Application Of Kalman Filter Research Articles

On AUV Control with the Aid of Position Estimation Algorithms Based on Acoustic Seabed Sensing and DOA Measurements.

This article discusses various approaches to the control of autonomous underwater vehicles (AUVs) with the aid of different velocity-position estimation algorithms. Traditionally this field is considered as the area of the extended Kalman filter (EKF) application: It became a universal tool for nonlinear observation models and its use is ubiquitous. Meanwhile, the specific characteristics of underwater navigation, such as an incomplete sets of measurements, constraints on the range metering or even impossibility of range measurements, observations provided by rather specific acoustic beacons, sonar observations, and other features seriously narrow the applicability of common instruments due to a high level of uncertainty and nonlinearity. The AUV navigation system, not being able to rely on a single source of position estimation, has to take into account all available information. This leads to the necessity of various complex estimation and data fusion algorithms, which are the matter of the present article. Here we discuss some approaches to the AUV position estimation such as conditionally minimax nonlinear filtering (CMNF) and unbiased pseudo-measurement filters (UPMFs) in conjunction with velocity estimation based on the seabed profile acoustic sensing. The presented estimation algorithms serve as a basis for a locally optimal AUV motion control algorithm, which is also presented.

Применение фильтра Калмана в задачах трекинга воздушных объектов

Применение фильтра Калмана в задачах трекинга воздушных объектов

Implicitly Localized MCMC Sampler to Cope With Non-local/Non-linear Data Constraints in Large-Size Inverse Problems

Many practical applications involve the resolution of large-size inverse problems, without providing more than a moderate-size sample to describe the prior probability distribution. In this situation, additional information must be supplied to augment the effective dimension of the available sample. This is the role played by covariance localization in the large-size applications of the ensemble Kalman filter. In this paper, it is suggested that covariance localization can also be efficiently applied to an approximate variant of the Metropolis/Hastings algorithm, by modulating the ensemble members by the large-scale patterns of other members. Modulation is used to design a (global) proposal probability distribution (i)~that can be sampled at a very low cost (proportional to the size of the state vector, with a small integer coefficient),(ii)~that automatically accounts for a localized prior covariance, and (iii)~that leads to an efficient sampler for the augmented prior probability distribution or for the posterior probability distribution. The resulting algorithm is applied to an academic example, illustrating (i)~the effectiveness of covariance localization, (ii)~the ability of the method to deal with nonlocal/nonlinear observation operators and non-Gaussian observation errors, (iii)~the possibility to deal with non-Gaussian (even discrete) prior marginal distributions, by including (stochastic) anamorphosis transformations, (iv)~the reliability, resolution and optimality of the updated ensemble, using probabilistic scores appropriate to a non-Gaussian posterior distribution, and (v)~the scalability of the algorithm as a function of the size of the problem. The evaluation of the computational complexity of the algorithm suggests that it could become numerically competitive with local ensemble Kalman filters, even in the absence of nonlocal constraints, especially if the localization radius is large. All codes necessary to reproduce the example application described in this paper are openly available from github.com/brankart/ensdam.

Application of baseline constraint Kalman filter to BeiDou precise point positioning

This paper proposes a baseline constrained PPP method to enhance the performance. The approach is based on constrained Kalman filter, and applied to BeiDou PPP in static, pseudo-kinematic, real kinematic modes. Both zero baseline and short baseline constrained PPP are verified in static mode, while a marine geodesy environment is designed to evaluate the performance in kinematic mode. The experiment results show that, compared to the PPP without constraint, the baseline constrained PPP can significantly improve the positional accuracy. Furthermore, the accuracy of baseline constrained static PPP can reach centimetre level, while the kinematic PPP can reach decimetre level.

