Kalman Smoother Algorithm Research Articles

Two-frame random phase shifting interferometry based on constrained Kalman filter without pre-filtering

This paper discusses a phase estimation algorithm in two-frame phase-shifting interferometry using a constrained Kalman filter without the need of pre-filtering operation for the background intensity removal. A state-space model is developed and state estimation is performed based on the extended Kalman filter. The Kalman smoother algorithm is utilized to improve the accuracy of state estimation. A comparative study is presented between the proposed and four state-of-art phase estimation methods. Both simulation and experimental results show good accuracy and noise robustness of the proposed method over a wide range of phase shifts.

Optimal frequency control for wind power-integrated power system based on parameter identification

Frequency control based on wind power is required by the grid code for maintaining system inertia level as well as frequency stability. However, synchronous generator (SG)-emulated frequency control of wind power will result in a nadir and second dip of frequency trajectory after a disturbance, which may threaten system safety. Optimizing the frequency trajectory of system to improve the nadir and avoid second dip usually relies on grid-wide information. But the information is hardly perfectly acquired in advance for real power system since it may change anytime. To address these problems, an optimal frequency control method for wind power-integrated power system based on parameter identification is proposed. Frequency characteristics of wind power-integrated are firstly analyzed based on the common frequency theory. Then the control framework of proposed method to eliminate the nadir and second dip of frequency trajectory is introduced. To realize this framework, system equivalent parameters like inertia and damp coefficient are identified by the extended Kalman smoother algorithm after each disturbance. These parameters are furtherly utilized to shape the transfer function of wind power-integrated power system as a first-order system. Finally, the implementation steps of proposed method are presented. The effectiveness of proposed method is verified by case studies.

An accurate target tracking method in wireless sensor networks

<span>Localization is a challenging research issue in various sectors of activity, particularly in dynamic indoor environment with high perturbation. Many existing localization techniques in wireless sensor networks are not efficient because of many constraints such as the high cost, the memory and energy limitation and the environmental noise effects. Thus, the development of novel methods of localization has become a great concern for the wireless sensor networks. In this paper, we propose a tracking method that combines regression tree and Kalman smoother filtering. Previously, regression tree has been suggested for static positioning by means of received signal strength indicator measurements. In this work, we employ this strategy to solve the mapping relation between these measurements and the target position by means of an optimized propagation model. Moreover, the predicted position considered as the observed information is introduced to the Kalman smoother algorithm, to have more precise state of the moving target. The proposed algorithm has been assessed and compared to other existing methods using real measurements of the received power by the moving target in an indoor environment. The evaluation shows that our solution outperforms other methods regarding localization accuracy.</span>

Adaptive Robust Least-Squares Smoothing Algorithm

The Kalman smoothing algorithm is widely use d in offline data processing in GNSS to improve filter calcu lation accuracy. When there are measurement outliers or b iased random models, the adaptive Kalman smoothing algo rithm can reduce their impact on the smoothing results to a certain extent. Nevertheless, the adaptive Kalman smoothi ng algorithm usually has difficulty obtaining optimal estim ation in a complex observation environment due to the inhe rent defects of the algorithm itself. Therefore, we propose a n adaptive robust least-squares smoothing algorithm. The row and column transformation of the least-square smooth noise covariance matrix is realized by constructing an orth ogonal space transformation matrix, and the noise covaria nce estimation problem of the Kalman filter is transformed into the problem of solving the variance covariance compo nent elements under a specific matrix structure. In additio n, by selecting the observation value with the largest stand ardized residual to determine whether it is gross error, we avoid the gross error misjudgment problem caused by the t wo-factor robust estimation method under least-square sm oothing, and further improve the smoothing accuracy. Fina lly, two experiments are studied to compare the performan ce of the new algorithm and the state-of-the-art algorithms. The proposed algorithm has demonstrated better perform ance in terms of robustness and estimation accuracy.

