Recursive Kalman Filter Algorithm Research Articles

Numerical Gaussian Process Kalman Filtering for Spatiotemporal Systems

We present a novel Kalman filter for spatiotemporal systems called the numerical Gaussian process Kalman filter (NGPKF). Numerical Gaussian processes have recently been introduced as a physics informed machine learning method for simulating time-dependent partial differential equations without the need for spatial discretization while also providing uncertainty quantification of the simulation resulting from noisy initial data. We formulate numerical Gaussian processes as linear Gaussian state space models. This allows us to derive the recursive Kalman filter algorithm under the numerical Gaussian process state space model. Using two case studies, we show that the NGPKF is more accurate and robust, given enough measurements, than a spatial discretization based KF.

Modification of Recursive Kalman Filter Algorithm for Adaptive Prediction of Cyber Resilience for Industrial Systems

This paper describes an approach to modification of the recursive Kalman filter algorithm to obtain adaptive prediction of time series from industrial systems. To ensure cyber resilience of modern industrial systems, it is necessary to detect anomalies in their work at an early stage. For this, data from industrial systems are presented as time series, and an adaptive prediction model combined with machine learning classification algorithm applies to identify anomalies. The effectiveness of the proposed approach is confirmed experimentally.

Online thermal parameter identification for permanent magnet synchronous machines

Temperature monitoring of permanent magnet synchronous machines (PMSMs) is of great importance because high temperatures can significantly shorten the lifetimes of motor components. Accurate temperature predictions can be achieved using reduced-order lumped parameter thermal networks (LPTNs) with accurate thermal parameters. In this study, an online estimation method based on the recursive Kalman filter algorithm is introduced for online identification of the thermal resistances in a three-node LPTN representing motor stator iron, stator winding and permanent magnet. The identification procedure requires a rotor temperature measurement, which is provided by an accurate pulse-width modulation-based estimation method. The proposed methodology is experimentally validated and applied to real-time fault detection of the motor cooling system.

Statistical methods for forecasting daily snow depths and assessing trends in inter-annual snow depth dynamics

This paper introduces a time-varying parameter regression model for modeling, forecasting, and assessing inter-annual trends in daily snow depths. The time-varying parameter regression is written in a simple state-space representation and forecasted using a Kalman filter. The recursive Kalman filter algorithm updates the time-varying parameter sequentially when a new data point becomes available and is a flexible forecasting technique. The proposed method is applied to a time series of daily snow depth observations recorded over a 103 year period at a station in Napoleon, North Dakota. The forecasts of the final ten years of data perform well when compared to the actual daily snow depths. Inter-annual snow depth trends indicate an increase in mid-winter snow depths followed by an earlier spring ablation.

Examining the Kalman filter in the field of noise and interference with the non-Gaussian distribution

We have developed a sequential recursive Kalman Filter algorithm to filter data in the field of the non-Gaussian noise distribution to be used in measurement instruments. A special feature of the constructed Kalman Filter algorithm to filter data with the non-Gaussian noises is the absence of a need to determine a priori the statistical characteristics of noise. The applicability of the developed Kalman filtering procedure was tested by processing different distribution laws: the Cauchy, Pareto noises, normal and logistic distributions. The effectiveness of the devised filtering procedure is confirmed by applying the filter when processing experimental data with different laws of noise distribution. We have conducted approbation of the developed procedure for the Kalman filtering based on data obtained experimentally, with respect to the superposition of noise distribution laws. The a priori estimate for a filtering error when the number of iterations exceeds 30 tends to zero. The devised filtering procedure employing the Kalman filter could be used when performing the metrological certification of measuring instruments under industrial conditions. Under such circumstances, measuring information could become noisy due to various noises, including those that are not governed by the Gaussian distribution law. The filter could be used when processing data from control systems over state parameters, implemented on the principle of a magnitude threshold control. The applied aspect of the scientific result obtained implies the possibility of extending the scope of application of the classic Kalman filter in measurement instruments. This is a prerequisite for the development of a generic filtering algorithm using the Kalman filter.

