Unscented Kalman Filter Filter Research Articles

Enhancing physically-based flood forecasts through fusion of long short-term memory neural network with unscented Kalman filter

Accurate flood forecasts are vital for reservoir operation and flood prevention. The unscented Kalman filter (UKF) excels in improving physically-based models flood forecasting but depends on precise noise estimation, posing challenges in complex uncertainty quantification. In this study, we propose a novel approach, the deep fusion of a long short-term memory (LSTM) neural network and unscented Kalman filter (LSTM-UKF), to enhance flood forecasts by adaptively updating hydrological model states. The LSTM efficiently learns noise-related information from the estimation of Kalman Gain, obviating the need for intricate uncertainty recognition and approximation. For comparative analysis, the LSTM-UKF and UKF filters are constructed to correct Xinanjiang (XAJ) hydrological model states. Both filters utilize streamflow observations to update the XAJ model states and facilitate its flood forecasting performance. Comprehensive evaluations were conducted using 3-hourly meteor-hydrological sequences from the Jianxi and Tianyi basins in China, focusing on the accuracy, stability, and reliability of multi-step-ahead flood forecasts. Results indicate that the LSTM-UKF performs superior to the UKF, with maximal advancements in Nash-Sutcliffe efficiency coefficient (NSE) by 9.1%, maximal reduction in root mean square error (RMSE) by 18.7%, and maximal decrease in mean absolute error (MAE) by 22.6%. Additionally, the LSTM-UKF exhibits better robustness and stability in non-stationary flood events. The proposed LSTM-UKF mitigates the over-reliance on noise estimates, reducing systematic biases and error accumulation in state estimates and enhancing hydrological model generalizability in operational flood prevention platforms and systems.

An online battery–state of charge estimation method using the varying forgetting factor recursive least square - unscented Kalman filter algorithm on electric vehicles

Accurate and fast estimation of the state of charge is important for the battery management system of electric vehicles. This paper proposes a method to estimate the state of charge of Lithium-ion batteries by the <span lang="EN-US">variable</span> forgetting factor recursive least square (VFFRLS) – unscented Kalman filter (UKF) algorithm in real-time without the off-line battery testing data. Since the state observation requires an accurate model, an equivalent circuit model was constructed. Then, the VFFRLS algorithm is used to identify online the battery model parameters based on voltage and current measurements. An advantage of this algorithm is that it requires less initial information and shorter identification time than offline parameter identification. After the model parameters are well identified, the unscented Kalman filter estimates the state of charge and minimizes noise characteristics and uncertainty in the parameter identification process. The VFFRLS algorithm applied in this paper has shown a good result with the model output error of less than 1%, and the identification achieves real-time response. The state of charge obtained by the UKF algorithm has shown satisfactory estimation results with fast convergence speed and small errors. The UKF filter provides the results with a 1.5% error from the reference and converges after 10 cycles.

Islanding Event Detection in Grid-Connected Distributed Generation Systems Using Unscented Kalman Filter

A pressing concern in modern smart grid systems revolves around islanding, leading to unpredictable system parameters and a decline in power quality. In response to this concern, we introduce a novel passive method for identifying islanding in grid-connected distributed generation units. This method utilizes the unscented Kalman filter (UKF) to assess the voltage signal captured at the DG position. The triphase voltage signal observed at the point of common coupling (PCC) is used as the test signal. The UKF extracts and filters the harmonic content of the voltage signal to produce a residual signal, which detects changes in the power system. The estimation of total harmonic distortion (THD) follows, and its fluctuations help discern between islanding and typical events. This suggested approach undergoes assessment through a test system simulated in MATLAB/Simulink across different situations. Outcome findings underscore the efficacy of the suggested approach in distinguishing between islanding and regular occurrences, ensuring enhanced reliability and resilience against incorrect operations by removing the zone of nondetection. In our detailed experiments, we found that the proposed unscented Kalman filter (UKF) technique improved islanding detection accuracy by approximately 90% over traditional methods, under varied conditions. Specifically, the nondetection zone (NDZ) was reduced by 95% when compared to the most commonly used passive methods. Furthermore, in scenarios with high harmonic content and noise, the UKF showcased a 90% improvement in reliability over conventional techniques.

Characteristic analysis and filtering algorithm design for UNGM model

The univariate non-stationary growth model (UNGM) is widely used in the verification of nonlinear filters, and the unscented Kalman filter (UKF) is often used as the reference filter for comparative analysis when using this model to evaluate the filter performance. However, due to the strong nonlinearity of UNGM and the change of model properties with different parameter settings, the estimation misalignment problem due to different reasons will occur when UKF is used for filtering. To solve these problems, this paper analyzes the complex characteristics of UNGM in filtering process, and proposes an UKF with sliding sampling module(SSUKF). The algorithm is optimized on the basis of UKF, and can effectively deal with the complex characteristics of UNGM by sampling and analyzing the filtering information in the filtering process and correcting the distribution of Sigma points in real time. SSUKF is applied to UNGM under different parameters and compared with UKF and bootstrap particle filter(BPF). The simulation results show that SSUKF can effectively solve the misalignment problem when UKF is applied to UNGM, and the calculation speed is better than BPF. Compared with UKF, SSUKF is suitable as a benchmark filter for evaluating the performance of nonlinear filters using UNGM.