Study of Auditory Brain Cognition Laws-Based Recognition Method of Automobile Sound Quality.

The research shows that subjective feelings of people, such as emotions and fatigue, can be objectively reflected by electroencephalography (EEG) physiological signals Thus, an evaluation method based on EEG, which is used to explore auditory brain cognition laws, is introduced in this study. The brain cognition laws are summarized by analyzing the EEG power topographic map under the stimulation of three kinds of automobile sound, namely, quality of comfort, powerfulness, and acceleration. Then, the EEG features of the subjects are classified through a machine learning algorithm, by which the recognition of diversified automobile sound is realized. In addition, the Kalman smoothing and minimal redundancy maximal relevance (mRMR) algorithm is used to improve the recognition accuracy. The results show that there are differences in the neural characteristics of diversified automobile sound quality, with a positive correlation between EEG energy and sound intensity. Furthermore, by using the Kalman smoothing and mRMR algorithm, recognition accuracy is improved, and the amount of calculation is reduced. The novel idea and method to explore the cognitive laws of automobile sound quality from the field of brain-computer interface technology are provided in this study.

Semi-Blind Channel Estimation and Data Detection for Multi-Cell Massive MIMO Systems on Time-Varying Channels

We study the problem of semi-blind channel estimation and symbol detection in the uplink of multi-cell massive MIMO systems with spatially correlated time-varying channels. An algorithm based on expectation propagation (EP) is developed to iteratively approximate the joint a posteriori distribution of the unknown channel matrix and the transmitted data symbols with a distribution from an exponential family. This distribution is then used for direct estimation of the channel matrix and detection of data symbols. A modified version of the popular Kalman filtering algorithm referred to as KF-M emerges from our EP derivation and it is used to initialize the EP-based algorithm. Performance of the Kalman smoothing algorithm followed by KF-M is also examined. Simulation results demonstrate that channel estimation error and the symbol error rate (SER) of the semi-blind KF-M, KS-M, and EP-based algorithms improve with the increase in the number of base station antennas and the length of the transmitted frame. It is shown that the EP-based algorithm significantly outperforms KF-M and KS-M algorithms in channel estimation and symbol detection. Finally, our results show that when applied to time-varying channels, these algorithms outperform the algorithms that are developed for block-fading channel models.

Trend-Aware Proactive Caching via Tensor Train Decomposition: A Bayesian Viewpoint

Content caching at base stations is an effective solution to cope with the unprecedented data traffic growth by prefetching contents near to end-users. To proactively servicing users, it is of high importance to extract predictive information from data requests. In this paper, we propose an accurate content request prediction algorithm for improving the performance of edge caching systems. In particular, we develop a Bayesian dynamical model through which a complex nonlinear latent temporal trend structure in the content requests can be accurately tracked and predicted. The dynamical model also leverages tensor train decomposition to capture content-location interactions to further enhance the accuracy of predictions. To infer the model’s parameters, we derive an approximation of the posterior distribution based on variational Bayes (VB) method with an embedded Kalman smoother algorithm. Based on the predictions of the proposed model, we design a cost-efficient proactive cooperative caching policy which adaptively utilizes network resources and optimizes the content delivery. The advantage of the proposed caching scheme is demonstrated via numerical results using two real-world datasets, which show that the developed Bayesian dynamical model substantially outperforms reference methods that ignore the temporal trends and content-location interactions.

State Estimation of Hemodynamic Model for fMRI Under Confounds: SSM Method.

Through hemodynamic models, the change of neuronal state can be estimated from functional magnetic resonance imaging (fMRI) signals. Usually, there are confounds in the fMRI signal, which will degrade the performance of the estimation for the neuronal state change. For the reason, this paper introduces a state-space model with confounds, from a conventional hemodynamic model. In this model, a successive state estimation method requires a state value vector, an error covariance, an innovation covariance, and a cross covariance to be re-derived. Thus, a confounds square-root cubature Kalman smoothing (CSCKS) algorithm is proposed in this paper. We use a Balloon-Windkessel model to generate simulation data and add confounds signals to evaluate the performance of the proposed algorithm. The experiment results show that when the signal-to-interference ratio is less than 21 dB, the CSCKS proposed in this paper reduced estimation error to 16%, whereas the traditional algorithm reduced it to only 73%.

