Filtering of Q(t) Measurement Data for Estimating Leakage Current

Bluetooth Low Energy (BLE) based Wireless Indoor Localization System (WILS) with high localization accuracy and high localization precision is a key requirement in enabling the Internet of Things (IoT) in today’s applications. In this paper, we investigated the effect of BLE signal variations on indoor localization caused by the change in BLE transmission power levels. This issue is not often discussed as most of the works on localization algorithms use the highest power levels but has important practical implications for energy efficiency, e.g., if a designer would like to trade-off localization performance and node lifetime. To analyze the impact, we used the established trilateration based localization model with two methods i.e., Centroid Approximation (CA) and Minimum Mean Square Error (MMSE). We observed that trilateration based localization with MMSE method outperforms the CA method. We further investigated the use of two filters i.e., Low Pass Filter (LPF) and Kalman Filter (KF) and evaluated their effects in terms of mitigating the random variations from BLE signal. In comparison to non-filter based approach, we observed a great improvement in localization accuracy and localization precision with a filter-based approach. Furthermore, in comparison to LPF based trilateration localization with CA, the performance of a KF based trilateration localization with MMSE is far better. An average of 1 m improvement in localization accuracy and approximately 50% improvement in localization precision is observed by using KF in trilateration based localization model with the MMSE method. In conclusion, with KF in trilateration based localization model with MMSE method effectively eliminates random variations in BLE RSS with multiple transmission power levels and thus results in a BLE based WILS with high accuracy and high precision.

The aim of this study is to evaluate the filtering techniques which can remove the noise involved in the time series. For this, Logistic series which is chaotic series and radar rainfall series are used for the evaluation of low-pass filter (LF) and Kalman filter (KF). The noise is added to Logistic series by considering noise level and the noise added series is filtered by LF and KF for the noise reduction. The analysis for the evaluation of LF and KF techniques is performed by the correlation coefficient, standard error, the attractor, and the BDS statistic from chaos theory. The analysis result for Logistic series clearly showed that KF is better tool than LF for removing the noise. Also, we used the radar rainfall series for evaluating the noise reduction capabilities of LF and KF. In this case, it was difficult to distinguish which filtering technique is better way for noise reduction when the typical statistics such as correlation coefficient and standard error were used. However, when the attractor and the BDS statistic were used for evaluating LF and KF, we could clearly identify that KF is better than LF.

This paper newly designs the RLS (recursive least-squares) fixed-lag smoother and filter, based on the innovation theory, in linear continuous-time stochastic systems. It is assumed that the signal is observed with additive white noise and the signal is uncorrelated with the observation noise. It is a characteristic that the estimators use the covariance information of the signal, in the form of the semi-degenerate kernel, and the observation noise. With respect to the RLS fixed-lag smoother, the algorithm for the estimation error variance function is developed to guarantee the stability of the fixed-lag smoother. The proposed estimators have the recursive property in calculating the fixed-lag smoothing and filtering estimates. Also, this paper proposes the Chandrasekhar-type RLS Wiener filter in linear wide-sense stationary stochastic system. Unlike the usual filter including the Riccati-type equations, the Chandrasekhar-type filter does not contain the Riccati-type differential equations and has an advantage of eliminating the possibility of the covariance matrix becoming nonnegative.

Many interplanetary mission concepts can benefit from autonomous orbit estimation, particularly during critical mission phases. Previous studies have examined the feasibility of optical navigation using nanosatellite class instruments. While promising, these techniques are not without drawbacks. Convergence of the navigation estimates are often sensitive to errors in initial state estimates. This thesis compares various methods to perform nonlinear estimation for autonomous optical navigation. These methods include an extended Kalman filter (EKF), an unscented Kalman filter (UKF), a particle filter (PF), a fixed-lag smoother (FLS), and moving horizon estimation (MHE). The EKF, UKF, and PF can be implemented in real time, while the FLS and MHE implement a delay into the estimation process. To compare the performance of each state estimator three initial reference scenarios around Mars were considered: a hyperbolic flyby, an elliptic orbit and a orbital maneuver using observations of Mars and its moons. Parameter estimation was also explored, where the mass of Mars was to be estimated as a reference parameter in both the hyperbolic and elliptical trajectories. One last reference scenario included a low Earth orbit (LEO) using observations of satellites in a geosynchronous equatorial orbit. In each case, the FLS and MHE showed similar or better performance over each state estimator but at the cost of an increased computation time with respect to the reference EKF. Similarly the UKF was able to provide improved results withe respect to the EKF. While, the PF provided poor estimates in the Mars trajectories but improvements were seen from the UKF and EKF in the LEO scenario.

A new memristor based on zinc oxide (ZnO) nanowires grown on the copper layer of a printed circuit board has been fabricated showing similar characteristics as memristive metal/oxide/metal structures. This device is then used with a capacitor and an inductor to form a first-order and a second-order lowpass filter to demonstrate the adaptability of the memristor. The memristor reacts to different input voltage bias and changes its resistance accordingly. The gain, damping and Q-factor of the lowpass filters are observed to be varying with small input voltages.

Nowadays, the integrated navigation system is very important in all kinds of aircraft, and the integrated navigation algorithm is the core of the integrated navigation system. The main research in this paper are as follows: (1) Introduce three low-pass filters to filter out the high-frequency noise collected by sensors. Then compare and analyze the performance of these three low-pass filters. (2) Adjust the Kalman filter parameters to improve the performance of the Kalman filter. The final conclusions are: (1) Through comparative analysis of the three low-pass filters, Wiener low-pass filter is the most suitable, which can better achieve the purpose of filtering out high-frequency noise. (2) By adjusting the parameters in the Kalman filter, a set of approximate optimal parameters is obtained. This set of parameters verifies that the performance of the Kalman filter can be improved.