Autonomous Orbit Determination System of Navigation Satellite Based on Spaceborne GPS Technology

In recent years, many low-orbit satellites have been widely used in the field of scientific research and national defense in China. In order to meet the demand of high-precision satellite orbit in China’s space, surveying and mapping, and other related fields, navigation satellites are of great significance. The UKF (unscented Kalman filter) method is applied to space targets’ spaceborne GPS autonomous orbit determination. In this paper, the UKF algorithm based on UT transformation is mainly introduced. In view of the situation that the system noise variance matrix is unknown or the dynamic model is not accurate, an adaptive UKF filtering algorithm is proposed. Simulation experiments are carried out with CHAMP satellite GPS data, and the results show that the filtering accuracy and stability are improved, which proves the algorithm’s effectiveness. The experimental results show that the Helmert variance component estimation considering the dynamics model can solve the problem of reasonable weight determination of BDS/GPS observations and effectively weaken the influence of coarse error and improve the accuracy of orbit determination. The accuracy of autonomous orbit determination by spaceborne BDS/GPS is 1.19 m and 2.35 mm/s, respectively.

A Novel State-of-Health Estimation for Lithium-Ion Battery via Unscented Kalman Filter and Improved Unscented Particle Filter

This paper aims to improve the rapidity and accuracy of the State of Health (SOH) assessment for lithium-ion battery. By integrating the Unscented Kalman Filter (UKF) and Improved Unscented Particle Filter (IUPF) algorithm, SOH can be effectively evaluated. The UKF algorithm is used to estimate the state of charge (SOC), the IUPF algorithm is employed to identify the ohmic internal resistance. The novelty of the proposed strategy relies on the 4-dimensional IUPF filter that is split into a 3-dimensional UKF filter and a 1-dimensional IUPF filter. Experimental results demonstrate that more accuracy and a faster rate of SOH estimation can be achieved via the UKFIUPF algorithm compared to the IUPF approach.

Initial Tracking Parameter Estimation of Magnetic Ship Based on PSO

We consider the problem of tracking a surface magnetic ship as it travels in a straight line path with the exertion of a magnetometer located at the seabed. Note that the initial filter parameters are prior information and the tracking performance depends on the initial filter parameters, and traditional estimation of initial filter parameters is to apply the filter bank algorithm, but there are several obvious defects in this method. In this paper, a novel algorithm based on the particle swarm optimization (PSO) algorithm is proposed to estimate initial parameters of the filter, and the model of uniformly magnetized ellipsoid is adopted to fit the magnetic field of the ship. The simulation results show that, under the condition of no prior information, the estimated ship parameters based on the observation of the single-observer are invalid, whereas the estimated ship parameters based on the observation of the double-observer are valid. Further, the estimated results of real-world recorded magnetic signals show that the ship parameters estimated by PSO based on the double-observer are also valid, as the estimated parameters are used as the initial parameters of the unscented Kalman filter (UKF), and a ship can be tracked effectively by the UKF filter. Moreover, the estimated half focal length can be used as a feature to distinguish noise environment, ships with different sizes, and mine sweepers.

A Theoretical Framework of Robust H-Infinity Unscented Kalman Filter and Its Application to Power System Dynamic State Estimation

This paper presents a new theoretical framework that, by integrating robust statistics and robust control theory, allows us to develop a robust dynamic state estimator of a cyber-physical system. This state estimator combines the generalized maximum-likelihood-type (GM) estimator, the unscented Kalman filter (UKF), and the H -infinity filter into a robust H -infinity UKF filter in the Krein space, which is able to handle large system uncertainties as well as suppress outliers while achieving a good statistical efficiency under Gaussian and non-Gaussian process and observation noises. Specifically, we first use the statistical linearization approach to build a linearlike regression model in the Krein space. Then, we show that the H -infinity UKF is just the Krein space Kalman filter that exhibits a bounded estimation error in presence of system uncertainties while minimizing the least squares criterion; consequently, it suffers from a lack of robustness to outliers and non-Gaussian noise. Because the GM estimator is able to handle outliers, but it may yield large estimation errors in the presence of system uncertainties, we propose to combine it with the H -infinity UKF in a robust H -infinity UKF. We carry out a theoretical analysis to demonstrate the connections that our filter has with the H -infinity UKF and the GM-UKF. The good performance of the new filter is demonstrated via extensive simulation performed on the IEEE 39-bus power system.