Robust Time-Varying Kalman State Estimators with Uncertain Noise Variances

This paper addresses the design of robust Kalman estimators (filter, predictor and smoother) for the time-varying system with uncertain noise variances. According to the unbiased linear minimum variance (ULMV) optimal estimation rule, the robust time-varying Kalman estimators are presented. Specially, two robust Kalman smoothing algorithms are presented by the augmented and non-augmented state approaches, respectively. They have the robustness in the sense that their actual estimation error variances are guaranteed to have a minimal upper bound for all admissible uncertainties of noise variances. Their robustness is proved by the Lyapunov equation approach, and their robust accuracy relations are proved. The corresponding steady-state robust Kalman estimators are also presented for the time-invariant system, and the convergence in a realization between the time-varying and steady-state robust Kalman estimators is proved by the dynamic error system analysis (DESA) method and the dynamic variance error system analysis (DVESA) method. A simulation example is given to verify the robustness and robust accuracy relations.

Estimating Non-stationary Common Factors: Implications for Risk Sharing

In this paper, we analyze and compare the finite sample properties of alternative factor extraction procedures in the context of non-stationary Dynamic Factor Models (DFMs). On top of considering procedures already available in the literature, we extend the hybrid method based on the combination of principal components and Kalman filter and smoothing algorithms to non-stationary models. We show that if the idiosyncratic noises are stationary, procedures based on extracting the factors using the non-stationary original series work better than those based on differenced variables. We apply the methodology to the analysis of cross-border risk sharing by fitting non-stationary DFM to aggregate Gross Domestic Product and consumption of a set of 21 industrialized countries from the Organization for Economic Co-operation and Development (OECD). The goal is to check if international risk sharing is a short- or long-run issue.

Functional Mixed-Effects Modeling of Longitudinal Duchenne Muscular Dystrophy Electrical Impedance Myography Data Using State-Space Approach.

Electrical impedance myography (EIM) is a quantitative and objective tool to evaluate muscle status. EIM offers the possibility to replace conventional physical functioning scores or quality of life measures, which depend on patient cooperation and mood. Here, we propose a functional mixed-effects model using a state-space approach to describe the response trajectories of EIM data measured on 16 boys with Duchenne muscular dystrophy and 12 healthy controls, both groups measured over a period of two years. The modeling framework presented imposes a smoothing spline structure on EIM data collected at each visit and taking into account of within subject correlations of these curves along the longitudinal measurements. The modeling framework is recast in a state-space approach, thereby allowing for the employment of computationally efficient diffuse Kalman filtering and smoothing algorithms for the model estimation, as well as the estimates of the posterior variance-covariance matrix for the construction of the Bayesian [Formula: see text] confidence bands. The proposed model allows us to simultaneously adjust for baseline variables, differentiate the longitudinal changes in the smooth functional response and estimate the subject and subject-time specific deviations from the population-averaged response curves. The code is made publicly available in the supplementary material. The modeling approach presented will potentially enhance EIM capability to serve as a biomarker for testing therapeutic efficacy in DMD and other clinical trials.

