Auswahl der wissenschaftlichen Literatur zum Thema „Unscented Kalman filter grand gain“

Abstract The photoelectric pod provides angular information and distance information for the UAV (Unmanned Aerial Vehicle), and the UAV uses it to estimate the status information of the moving target. Since the measurement information of the photoelectric pod is the angle of sight and relative distance, the measurement equation contains some nonlinear functions in the Cartesian coordinate system, and the output frequency of the photoelectric pod is low. The improved unscented Kalman filter combines the function of prediction and correction, introduces the prior information of the target acceleration constraint, and uses the offline data to obtain steady gain, and then estimates the target state online. The simulation result show that the algorithm can track the target and need less time compared with the traditional unscented Kalman filter.

Smart grids have brought new possibilities in power grid operations for control and monitoring. For this purpose, state estimation is considered as one of the effective techniques in the monitoring and analysis of smart grids. State estimation uses a processing algorithm based on data from smart meters. The major challenge for state estimation is to take into account this large volume of measurement data. In this article, a novel smart distribution network state estimation algorithm has been proposed. The proposed method is a combined high-gain state estimation algorithm named adaptive extended Kalman filter (AEKF) using extended Kalman filter (EKF) and unscented Kalman filter (UKF) in order to achieve better intelligent utility grid state estimation accuracy. The performance index and the error are indicators used to evaluate the accuracy of the estimation models in this article. An IEEE 37-node test network is used to implement the state estimation models. The state variables considered in this article are the voltage module at the measurement nodes. The results obtained show that the proposed hybrid algorithm has better performance compared to single state estimation methods such as the extended Kalman filter, the unscented Kalman filter, and the weighted least squares (WLS) method.

This paper proposes an innovative simultaneous localization and mapping (SLAM) algorithm which combines a strong tracking filter (STF), an unscented Kalman filter (UKF), and a particle filter (PF) to deal with the low accuracy of unscented FastSLAM (UFastSLAM). UFastSLAM lacks the capacity for online self-adaptive adjustment, and it is easily influenced by uncertain noise. The new algorithm updates each Sigma point in UFastSLAM by an adaptive algorithm and obtains optimized filter gain by the STF adjustment factor. It restrains the influence of uncertain noise and initial selection. Therefore, the state estimation would converge to the true value rapidly and the accuracy of system state estimation would be improved eventually. The results of simulations and practical tests show that strong tracking unscented FastSLAM (STUFastSLAM) has a significant improvement in accuracy and robustness.

This paper presents parameters estimation techniques for coupled industrial tanks using the mixed Unscented Kalman Filter (UKF) and Differential Evolution (DE) method. UKF have known to be a typical estimation technique used to estimate the state vectors and parameters of nonlinear dynamical systems and DE is one of the most powerful stochastic real-parameter optimization algorithms. Meanwhile, liquid tank systems play important role in industrial application such as in food processing, beverage, dairy, filtration, effluent treatment, pharmaceutical industry, water purification system, industrial chemical processing and spray coating. The aim is to model the coupled tank system using mixed UKF and DE method to estimate the parameters of the tank. First, a non-linear mathematical model is developed. Next, its parameters are identified using mixed Unscented Kalman Filter (UKF) and Differential Evolution (DE) based on the experimental data. DE algorithm is integrated into the UKF algorithm to optimize the Kalman gain obtained. The obtained results demonstrate good performances.

In this paper, a new hybrid unscented Kalman (UKF) and unscented [Formula: see text](U[Formula: see text]F) filter is presented that can adaptively adjust its performance better than that of either UKF and/or U[Formula: see text], accordingly. In this way, two Takagi-Sugeno-Kang (TSK) fuzzy logic systems are presented to adjust automatically some weights that combine those UK and U[Formula: see text] filters, independent of the dynamics of the problem. Such adaptive fuzzy hybrid unscented Kalman/[Formula: see text] filter (AFUK[Formula: see text]) is based on the combination of gain, a priori state estimation, and a priori measurement estimation. The simulation results of an inverted pendulum and a re-entry vehicle tracking problem clearly demonstrate robust and better performance of this new AFUK[Formula: see text] filter in comparison with those of both UKF and U[Formula: see text]F, appropriately. It is shown that, therefore, the new presented AFUK[Formula: see text] filter can simply eliminate the need for either UKF or U[Formula: see text] F effectively in the presence of Gaussian and/or non-Gaussian noises.