Application of augmented Kalman filter to identify unbalance load of rotor-bearing system: Theory and experiment

Rotor dynamic balancing technology with online, no start-stop, no trial weights is an important research topic in rotor dynamics, and its key problem is how to identify the rotor unbalance state online. Rotor unbalance parameter identification is often ill-conditioned mathematically, so a small amount of errors such as measurement and modeling will worsen the identification accuracy. For this reason, a new unbalance loads identification method using the rotor finite element (FE) model combined with augmented Kalman filter (AKF) algorithms is proposed. This method is a deterministic-stochastic, time-domain method and is insensitive to measurement and modeling errors. The research results show that the proposed method can well identify the unbalance parameters online and in real time. Meanwhile, the errors of dynamic model and measurement signal could be considered and effectively filtered out in real time, thus the accuracy of unbalance estimation is improved.

Application of Kalman filter to Model-based Prognostics for Solenoid Valve

Solenoid valves (SVs) are electromechanical components, which are used as actuators in various application environments and play crucial roles in control systems, and their breakdown may result in a system crash. Therefore, this paper explores a Kalman filter (KF)-based method to predict the remaining useful life (RUL) of SVs, so that the SVs can be replaced or maintained before their failure bringing a catastrophic consequence for engineering system. In this paper, a degradation signal is extracted from the driven current, which can be monitored conveniently with a non-contact current sensor. Based on an empirical linear degradation model, the KF is adopted to track the degradation state and the degradation rate and to capture the uncertainties. The Monte Carlo sampling and kernel density estimation are used to propagate the uncertainties and estimate the probability distribution of RUL, respectively. To verify our methods, a degradation experiment is designed. The experiment results show that the degradation signal extracted from the driven current can indeed reflect the degradation state of SVs. By comparing the proposed method with other state of the arts prognostic approaches, it shows that the proposed KF method preforms better and has a higher prediction accuracy than other methods.

NIRK-based Cholesky-factorized square-root accurate continuous-discrete unscented Kalman filters for state estimation in nonlinear continuous-time stochastic models with discrete measurements

This paper further advances the idea of accurate Gaussian filtering towards efficient unscented-type Kalman methods for estimating continuous-time nonlinear stochastic systems with discrete measurements. It implies that the differential equations evolving sigma points utilized in computations of the predicted mean and covariance in time-propagations of the Gaussian distribution are solved accurately, i.e. with negligible error. The latter allows the total error of the unscented Kalman filtering technique to be reduced significantly and gives rise to the novel accurate continuous-discrete unscented Kalman filtering algorithm. At the same time, this algorithm is rather vulnerable to round-off and numerical integration errors committed in each state estimation run because of the need for the Cholesky decomposition of covariance matrices involved. Such a factorization will always fail when the covariance's positivity is lost. This positivity lost issue is commonly resolved with square-root filtering implementations, which propagate not the full covariance matrix but its square root (Cholesky factor) instead. Unfortunately, negative weights encountered in applications of the accurate continuous-discrete unscented Kalman filter to high-dimensional stochastic systems preclude from designing conventional square-root methods. In this paper, we address this problem with low-rank Cholesky factor update procedures or with hyperbolic QR transforms used for yielding J-orthogonal square roots. Our novel square-root algorithms are justified theoretically and examined numerically in an air traffic control scenario.

A Simplified Model-Based State-of-Charge Estimation Approach for Lithium-Ion Battery With Dynamic Linear Model

The performance of model-based state-of-charge (SOC) estimation method relies on an accurate battery model. Nonlinear models are thus proposed to accurately describe the external characteristics of the lithium-ion battery. The nonlinear estimation algorithms and online parameter identification methods are needed to guarantee the accuracy of the model-based SOC estimation with nonlinear battery models. A new approach forming a dynamic linear battery model is proposed in this paper, which enables the application of the linear Kalman filter for SOC estimation and also avoids the usage of online parameter identification methods. With a moving window technology, partial least squares regression is able to establish a series of piecewise linear battery models automatically. One element state-space equation is then obtained to estimate the SOC from the linear Kalman filter. The experiments on a LiFePO4 battery prove the effectiveness of the proposed method compared with the extended Kalman filter with two resistance and capacitance equivalent circuit model and the adaptive unscented Kalman filter with least squares support vector machines.