Discrimination of water quality monitoring sites in River Vouga using a mixed-effect state space model

The surface water quality monitoring is an important concern of public organizations due to its relevance to the public health. Statistical methods are taken as consistent and essential tools in the monitoring procedures in order to prevent and identify environmental problems. This work presents the study case of the hydrological basin of the river Vouga, in Portugal. The main goal is discriminate the water monitoring sites using the monthly dissolved oxygen concentration dataset between January 2002 and May 2013. This is achieved through the extraction of trend and seasonal components in a linear mixed-effect state space model. The parameters estimation is performed with both maximum likelihood method and distribution-free estimators in a two-step procedure. The application of the Kalman smoother algorithm allows to obtain predictions of the structural components as trend and seasonality. The water monitoring sites are discriminated through the structural components by a hierarchical agglomerative clustering procedure. This procedure identified different homogenous groups relatively to the trend and seasonality components and some characteristics of the hydrological basin are presented in order to support the results.

Phase derivative estimation from a single interferogram using a Kalman smoothing algorithm.

We report a technique for direct phase derivative estimation from a single recording of a complex interferogram. In this technique, the interference field is represented as an autoregressive model with spatially varying coefficients. Estimates of these coefficients are obtained using the Kalman filter implementation. The Rauch-Tung-Striebel smoothing algorithm further improves the accuracy of the coefficient estimation. These estimated coefficients are utilized to compute the spatially varying phase derivative. Stochastic evolution of the coefficients is considered, which allows estimating the phase derivative with any type of spatial variation. The simulation and experimental results are provided to substantiate the noise robustness and applicability of the proposed method in phase derivative estimation.

Short-Term Observation Data Process of all in View Based on the Kalman Smoothing Algorithm

All in view method is one of the important methods used for time synchronization, and it takes advantage of all the visible satellite time data for time synchronization at the same time. This paper analyzes all in view method and uses Kalman smoothing algorithm to deal with the observation data. This paper simulates the Kalman smoothing algorithm with the data from BIPM. The simulation comparison is made between Kalman smoothing algorithm and Vondrak smoothing algorithm, and the time-consuming comparison to deal with the same data is also been showed here. The simulation results show that, Kalman smoothing algorithm has almost the same accuracy of the Vondrak smoothing algorithm to deal with the observation data of all in view, but its time-consuming is shorter

On the influence of model nonlinearity and localization on ensemble Kalman smoothing

Ensemble‐based Kalman smoother algorithms extend ensemble Kalman filters to reduce the estimation error of past model states utilizing observational information from the future. Like the filters they extend, current smoothing algorithms are optimal only for linear models. However, the ensemble methods are typically applied with high‐dimensional nonlinear models, which also require the application of localization in the data assimilation. In this article, the influence of the model nonlinearity and of the application of localization on the smoother performance is studied. Numerical experiments show that the observational information can be successfully utilized over smoothing lags several times the error doubling time of the model. Localization limits the smoother lag by spatial decorrelation. However, if the localization is well tuned, the usable lag of the smoother, and hence the usable amount of observational information, is maximized. The localization reduces the estimation errors of the smoother even more than those of the filter. As the smoother reuses the transformation matrix of the filter, it profits from increases of the ensemble size more strongly than the filter. With respect to inflation and localization, the experiments also show that the same configuration that yields the smallest estimation errors for the filter without smoothing also results in the smallest errors of the smoothed states. Thus, smoothing only adds the lag as a further tunable parameter.

Modeling Bivariate Longitudinal Hormone Profiles by Hierarchical State Space Models

The hypothalamic-pituitary-adrenal (HPA) axis is crucial in coping with stress and maintaining homeostasis. Hormones produced by the HPA axis exhibit both complex univariate longitudinal profiles and complex relationships among different hormones. Consequently, modeling these multivariate longitudinal hormone profiles is a challenging task. In this article, we propose a bivariate hierarchical state space model, in which each hormone profile is modeled by a hierarchical state space model, with both population-average and subject-specific components. The bivariate model is constructed by concatenating the univariate models based on the hypothesized relationship. Because of the flexible framework of state space form, the resultant models not only can handle complex individual profiles, but also can incorporate complex relationships between two hormones, including both concurrent and feedback relationship. Estimation and inference are based on marginal likelihood and posterior means and variances. Computationally efficient Kalman filtering and smoothing algorithms are used for implementation. Application of the proposed method to a study of chronic fatigue syndrome and fibromyalgia reveals that the relationships between adrenocorticotropic hormone and cortisol in the patient group are weaker than in healthy controls. Supplementary materials for this article are available online.

