investigation

Propeller synchrophasing is an effective way of reducing interior noise and vibration of turboprop-driven aircraft. However, synchrophasing has achieved limited success in practice for the reason that the predetermined phase angles are not acoustically optimized for maximum noise reduction during all flight conditions. An investigation has been conducted out which includes two folds: first, the noise vector based on laboratory experimental data has been modeled and second, optimal phase to acquire minimum noise is obtained via optimization search. An improved identification method of vector noise model which can be less dependent to noise phase message is presented. Compared with traditional methods, this method can greatly reduce the real-time requirement between phase optimization model and control model or sound acquiring model, so it can eliminate the influence which communication delay brings on identification precision. A synchrophasing experimental platform is established to verify the vector noise modeling. It adopts two propellers-driven servo motors to simulate the interior noise environment of the aircraft. The influence of the date sampling condition on identification is also researched. Ant colony optimization with two improvements is applied to phase optimization of four propellers. Simulation results show that the improved algorithm requires much less calculation.

Eliminating 1/f noise in oscillators.

We study 1/f and narrow-bandwidth noise in precision oscillators based on high-quality factor resonators and feedback. The dynamics of such an oscillator are well described by two variables, an amplitude and a phase. In this description we show that low-frequency feedback noise is represented by a single noise vector in phase space. The implication of this is that 1/f and narrow-bandwidth noise can be eliminated by tuning controllable parameters, such as the feedback phase. We present parameter values for which the noise is eliminated and provide specific examples of noise sources for further illustration.

Performance analysis of random angle based quantization modulation

The random angle based quantization modulation (RAQM) is a new watermarking method invariant to valumetric scaling attack. In this paper, the performance of RAQM is theoretically evaluated in two aspects: the embedding distortion and the decoding performance against additive noise attack. The analyses are developed under the assumptions that the host and noise vectors are mutually independent and both of them have independently and identically distributed components. We establish the stochastic models for several concerned signals. Based on them, the expressions of the embedding distortion and the decoding bit-error probability are derived in closed form. We also present the simplified but effective approximations to these analytical results. The analyses allow us to get more insight into the impact of various factors on the performance of RAQM. Numerical simulations confirm the validity of our analyses and exhibit the performance advantage of RAQM over similar modulation techniques.