Adaptive Kalman Filter for Noise Estimation and Identification with Bayesian Approach

Bayesian approach can be used for parameter identification and extraction in state space models and its ability for analyzing sequence of data in dynamical system is proved in different literatures. In this paper, adaptive Kalman filter with Bayesian approach for identification of variances in measurement parameter noise is developed. Next, it is applied for estimation of the dynamical state and measurement data in discrete linear dynamical system. This algorithm at each step time estimates noise variance in measurement noise and state of system with Kalman filter. Next, approximation is designed at each step separately and consequently sufficient statistics of the state and noise variances are computed with a fixed-point iteration of an adaptive Kalman filter. Different simulations are applied for showing the influence of noise variance in measurement data on algorithm. Firstly, the effect of noise variance and its distribution on detection and identification performance is simulated in Kalman filter without Bayesian formulation. Then, simulation is applied to adaptive Kalman filter with the ability of noise variance tracking in measurement data. In these simulations, the influence of noise distribution of measurement data in each step is estimated, and true variance of data is obtained by algorithm and is compared in different scenarios. Afterwards, one typical modeling of nonlinear state space model with inducing noise measurement is simulated by this approach. Finally, the performance and the important limitations of this algorithm in these simulations are explained. 

Error Correction Method for 2D Ultra-Wideband Indoor Wireless Positioning System Using Logarithmic Error Model

Indoor positioning technologies have been evolved rapidly. They augment the Global Positioning System (GPS) which requires line-of-sight to the sky to track the location of people or objects. In this study, we developed an error correction method for an indoor real-time location system (RTLS) based on an ultra-wideband (UWB) sensor from Decawave. Multiple stationary nodes (anchor) were installed throughout the workspace. The distance between stationary and moving nodes (tag) can be measured using a two-way-ranging (TWR) scheme. The result has shown that the uncorrected ranging error from the sensor system can be as large as 1 m. To reduce ranging error and thus increase positioning accuracy, we present an online correction algorithm using the Kalman filter. The results from experiments have shown that the system can reduce ranging error down to 5 cm.

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.

State Estimation Based on Unscented Kalman Filter for Burgers’ Equation

Controlling the flow of fluids is a challenging problem that arises in many fields. Burgers’ equation is a fundamental equation for several flow phenomena such as traffic, shock waves, and turbulence. The optimal feedback control method, so-called model predictive control, has been proposed for Burgers’ equation. However, the model predictive control method is inapplicable to systems whose all state variables are not exactly known. In practical point of view, it is unusual that all the state variables of systems are exactly known, because the state variables of systems are measured through output sensors and limited parts of them can be only available. In fact, it is usual that flow velocities of fluid systems cannot be measured for all spatial domains. Hence, any practical feedback controller for fluid systems must incorporate some type of state estimator. To apply the model predictive control to the fluid systems described by Burgers’ equation, it is needed to establish a state estimation method for Burgers’ equation with limited measurable state variables. To this purpose, we apply unscented Kalman filter for estimating the state variables of fluid systems described by Burgers’ equation. The objective of this study is to establish a state estimation method based on unscented Kalman filter for Burgers’ equation. The effectiveness of the proposed method is verified by numerical simulations.

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.

Motion-Based Detection and Tracking of Multiple Pedestrians

Tracking of moving people has gained a matter of great importance due to rapid technological advancements in the field of computer vision. The objective of this study is to design a motion based detection and tracking multiple walking pedestrians randomly in different directions. In our proposed method, Gaussian mixture model (GMM) is used to determine moving persons in image sequences. It reacts to changes that take place in the scene like different illumination; moving objects start and stop often, etc. Background noise in the scene is eliminated through applying morphological operations and the motions of tracked people which is determined by using the Kalman filter. The Kalman filter is applied to predict the tracked location in each frame and to determine the likelihood of each detection. We used a benchmark data set for the evaluation based on a side wall stationary camera. The actual scenes from the data set are taken on a street including up to eight people in front of the camera in different two scenes, the duration is 53 and 35 seconds, respectively. In the case of walking pedestrians in close proximity, the proposed method has achieved the detection ratio of 87%, and the tracking ratio is 77 % successfully. When they are deferred from each other, the detection ratio is increased to 90% and the tracking ratio is also increased to 79%.

