Kalman Filter Design Research Articles

A Novel Step‐by‐Step High‐Order Extended Kalman Filter Design for a Class of Complex Systems with Multiple Basic Multipliers

A novel step-by-step linearization highorder Extended Kalman filter SH-EKF is designed for a class of nonlinear systems composed of linear functions and the product of several separable basic functions. The basic functions in the state and measurement models are defined as latent variables; the state and measurement models are equivalently formulated into pseudo-linear models based on the combination of the original variable and the latent variables; latent variables are regarded as new variables, and a dynamic linear model between each latent variable and other latent variables with original state is established; the measurement model is rewritten into the first-order linear product form between the current state and each latent variable; latent variables are solved by Kalman filter step by step, and a stepwise linearized high-order extended Kalman filter is designed. Illustration examples are presented to demonstrate the effectiveness of the new algorithm.

Computational Approach For Real-Time Interval Type-2 Fuzzy Kalman Filtering and Forecasting via Unobservable Spectral Components of Experimental Data

In this paper, a methodology for design of Kalman filter, using interval type-2 fuzzy systems, in discrete time domain, via spectral decomposition of experimental data, is proposed. The adopted methodology consists of recursive parametric estimation of local state space linear submodels of interval type-2 fuzzy Kalman filter for tracking and forecasting of the dynamics inherited to experimental data, using an interval type-2 fuzzy version of Observer/Kalman Filter Identification (OKID) algorithm. The partitioning of the experimental data is performed by interval type-2 fuzzy Gustafson–Kessel clustering algorithm. The interval Kalman gains in the consequent proposition of interval type-2 fuzzy Kalman filter are updated according to unobservable components computed by recursive spectral decomposition of experimental data. Results illustrate the efficiency of proposed methodology, as compared to other approach widely cited in the literature, for filtering and tracking the state variables of Lorenz’s chaotic attractor in a noisy environment, and its applicability for adaptive and real-time forecasting the dynamic spread behavior of novel coronavirus 2019 (COVID-19) outbreak in state of Maranhão and Brazil.

An Optimal Kalman-Consensus Filter for Distributed Implementation Over a Dynamic Communication Network

With the rising number of applications for sensor networks comes a need for more accurate cooperative fusion algorithms. In this paper, a distributed and optimal state estimator is presented for implementation through a dynamically switching, yet strongly connected, directed communication network to cooperatively estimate the state of a dynamic system. The Kalman-Consensus filter approach is used to incorporate a consensus protocol of neighboring state estimates into the traditional Kalman filter. It has been known that the main difficulty associated with implementing such an optimal solution is its fully coupled covariance matrix. Presented is a distributed computation of the covariance matrix at every node achieved by taking advantage of its independence from state estimates. Reductions to the distributed covariance computations are achieved through shared processing made available by the strongly connected digraph. Should the digraph change over time, a distributed topology estimation algorithm is included to facilitate the implementation of the proposed Kalman-Consensus filters. Together, these advances render a distributed and optimal solution to the consensus-based cooperative Kalman filter design problem. Convergence and stability of the proposed algorithms are analyzed and analytically concluded with performance verified through simulation of an illustrative example.

Model Predictive Control and Adaptive Kalman Filter Design for an Underground Coal Gasification Process

The control of a nonlinear system such as an underground coal gasification (UCG) process is a challenging task. Several nonlinear design approaches are implemented to improve the tracking performance of the UCG process, however, the nonlinear techniques make implementation complex and computationally inefficient. In this work, a constrained linear model predictive control (MPC) is designed for the UCG process to track the desired trajectory of the heating value, while satisfying actuator constraints pertaining to UCG. The unknown states required for MPC design are reconstructed by using linear adaptive Kalman filter (AKF) and unscented Kalman filter (UKF). The design of MPC and AKF is based on the quasi-linear model of the UCG process. A fair comparison between different control strategies is conducted which include MPC– AKF, MPC– UKF, MPC– gain scheduled modified Utkin observer (GSMUO) and dynamic integral sliding mode control (DISMC)–GSMUO. The quantitative analysis and simulation results show that MPC- AKF outperforms its counterparts by yielding the least tracking error and average control energy. This conclusion holds, even in the presence of an external disturbance, parametric variations, and measurement and process noises. Moreover, MPC- AKF yields 51%, 44% and 46% improvement in absolute relative root-mean-squared error with reference to MPC– UKF, MPC– GSMUO and DISMC–GSMUO, respectively. A quantitative analysis has also been carried for AKF and UKF, which shows that the performance of AKF is more robust against changes in the initial values of measurement and process covariances.

