Kalman Filter Theory Research Articles

Kriging-based multi-fidelity optimization via information fusion with uncertainty

In this paper, a Multi-fidelity optimization method via information fusion with uncertainty (MFOIFU) is proposed. MFOIFU combines prediction uncertainty of kriging and model uncertainty, aiming at reducing computational cost of optimization and guaranteeing reliability of the optima. Firstly, the uncertainty of Low-fidelity (LF) and High-fidelity (HF) models is confirmed, respectively. After that, the optimal estimation theory of Kalman filter is employed to fuse information from LF and HF models. Then, the fused model is optimized and a distinctive updating strategy is presented to supplement feasible solutions. The newly introduced MFOIFU is verified through eight benchmark examples. Results showed that MFOIFU has some advantages over the Single high-fidelity optimization (SHO) method and some of the well-established multi-fidelity methods on computational expense and optimization efficiency. Finally, the MFOIFU method is successfully applied to the shell structure design of an Autonomous underwater vehicle (AUV).

Research of Snr Estimation and Prediction Method Used in Cognitive Radio

Cognitive radio is widely researched and concerned because of its cognitive and reconfigurable features. Cognitive radio can judge and evaluate channel quality, and adjust communication parameters in time to adapt to channel changes. One of the key factors to evaluate the channel status is the signal-to-noise ratio (SNR).This paper introduces a SNR estimation algorithm (M2M4 method), on the basis of Kalman filter theory, the SNR prediction algorithm is induced. The simulation results show that in the range of SNR (0 ~ 15dB), the estimation and prediction method exhibited low error rates, and the channel quality can be assessed in real time, so that the method can be used to estimate the channel quality of cognitive radio communication system.

Entropy optimization based filtering for non-Gaussian stochastic systems

This paper is concerned with the entropy optimization based filter design for a class of multivariate dynamic stochastic systems with simultaneous presence of non-Gaussian process noise and measurement noise. The filter consists of time update and measurement update two steps, where the selection of the filter gain in the measurement update equation is a key issue to be addressed. Different from the classic Kalman filter theory, entropy rather than variance is employed as the filtering performance criterion due to the non-Gaussian characteristic of the estimation error. Following the establishment of the relationship between the probability density functions of random noises and estimation error, two kinds of entropy based performance indices are provided. On this basis, the corresponding optimal filter gains are obtained respectively by using the gradient optimization technique. Finally, some numerical simulations are provided to demonstrate the effectiveness of the proposed filtering algorithms.

Metrics unreliability and marketing overspending

The adverse consequences of measurement unreliability on statistical issues (e.g., inconsistency, attenuation bias) are well known. Yet there exists sparse literature, if any, on how unreliable metrics affect strategic marketing decisions: optimal marketing budget, its optimal allocation to advertising and promotions, and overspending. Consequently, researchers and managers do not know: How to estimate dynamic demand models using unreliable data? How to optimally combine multiple noisy and biased metrics? How to optimally set the total marketing budget and optimally allocate it to advertising and promotions activities using unreliable sales metrics?To answer these open questions, first, based on Kalman filtering theory, we show how to estimate and infer dynamic demand models using unreliable sales metrics. Then, we furnish evidence of significant measurement noise in both retail audit and company's internal data to track brand sales. We replicate these results across six largest political regions in the emerging Indian markets for a major hair care brand. Next, we analytically derive the optimal weights to combine noisy and biased metrics to infer the latent demand. This result uncovers a counter-intuitive insight that two independent noisy metrics are better than one even when the second metric is noisier. In other words, a composite metric serves as noise reduction device as it is more reliable than individual noisy metrics. Subsequently, we derive closed-form expressions for the optimal budget and its optimal allocation to advertising and promotions activities in the presence of unreliable sales metrics. Based on these results, we discover that marketing overspending increase as metrics unreliability increases. Furthermore, overconfidence —the presumption that the metrics are reliable— leads to overspending on advertising and promotions. Managers should reduce advertising and promotional spending when sales metrics are noisy. Finally, we provide a simple correction factor that managers can use to eliminate overspending.