Реализация расширенного фильтра Калмана для нелинейной модели двухзвенного маятника

Реализация расширенного фильтра Калмана для нелинейной модели двухзвенного маятника

Review of Kalman Filter Employment in the NAIRU Estimation

The aim of the paper is to provide a recent overview of Kalman filter employment in the non-accelerating inflation rate of unemployment (NAIRU) estimation. The NAIRU plays a key part in an economic system. A certain unemployment rate which is consistent with a stable rate of inflation is one of the conditions for economic system stability. Since the NAIRU cannot be directly observed and measured, it is one of the most fitting problems for the Kalman filter application. The search for original, NAIRU focused and Kalman filter employment studies was performed in three scientific databases: Web of Science, Scopus, and ScienceDirect. A sample of 152 papers was narrowed down to 25 studies, which were described in greater detail regarding the focus, methods, model features, limitations, and other characteristics. A group of studies using a purely statistical approach of decomposing unemployment into a trend and cyclical component was identified. The next group uses the reduced-form approach which is sometimes combined with statistical decomposition. In such cases, the models are usually based on the backward-looking Phillips curve. Nevertheless, the forward-looking, New Keynesian or rarely hybrid New Keynesian variant can also be encountered.

An Integrated Adaptive Kalman Filter for High-Speed UAVs

In order to solve the problems of filtering divergence and low accuracy in Kalman filter (KF) applications in a high-speed unmanned aerial vehicle (UAV), this paper proposed a new method of integrated robust adaptive Kalman filter: strong adaptive Kalman filter (SAKF). The simulation of two high-dynamic conditions and a practical experiment were designed to verify the new multi-sensor data fusion algorithm. Then the performance of the Sage–Husa adaptive Kalman filter (SHAKF), strong tracking filter (STF), H∞ filter and SAKF were compared. The results of the simulation and practical experiments show that the SAKF can automatically select its filtering process under different conditions, according to an anomaly criterion. SAKF combines the advantages of SHAKF, H∞ filter and STF, and has the characteristics of high accuracy, robustness and good tracking skill. The research has proved that SAKF is more appropriate in high-speed UAV navigation than single filter algorithms.

Ensemble estimates of the wave state related parameters in a sea spray parameterization scheme

Uncertainties of the wave state parameters in a sea spray parameterization scheme can be a major source of errors for air-sea turbulent (momentum, sensible and latent) fluxes parameterizations resulting in biases in numerical ocean simulations and forecasts. In this study, we explore applications of the ensemble adjustment Kalman filter (EAKF) data assimilation method to optimize the wave states parameters the 1-D POM ocean model for a full range of wind speed conditions. Thus, we assimilate sea surface temperature (SST) synthesized observations to improve our estimates of the SST analysis and prediction skill from low to high winds. Two types of experiments are conducted. In the first type, in a “twin” experiment framework, the SST “observations” generated by a “truth” model are assimilated into an imperfect, biased model to investigate the extent to which the parameters are able to be optimized, with respect to the “truth” values based on data from Station Papa and the Kuroshio Extension Observatory (KEO). In the second type, real SST observations from KEO are assimilated to obtain optimized parameters. With these optimized parameters, the SST analysis and prediction errors are significantly reduced, especially for high wind conditions.