Accurate estimation of line-of-sight rate under strong impact interference effect

In the process of the terminal guidance of a kinetic kill vehicle (KKV), it is very important to accurately estimate the line-of-sight (LOS) rate via the measurements of a target seeker onboard the KKV. The strong impact interference caused by the large lateral thrust produced by the thrusters on the KKV is a main factor that affects the measurements on the LOS angle. A method to estimate the impact interference and the LOS rate together via a Kalman filter is proposed to improve the estimation precision of the LOS rate. The observability of the system describing the missile-target relative motion model and the impact interference model is proved, and then a Kalman filter is designed. In the Kalman filter design, the continuous-discrete and two-stage filtering techniques are used because the system model is time-variant and high-order. Numerical simulation results show that by estimating the impact interference, the estimation precision of the LOS rate is increased, and so the miss distance of the KKV under the strong impact interference is reduced. The proposed continuous-discrete two-stage Kalman filter shows higher estimation precision and lower computational cost than the naive discrete augmented state Kalman filter.

Global Gravitational Search Algorithm-Aided Kalman Filter Design for Volterra-Based Nonlinear System Identification

This paper proposes an efficient global gravitational search (GGS) algorithm-assisted Kalman filter (KF) design, called a GGS-KF technique, for accurate estimation of the Volterra-type nonlinear systems. KF is a well-known estimation technique for the dynamic states of the system. The best estimate is achieved if the system dynamics and noise statistical model parameters are available at the beginning. However, to estimate the real-time problems, these parameters are unstipulated or partly known. Due to this limitation, the performance of the KF degrades or sometimes diverges. In this work, two steps have been proposed for unknown system identification while overcoming the difficulty encountered in KF. The first step is to optimise the parameters of the KF using the GGS algorithm by considering a properly balanced fitness function. The second step is to estimate the unknown coefficients of the system by using the basic KF method with the optimally tuned KF parameters obtained from the first step. The proposed GGS-KF technique is tested on five different Volterra systems with various levels of noisy (10 dB, 15 dB and 20 dB) and noise-free input conditions. The simulation results confirm that the GGS-KF-based identification approach results in the most accurate estimations compared to the conventional KF and other reported techniques in terms of parameter estimation error, mean-squared error (MSE), fitness percentage (FIT%), mean-squared deviation (MSD), and cumulative density function (CDF). To validate the practical applicability of the proposed technique, two benchmark systems have also been identified based on the original data sets.

An Unscented Kalman Filter Based on-line Diagnostic Approach For PEM Fuel Cell Flooding

Poor water management usually leads to various degrees of flooding in the hydrogen type fuel cell, affecting both the instantaneous performance and the long-term durability of the system adversely. While a lot of fuel cell diagnostic tools exist that could be utilized for the flooding diagnostics, most of these approaches are intrusive, requiring special modification to the fuel cell that affects its integrity, or special equipment (e.g. AC spectrometer) that adds to the complexity and cost of the system, and therefore are not considered to be a viable solution for the on-board integration of the diagnostic scheme.This paper proposes a model based approach for the fuel cell flooding diagnostics problem, utilizing only the cell current and voltage, and the inlet pressures of the fuel cell as the input signals of the diagnostic scheme. A diagnostic-oriented fuel cell system dynamic model is developed to incorporate the effects of the fault, i.e. the flooding, on the system dynamics. For simplicity, only the cathode channel flooding, the cathode gas diffusion layer (GDL) flooding, and the anode channel flooding are considered while we neglect the mass transport loss through the anode GDL. The cathode channel flooding and the GDL flooding diagnostic problems are decoupled and formulated as standard joint state and parameter estimation problems, with the amounts of the liquid water treated as varying system parameters to be identified. The unscented Kalman Filter technique has been applied to solve these problems. Simulation results validate the applicability of the cascading unscented Kalman filter design for flooding diagnostics.

Design of unscented Kalman filter based on the adjustments of the number and placements of the sampling points

This paper addresses a general sampling method of the unscented Kalman filter (UKF) for nonlinear state estimation. The sampling method for standard UKF is analyzed, and we propose a theorem to address the conditions that UKF provides a third order accuracy in terms of Taylor series expansion for expectation estimation by changing the number and placements of the sampling points. This theorem can be used to develop new UKF. Based on this theorem, we propose a method to design the placements of the sampling points, including the directions and lengths by optimization strategies. Simulation studies demonstrate that the proposed UKF is effective and can significantly improve the filter performance.

Extended Kalman Filter (EKF) Design for Vehicle Position Tracking Using Reliability Function of Radar and Lidar.

