Investigation of Improved Chaotic Signal Tracking by Echo State Neural Networks and Multilayer Perceptron via Training of Extended Kalman Filter Approach

This paper presents a prediction performance of feedforward Multilayer Perceptron (MLP) and Echo State Networks (ESN) trained with extended Kalman filter. Feedforward neural networks and ESN are powerful neural networks which can track and predict nonlinear signals. However, their tracking performance depends on the specific signals or data sets, having the risk of instability accompanied by large error. In this study we explore this process by applying different network size and leaking rate for prediction of nonlinear or chaotic signals in MLP neural networks. Major problems of ESN training such as the problem of initialization of the network and improvement in the prediction performance are tackled. The influence of coefficient of activation function in the hidden layer and other key parameters are investigated by simulation results. Extended Kalman filter is employed in order to improve the sequential and regulation learning rate of the feedforward neural networks. This training approach has vital features in the training of the network when signals have chaotic or non-stationary sequential pattern. Minimization of the variance in each step of the computation and hence smoothing of tracking were obtained by examining the results, indicating satisfactory tracking characteristics for certain conditions. In addition, simulation results confirmed satisfactory performance of both of the two neural networks with modified parameterization in tracking of the nonlinear signals.

Parameter Estimation of Diode Circuit Using Extended Kalman Filter

This paper presents parameter estimation of a single-phase rectifier using extended Kalman filter (EKF). The state space model has been obtained using Kirchhoff’s current law (KCL) and Kirchhoff’s voltage law (KVL). The capacitor voltage and diode current of the circuit have been estimated using EKF. Simulation results validate the better accuracy of the proposed method as compared to the least mean square method (LMS). Further, EKF has the advantage that it can be used for nonlinear systems.

Relative Navigation with Laser-Based Intermittent Measurement for Formation Flying Satellites

This study presents a precise relative navigational method for satellites flying in formation using laser-based intermittent measurement data. The measurement data for the relative navigation between two satellites consist of a relative distance measured by a laser instrument and relative attitude angles measured by attitude determination. The relative navigation solutions are estimated by both the Extended Kalman filter (EKF) and unscented Kalman filter (UKF). The solutions estimated by the EKF may become inaccurate or even diverge as measurement outage time gets longer because the EKF utilizes a linearization approach. However, this study shows that the UKF with the appropriate scaling parameters provides a stable and accurate relative navigation solutions despite the long measurement outage time and large initial error as compared to the relative navigation solutions of the EKF. Various navigation results have been analyzed by adjusting the scaling parameters of the UKF.

Analysis of Translational Ship Oscillations in a Realistic Environment

To acquire accurate ship motions at the center of gravity, a single low-cost inertial sensor is utilized and applied on board to measure ship oscillating motions. As observations, the three axes accelerations and three axes rotational rates provided by the sensor are used. The mathematical model of processing the observation data includes determination of the distance vector between the sensor and the center of gravity in x, y, and z directions. After setting up the transfer matrix from sensor’s own coordinate system to the ship’s body frame, an extended Kalman filter is applied to deal with nonlinearities between the ship motion in the body frame and the observation information in the sensor’s frame. As a side effect, the method eliminates sensor noise and other unwanted errors. Results are not only roll and pitch, but also linear motions, in particular heave and surge at the center of gravity. For testing, we resort to measurements recorded on a small vessel in a well-defined sea state. With response amplitude operators computed numerically by a commercial software (Seaway), motion characteristics are estimated. These agree well with the measurements after processing with the suggested method.

Adaptive Extended Kalman Filter for Ballistic Missile Tracking

In the current work, adaptive extended Kalman filter (AEKF) is presented for solution of ground radar based ballistic missile (BM) tracking problem in re-entry phase with unknown ballistic coefficient. The estimation of trajectory of any BM in re-entry phase is extremely difficult, because of highly non-linear motion of BM. The estimation accuracy of AEKF has been tested for a typical test target tracking problem adopted from literature. Further, the approach of AEKF is compared with extended Kalman filter (EKF). The simulation result indicates the superiority of the AEKF in solving joint parameter and state estimation problems.

