Parameter estimation for a bilinear time series model

Journal ArticleABSTRACT This paper presents a direct approach to the estimation of the parameters associated with a bilinear time series model. The approach depends critically on the expressions for certain higher-order statistics of the signals that satisfy the bilinear model. These expressions are linear in most of the parameters of the model. The parameters are then estimated from an overdetermined set of equations. Results of an experiment that employs our technique and demonstrates its good properties are also included in the paper

Estimation of Autoregressive Parameters from Noisy Observations Using Iterated Covariance Updates

Estimating the parameters of the autoregressive (AR) random process is a problem that has been well-studied. In many applications, only noisy measurements of AR process are available. The effect of the additive noise is that the system can be modeled as an AR model with colored noise, even when the measurement noise is white, where the correlation matrix depends on the AR parameters. Because of the correlation, it is expedient to compute using multiple stacked observations. Performing a weighted least-squares estimation of the AR parameters using an inverse covariance weighting can provide significantly better parameter estimates, with improvement increasing with the stack depth. The estimation algorithm is essentially a vector RLS adaptive filter, with time-varying covariance matrix. Different ways of estimating the unknown covariance are presented, as well as a method to estimate the variances of the AR and observation noise. The notation is extended to vector autoregressive (VAR) processes. Simulation results demonstrate performance improvements in coefficient error and in spectrum estimation

CAMP: An Algorithm to Recover Sparse Signals with Unknown Clustering Pattern Using Approximate Message Passing

Recovering clustered sparse signals with an unknown sparsity pattern for the single measurement vector (SMV) problems is considered. The notion of sparsity in this context is referred to the signals having very few non-zero elements in some known basis. In the SMV, the objective is to recover a sparse or compressible signal from a small set of linear non-adaptive measurements. The case considered in this paper is that the signal of interest is not only sparse but also has an unknown clustered pattern, which occurs in many practical situations. In this case, we propose a sparse Bayesian learning algorithm simplified by the approximate message passing to reduce the complexity of the algorithm. In order to encourage the probably existing clustered sparsity pattern, we define a prior which provides a measure of contiguity over the supports of the solution. We refer to the proposed algorithm as CAMP, where the letter C stands for clustered sparsity pattern and AMP denotes approximate message passing. Simulation results show an encouraging result

Exploration vs. Data Refinement via Multiple Mobile Sensors

We examine the deployment of multiple mobile sensors to explore an unknown region to map regions containing concentration of a physical quantity such as heat, electron density, and so on. The exploration trades off between two desiderata: to continue taking data in a region known to contain the quantity of interest with the intent of refining the measurements vs. taking data in unobserved areas to attempt to discover new regions where the quantity may exist. Making reasonable and practical decisions to simultaneously fulfill both goals of exploration and data refinement seem to be hard and contradictory. For this purpose, we propose a general framework that makes value-laden decisions for the trajectory of mobile sensors. The framework employs a Gaussian process regression model to predict the distribution of the physical quantity of interest at unseen locations. Then, the decision-making on the trajectories of sensors is performed using an epistemic utility controller. An example is provided to illustrate the merit and applicability of the proposed framework

Sparse Recovery with Unknown Sparsity Pattern via Multiple Measurement Vectors

In this work, we investigate finding the supports of sparse signals via multiple measurement vectors (MMVs). MMV can be thought as a collection of single measurement vectors (SMVs), in which all the SMVs share the same sparsity pattern, referred to as joint sparsity in the literature. The term sparse is referred to the signals that have very few non-zero (active) elements. The SMV problem is essentially a computational problem related to compressive sensing (CS) with the core idea of providing the possibility of measuring and representing a sparse or compressible signal from a small set of non-adaptive linear measurements. Here, we first propose a hierarchical Bayesian model to solve the MMV problem in the presence of noise. Our model decouples the signal into two parts; the supports of the solution and the amplitudes of the non-zero elements in the solution. Supports of the signal are the location of non-zero elements in the solution. In some applications such as magnetoencephalography (MEG), the signal of interest is not only sparse but also exhibits a clustered sparsity pattern. For example, MEG investigates the locations where most brain activities are produced. The brain activities exhibit contiguity, meaning that they occur in localized regions. Such unknown clustered sparsity pattern can be considered as a prior information in our proposed model. For this purpose, we modify our model by incorporating a parameter that accounts for the measure of contiguity (number of transitions) in the supports of the solution. The emphasizing factor on the contiguity measure of the supports will also be learned in our algorithm. Based on the experimental results, we show that our model is capable of learning the unknown sparsity clustered pattern. In this case, we evaluate the performance of our algorithm via receiver operating curves (ROCs)