Detection and distance measurement using sensors is not always accurate. Sensor fusion makes up for this shortcoming by reducing inaccuracies. This study, therefore, proposes an extended Kalman filter (EKF) that reflects the distance characteristics of lidar and radar sensors. The sensor characteristics of the lidar and radar over distance were analyzed, and a reliability function was designed to extend the Kalman filter to reflect distance characteristics. The accuracy of position estimation was improved by identifying the sensor errors according to distance. Experiments were conducted using real vehicles, and a comparative experiment was done combining sensor fusion using a fuzzy, adaptive measure noise and Kalman filter. Experimental results showed that the study’s method produced accurate distance estimations.

Design of a robust central difference kalman filter in the presence of uncertainties and unknown measurement errors

In this study, a novel RCDKF11Robust Central Difference Kalman Filter. is proposed for nonlinear plants. The system under consideration is a comprehensive case where the norm bounded uncertainties are supposed in both the state and output equations. Since the filtering methodology has been suggested based on the Stirling formula, it requires no derivative or Jacobian matrix computations. Furthermore, the mean value of uncertainties has been eliminated in the development of the filter structure. Different types of uncertainties are incorporated in the standard formulation of CDKF and it is demonstrated that the upper bound of covariance matrices can be derived according to them. In contrast to the similar works, the stability of the proposed filtering strategy is proved by the Lyapunov theory and the upper bound of state estimation error covariance is found for all admissible uncertainties. To demonstrate the performance of the introduced estimation algorithm, it will be evaluated on the attitude determination system of a three-axis satellite including a star camera and gyro sensor. The simulation results of the proposed filter are compared with the conventional CDKF,22Central Difference Kalman Filter. NRF,33Nonlinear Robust Filter. EKF44Extended Kalman Filter. and PF55Particle Filter. and the better efficiency of the developed method is established.

Kalman filter and satellite attitude control system analytical design

The article considers a certain form of suboptimal Kalman-Bucy filter (KBF), with bounded grows of memory (FBGM) and its application for satellite control system analytical design. The FBGM is robust and simple. Due to these qualities it can be easily practically implemented. This is especially important for airspace applications, where on-board computers (OBC), despite of the huge progress achieved in their characteristics, still have restricted resources. Since FBGM in the steady state can be made optimal KBF, it is used for, so called, analytical design (AD) of ACS, to estimate its potentially achievable performance in an idealistic case. This case assumes that all restrictions and constraints are removed and not taking into account as for the real system design process. Various schemes of filter usage in conjunction with the controller in closed negative feedback control loop are discussed. The emphasis is on analytical design; however, taking into account engineering aspects, the solution found can be implemented in real system as well.

Kalman filter and satellite attitude control system analytical design

Kalman filter and satellite attitude control system analytical design

ASENKRON MOTORUN İNDİRGENMİŞ-DERECELİ UYARLAMALI GENİŞLETİLMİŞ KALMAN FİLTRESİ İLE DURUM VE PARAMETRE KESTİRİMİ

In this study, the design of reduced-order adaptive extended Kalman filter (EKF) for speed-sensorless control of induction motors (IMs) is performed, and its performance is tested using it in a speed-sensorless direct vector controlled drive system under simulations. The proposed observer estimates the stator stationary axis components of rotor fluxes and rotor mechanical speed required for vector control in addition to disturbance load torque. On the other hand, estimation performance of EKFs depends on the correct selection of system ( ) and measurement ( ) error covariance matrices. In the literature, these matrices are generally assumed as constant and determined by the trial-and-error method. However, those matrices are affected by operating conditions of IM and should be updated according to operating conditions in order to obtain higher performance estimations. Since the simultaneously update of both and may lead to divergence or tracking problems, only is updated considering operating conditions by adaptive EKF (AEKF) algorithm having a forgetting factor. In addition, AEKF has been designed as reduced-order with the aim of reduction of its computational burden for real-time applications.

Discrete-Time Kalman Filter Design for Linear Infinite-Dimensional Systems

As the optimal linear filter and estimator, the Kalman filter has been extensively utilized for state estimation and prediction in the realm of lumped parameter systems. However, the dynamics of complex industrial systems often vary in both spatial and temporal domains, which take the forms of partial differential equations (PDEs) and/or delay equations. State estimation for these systems is quite challenging due to the mathematical complexity. This work addresses discrete-time Kalman filter design and realization for linear distributed parameter systems. In particular, the structural- and energy-preserving Crank–Nicolson framework is applied for model time discretization without spatial approximation or model order reduction. In order to ensure the time instance consistency in Kalman filter design, a new discrete model configuration is derived. To verify the feasibility of the proposed design, two widely-used PDEs models are considered, i.e., a pipeline hydraulic model and a 1D boundary damped wave equation.