The Enhancement of Target Localization Using Ship-Borne Electro-Optical Stabilized Platform

Electro-optical (EO) stabilized platforms have been widely used for surveillance and reconnaissance on various types of vehicles, from surface ships to unmanned air vehicles (UAVs). EO stabilized platforms usually consist of an assembly of structure, bearings, and motors called gimbals in which a gyroscope is installed. EO elements such as a CCD camera and IR camera, are mounted to a gimbal, which has a range of motion in elevation and azimuth and can designate and track a target. In addition, a laser range finder (LRF) can be added to the gimbal in order to acquire the precise slant range from the platform to the target. Recently, a versatile functionality of target localization is needed in order to cooperate with the weapon systems that are mounted on the same platform. The target information, such as its location or velocity, needed to be more accurate. The accuracy of the target information depends on diverse component errors and alignment errors of each component. Specially, the type of moving platform can affect the accuracy of the target information. In the case of flying platforms, or UAVs, the target location error can be increased with altitude so it is important to measure altitude as precisely as possible. In the case of surface ships, target location error can be increased with obliqueness of the elevation angle of the gimbal since the altitude of the EO stabilized platform is supposed to be relatively low. The farther the slant ranges from the surface ship to the target, the more extreme the obliqueness of the elevation angle. This can hamper the precise acquisition of the target information. So far, there have been many studies on EO stabilized platforms of flying vehicles. However, few researchers have focused on ship-borne EO stabilized platforms of the surface ship. In this paper, we deal with a target localization method when an EO stabilized platform is located on the mast of a surface ship. Especially, we need to overcome the limitation caused by the obliqueness of the elevation angle of the gimbal. We introduce a well-known approach for target localization using Unscented Kalman Filter (UKF) and present the problem definition showing the above-mentioned limitation. Finally, we want to show the effectiveness of the approach that will be demonstrated through computer simulations.

Performance Evaluation of GPS \ INS Main Integration Approach

This paper introduces a comparative study between the main GPS\INS coupling schemes, this will include the loosely coupled and tightly coupled configurations, several types of situations and operational conditions, in which the data fusion process is done using Kalman filtering. This will include the importance of sensors calibration as well as the alignment of the strap down inertial navigation system. The limitations of the inertial navigation systems are investigated.

1G2A IMU\GPS Integration Algorithm for Land Vehicle Navigation

A general decline in the cost, size, and power requirements of electronics is accelerating the adoption of integrated GPS/INS technologies in consumer applications such Land Vehicle Navigation. Researchers have looking for ways to eliminate additional components from product designs. One possibility is to drop one or more of the relatively expensive gyroscopes from microelectromechanical system (MEMS) versions of inertial measurement units (IMUs). For land vehicular use, the most important gyroscope is the vertical gyro that senses the heading of the vehicle and two horizontal accelerometers for determining the velocity of the vehicle. This paper presents a simplified integration algorithm for strap down (ParIMU)\GPS combination, with data post processing for the determination of 2-D components of position (trajectory), velocity and heading. In the present approach we have neglected earth rotation and gravity variations, because of the poor gyroscope sensitivities of the low-cost IMU and because of the relatively small area of the trajectory.

Fuzzy Based Stabilizer Control System for Quad-Rotor

In this paper the design, development and testing of a stabilizer control system for a Quad-rotor is presented which is focused on the maneuverability. The mechanical design is performed along with the design of the controlling algorithm which is devised using fuzzy logic controller. The inputs for the system are the angular positions and angular rates of the Quad-rotor relative to three axes. Then the output data is filtered from an accelerometer and a gyroscope through a Kalman filter. In the development of the stability controlling system Mandani fuzzy model is incorporated. The results prove that the fuzzy based stabilizer control system is superior in high dynamic disturbances compared to the traditional systems which use PID integrated stabilizer control systems.

Kalman Filter for Bilinear Systems with Application

In this paper, we present a new kind of the bilinear systems in the form of state space model. The evolution of this system depends on the product of state vector by its self. The well known Lotak Volterra and Lorenz models are special cases of this new model. We also present here a generalization of Kalman filter which is suitable to work with the new bilinear model. An application to real measurements is introduced to illustrate the efficiency of the proposed algorithm.

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.

Low Cost IMU \ GPS Integration Using Kalman Filtering for Land Vehicle Navigation Application