TDOA/FDOA based target tracking with imperfect position and velocity data of distributed moving sensors

This paper addresses the target tracking problem using time difference of arrival (TDOA) and frequency difference of arrival (FDOA) measured by moving sensor network whose position and velocity are noise contaminated. It is a known fact that the existing approaches to this problem still have two unsolved technical issues; the unsatisfactory convergence behavior of the tracking filter mainly caused by severe nonlinearity of the problem itself and the tracking performance degradation due to the sensor position and velocity errors. In order to resolve these matters radically, the given target tracking problem is formulated as the robust state estimation problem of the linear system with stochastic uncertainties in its measurement matrix and solved by using the robust Kalman filter theory. The proposed scheme enables us to overcome the inherent limitations of the conventional nonlinear filters for its linear filter structure. It can also prevent the performance degradation due to imperfect sensor position and velocity information. Through the simulations, the effectiveness and reliable target tracking performance of the proposed method are demonstrated.

Bootstrapping the Ultimate Claims of Cumulative Claims Payments and Incurred Losses Data Using Kalman-Filter Theory

The prediction of outstanding loss liabilities for non-life run-off portfolios and the quantification of the prediction error is one of the most important actuarial tasks in non-life insurance. In this paper we consider this prediction problem in a bivariate context. More precisely, we derive the predictive bootstrap distribution of the aggregated claims reserve based on cumulative claims payments and incurred losses data using Kalman-filter theory. With the predictive bootstrap distribution we are able to calculate all risk measures such as Value-at-Risk, Expected-Shortfall or Conditional-Tail-Expectation. An example is given at the end with a calculation of the bootstrap distribution and various risk measures are presented.

Flow field estimation analysis based on the Kalman filter FEM for selection of tidal stream power generator locations

In this paper, we present a shallow water flow field estimation analysis, based on the Kalman filter FEM, for locating the optimal positions for tidal stream power generation systems. In our flow field analysis, we adopt the shallow water equation as the governing equation. The Galerkin and the selective lumping methods are employed as discretization techniques in space and time, respectively. The Kalman filter theory is applied to estimate the flow field. As a numerical example, we carry out a flow estimation analysis for Tokyo Bay. The high estimation accuracy of the flow field estimation based on the Kalman filter FEM is confirmed by comparison with conventional FEM. The electric power generation potential is also computed using the estimated flow field.

Distribution Voltage Regulation Through Active Power Curtailment With PV Inverters and Solar Generation Forecasts

Distribution voltage profiles are subjected to overvoltage limit violations from high penetration of grid-connected photovoltaic (PV) systems. Such voltage rises seen at the point of PV interconnection can be mitigated by adaptively changing the active and/or reactive power injection from the PV inverter. This work proposes a local voltage regulation technique that utilizes very short-term (15 s) PV power forecasts to circumvent imminent upper voltage limit violation or an overvoltage scenario. To provide these PV generation forecasts, a hybrid forecasting method is formulated based on Kalman filter theory, which applies physical PV generation modeling using high-resolution (15 s) data from on-site measurements. The proposed algorithm employs an active power curtailment based on these PV power forecasts, when the reactive power estimate given by a droop-based method cannot provide the desired voltage regulation within predefined power factor limits. The curtailment threshold values are calculated in such a way that this voltage regulation technique can reduce possible voltage limit violations. The effectiveness of the proposed method is demonstrated with case studies developed on a standard test feeder with realistic load and PV generation profiles.

東京湾における潮流発電ポテンシャル算定に対するカルマンフィルタFEMの適用

In recent years, tidal stream power generation is attracting attention as renewable energy. When a turbine submerged in the sea is rotated by a tidal current, kinetic energy is transformed to electric energy in this power generation method. In this paper, we present a flow field estimation analysis based on the Kalman filter FEM for locating the optimal positions for tidal stream power generation systems. We employed the shallow water equation as the governing equation. The Galerkin and the selective lumping methods are used as discretization techniques in space and time, respectively. The Kalman filter theory is applied to estimate the flow field. As a numerical example, we carried out a flow estimation analysis for Tokyo Bay and the electric power generation potential is calculated using the estimated flow field. It was confirmed that the estimation accuracy of the flow field estimation analysis by the Kalman filter FEM is higher than that by the conventional FEM.