Beating the Odds - A State Space Model for predicting match results in the Australian Football League

This thesis investigates whether state space models have the potential to pre- dict the outcome of Australian Rules Football matches and can produce significant positive return over the bookmaker’s odds. The point of departure is a sample of 18 Australian football teams over the period 2012 to 2016. Modeling and predicting a football match is a challenging task, since the model should incorporate two di ↵ er- ent random processes. Firstly, the evolution of parameters, i.e. the team strengths change over time as it incorporates changes in team composition, coaching, train- ing ground, injuries etc. Secondly, the distribution of ranking data with these time-varying propensities changes stochastically over time. Given that we cannot observe all team-specific and location-specific factors, a dynamic state space model for team strengths is introduced. The team strengths are assumed to follow an order-one autoregressive process and are estimated using a recursive Kalman filter algorithm. Smoothed state estimates are applicable for ranking teams and predict- ing future outcomes of the matches. We show that beating the bookmaker’s odds is a challenging task indicating that the betting markets are e cient. Keywords : Sport Analytics; Kalman Filter Algorithm; State Space models; Predictive inference; Ranking; Australian Rules Football.

Change Point Detection and Estimation of the Two-Sided Jumps of Asset Returns Using a Modified Kalman Filter

In the first part of the paper, the positive and negative jumps of NASDAQ daily (log-) returns and three of its stocks are estimated based on the methodology presented by Theodosiadou et al. 2016, where jumps are assumed to be hidden random variables. For that reason, the use of stochastic state space models in discrete time is adopted. The daily return is expressed as the difference between the two-sided jumps under noise inclusion, and the recursive Kalman filter algorithm is used in order to estimate them. Since the estimated jumps have to be non-negative, the associated pdf truncation method, according to the non-negativity constraints, is applied. In order to overcome the resulting underestimation of the empirical time series, a scaling procedure follows the stage of truncation. In the second part of the paper, a nonparametric change point analysis concerning the (variance–) covariance is applied to the NASDAQ return time series, as well as to the estimated bivariate jump time series derived after the scaling procedure and to each jump component separately. A similar change point analysis is applied to the three other stocks of the NASDAQ index.

Multisensor-Based Periodic Estimation in Sensor Networks With Transmission Constraint and Periodic Mixed Storage

In this paper, we consider a periodic estimation problem in sensor networks with a shared communication channel. The transmission constraint is inevitable in a single-channel-based sensor network if the sensors are heterogeneous or deployed far away from each other. A novel stochastic competitive transmission strategy is presented to deal with the transmission constraint, such that the sensors communicate with the fusion center (FC) in a strict asynchronous manner. A periodic mixed storage strategy combing the zero-input and the hold-input mechanisms is presented to describe periodic updating of the stored information in the sensors' buffers. A recursive Kalman filtering algorithm is derived for the FC to periodically generate estimates of state variables describing an object by using a linear continuous-time stochastic model. Two simulation examples are presented to show the effectiveness of the proposed results.

Coordination mechanism based on mobile actuator design for wireless sensor and actuator networks

Wireless sensor and actuator networks combine a large number of sensors and a lower number of actuators that are connected with wireless medium, providing distributed sensing and executing appropriate tasks in a special region of interest. To accomplish effective sensing and acting tasks, efficient coordination mechanism among the nodes is required. As an attempt in this direction, this paper develops a collaborative control and estimation mechanism, which addresses the nodes coordination in a distributed manner. First, we propose a regional controllability-based virtual force algorithm as an actuator deployment strategy to enhance area coverage after an initial random placement of actuators. During this process, a dynamic coordination mechanism is adopted to control nodes. This mechanism incorporates two components, namely, proportional-integral-derivative neural network and recursive least squares-based Kalman filter algorithms. Taking advantage of feedback control and online learning technology, the proposed coordination mechanism schedules the corresponding nodes on the basis of the characteristics of current events, utilizes proportional-integral-derivative neural network controller inside each actuator to improve system transient and steady-state responses, and deals with system state/parameter estimation problems according to the recursive least squares-based Kalman filter algorithm, so as to achieve better control accuracy. Simulations demonstrate the effectiveness of our proposed methods. Copyright © 2013 John Wiley & Sons, Ltd.