For various target tracking applications, it is well known that the Kalman filter is the optimal estimator(in the minimum mean-square sense) to predict and estimate the state(position and/or velocity) of linear dynamical systems driven by Gaussian stochastic noise. In the case of nonlinear systems, Extended Kalman filter(EKF) and/or Unscented Kalman filter(UKF) are widely used, which can be viewed as approximations of the(linear) Kalman filter in the sense of the conditional expectation. However, to implement EKF and UKF, the exact dynamical model information and the statistical information of noise are still required. In this paper, we propose the recurrent neural-network based Kalman filter, where its Kalman gain is obtained via the proposed GRU-LSTM based neural-network framework that does not need the precise model information as well as the noise covariance information. By the proposed neural-network based Kalman filter, the state estimation performance is enhanced in terms of the tracking error, which is verified through various linear and nonlinear tracking problems with incomplete model and statistical covariance information.

This paper aims to improve the stability and robustness of the state-of-charge estimation algorithm for lithium-ion batteries. A new internal resistance-polarization circuit model is constructed on the basis of the Thevenin equivalent circuit to characterize the difference in internal resistance between charge and discharge. The extended Kalman filter is improved through adding an adaptive noise tracking algorithm and the Kalman gain in the unscented Kalman filter algorithm is improved by introducing a dynamic equation. In addition, for benignization of outliers of the two above-mentioned algorithms, a new dual Kalman algorithm is proposed in this paper by adding a transfer function and through weighted mutation. The model and algorithm accuracy is verified through working condition experiments. The result shows that: the errors of the three algorithms are all maintained within 0.8% during the initial period and middle stages of the discharge; the maximum error of the improved extension of Kalman algorithm is over 1.5%, that of improved unscented Kalman increases to 5%, and the error of the new dual Kalman algorithm is still within 0.4% during the latter period of the discharge. This indicates that the accuracy and robustness of the new dual Kalman algorithm is better than those of traditional algorithm.

Autonomous underwater vehicle (AUV) acoustic navigation is challenged by unknown system noise and gross errors in the acoustic observations caused by the complex marine environment. Since the classical unscented Kalman filter (UKF) algorithm cannot control the dynamic model biases and resist the influence of gross errors, an adaptive robust UKF based on the Sage-Husa filter and the robust estimation technique is proposed for AUV acoustic navigation. The proposed algorithm compensates the system noise by adopting the Sage-Husa noise estimation technique in an online manner under the condition that the system noise matrices are kept as positive or semi positive. In order to control the influence of gross errors in the acoustic observations, the equivalent gain matrix is constructed to improve the robustness of the adaptive UKF for AUV acoustic navigation based on Huber’s equivalent weight function. The effectiveness of the algorithm is verified by the simulated long baseline positioning experiment of the AUV, as well as the real marine experimental data of the ultrashort baseline positioning of an underwater towed body. The results demonstrate that the adaptive UKF can estimate the system noise through the time-varying noise estimator and avoid the problem of negative definite of the system noise variance matrix. The proposed adaptive robust UKF based on the Sage-Husa filter can further reduce the influence of gross errors while adjusting the system noise, and significantly improve the accuracy and stability of AUV acoustic navigation.

