Nonstationary phase boundary estimation in electrical impedance tomography using unscented Kalman filter

In this paper, an adaptive unscented Kalman filter (AUKF) is developed for state estimation on a tractor-trailer system. For nonlinear systems, the unscented Kalman filter (UKF) is a well-known approach for observer design. Some research has shown the UKF can be more accurate than extended Kalman filter (EKF) with similar computation burden. However, the performance of traditional Kalman filter may deteriorate when process noise changes or sudden disturbance occurs due to the fixed process noise covariance (Q matrix) in the filter. An adaptive gain is calculated to compensate for the mismatch between the actual residual covariance and the deduced value from the filter, ensuring that the sequence of residual is uncorrelated. An estimated Q matrix is referred in the adaptive gain calculation at each sample. Simulation is done in various situations. The positions of trailer are used as measurements. Compared with the standard UKF (SUKF) and another adaptive UKF, the proposed algorithm has better result.

For the purpose of improving the performance of unscented Kalman filter (UKF) under the condition without accurate system noise statistics, this paper presents a new adaptive UKF based on the maximum likelihood principle. According to the maximum likelihood principle, the estimation of system noise statistics is determined by minimizing the negative of log likelihood function of innovation sequences. Subsequently, the estimated system noise statistics are fed back to the standard UKF to overcome its limitation. The proposed adaptive UKF can enhance the adaptive capability of standard UKF through the online estimation of system noise statistics. The effectiveness and advantage of the proposed algorithm are verified by the numerical simulations and comparison analysis.

Dynamic inverse obstacle problems with electrical impedance tomography

Requirements of highly precise pointing performance have been imposed on recently developed spacecrafts for a variety of missions. The stringent requirements have called on on-orbit estimation of spacecraft dynamics parameters and calibration of on-board sensors as indispensible practices. Consequently, on-orbit estimation of the mass moment of inertia of spacecraft has been a major issue mostly due to the changes by solar panel deployment and a large portion of fuel consumption (Creamer et al., 1996; Ahmed et al., 1998; Bordany et al., 2000; VanDyke et al., 2004; Myung et al., 2007; Myung & Bang, 2008; Sekhavat et al., 2009). As for measurement sensors, on-board calibration of alignment and bias errors of attitude and rate sensors is one of the main concerns of attitude sensor calibration researches (Pittelkau, 2001 & 2002, Lai et al., 2003). Pittelkau (2002) proposed an attitude estimator based on the Kalman filter (Kalman, 1960), in which spacecraft attitude quaternion, rate sensor misalignment and bias, and star tracker misalignments are taken into consideration as states, whereas the body rate is dealt as a synthesized signal by the estimates. Lai at al. (2003) derived a method for alignment estimation of attitude and rate sensors based on the unscented Kalman filter (UKF) (Julier and Uhlmann, 1997). Ma and Jiang (2005) presented spacecraft attitude estimation and calibration based only magnetometer measurements using an UKF. An interesting point is that we need predesigned 3-axis excitation manoeuvres of spacecraft for both dynamics parameter estimation and sensor calibration. Therefore, this study is motivated to merge above estimation and calibration processes into a single filtering problem. It is noteworthy that poor information of moments of inertia is to be treated as a system uncertainty while the rate sensor model errors are to be incorporated into the measurement process. As a filtering algorithm, this study employs a UKF. Extended Kalman filters (EKFs) have been successfully applied to the nonlinear attitude estimation problem (Crassidis et al., 2007). Hybrid estimation using the EKF has been reported by Myung at al. (2007). However, the EKF estimates using the first order linearization, which may lead to instability of the filter (ValDyke et al., 2004). The UKF approximates the nonlinear model to the second order by spreading points 1 sigma apart from the a priori mean. Performing nonlinear