New Bayesian Compressive Sensing Algorithms for Sparse Signal Recovery

Compressive sensing (CS) is one of the evolving areas in signal acquisition and reconstruction with many applications including the study of brain activities, recovery of multi-band signals, separating the foreground and background components from the collection of noisy frames of a video recording, reconstruction of hand-written digits, taking images using one-pixel camera, and so forth. It is a promising technique in processing compressible or sparse signals by requiring far few samples than the well-known Nyquist rate. Sparse signals have very few non-zero elements. In CS the goal is to efficiently measure and then reconstruct the signal under the assumption that the underlying signal of interest is sparse but the number and location of the non-zeros are unknown. Here, we provide some of our recently proposed algorithms in this area using Bayesian approach. Bayesian learning models are powerful and flexible to incorporate the prior knowledge on the characteristics of the underlying signals. We evaluate the performance of our proposed algorithms compared to other existing algorithms in terms of the detection and false-alarm rate via receiver operating curves (ROC) on the synthetically generated data. We also illustrate the performance based on some real-world data

Bayesian Compressive Sensing of Sparse Signals with Unknown Clustering Patterns

We consider the sparse recovery problem of signals with an unknown clustering pattern in the context of multiple measurement vectors (MMVs) using the compressive sensing (CS) technique. For many MMVs in practice, the solution matrix exhibits some sort of clustered sparsity pattern, or clumpy behavior, along each column, as well as joint sparsity across the columns. In this paper, we propose a new sparse Bayesian learning (SBL) method that incorporates a total variation-like prior as a measure of the overall clustering pattern in the solution. We further incorporate a parameter in this prior to account for the emphasis on the amount of clumpiness in the supports of the solution to improve the recovery performance of sparse signals with an unknown clustering pattern. This parameter does not exist in the other existing algorithms and is learned via our hierarchical SBL algorithm. While the proposed algorithm is constructed for the MMVs, it can also be applied to the single measurement vector (SMV) problems. Simulation results show the effectiveness of our algorithm compared to other algorithms for both SMV and MMVs

Source Localization and Room Mapping Using Information Derived from Independent Component Analysis

Convolutive independent component analysis (ICA) algorithms, which have proven capable at separating convolutively mixed signals, can also provide information about the geometry of the setting. This geometry includes source location information and wall locations (room shape). From the multi-input/multi-output impulse responses learned from convolutive ICA, peaks indicating direct path or reflection delays are extracted. The location of sensors (or sources) is obtained using hyperbolic geometry based on direct path time delays. Delays from re-flected paths learned from the impulses responses correspond geometrically to ellipses, which are tangent at the reflecting point. Ellipse tangent directions are clustered to determine wall locations. Following a summary of the method, experi-ments are presented on actual room measurements

Anomaly Detection on Small Wind Turbine Blades Using Deep Learning Algorithms

Wind turbine blade maintenance is expensive, dangerous, time-consuming, and prone to misdiagnosis. A potential solution to aid preventative maintenance is using deep learning and drones for inspection and early fault detection. In this research, five base deep learning architectures are investigated for anomaly detection on wind turbine blades, including Xception, Resnet-50, AlexNet, and VGG-19, along with a custom convolutional neural network. For further analysis, transfer learning approaches were also proposed and developed, utilizing these architectures as the feature extraction layers. In order to investigate model performance, a new dataset containing 6000 RGB images was created, making use of indoor and outdoor images of a small wind turbine with healthy and damaged blades. Each model was tuned using different layers, image augmentations, and hyperparameter tuning to achieve optimal performance. The results showed that the proposed Transfer Xception outperformed other architectures by attaining 99.92% accuracy on the test data of this dataset. Furthermore, the performance of the investigated models was compared on a dataset containing faulty and healthy images of large-scale wind turbine blades. In this case, our results indicated that the best-performing model was also the proposed Transfer Xception, which achieved 100% accuracy on the test data. These accuracies show promising results in the adoption of machine learning for wind turbine blade fault identification

VERY FAST TREE-STRUCTURED VECTOR QUANTIZATION

Very fast tree-structured vector quantization employs scalar quantization decisions at each level, but chooses the dimension on which to quantize based on the coordinate direction of maximum variance. Because the quantization is scalar, searches are no more complex than scalar quantization - providing significant improvement in complexity over full-searched or even tree-structured vector quantization - but the method preserves the shape and memory advantages of conventional vector quantization. However, the space filling advantage of VQ is forfeited, since each Voronoi cell is a rectangular cuboid