Notre travail consiste à étudier les propriétés du filtre unscented Kalman filter "UKF" et son adaptation en tant qu'observateur non linéaire. Il a été développé mais, bien que donnant en pratique de meilleurs résultats, aucune preuve de convergence n’existe qui garantit son utilisation.Un résultat négatif a été obtenu (sa non-convergence). Ce qui nous a conduit à proposer une nouvelle version : "unscented Kalman observer" pour les systèmes à temps continu dans un cadre déterministe. Nous avons montré sa convergence, lorsque les erreurs d'estimations initiales sont suffisamment petites. Cette démonstration repose essentiellement sur l'existence de bornes de la solution de l'équation de Riccati qui est perturbé par un terme non Linéaire.On a aussi développer une version grand gain de l'observateur UKF, qui est un compromis entre le filtre de Kalman étendu grand gain (EKF) et le unscented Kalman filter grand grand (HG-UKF). Toutes ces propriétés sont illustrées sur l'exemple de la colonne de distillation binaire et sur un exemple de géolocalisation
The present thesis is a study of the convergence of the unscented Kalman filter. A convergence analysis of the modified unscented Kalman filter ( used as an observer for a class of nonlinear deterministic continuous time systems, is presented. Under certain conditions, the extended Kalman filter ( is an exponential observer for non linear systems, i.e., the dynamics of the estimation error is exponentially stable. It is shown that unlike the EKF, the UKF is not an expo nentially converging observer. A modification of the UKF the unscented Kalman observer ( is proposed, which is a better candidate for an observer, we proved the exponentialconvergence of the UKO and also shown that the high gain UKF observer as a compromise between the high gain extended Kalman filter (HG EKF) and the high gain unscented Kalman filter (HG UKF). All these properties are illustrated on the example of the binary distillation column and on an example of geolocalization

The work concerns the "observability problem"--the reconstruction of a dynamic process's full state from a partially measured state-- for nonlinear dynamic systems. The Extended Kalman Filter (EKF) is a widely-used observer for such nonlinear systems. However it suffers from a lack of theoretical justifications and displays poor performance when the estimated state is far from the real state, e.g. due to large perturbations, a poor initial state estimate, etc. . . We propose a solution to these problems, the Adaptive High-Gain (EKF). Observability theory reveals the existence of special representations characterizing nonlinear systems having the observability property. Such representations are called observability normal forms. A EKF variant based on the usage of a single scalar parameter, combined with an observability normal form, leads to an observer, the High-Gain EKF, with improved performance when the estimated state is far from the actual state. Its convergence for any initial estimated state is proven. Unfortunately, and contrary to the EKF, this latter observer is very sensitive to measurement noise. Our observer combines the behaviors of the EKF and of the high-gain EKF. Our aim is to take advantage of both efficiency with respect to noise smoothing and reactivity to large estimation errors. In order to achieve this, the parameter that is the heart of the high-gain technique is made adaptive. Voila, the Adaptive High-Gain EKF. A measure of the quality of the estimation is needed in order to drive the adaptation. We propose such an index and prove the relevance of its usage. We provide a proof of convergence for the resulting observer, and the final algorithm is demonstrated via both simulations and a real-time implementation. Finally, extensions to multiple output and to continuous-discrete systems are given.