Study on high-precision regional monitoring method of high-grade highways subsidence under the influence of underground mining

High-grade highways are the foundation of regional economic development. How to monitor the deformation of high-grade highways under the influence of underground mining and guarantee their safe operation is very important and is directly relevant to regional economic development. Considering that Differential interferometric synthetic aperture radar (D-InSAR) technology has low monitoring accuracy around the maximum subsidence and high-accuracy levelling can only monitor the deformation of finite number points, the method of assimilating the D-InSAR data and levelling monitoring data based on Kalman filtering theory is proposed to improve precision of regional monitoring. Research results indicate that data assimilation results based on ensemble Kalman filter are much better than the inversion results and D-InSAR data. When applied to Zouji Highway of Jining, the total RMS is 17.7 mm after assimilating the D-InSAR data and levelling monitoring data, which can meet accuracy requirements of deformation monitoring of high-grade highways. Research results are of theoretical and practical significance to guarantee safe operation of high-grade highways under the influence of mining activities.

A multi-functional dynamic state estimator for error validation: measurement and parameter errors and sudden load changes

We propose a new and efficient algorithm to detect, identify, and correct measurement errors and branch parameter errors of power systems. A dynamic state estimation algorithm is used based on the Kalman filter theory. The proposed algorithm also successfully detects and identifies sudden load changes in power systems. The method uses three normalized vectors to process errors at each sampling time: normalized measurement residual, normalized Lagrange multiplier, and normalized innovation vector. An IEEE 14-bus test system was used to verify and demonstrate the effectiveness of the proposed method. Numerical results are presented and discussed to show the accuracy of the method.

Robust consensus for linear multi‐agent systems with noises

This study investigates robust consensus problem for multi-agent systems (MASs) with both system and communication noises. The agent state is estimated based on the noisy measurement information by applying Kalman-filtering theory, and then the estimated state is sent to the neighbour agents through a noisy communication environment. A consensus protocol is proposed based on the relative estimated state, under which the consensus error of the MASs can be characterised precisely via the unique solution of a Lyapunov equation. In addition, the consensusability via dynamic output feedback control of the MASs without noises is studied. Finally, simulation examples are given to show the correctness of the proposed results.

Active disturbance rejection control for voltage stabilization in open-cathode fuel cells through temperature regulation

Temperature regulation is an important control challenge in open-cathode fuel cell systems. In this paper, a feedback controller, combined with a novel output-injection observer, is designed and implemented for fuel cell stack temperature control. The first functionality of the observer is to smooth the noisy temperature measurements. To this end, the observer gain is calculated based on Kalman filter theory which, in turn, results in a robust temperature estimation despite temperature model uncertainties and measurement noise. Furthermore, the observer is capable of estimating the output voltage model uncertainties. It is shown that temperature control not only ensures the fuel cell temperature reference is properly tracked, but, along with the uncertainty estimator, can also be used to stabilize the output voltage. Voltage regulation is of great importance for open-cathode fuel cells, which typically suffer from gradual voltage decay over time due to their dead-end anode operation. Moreover, voltage control ensures predictable and fixed fuel cell output voltages for given current values, even in the presence of disturbances. The observer stability is proved using Lyapunov theory, and the observer's effectiveness in combination with the controller is validated experimentally. The results show promising controller performances in regulating fuel cell temperature and voltage in the presence of model uncertainties and disturbances.

Nonlinear state estimation for suspension control applications: a Takagi-Sugeno Kalman filtering approach

A new nonlinear state estimation approach, which combines classical Kalman filter theory and Takagi-Sugeno (TS) modeling, is proposed in this paper. To ensure convergence of the TS observer, conditions are derived that explicitly account for the TS model's confined region of validity. Thereby, the secured domain of attraction (DA) of the TS error dynamics is maximized within given bounds. The TS Kalman filtering concept is then applied to a hybrid vehicle suspension configuration, whose nonlinear dynamics are exactly represented by a continuous-time TS system. The benefit of the novel estimation technique is analyzed in comparison with the well-known EKF and UKF variants in simulations and experiments of a passive and an actively controlled suspension configuration in a quarter-car set-up. Employing a real road profile as disturbance input, the TS Kalman filter shows the highest estimation quality of the concepts studied. Moreover, as its computational complexity adds up to only one third of the one involved with the classical methods, the new approach operates remarkably efficient.