Application of adaptive square root cubature Kalman filter in turbofan engine gas path performance monitoring

Kalman filters are very popular in turbofan engine community for health monitoring purposes. In this study, in order to get better performance in terms of filtering accuracy and noise adaptability, an Adaptive Square Root Cubature Kalman Filter (ASRCKF) was proposed to estimate health parameters of the turbofan engine gas path components. In the ASRCKF algorithm, the mean value and covariance of the engine nonlinear function were calculated by cubature rule-based numerical integration method and used as a substitute for nonlinear model in nonlinear Kalman filter. The latest information of measurement parameters in the recursion and filtering process was used to estimate and self-adjust the noises cross-covariance by removable window method to get higher filtering accuracy. Compared with the Extended Kalman Filter (EKF) and Square Root Cubature Kalman Filter (SRCKF), the simulation results in the gradual and rapid deterioration process of turbofan engine gas path components indicate that the higher accuracy and faster convergence can be obtained through ASRUKF, which can be used in health parameters estimation and condition monitoring of turbofan engine gas path.1

A Kalman filter application for rainfall estimation using radar reflectivity measurements

The rainfall amount observed at a given location mostly depend on the cloud density, which can be quantified with the reflectivity values observed by meteorology weather radars. In this study, we aim to estimate the rainfall amount using a Kalman filter with radar reflectivity measurements. We first assume that the amount of rainfall observed at automatic weather observation stations (AWOSs) are elements of an unknown state vector and consider the Kalman filter process model as the true rainfall amounts observed at these AWOSs over time. For the measurement model of the Kalman filter, we use the radar reflectivity values observed at each AWOS location. For the execution of the Kalman filter, a number of rainfall amount and radar reflectivity value pairs are first required to learn the process and measurement models of the Kalman filter. The estimation performance of the proposed Kalman filter is then compared with empirical reflectivity (Z) - rainfall (R) relationships. Numerical results show that when the Kalman filter is executed with radar reflectivity measurements observed around a large number of AWOS locations, the mean squared errors of the Kalman filter rainfall estimates are smaller than the ones obtained with empirical ZR relationships.

Estimating Residential and Industrial City Gas Demand Function in the Republic of Korea—A Kalman Filter Application

This paper analyzes the city gas demand function in Korea from 1998 to 2018. The demand function of city gas is derived by a Kalman filter method, and price and income elasticities varying with time are estimated. In the case of residential city gas, the price elasticity gradually decreased to a value of approximately 0.57, while income elasticity increased to approximately 1.48 from 1998 to 2018. Alternatively, industrial city gas demand’s price and income elasticities have been estimated as inelastic, as their absolute values were less than unity over time. The absolute values of price and income elasticities are estimated to be larger for residential than industrial city gas, and thus, city gas consumers are more likely to respond to changes in price and income for residential than industrial city gas. There is a substantial income effect on demand for residential city gas in Korea, whereas industrial city gas is found to have relatively small income and price effects. The results of this study provide policy makers with a Kalman filter method to access more accurate information on the city gas demand function’s elasticities, which change with time.

Compensation of asynchronous time of flight measurements in a long baseline navigation

In a long baseline (LBL) acoustic positioning system, a navigation subject estimates its own position at a time based on the ranges between itself and the LBL transponders. To obtain the ranges, each transponder sends acoustic wave to the subjects receiver. Here, a range equals to time required by the wave to travel between these two points multiplied by the wave propagation speed. This method is known as the time of flight (ToF) measurement. One of the ideals in carrying out a ToF is that the navigation subject would remain still throughout the measurement. Corollary, position estimation based on the ToF holds on the same ideal. However, an acoustic wave propagates in a very low speed. Due to this characteristic, the displacement of a moving navigation subject like an autonomous underwater vehicle (AUV) may not be negligible and becomes a source of bias for the range estimations. The AUV motion would also lead to asynchronous ToFs, i.e. acoustic waves sent by transponders arrive at the AUV in different time epochs. In this paper, we present LBL navigation for an AUV that deals with uncertainty due to motion of the AUV. Here, state estimator is modeled while considering the bias for each ToF. Once we obtain the state space representation, we apply Kalman filter to estimate the AUV position and speed. By simulation, we demonstrate that the estimator follows the actual states with good accordance.

Accurate and Cost-Effective Micro Sun Sensor based on CMOS Black Sun Effect.