Estimation of the Temperatures in an Asynchronous Machine Using Extended Kalman Filter

In order to monitor the thermal behavior of an asynchronous machine with squirrel cage rotor, a 9th-order extended Kalman filter (EKF) algorithm is implemented to estimate the temperatures of the stator windings, the rotor cage and the stator core. The state-space equations of EKF are established based on the electrical, mechanical and the simplified thermal models of an asynchronous machine. The asynchronous machine with simplified thermal model in Dymola is compiled as DymolaBlock, a physical model in MATLAB/Simulink. The coolant air temperature, three-phase voltages and currents are exported from the physical model and are processed by EKF estimator as inputs. Compared to the temperatures exported from the physical model of the machine, three parts of temperatures can be estimated quite accurately by the EKF estimator. The online EKF estimator is independent from the machine control algorithm and can work under any speed and load condition if the stator current is nonzero current system.

Lithium-Ion Battery State of Charge Estimation Using One State Hysteresis Model with Nonlinear Estimation Strategies

Battery state of charge (SOC) estimation is an important parameter as it measures the total amount of electrical energy stored at a current time. The SOC percentage acts as a fuel gauge if it is compared with a conventional vehicle. Estimating the SOC is, therefore, essential for monitoring the amount of useful life remaining in the battery system. This paper looks at the implementation of three nonlinear estimation strategies for Li-Ion battery SOC estimation. One of the most common behavioral battery models is the one state hysteresis (OSH) model. The extended Kalman filter (EKF), the smooth variable structure filter (SVSF), and the time-varying smoothing boundary layer SVSF are applied on this model, and the results are compared.

Offline Parameter Identification and State-of-Charge Estimation for Healthy and Aged Electric Vehicle Batteries Based on the Combined Model

Recently, Electric Vehicles (EVs) have received extensive consideration since they offer a more sustainable and greener transportation alternative compared to fossil-fuel propelled vehicles. Lithium-Ion (Li-ion) batteries are increasingly being deployed in EVs because of their high energy density, high cell-level voltage, and low rate of self-discharge. Since Li-ion batteries represent the most expensive component in the EV powertrain, accurate monitoring and control strategies must be executed to ensure their prolonged lifespan. The Battery Management System (BMS) has to accurately estimate parameters such as the battery State-of-Charge (SOC), State-of-Health (SOH), and Remaining Useful Life (RUL). In order for the BMS to estimate these parameters, an accurate and control-oriented battery model has to work collaboratively with a robust state and parameter estimation strategy. Since battery physical parameters, such as the internal resistance and diffusion coefficient change depending on the battery state-of-life (SOL), the BMS has to be adaptive to accommodate for this change. In this paper, an extensive battery aging study has been conducted over 12-months period on 5.4 Ah, 3.7 V Lithium polymer cells. Instead of using fixed charging/discharging aging cycles at fixed C-rate, a set of real-world driving scenarios have been used to age the cells. The test has been interrupted every 5% capacity degradation by a set of reference performance tests to assess the battery degradation and track model parameters. As battery ages, the combined model parameters are optimized and tracked in an offline mode over the entire batteries lifespan. Based on the optimized model, a state and parameter estimation strategy based on the Extended Kalman Filter (EKF) and the relatively new Smooth Variable Structure Filter (SVSF) have been applied to estimate the SOC at various states of life.

Fault Detection and Isolation in Attitude Control Subsystem of Spacecraft Formation Flying Using Extended Kalman Filters

In this paper, the problem of fault detection and isolation in the attitude control subsystem of spacecraft formation flying is considered. In order to design the fault detection method, an extended Kalman filter is utilized which is a nonlinear stochastic state estimation method. Three fault detection architectures, namely, centralized, decentralized, and semi-decentralized are designed based on the extended Kalman filters. Moreover, the residual generation and threshold selection techniques are proposed for these architectures.

State Estimation of a Biotechnological Process Using Extended Kalman Filter and Particle Filter

This paper deals with advanced state estimation algorithms for estimation of biomass concentration and specific growth rate in a typical fed-batch biotechnological process. This biotechnological process was represented by a nonlinear mass-balance based process model. Extended Kalman Filter (EKF) and Particle Filter (PF) was used to estimate the unmeasured state variables from oxygen uptake rate (OUR) and base consumption (BC) measurements. To obtain more general results, a simplified process model was involved in EKF and PF estimation algorithms. This model doesn’t require any special growth kinetic equations and could be applied for state estimation in various bioprocesses. The focus of this investigation was concentrated on the comparison of the estimation quality of the EKF and PF estimators by applying different measurement noises. The simulation results show that Particle Filter algorithm requires significantly more computation time for state estimation but gives lower estimation errors both for biomass concentration and specific growth rate. Also the tuning procedure for Particle Filter is simpler than for EKF. Consequently, Particle Filter should be preferred in real applications, especially for monitoring of industrial bioprocesses where the simplified implementation procedures are always desirable.