Fault Diagnosis of Induction Motors Using a Recursive Kalman Filtering Algorithm

This study describes an adaptive order-tracking fault diagnosis method using recursive Kalman filtering algorithm. In this paper, a high-resolution order tracking technique based on adaptive Kalman filter is proposed for detecting the fault in an induction motor bearing. The order tracking problem has been treated as the tracking of frequency-varying bandpass signals. The algorithm is implemented on the real digital signal obtained from the vibration of induction motor to evaluate the efficiency of the proposed method. Ordered amplitudes are estimated with high-accuracy when experimental implementation is done. The results of the experiments indicate that the proposed methodology has been validated for several cases in fault diagnosis of an induction motor

Tool wear monitoring using artificial neural network based on extended Kalman filter weight updation with transformed input patterns

The condition of the tool in a turning operation is monitored by using artificial neural network (ANN). The recursive Kalman filter algorithm is used for weight updation of the ANN. To monitor the status of the tool, tool wear patterns are collected. The patterns are transformed from n-dimensional feature space to a lower dimensional space (two dimensions). This is done by using two discriminant vectors $${\varphi_{1 }}$$ and $${\varphi_{2}}$$ . These discriminant vectors are found by optimal discriminant plane method. Thirty patterns are used for training the ANN. A comparison between the classification performances of the ANN trained without reducing the dimensions of the input patterns and with reduced dimensions of the input patterns is done. The ANN trained with transformed tool wear patterns gives better results in terms of improved classification performance in less iteration, when compared with the results of the ANN trained without transforming the dimensions of the input patterns to a lower dimension.

Algorithms of Mobile Object Location with Satellite Systems

Comparison of tow most frequently used algorithms for mobile object place location with satellite systems is shown in this work. First is the minimum mean-square (MMS) recursive algorithm. Second is recursive Kalman filtering algorithm. Estimation of algorithms was obtained by modeling mobile object place location with satellite systems in various dynamic and noise signal situations. Is show, that no one of algorithms is working perfect in all situations and thy can be used complex in mobile systems. Ill. 5, bibl. 4 (in English, summaries in Lithuanian, English, Russian).

An application of a recursive Kalman filtering algorithm in rotating machinery fault diagnosis

In this paper, an application of adaptive order tracking fault diagnosis technique based on recursive Kalman filtering algorithm is presented. Order tracking fault diagnosis technique is one of the important tools for fault diagnosis of rotating machinery. Conventional methods of order tracking are primarily based on Fourier analysis with reference to shaft speed. In this study, a high-resolution order tracking method with adaptive Kalman filter is used to diagnose the fault in a gear set and damaged engine turbocharger wheel blades. The adaptive Kalman filtering algorithm can overcome the problems encountered in conventional methods. The problem is treated as the tracking of frequency-varying bandpass signals. Ordered amplitudes can be calculated with high resolution after experimental implementation. Experiments are also carried out to evaluate the proposed system in gear-set defect diagnosis and engine turbocharger wheel blades damaged under various conditions. The experimental results indicate that the proposed algorithm is effective in fault diagnosis of both cases.

A hybrid wavelet-Kalman filter method for load forecasting

Abstract This paper presents a wavelet transform method for load forecasting. The stochastic nature of the wavelet coefficients for the daily load variation is studied by the decomposition scheme of multiresolution analysis (MRA). The study indicates that the stochastic process of the wavelet coefficients can be modeled as a random walk process. Therefore, the wavelet coefficients are modeled as the state variables of Kalman filters. The best estimation of the wavelet coefficients is obtained by the recursive Kalman filter algorithm. The predicted daily load is the inverse of the predicted wavelet coefficients. Based on the above procedure, two models (weather insensitive and sensitive models) are presented in this paper. Results from an actual system are also presented.

Guanidinium-induced differential kinetic denaturation of alkaline phosphatase isozymes

This paper examines the solution kinetics of bovine intestinal and liver alkaline phosphatase (ALP) isozymes. 4-Methylumbelliferyl phosphate is used as the substrate to study the differential kinetic behavior of ALP isozymes in the presence of guanidinium hydrochloride, a denaturant. The recursive Kalman filter algorithm for parameter estimation is used for analysis of the resulting kinetic data. A two-component first-order kinetic model with a zero-order component is used to successfully quantify intestinal and liver isozymes in synthetic mixtures. This work serves as a basis for the development of an electrophoresis separation method for ALP isozyme quantification with differential kinetic detection.