Nonlinear System Identification of Floating Structures Using Time-Varying ARX-Based Volterra Model

This work presents a newapproach for nonlinear system identification of floating structures using time-varyingautoregressive with exogenous input (TVARX)–based Volterra model. This methodutilizes time series of measured wave heights as system input and surge motionas system output. Solution to the proposed approach is also proposed via Kalmansmoother algorithm. The efficacy of the proposed method is then applied in ascaled 1:100 model of a prototype truss spar. It is shown that surge motionobtained from the identification results has good agreement with theexperimental results either in time or frequency domain

ASSESSING THE FEASIBILITY OF UAV-BASED LIDAR FOR HIGH RESOLUTION FOREST CHANGE DETECTION

Abstract. Airborne LiDAR data has become an important tool for both the scientific and industry based investigation of forest structure. The uses of discrete return observations have now reached a maturity level such that the operational use of this data is becoming increasingly common. However, due to the cost of data collection, temporal studies into forest change are often not feasible or completed at infrequent and at uneven intervals. To achieve high resolution temporal LiDAR surveys, this study has developed a micro-Unmanned Aerial Vehicle (UAV) equipped with a discrete return 4-layer LiDAR device and miniaturised positioning sensors. This UAV has been designed to be low-cost and to achieve maximum flying time. In order to achieve these objectives and overcome the accuracy restrictions presented by miniaturised sensors a novel processing strategy based on a Kalman smoother algorithm has been developed. This strategy includes the use of the structure from motion algorithm in estimating camera orientation, which is then used to restrain IMU drift. The feasibility of such a platform for monitoring forest change is shown by demonstrating that the pointing accuracy of this UAV LiDAR device is within the accuracy requirements set out by the Australian Intergovernmental Committee on Surveying and Mapping (ICSM) standards.

Heart Rate Variability Dynamics During Low-Dose Propofol and Dexmedetomidine Anesthesia

Heart rate variability (HRV) has been observed to decrease during anesthesia, but changes in HRV during loss and recovery of consciousness have not been studied in detail. In this study, HRV dynamics during low-dose propofol (N = 10) and dexmedetomidine (N = 9) anesthesia were estimated by using time-varying methods. Standard time-domain and frequency-domain measures of HRV were included in the analysis. Frequency-domain parameters like low frequency (LF) and high frequency (HF) component powers were extracted from time-varying spectrum estimates obtained with a Kalman smoother algorithm. The Kalman smoother is a parametric spectrum estimation approach based on time-varying autoregressive (AR) modeling. Prior to loss of consciousness, an increase in HF component power indicating increase in vagal control of heart rate (HR) was observed for both anesthetics. The relative increase of vagal control over sympathetic control of HR was overall larger for dexmedetomidine which is in line with the known sympatholytic effect of this anesthetic. Even though the inter-individual variability in the HRV parameters was substantial, the results suggest the usefulness of HRV analysis in monitoring dexmedetomidine anesthesia.

Fixed-Interval Kalman Smoothing Algorithms in Singular State–Space Systems

Fixed-interval Bayesian smoothing in state---space systems has been addressed for a long time. However, as far as the measurement noise is concerned, only two cases have been addressed so far : the regular case, i.e., with positive definite covariance matrix; and the perfect measurement case, i.e., with zero measurement noise. In this paper we address the smoothing problem in the intermediate case where the measurement noise covariance is positive semi definite with arbitrary rank. We exploit the singularity of the model in order to transform the original state---space system into a pairwise Markov model with reduced state dimension. Finally, the a posteriori Markovianity of the reduced state enables us to propose a family of fixed-interval smoothing algorithms.