Robust weighted fusion steady-state kalman predictors with uncertain noise variances

In this paper, a direct approach of designing robust weighted fusion steady-state Kalman predictors with uncertain noise variances is presented. Based on the steady-state Kalman filtering theory, using the minimax robust estimation principle, the local and six weighted fusion robust steady-state Kalman predictors are proposed based on the worst case systems with the conservative upper bounds of noise variances. They include the three robust weighted state fusers, two robust weighted measurement fusers, and a modified robust covariance intersection (CI) fuser. Their actual prediction error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. A Lyapunov equation approach for robustness analysis and the concept of the robust accuracy are presented and their robust accuracy relations are proved. A simulation example verifies the accuracy relations and robustness.

Observer-based robust consensus control for multi-agent systems with noises

This study deals with the problem of consensus error calculation for linear multi-agent systems (MASs) with system noises and measurement noises. It is supposed that there exist communication noises when the information exchanges among distinct agents. The agents cannot reach consensus due to the existence of the system noises. We aim to design proper distributed control protocol to calculate the consensus error for the MASs. The states of each agent and its neighbors are estimated by applying Kalman-filtering theory. The distributed control protocol is designed by employing the estimated state information. Then the consensus error is calculated via the unique solution of a Lyapunov equation. Finally, a simulation example is presented to verify the correctness of the proposed results.

Trend Without Hiccups - A Kalman Filter Approach

Have you ever felt miserable because of a sudden whipsaw in the price that triggered an unfortunate trade? In an attempt to remove this noise, technical analysts have used various types of moving averages (simple, exponential, adaptive one or using Nyquist criterion). These tools may have performed decently but we show in this paper that this can be improved dramatically thanks to the optimal filtering theory of Kalman filters (KF). We explain the basic concepts of KF and its optimum criterion. We provide a pseudo code for this new technical indicator that demystifies its complexity. We show that this new smoothing device can be used to better forecast price moves as lag is reduced. We provide 4 Kalman filter models and their performance on the SP500 mini-future contract. Results are quite illustrative of the efficiency of KF models with better net performance achieved by the KF model combining smoothing and extremum position.

Robust Uncertainty Control of the Simplified Kalman Filter for Acoustic Echo Cancelation

One of the main difficulties in acoustic echo cancelation (AEC) is the adaptation strategy of the adaptive filter in different situations. Recently, the Kalman filter theory has been introduced to accommodate for the adaptation control in AEC applications, due to its optimal performance in many system identification problems. In this paper, a frequency-domain simplified Kalman filter for partitioned-block-based AEC is studied. The contribution is twofold. First, the relationship between the Kalman filter and an optimal variable step-size algorithm is revealed, which contributes to the motivation of this paper. Second, the influence of system uncertainty on the performance of the Kalman filter is analyzed, and a new uncertainty control method is developed. Simulation results confirm the superiority of the proposed method to the conventional ones.

カルマンフィルタ有限要素法による浅水域における流れ場の推定精度の検証（観測変数・観測点の数および位置が推定精度に与える影響）

In this study, the estimation of the flow field in open channel is carried out based on the finite element method and the Kalman filter theory. As the governing equation, the shallow water equation is employed, and the finite element and the selective lumping methods are applied to discretize the governing equation in space and time, respectively. The estimation of the distribution of the velosity vector and the water elevation is carried out by using the equations obtained by the Kalman filter theory. In the numerical experiments, the open channel flow is treated, and some examinations are carried out by changing the observation variables, number and posision of observation points.

305 カルマンフィルタ有限要素法による流れ場の推定解析における計測点配置に関する検討(OS4-2 次世代シミュレーション技術の開拓)

The Kalman filter developed by R. E. Kalman and R. S. Bucy is states estimation theory in the target domain and has been employed in various field of engineering. In general, observation data in any system include observation noise and the computational model include system noise. These noises can be eliminated by using a Kalman filter. The finite element equation is applied to derive the state transition matrix in the system equation of the Kalman filter. As the fundamental study, the estimation of the flow field in open channel is carried out based on the finite element method and the Kalman filter theory. In addition, as the governing equation, the shallow water equations are employed, and the finite element and the selective lumping methods are applied to discretize the governing equations in space and time, respectively. The open channel model is employed in the numerical experiment, and some examinations are carried out by changing the observation variables, number and position of observation points.