This thesis is a reconciliation between multiple bodies of work with a shared objective that is ``to identify the active support" under different environment settings. The applications of focus within this thesis will be placed on electrical impedance tomography (EIT) and direction-of-arrival (DOA) estimation. The term ``active support" or only ``support" is commonly used in compressed sensing and sparse signal recovery communities which is essentially referring to ``the most contributing parameters" in a system of linear equations. Although with a common objective shared among the works that have been done within this thesis, this thesis can be divided into two major parts based on applications’ environment. The first part is the support identification under a process expressible by Fredholm integral equation of the first kind. For this problem, a research topic that is known as ``Electrical impedance tomography (EIT)," is chosen as a representative application for a collection of problems expressible by this integral equation. The physical laws (Physics) of EIT can be explained by Maxwell's equations under quasi-static environment. Under such condition, the energy dissipated from the source is spread throughout the region (domain) in a non-linear fashion. Together with the absent of phase or time delay information, the image reconstruction task for EIT usually faces the issue of low signal-to-noise-ratio (SNR) and support ambiguity. Multiple real-life applications typically fall under this category of problems such as medical and geophysical subsurface imaging, deconvolution, and image deblurring. The EIT is an imaging technique that estimates a distribution of electrical admittivity $\gamma$ of a ``subject under test (SUT)" sometimes called as ``medium" based on an inference from data captured from the medium's boundary. Although the name would suggests the value of `impedance' to be measured, in most practical scenario its reciprocal which is `admittance' (admittivity value) is commonly calculated instead. The admittivity value $\gamma$ encapsulates the information of medium's conductivity ($\sigma$) and permittivity ($\epsilon$) with the following expression $\gamma = \sigma + i\omega\epsilon$, where $\omega=2\pi f$ is the angular frequency (rad/s) and $f$ is frequency in Hz. The ``tomographic reconstruction" or ``the process of estimating the medium's internal admittivity distribution" can be accomplished by solving a mathematical problem that is commonly known as an ``inverse problem." Due to a quasi-static nature of this imaging modality, the image reconstruction of the EIT is known to be one of the most severely ill-posed inverse problems. The image reconstruction problem of EIT will be analyzed through two different viewpoints. Firstly, this problem will be analyzed through the lens of a discrete ill-posed inverse problem from the applied mathematics community viewpoint. Secondly, this problem will be re-analyzed through the lens of array signal processing/beamforming framework from the signal processing community viewpoint. While exploring the EIT image reconstruction techniques, it was observed that although the EIT system can be implemented economically, the implementation process is not completely straightforward. Therefore, a framework of a simple and reliable EIT prototyping system that could provide means to collect different data format (e.g. single measurement vector (SMV) and multiple measurement vectors (MMV)) were implemented in this thesis. This robust, economical, and straightforward implementation framework was developed with an aim that it could be beneficial for those who are interested in image reconstruction and inverse algorithms without the access of a full functioning commercialized EIT system. The second part is the support identification for DOA estimation under Gaussian and $\alpha-$stable distributed noises. Several improvements of a robust beamforming technique called MUSIC-like algorithm had been further investigated which helps improve the algorithm's performance. The main focus of this part is the performance improvement of the algorithm that can be used for support identification task under different noise scenarios. Three different approaches for estimating a relaxation parameter, an essential parameter used in the MUSIC-like algorithm, are presented. By experimenting with different approaches, an adaptive framework for relaxation parameter was observed to have the potential for further improvement. The performance of the MUSIC-like algorithm was then further explored through the directional adaptive framework under both Gaussian and $\alpha-$stable distributed noise. It was also compared with the conventional MUSIC algorithm coupled with a pre-conditioned covariance matrix.

Due to the complexity of hydrodynamic forces during maneuvering, the parameter estimation of the hydrodynamic model of vessel is challenging. This paper proposed a simplified three-degree-of-freedom (3DOF) hydrodynamic model of a two-thruster vessel. Based on experiment data, a comparative study on Extended Kalman filter (EKF) and Unscented Kalman filter (UKF) performance in non-linear parameter estimation is conducted. Via the comparison of model accuracy, the feasibility and possible profits of UKF are demonstrated.

In this paper, vision-based relative navigation of two spacecraft is addressed using the sparse Gauss-Hermite quadrature filter. The relative navigation provides the estimation of the relative attitude and relative orbit between spacecraft, which is a challenging filtering problem since it is a highly nonlinear and high dimensional estimation problem. Many filters have been used to solve this problem, such as, the extended Kalman filter (EKF) and the unscented Kalman filter (UKF). However, these filters are not accurate enough when the initial uncertainty is large or the nonlinearity is significant. Moreover, although the conventional Gauss-Hermite quadrature filter is more accurate than the UKF, it cannot be used since a huge number of points is required. It is shown in this paper that the sparse Gauss-Hermite quadrature filter can achieve better estimation accuracy than the EKF, the UKF, and the cubature Kalman filter without excessive computation load.

In this paper, the state trajectories of a hypersonic vehicle is estimated using a new generalized cubature Kalman filter. This new nonlinear estimation technique is based on a class of arbitrary-degree cubature rules to compute the multivariate integrals in the Bayesian filtering algorithm and can achieve higher degree of estimation accuracy. The performance of this new cubature Kalman filter is compared with the Extended Kalman filter, the unscented Kalman filter and the conventional third-degree cubature Kalman filter. The simulation results demonstrate that the proposed filter outperforms those three filters in estimation accuracy and convergence rate. It is also computationally more efficient than many other point-based estimation techniques.