Navigation and Guidance System Architectures for Small Unmanned Aircraft Applications

Two multisensor system architectures for navigation and guidance of small Unmanned Aircraft (UA) are presented and compared. The main objective of our research is to design a compact, light and relatively inexpensive system capable of providing the required navigation performance in all phases of flight of small UA, with a special focus on precision approach and landing, where Vision Based Navigation (VBN) techniques can be fully exploited in a multisensor integrated architecture. Various existing techniques for VBN are compared and the Appearance-Based Navigation (ABN) approach is selected for implementation. Feature extraction and optical flow techniques are employed to estimate flight parameters such as roll angle, pitch angle, deviation from the runway centreline and body rates. Additionally, we address the possible synergies of VBN, Global Navigation Satellite System (GNSS) and MEMS-IMU (Micro-Electromechanical System Inertial Measurement Unit) sensors, and the use of Aircraft Dynamics Model (ADM) to provide additional information suitable to compensate for the shortcomings of VBN and MEMS-IMU sensors in high-dynamics attitude determination tasks. An Extended Kalman Filter (EKF) is developed to fuse the information provided by the different sensors and to provide estimates of position, velocity and attitude of the UA platform in real-time. The key mathematical models describing the two architectures i.e., VBN-IMU-GNSS (VIG) system and VIGADM (VIGA) system are introduced. The first architecture uses VBN and GNSS to augment the MEMS-IMU. The second mode also includes the ADM to provide augmentation of the attitude channel. Simulation of these two modes is carried out and the performances of the two schemes are compared in a small UA integration scheme (i.e., AEROSONDE UA platform) exploring a representative cross-section of this UA operational flight envelope, including high dynamics manoeuvres and CAT-I to CAT-III precision approach tasks. Simulation of the first system architecture (i.e., VIG system) shows that the integrated system can reach position, velocity and attitude accuracies compatible with the Required Navigation Performance (RNP) requirements. Simulation of the VIGA system also shows promising results since the achieved attitude accuracy is higher using the VBN-IMU-ADM than using VBN-IMU only. A comparison of VIG and VIGA system is also performed and it shows that the position and attitude accuracy of the proposed VIG and VIGA systems are both compatible with the RNP specified in the various UA flight phases, including precision approach down to CAT-II.

On the Modeling and State Estimation for Dynamic Power System

This paper investigates a method for the state estimation of nonlinear systems described by a class of differential-algebraic equation (DAE) models using the extended Kalman filter. The method involves the use of a transformation from a DAE to ordinary differential equation (ODE). A relevant dynamic power system model using decoupled techniques will be proposed. The estimation technique consists of a state estimator based on the EKF technique as well as the local stability analysis. High performances are illustrated through a simulation study applied on IEEE 13 buses test system.

Function Approximation with Radial Basis Function Neural Networks via FIR Filter

Recent experimental evidences have shown that because of a fast convergence and a nice accuracy, neural networks training via extended kalman filter (EKF) method is widely applied. However, as to an uncertainty of the system dynamics or modeling error, the performance of the method is unreliable. In order to overcome this problem in this paper, a new finite impulse response (FIR) filter based learning algorithm is proposed to train radial basis function neural networks (RBFN) for nonlinear function approximation. Compared to the EKF training method, the proposed FIR filter training method is more robust to those environmental conditions. Furthermore , the number of centers will be considered since it affects the performance of approximation.

Low-Cost and Highly Accurate Motion Models for Three-Dimensional Local Landmark-based Autonomous Navigation

Recently, the Spherical Motion Models (SMM-s) have been introduced [1]. These new models have been developed for 3D local landmark-base Autonomous Navigation (AN). This paper is revealing new arguments and experimental results to support the SMM-s characteristics. The accuracy and the robustness in performing a specific task are the main concerns of the new investigations. To analyze their performances of the SMM-s, the most powerful tools of estimation theory, the extended Kalman filter (EKF) and unscented Kalman filter (UKF), which give the best estimations in noisy environments, have been employed. The Monte Carlo validation implementations used to test the stability and robustness of the models have been employed as well.