In recent years, the Moon has been identified as a key testing ground to develop and enhance technologies for future deep-space missions, resulting in an ever-growing number of planned Moon-targeted launches from both space agencies and commercial actors. Despite having different objectives, all these users share the need to maintain accurate and reliable state estimates. In this regard, The European Space Agency (ESA) has launched the Moonlight initiative to foster the development of a dedicated Lunar Communication and Navigation System (LCNS) exploiting a small satellite constellation in lunar orbits. LCNS will deliver cost-efficient and high-performance navigation and communication services to future lunar exploration missions, enabling users simplifying their design and lowering the size, mass and power demands of the navigation payload. Additionally, the deployment of a third-party constellation may facilitate the on-board implementation of autonomous lunar navigation systems, enabling rovers, landers and spacecraft to explore the lunar environment with no need for constant human control. At the beginning of the constellation setup, a key challenge will be the limited availability of navigation signals, due to the significantly smaller number of LCNS servicing satellites with respect to well-established Earth Global Navigation Satellite Systems (GNSS). In particular, the initial architecture will focus on maximizing the navigation performance of surface and Low Lunar Orbital (LLO) users at latitudes around the South Pole region, which is the subject of great scientific interest. Nevertheless, even for South Pole users, the LCNS constellation will still be too small to provide a continuous view of at least 4 satellites at any location, requiring the development of tailored navigation algorithms to cope with the mission requirements. To overcome these limitations, the paper investigates strategies to mitigate the impact of these reduced-servicers-visibility windows on the estimation process by exploiting sensor fusion techniques to integrate the one-way ranging LCNS signals with a suite of well-known sensors, which might include Inertial Measurement Units (IMUs), optical cameras, altimeters and Two-Way Ranging (TWR) with the Lunar Gateway (LOP-G). The observability gain provided by each sensor is analyzed as a function of the relative servicer-user dynamics, the required pointing strategy and the measurements availability. Different inclinations of LLO are analyzed to investigate the most favorable LCNS receiver antenna pointing direction that maximizes the overall number of visible satellites throughout the simulation window. Additionally, sensors mounting location on-board the spacecraft is discussed in relationship to the LLO inclination and satellite attitude, to identify possible operational constraints that may influence the observables availability and to identify the best suited sensors clustering for a given mission profile and operational needs. The simulation architecture consists of a high-fidelity non-Keplerian dynamics propagator, which accounts for irregular lunar gravity field and Solar Radiation Pressure (SRP) perturbations; a sensor suite to have a truthful noisy representation of the available spacecraft measurements; a dedicated sequential navigation filter. Each proposed navigation scheme underwent a Montecarlo testing campaign to comprehensively fix and tune the algorithm gains and parameters. The sensitivity of the navigation solution on the measurement noise has been assessed for each type of observable, allowing for a direct link between commercial sensor properties and the resulting navigation errors and uncertainties. A tightly coupled approach is exploited to directly fuse the LCNS one-way ranging measurements with other sensors data, making the observables availability hold irrespective of the actual number of visible LCNS satellites. The filter is constructed to estimate both the spacecraft state and the receiver clock bias and drift, allowing to properly account for the de-synchronization of the generally low-cost user clocks with respect to the high precision atomic clocks on-board of the LCNS constellation. The outcomes show that with the sole LCNS signals and a proper pointing strategy exploitation, the navigation error swings between 10 meters, with 4 visible satellites, and 1 km when the user is above the lunar North Pole and the LCNS servicers are obstructed by the Moon. Each of the analyzed sensors further improves these statistics: for low altitude LLO users, an altimeter provides continuous discrete altitude measurements that can improve the overall error up to 60%, especially if long LCNS-unavailability windows are present. On the other hand, although TWR with LOP-G effectively offers an additional high precision observable, its availability is often synchronized with that of the LCNS satellites: being on a Southern Near Rectilinear Halo Orbit (S-NRHO), the Gateway can only provide measurements for users located above the Lunar North Pole only for a day per week. Additionally, the performance of a variety of Runge-Kutta (RK) explicit integration schemes and dynamic approximations is tested for both Extended Kalman Filters (EKF) and Unscented Kalman Filters (UKF). A trade-off between solution accuracy and computation burden (i.e., number of required dynamic function evaluations) is performed to accommodate the needs of different spacecraft classes and available hardware. The results highlight that for filters running at 1 Hz a two-stage Heun integration method halves the CPU time required for the computations while bounding the propagation error difference with respect to Verner’s “Most Efficient” 8(7) scheme to less than 5 meters. On the other hand, at lower filter frequencies (e.g., 1/60 Hz), the same difference grows up to hundreds of meters, thus requiring a more accurate integration to properly navigate. The paper exhaustively presents that with the proper navigation sensors, autonomous lunar navigation exploiting a dedicated Moon-centered GNSS-like infrastructure can provide accurate and reliable state estimates, paving the way to a new generation of lunar exploration missions with enhanced autonomy and reliability. The present study has been carried out in collaboration with Telespazio.