Target tracking is one among the foremost aspects usually utilized in microwave radar applications, police investigation, communication, embedded systems, etc. In particular, tracking is crucial in single as well as multiple object environments. The target Motion is analyzed by mathematical model of a physical system. To obtain dynamics of a moving target such as location, momentum, expedition…etc. one of the most used approaches in target chase is random estimation approach. Stochastic (random) estimation is estimators are Interactive multiple model filter, particle filter, Unscented Kalman filter, Extended Kalman filter, Kalman filter,….etc. The stochastic estimator provides the estimate of the unknown dynamics of the system. For acquiring better gauge of the objective, channel ought to be adjusted. It is very important to tune the parameters observation noise (measurement noise) and plant noise (process noise) for better estimation of dynamics of the system especially in tracking applications. Tuning of measurement noise and plant noise can be done through Optimization techniques. To investigate the execution examination of Kalman filter and Extended Kalmanfilter using fine tuning approaches for both single and multi-target tracking are analyzed in this paper.

A real-time EIT imaging system based on the split augmented Lagrangian shrinkage algorithm

For mobile robotics, head gear in augmented reality (AR) applications or computer vision, it is essential to continuously estimate the egomotion and the structure of the environment. This paper presents the system developed in the SmartTracking project, which simultaneously integrates visual and inertial sensors in a combined estimation scheme. The sparse structure estimation is based on the detection of corner features in the environment. From a single known starting position, the system can move into an unknown environment. The vision and inertial data are fused, and the performance of both Unscented Kalman filter and Extended Kalman filter are compared for this task. The filters are designed to handle asynchronous input from visual and inertial sensors, which typically operate at different and possibly varying rates. Additionally, a bank of Extended Kalman filters, one per corner feature, is used to estimate the position and the quality of structure points and to include them into the structure estimation process. The system is demonstrated on a mobile robot executing known motions, such that the estimation of the egomotion in an unknown environment can be compared to ground truth.

This paper presents the efficient Unscented Kalman filter (UKF) based estimation and control of a 3-DOF Omni bundle robot. The angular trajectory tracking becomes more difficult under highly non-linear measurement noise and process noise. A rapidly converging Unscented Kalman Filter (UKF) is presented in the paper. The extended Kalman filter (EKF) provides less accurate results in the highly non-linear system and sometime may become unstable because of convergence related issues, whereas in UKF the results in the non-linear system are better than EKF. UKF is more accurate in state and noise estimation. The computed torque technique is taken as a model to apply UKF. After, estimation the noise is removed. The experiment is conducted on Omni bundle with process and measurement noise. The results prove the superiority of presented UKF over conventional UKF and EKF.

Radar systems are used for estimating the position and velocity of aircraft and ships from range and bearing measurements. In this article, we consider two motion models for a civilian aircraft: a constant velocity model and a coordinated turn model. Both kinematics models are written in state-space terms, where the velocity perturbations are modeled by a white noise acceleration model. In order to estimate the aircraft states given noisy measurements obtained from sensor outputs, we follow a Bayesian statistical approach that calculates the estimators of the unknown states. In our simulation, we recreate an air traffic control scenario and implement two nonlinear filtering algorithms in order to perform target tracking of the aircraft. The nonlinear Bayesian-based filters for this target tracking problem are the unscented Kalman filter and the Gauss-Hermite Kalman filter. Finally, the performance of both nonlinear filters is evaluated with a performance metric, root mean squared error, in Monte-Carlo runs.KeywordsTarget trackingUnscented Kalman filterGauss-Hermite Kalman filter

Fast non-intrusive estimation of liquid-phase interface and boundary heat flux in participating media by the Kalman filtering methods

State of Charge (SOC) estimation plays a crucial role in managing the performance and longevity of electric vehicle (EV) batteries. Various estimation techniques, including various Kalman Filters (KF), have been employed for this purpose. The mathematical process and limits of different KF family algorithms are analysed. In this study, an impact of nonlinear KF parameters on SOC estimation accuracy for EV batteries is analyzed. Specifically, the performance of Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), and Particle Filter (PF) is examined. EKF is most preferred for SOC estimation whereas introducing sigma points in UKF is the basic difference between EKF and UKF. In comparison to EKF and UKF, PF is more flexible since it applies to nonlinear systems with non-Gaussian distributions. Utilising a sequence of noisy measurements, KF is a recursive method that approximates the state of a dynamic system. It requires accurate parameters such as process noise covariance (Q) and measurement noise covariance (R) to work effectively. In this work, the effect of these parameters on state of charge estimation using nonlinear KFs has been analysed under different settings of noise covariance matrices. Tuning these parameters is essential for optimizing the performance of the KF and ensuring accurate and reliable state estimation in real-world applications. To find parameter values that provide the best balance between accuracy, robustness, and computational efficiency, the tuning process involves experimentation, simulation, and validation using real-world data. According to the results observed, the filter parameters such as three diagonal elements of Q are selected as 2e-8, 0.005, 0.003 and R as 2e-6. By evaluating the state estimation accuracy under different driving scenarios, robustness and sensitivity of filtering technique in estimating SOC for EV batteries has been studied. This analysis contributes to the optimization of SOC estimation algorithms, enhancing the reliability and efficiency of EV battery management systems.