Extraction and Filter Algorithm of Guidance Information for Full-strapdown Seeker on Rotation Missile

Strapdown seekers are superior to platform seekers for their simple structure, high reliability and light weight but cannot measure the line-of-sight angle rate information for the guidance of rotation missile directly. This paper aims at the engineering application of full-strapdown seekers on rotation missile problem. Firstly, a line-of-sight angle rate solution model is established. Based on the MATLAB, the extended Kalman filter (EKF) algorithm and unscented Kalman filter (UKF) algorithm are used to estimate the line-of-sight angle rate information of the full-strapdown seekers. The results show that using EKF filter and UKF filter both can obtain effective guidance information and the UKF’s effect is better.

A Seventh‐Degree Cubature Kalman Filter

AbstractThe fifth‐degree cubature Kalman filter (CKF) has been proved to be a kind of algorithm that has higher precision than the third‐degree CKF and unscented Kalman filter (UKF). In order to further improve the performance of CKF, the seventh‐degree CKF is proposed in this paper by expanding the spherical‐radial rule, and a new kind of deterministic sampling method is derived based on the seventh‐degree cubature rule. Through the comparison in target tracking simulation, the seventh‐degree CKF methods are shown to be able to enhance filtering precision compared to the fifth‐degree CKF, the third‐degree CKF and the UKF filter.

An Unscented Kalman-Particle Hybrid Filter for Space Object Tracking

Optimal and consistent estimation of the state of space objects is pivotal to surveillance and tracking applications. However, probabilistic estimation of space objects is made difficult by the non-Gaussianity and nonlinearity associated with orbital mechanics. In this paper, we present an unscented Kalman-particle hybrid filtering framework for recursive Bayesian estimation of space objects. The hybrid filtering scheme is designed to provide accurate and consistent estimates when measurements are sparse without incurring a large computational cost. It employs an unscented Kalman filter (UKF) for estimation when measurements are available. When the target is outside the field of view (FOV) of the sensor, it updates the state probability density function (PDF) via a sequential Monte Carlo method. The hybrid filter addresses the problem of particle depletion through a suitably designed filter transition scheme. To assess the performance of the hybrid filtering approach, we consider two test cases of space objects that are assumed to undergo full three dimensional orbital motion under the effects of J 2 and atmospheric drag perturbations. It is demonstrated that the hybrid filters can furnish fast, accurate and consistent estimates outperforming standard UKF and particle filter (PF) implementations.

Gaussian Process Regression for Sensorless Grip Force Estimation of Cable Driven Elongated Surgical Instruments.

Haptic feedback is a critical but a clinically missing component in robotic Minimally Invasive Surgeries. This paper proposes a Gaussian Process Regression(GPR) based scheme to address the gripping force estimation problem for clinically commonly used elongated cable-driven surgical instruments. Based on the cable-driven mechanism property studies and surgical robotic system properties, four different Gaussian Process Regression filters were designed and analyzed, including: one GPR filter with 2-dimensional inputs, one GPR filter with 3-dimensional inputs, one GPR Unscented Kalman Filter (UKF) with 2-dimensional inputs, and one GPR UKF with 3-dimensional inputs. The four proposed methods were compared with the dynamic model based UKF filter on a 10mm gripper on the Raven-II surgical robot platform. The experimental results demonstrated that the four proposed methods outperformed the dynamic model based method on precision and reliability without parameter tuning. And surprisingly, among the four methods, the simplest GPR Filter with 2-dimensional inputs has the best performance.

Fault detection and identification of non‐linear hybrid system using self‐switched sigma point filter bank

This study proposes a scheme for fault detection and identification (FDI) of a class of non-linear hybrid systems. For fault detection, the proposed method uses a self-switched unscented Kalman filter (UKF) where a component filter with the appropriate dynamic model is chosen to suit the current mode of the hybrid plant. The mode of the hybrid plant, usually defined by system states, is deduced based on the state estimates. The statistical tests of measured datasets are used to detect and identify the fault parameters. For fault identification, a bank of such switched UKF filters is used. A three-tank system has been used to demonstrate the effectiveness of the scheme. Different types of faults, that is, leakage, clogging and abrupt changes in inflow (actuator fault) have been considered. t-Statistical test has been performed on the residuals for FDI and threshold calculation purposes. It is shown that all the types of faults can be successfully detected and identified by the proposed method. The performance of the proposed system is compared with the same for an extended Kalman filter-based FDI system. It has been shown that the UKF-based scheme has lower latency and higher range coverage.