A lightweight autonomous MAV for indoor search and rescue

AbstractMicro Aerial Vehicles (MAVs) have great potentials to be applied for indoor search and rescue missions. In this paper, we propose a modular lightweight design of an autonomous MAV with integrated hardware and software. The MAV is equipped with the 2D laser scanner, camera, mission computer and flight controller, running all the computation onboard in real time. The onboard perception system includes a laser‐based SLAM module and a custom‐designed visual detection module. A dual Kalman filter design provides robust state estimation by multiple sensor fusion. Specifically, the fusion module provides robust altitude measurement in the circumstance of surface changing. In addition, indoor‐outdoor transition is explicitly handled by the fusion module. In order to efficiently navigate through obstacles and adapt to multiple tasks, a task tree‐based mission planning method is seamlessly integrated with path planning and control modules. The MAV is capable of searching and rescuing victims from unknown indoor environments effectively. It was validated by our award‐winning performance at the 2017 International Micro Air Vehicle Competition (IMAV 2017), held in Toulouse, France. The performance video is available on https://youtu.be/8H19ppS_VXM.

Kalman Filter-Based Channel Estimation for Mobile-to-Mobile and Relay Networks

This letter deals with channel estimation in mobile-to-mobile communications, possibly including amplify and forward mobile relays, assuming a two-dimensional scattering environment. A second-order autoregressive [AR(2)] model with the Kalman filter is used to estimate the channel gain of the global multihop channel. The parameters of the AR(2) model can be tuned by using a classic correlation matching criterion. Alternatively, the use of a minimization of the asymptotic variance criterion permits a strong performance improvement, although the corresponding analytical study is still missing in the literature—which is the topic of this letter. The closed-form expressions for the optimal tuning of the AR(2) parameters and mean square error performance have been first established as a function of the second and fourth moments of the Doppler spectrum of the global channel. Because the analytical formulas of these moments were not given in the literature, we derive them by exploiting cumulant property of convolution of density functions, after decomposition of the global channel as a cascade of Jakes Doppler power spectral density channels. Consequently, the provided closed-form formula are helpful for the design of Kalman filters for a given state of the source, destination, and mobile relays [Doppler spread and signal to noise ratio].

Design and implementation of hybrid Kalman filter for state estimation of power system under unbalanced loads

State estimation technique plays a vital role in predicting the stability of the power system and is done by estimating the primary variables (states) of the system. Voltage magnitudes (V) and angles (δ) at network buses define the state of a power system. Supervisory control and data acquisition is used to monitor and control the power system state variables where in accurate state variable estimation is quite complex due to the presence of noise in the measured data. State estimation (SE) using conventional techniques such as weighted least square, regularised least square, Kalman filter predict the state vectors with still random error due to its parametric limitations. This study proposes hybrid Kalman filter based SE where the limitation in efficient handling of more number of variables using Kalman filter is addressed by regularising the state variables with constrains and the results are validated for 62-bus Indian utility system. The simulation results explain the operational efficiency of the hybrid Kalman filtering method under various load variation conditions and the results are compared with SE using conventional Kalman filtering method.

Unscented Kalman filter for continuous‐time nonlinear fractional‐order systems with process and measurement noises

AbstractThis study proposes the design of unscented Kalman filter for a continuous‐time nonlinear fractional‐order system involving the process noise and the measurement noise. The nonlinear fractional‐order system is discretized to get the difference equation. According to the unscented transformation, the design method of unscented Kalman filter for a continuous‐time nonlinear fractional‐order system is provided. Compared with the extended Kalman filter, the proposed method can obtain a more accurate estimation effect. For fractional‐order systems containing non‐differentiable nonlinear functions, the method proposed in this paper is still effective. The unknown parameters are also discussed by the augmented vector method to achieve the state estimation and parameter identification. Finally, two examples are offered to verify the effectiveness of the proposed unscented Kalman filter for nonlinear fractional‐order systems.

Observer and filter design for linear transport-reaction systems

The present work extends known finite dimensional Luenberger observer and Kalman filter designs to the realm of linear transport-reaction systems frequently present in chemical engineering practice. A unified modelling framework for distributed parameter systems (DPS) which does not account for any type of spatial approximation or order reduction is developed. The Cayley–Tustin transformation of continuous linear distributed parameter system yields structure and properties preserving discrete distributed parameter models, amenable to observer and filter design developments. Designs presented here explore well known state reconstruction methodologies starting from least square estimation, continuous and discrete Luenberger observers and one-step predictor Kalman filter realization. Simple implementation and realization account for the appealing nature of the discrete system observers and filter designs for linear transport-reaction systems. The simulation scenarios cover the majority of representative examples found in the common engineering process control practice.

Distributed adaptive Kalman filter based on variational Bayesian technique

In this paper, distributed Kalman filter design is studied for linear dynamics with unknown measurement noise variance, which modeled by Wishart distribution. To solve the problem in a multi-agent ...