Land vehicle navigation system technology is a subject of great interest today. Global Positioning System (GPS) is a common choice for positioning in such systems. However, GPS alone is incapable of providing continuous and reliable positioning, because of its inherent dependency on external electromagnetic signals. Inertial Navigation is the implementation of inertial sensors to determine the position and orientation of a vehicle. As such, inertial navigation has unbounded error growth since the error accumulates at each step. Thus in order to contain these errors some form of external aiding is required. The availability of low cost Micro-Electro-Mechanical-System (MEMS) inertial sensors is now making it feasible to develop Inertial Navigation System (INS) using an inertial measurement unit (IMU), in conjunction with GPS to fulfill the demands of such systems. Typically IMU’s are very expensive systems; however this INS will use “low cost” components. Unfortunately with low cost also comes low performance and is the main reason for the inclusion of GPS and Kalman filtering into the system. The aim of this paper is to develop a GPS/MEMS INS integrated system, which is able to provide a navigation solution with accuracy levels appropriate for land vehicle navigation. The primary piece of equipment used was a MEMS-based Crista IMU (from Cloud Cap Technology Inc.) and a Garmin GPS 18 PC (which is both a receiver and antenna). The integration of GPS with INS can be implemented using a Kalman filter in loosely coupled mode. In this integration mode the INS error states, together with any navigation state (position, velocity, and attitude) and other unknown parameters of interest, are estimated using GPS measurements. All important equations regarding navigation are presented along with discussion.

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.

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.

A Stable Pose Estimation Method for the Biped Robot using Image Information

This paper proposes a balance control scheme for a biped robot to trace an arbitrary path using image information. While moving, it estimates the zero moment point(ZMP) of the biped robot in the next step using a Kalman filter and renders an appropriate balanced pose of the robot. The ZMP can be calculated from the robot's pose, which is measured from the reference object image acquired by a CCD camera on the robot's head. For simplifying the kinematical model, the coordinates systems of individual joints of each leg are aligned and the robot motion is approximated as an inverted pendulum so that a simple linear dynamics, 3D-LIPM(3D-Linear Inverted Pendulum Mode) can be applied. The efficiency of the proposed algorithm has been proven by the experiments performed on unknown trajectory.

A Novel Non-Uniformity Correction Algorithm Based On Non-Linear Fit

Infrared focal plane arrays (IRFPA) sensors, due to their high sensitivity, high frame frequency and simple structure, have become the most prominently used detectors in military applications. However, they suffer from a common problem called the fixed pattern noise (FPN), which severely degrades image quality and limits the infrared imaging applications. Therefore, it is necessary to perform non-uniformity correction (NUC) on IR image. The algorithms of non-uniformity correction are classified into two main categories, the calibration-based and scene-based algorithms. There exist some shortcomings in both algorithms, hence a novel non-uniformity correction algorithm based on non-linear fit is proposed, which combines the advantages of the two algorithms. Experimental results show that the proposed algorithm acquires a good effect of NUC with a lower non-uniformity ratio.

Two Stage Control Method Using a Disturbance Observer and a Kalman Filter

This paper describes the two stage control using a disturbance observer and a Kalman filter. The system feedback uses the estimated state when it controls the speed. After the change-over point, its feedback uses the controlled plant output when it controls the position. To change the system continually, a change-over point has to be determined pertinently, and the controlled plant input has to be adjusted by the addition of the appropriate value. The proposed method has noise-reduction effect. It changes the system continually, even if the controlled plant identification has the error. Although the conventional method needs a speed sensor, the proposed method does not need it. The proposed method has a superior robustness compared with the conventional two stage control.

Neuro-Fuzzy Network Based On Extended Kalman Filtering for Financial Time Series

The neural network's performance can be measured by efficiency and accuracy. The major disadvantages of neural network approach are that the generalization capability of neural networks is often significantly low, and it may take a very long time to tune the weights in the net to generate an accurate model for a highly complex and nonlinear systems. This paper presents a novel Neuro-fuzzy architecture based on Extended Kalman filter. To test the performance and applicability of the proposed neuro-fuzzy model, simulation study of nonlinear complex dynamic system is carried out. The proposed method can be applied to an on-line incremental adaptive learning for the prediction of financial time series. A benchmark case studie is used to demonstrate that the proposed model is a superior neuro-fuzzy modeling technique.

GPS INS Integration Application in Flight Management System

Flight management system (FMS) is a specialized computer system that automates a wide variety of in-flight tasks, reducing the workload on the flight crew to the point that modern aircraft no longer carry flight engineers or navigators. The primary function of FMS is to perform the in-flight management of the flight plan using various sensors (such as GPS and INS often backed up by radio navigation) to determine the aircraft's position. From the cockpit FMS is normally controlled through a Control Display Unit (CDU) which incorporates a small screen and keyboard or touch screen. This paper investigates the performance of GPS/ INS integration techniques in which the data fusion process is done using Kalman filtering. This will include the importance of sensors calibration as well as the alignment of the strap down inertial navigation system. The limitations of the inertial navigation systems are investigated in order to understand why INS sometimes is integrated with other navigation aids and not just operating in standalone mode. Finally, both the loosely coupled and tightly coupled configurations are analyzed for several types of situations and operational conditions.