An accurate and cost-effective micro sun sensor based on the extraction of the sun vector using a phenomenon called the “black sun” is presented. Unlike conventional image-based sun sensors where there is difficulty in accurately detecting the sun center, the black sun effect allows the sun center to be accurately extracted even with the sun image appearing irregular and noisy due to glare. This allows the proposed micro sun sensor to achieve high accuracy even when a 1 mm × 1 mm CMOS image sensor with a resolution of 250 × 250 pixels is used. The proposed micro sun sensor is implemented in two application modes: (1) a stationary mode targeted at tracking the sun for heliostats or solar panels with a fixed pose of single image sensor of 1 mm × 1 mm × 1.74 mm in size and (2) a non-stationary mode targeted at determining the orientation of moving platforms with six sensors on the platform, which is configured in an icosahedron geometry of 23 mm × 23 mm × 12 mm in size. For the stationary mode, we obtained an accuracy of 0.013° by applying Kalman filter to the sun sensor measurement for a particular sensor orientation. For the non-stationary mode, we obtained an improved accuracy of 0.05° by fusing the measurements from three sun sensors available at any instant of time. Furthermore, experiments indicate that the black sun effect makes the precision of sun vector extraction independent of the sun location captured on the image plane.

Kalman Filter Demystified: From Intuition to Probabilistic Graphical Model to Real Case in Financial Markets

In this paper, we revisit the Kalman filter theory. After giving the intuition on a simplified financial markets example, we revisit the maths underlying it. We then show that Kalman filter can be presented in a very different fashion using graphical models. This enables us to establish the connection between Kalman filter and Hidden Markov Models. We then look at their application in financial markets and provide various intuitions in terms of their applicability for complex systems such as financial markets. Although this paper has been written more like a self contained work connecting Kalman filter to Hidden Markov Models and hence revisiting well known and establish results, it contains new results and brings additional contributions to the field. First, leveraging on the link between Kalman filter and HMM, it gives new algorithms for inference for extended Kalman filters. Second, it presents an alternative to the traditional estimation of parameters using EM algorithm thanks to the usage of CMA-ES optimization. Third, it examines the application of Kalman filter and its Hidden Markov models version to financial markets, providing various dynamics assumptions and tests. We conclude by connecting Kalman filter approach to trend following technical analysis system and showing their superior performances for trend following detection.

Application of MCC-based Robust High-degree Cubature Kalman Filter in Integrated Navigation System

As the integrated navigation system is a nonlinear system, in the case of non-gaussian noise, the traditional nonlinear gaussian filtering algorithm has a serious problem of decreasing filtering precision. In this paper, a new robust high-degree Cubature Kalman filtering algorithm is proposed, which takes into account the nonlinearity of the system and non-gaussian noise. The algorithm improves the measurement updating process by using the Maximum correntropy criterion(MCC), and converts the traditional measurement updating problem into the linear regressione quation solving problem. Combines the advantages of Maximum correntropy criterion and Cubature Kalman filter to deal with non-Gaussian and nonlinear systems. The proposed algorithm is applied to the SINS/GPS integrated navigation system, the simulation results show that the proposed algorithm’s filtering performance is greatly affected by the kernel width. Under the condition of gaussian mixture noise, the new robust high-degree Cubature Kalman filter based on Maximum correntropy criterion(MCC-HCKF) is more robust and has higher filtering precision than the traditional high-degree Cubature Kalman filter(HCKF).

Three-dimensional dynamic monitoring of environmental cost based on state-space model

This paper discusses the applicability of Kalman filter in 3D dynamic monitoring of environmental cost. By selecting Kalman filtering algorithm which is suitable for dynamic environmental cost monitoring, the three-dimensional state-space model of environmental cost and the three-dimensional observation system were established based on the analysis and test of the three-dimensional dynamic data of environmental cost. In addition, by analyzing the algorithm of 3D dynamic monitoring model of environmental cost, a three-dimensional state-space monitoring model of environmental cost based on Kalman filter was constructed. Finally, empirical research study of the cement manufacturing enterprise of Ezhou city of Hubei province was carried out.