A Robust Unscented Kalman Filter for Nonlinear Dynamical Systems with Colored Noise

The Unscented Kalman filter (UKF) is the commonest filter for state estimation of a discrete-time nonlinear system corrupted with noise. If the process noise and measurement noise of nonlinear system are Gaussian and white, the UKF filter will be optimal. While the process or measurement noises are colored noise, the UKF filter will be instead suboptimal. In this paper, a robust UKF (R-UKF) filter is proposed in order to solve this problem. The proposed filter allows that the conventional UKF is applied for discrete-time nonlinear system corrupted with colored noise. Simulation results show that the R-UKF has better performance in estimation of the corrupted state of dynamical system by colored noise in comparison with those of using conventional UKF algorithm. 

Reconstructing Mammalian Sleep Dynamics with Data Assimilation

Data assimilation is a valuable tool in the study of any complex system, where measurements are incomplete, uncertain, or both. It enables the user to take advantage of all available information including experimental measurements and short-term model forecasts of a system. Although data assimilation has been used to study other biological systems, the study of the sleep-wake regulatory network has yet to benefit from this toolset. We present a data assimilation framework based on the unscented Kalman filter (UKF) for combining sparse measurements together with a relatively high-dimensional nonlinear computational model to estimate the state of a model of the sleep-wake regulatory system. We demonstrate with simulation studies that a few noisy variables can be used to accurately reconstruct the remaining hidden variables. We introduce a metric for ranking relative partial observability of computational models, within the UKF framework, that allows us to choose the optimal variables for measurement and also provides a methodology for optimizing framework parameters such as UKF covariance inflation. In addition, we demonstrate a parameter estimation method that allows us to track non-stationary model parameters and accommodate slow dynamics not included in the UKF filter model. Finally, we show that we can even use observed discretized sleep-state, which is not one of the model variables, to reconstruct model state and estimate unknown parameters. Sleep is implicated in many neurological disorders from epilepsy to schizophrenia, but simultaneous observation of the many brain components that regulate this behavior is difficult. We anticipate that this data assimilation framework will enable better understanding of the detailed interactions governing sleep and wake behavior and provide for better, more targeted, therapies.

Model based learning of sigma points in unscented Kalman filtering

The unscented Kalman filter (UKF) is a widely used method in control and time series applications. The UKF suffers from arbitrary parameters necessary for sigma point placement, potentially causing it to perform poorly in nonlinear problems. We show how to treat sigma point placement in a UKF as a learning problem in a model based view. We demonstrate that learning to place the sigma points correctly from data can make sigma point collapse much less likely. Learning can result in a significant increase in predictive performance over default settings of the parameters in the UKF and other filters designed to avoid the problems of the UKF, such as the GP-ADF. At the same time, we maintain a lower computational complexity than the other methods. We call our method UKF-L.

A comparison of simultaneous state and parameter estimation schemes for a continuous fermentor reactor

This article proposes a maximum likelihood algorithm for simultaneous estimation of state and parameter values in nonlinear stochastic state-space models. The proposed algorithm uses a combination of expectation maximization, nonlinear filtering and smoothing algorithms. The algorithm is tested with three popular techniques for filtering namely particle filter (PF), unscented Kalman filter (UKF) and extended Kalman filter (EKF). It is shown that the proposed algorithm when used in conjunction with UKF is computationally more efficient and provides better estimates. An online recursive algorithm based on nonlinear filtering theory is also derived and is shown to perform equally well with UKF and ensemble Kalman filter (EnKF) algorithms. A continuous fermentation reactor is used to illustrate the efficacy of batch and online versions of the proposed algorithms.

A land surface soil moisture data assimilation system based on the dual‐UKF method and the Community Land Model

Many studies have shown the deficiencies of the extended Kalman filter (EKF), even though it has become a standard technique used in nonlinear estimation. In the EKF method, the state distribution is propagated analytically through the first‐order linearization of the nonlinear system, which can introduce large errors in variable estimation and may lead to suboptimal performance and sometimes divergence of the filter. The unscented Kalman filter (UKF) addresses these problems using a deterministic sampling approach to capture the posterior mean and covariance accurate to the third order for any nonlinearity, while the dual‐UKF method uses two UKF filters (one for state variables and one for parameters, in contrast to only one filter in the usual UKF) to simultaneously optimize the model states and parameters using observational data. In this paper, we employ the dual‐UKF method to account for the effects of land surface subgrid‐scale heterogeneity and soil water thawing and freezing and implement it into the NCAR Community Land Model version 2.0 to build a data assimilation system for assimilating satellite observations of soil moisture. Experiments for two sites in north and south China show that this dual‐UKF‐based assimilation system outperforms the usual UKF‐ and EKF‐based methods in reproducing the temporal evolution of daily soil moisture, especially under freezing conditions. Furthermore, the improvement also propagates, albeit to a lesser extent, to lower layers where observations are unavailable.