A New Version of Unscented Kalman Filter

This paper presents a new algorithm which yields a nonlinear state estimator called iterated unscented Kalman filter. This state estimator makes use of both statistical and analytical linearization techniques in different parts of the filtering process. It outperforms the other three nonlinear state estimators: unscented Kalman filter (UKF), extended Kalman filter (EKF) and iterated extended Kalman filter (IEKF) when there is severe nonlinearity in system equation and less nonlinearity in measurement equation. The algorithm performance has been verified by illustrating some simulation results.

Deterministic Method to Assess Kalman Filter Passive Ranging Solution Reliability

For decades, the defense business has been plagued by not having a reliable, deterministic method to know when the Kalman filter solution for passive ranging application is reliable for use by the fighter pilot. This has made it hard to accurately assess when the ranging solution can be used for situation awareness and weapons use. To date, we have used ad hoc rules-of-thumb to assess when we think the estimate of the Kalman filter standard deviation on range is reliable. A reliable algorithm has been developed at BAE Systems Electronics & Integrated Solutions that monitors the Kalman gain matrix elements – and a patent is pending. The “settling" of the gain matrix elements relates directly to when we can assess the time when the passive ranging solution is within the 10 percent-of-truth value. The focus of the paper is on surface-based passive ranging – but the method is applicable to airborne targets as well.

Cascade Kalman Filter Configuration for Low Cost IMU/GPS Integration in Car Navigation Like Robot

This paper introduces a low cost INS/GPS algorithm for land vehicle navigation application. The data fusion process is done with an extended Kalman filter in cascade configuration mode. In order to perform numerical simulations, MATLAB software has been developed. Loosely coupled configuration is considered. The results obtained in this work demonstrate that a low-cost INS/GPS navigation system is partially capable of meeting the performance requirements for land vehicle navigation. The relative effectiveness of the kalman filter implementation in integrated GPS/INS navigation algorithm is highlighted. The paper also provides experimental results; field test using a car is carried out.

Single-Camera EKF-vSLAM

This paper presents an Extended Kaman Filter implementation of a single-camera Visual Simultaneous Localization and Mapping algorithm, a novel algorithm for simultaneous localization and mapping problem widely studied in mobile robotics field. The algorithm is vision and odometry-based, The odometry data is incremental, and therefore it will accumulate error over time, since the robot may slip or may be lifted, consequently if the odometry is used alone we can not accurately estimate the robot position, in this paper we show that a combination of odometry and visual landmark via the extended Kalman filter can improve the robot position estimate. We use a Pioneer II robot and motorized pan tilt camera models to implement the algorithm.

Acoustic Source Localization Based On the Extended Kalman Filter for an Underwater Vehicle with a Pair of Hydrophones

In this study, we consider a special situation that only a pair of hydrophone on a moving underwater vehicle is available to localize a fixed acoustic source of far distance. The trigonometry can be used in this situation by using two different DOA of different locations. Notice that the distance between the two locations should be measured. Therefore, we assume that the vehicle is sailing straightly and the moving distance for each unit time is measured continuously. However, the accuracy of the localization using the trigonometry is highly dependent to the accuracy of DOAs and measured moving distances. Therefore, we proposed another method based on the extended Kalman filter that gives more robust and accurate localization result.

Static Single Point Positioning Using The Extended Kalman Filter

Global Positioning System (GPS) technology is widely used today in the areas of geodesy and topography as well as in aeronautics mainly for military purposes. Due to the military usage of GPS, full access and use of this technology is being denied to the civilian user who must then work with a less accurate version. In this paper we focus on the estimation of the receiver coordinates ( X, Y, Z ) and its clock bias ( δtr ) of a fixed point based on pseudorange measurements of a single GPS receiver. Utilizing the instantaneous coordinates of just 4 satellites and their clock offsets, by taking into account the atmospheric delays, we are able to derive a set of pseudorange equations. The estimation of the four unknowns ( X, Y, Z , δtr ) is achieved by introducing an extended Kalman filter that processes, off-line, all the data collected from the receiver. Higher performance of position accuracy is attained by appropriate tuning of the filter noise parameters and by including other forms of biases.