The performance of the Kalman Filter (KF) technique is most appropriate when both the process and observation are considered as white Gaussian noise. But in real time applications, this assumption is not always true. Two sorts of Kalman Filtering techniques i.e Augmented Kalman Filtering and Second Moment Information bases Kalman Filtering with colored system noise i.e (process noise and observation noise) are examined in this paper. Augmented Kalman Filtering (AKF) with colored measurement noise is shortly analyzed. Modified Kalman Filtering method (SMIKF) is proposed for colored process and observation noise. In order to check the performance of the system a real-time Mass-Spring Damper system having colored system noises is considered. The computational burdens of the proposed scheme is compared with AKF. The simulation results endorse the Performance of the suggested algorithm.

Design of recursive least-squares fixed-lag smoother using covariance information in linear continuous stochastic systems

A fixed-lag Kalman smoother can be used for target trajectory reconstruction in postmission data analysis from noisy sensor data, where lag is the time difference between the time of the latest available measurement (or the latest measurement used for estimation) and the time of the smoothed estimate. Based on the steady-state conditions of a Kalman smoother, a recursive method for calculating the steady-state gains and covariance matrix of a fixed-lag alpha-beta smoother is derived and presented. The equations derived for the alpha-beta fixed-lag smoother were verified using a Kalman smoother in steady-state, and the results are used to characterize the benefits achieved with fixed-lag smoothing.

For linear discrete state-space models, under certain conditions, the linear least mean squares (LLMS) filter estimate has a recursive format, a.k.a. the Kalman filter (KF). Interestingly, the linear minimum variance distortionless response (LMVDR) filter, when it exists, shares exactly the same recursion as the KF, except for the initialization. If LMVDR estimators are suboptimal in mean-squared error sense, they do not depend on the prior knowledge on the initial state. Thus, the LMVDR estimators may outperform the usual LLMS estimators in case of misspecification of the prior knowledge on the initial state. In this perspective, we establish the general conditions under which existence of the LMVDRF is guaranteed. An immediate benefit is the introduction of LMVDR fixed-point and fixed-lag smoothers (and possibly other smoothers or predictors), which has not been possible so far. Indeed, the LMVDR fixed-point smoother can be used to compute recursively the solution of a generalization of the deterministic least-squares problem.

Wavelet transforms that have an adaptive low-pass filter are useful in applications that require the signal singularities, sharp transitions, and image edges to be left intact in the low-pass signal. In scalable image coding, the spatial resolution scalability is achieved by reconstructing the low-pass signal subband, which corresponds to the desired resolution level, and discarding other high-frequency wavelet subbands. In such applications, it is vital to have low-pass subbands that are not affected by smoothing artifacts associated with low-pass filtering. We present the mathematical framework for achieving 1-D wavelet transforms that have a spatially adaptive low-pass filter (SALP) using the prediction-first lifting scheme. The adaptivity decisions are computed using the wavelet coefficients, and no bookkeeping is required for the perfect reconstruction. Then, 2-D wavelet transforms that have a spatially adaptive low-pass filter are designed by extending the 1-D SALP framework. Because the 2-D polyphase decompositions are used in this case, the 2-D adaptivity decisions are made nonseparable as opposed to the separable 2-D realization using 1-D transforms. We present examples using the 2-D 5/3 wavelet transform and their lossless image coding and scalable decoding performances in terms of quality and resolution scalability. The proposed 2-D-SALP scheme results in better performance compared to the existing adaptive update lifting schemes.

Many technologies need to be established to realize autonomous ships. In particular, accurate state estimation in real time is one of the most important technologies. In the ship and ocean engineering fields, there have been many studies on state estimation using nonlinear Kalman filters. Several methods have been proposed for nonlinear Kalman filters. However, there is insufficient verification on the selection of which filter should be applied among them. Therefore, this study aims to validate the filter selection to provide a guideline for filter selection. The effects of modeling error, observation noise, and type of maneuvers on the estimation accuracy of the unscented Kalman filter (UKF) and ensemble Kalman filter (EnKF) used in this study were investigated. In addition, it was verified whether filtering could be performed in real time. The results show that modeling error significantly impacts the estimation accuracy of the UKF and EnKF. However, the observation noise and types of maneuvers did not have an impact like the modeling error. Thus, we obtained the guideline that UKF and EnKF should be used differently depending on the required computation time. We also obtained that keeping the modeling error sufficiently small is essential to improving the estimation accuracy.

In view of the problems of route selection and driving stability of intelligent vehicle in the process of turning, a state model of intelligent vehicle turning system control based on Kalman filter is proposed. Taking intelligent vehicle as the research object, according to the route of intelligent vehicle passing through a certain bend at uniform speed, the corresponding state transition model of intelligent vehicle’s speed and position is established, and the state model of intelligent vehicle’s bend system is analyzed, and the system state equation of intelligent vehicle in the process of bend movement based on Kalman filter is obtained. According to the state equation of the system, it can effectively monitor the speed, position and trajectory of the intelligent vehicle on the bend. Combining with Kalman filter algorithm, it can effectively reduce the noise of the control process and observation noise. It can be used to achieve more stable and accurate control of the intelligent vehicle in the bend movement.

Under the usual assumptions of normality, the recursive estimator known as the Kalman filter gives excellent results and has found an extremely broad field of application--not only for estimating the state of a stochastic dynamic system, but also for estimating model parameters as well as detecting abrupt changes in the states or the parameters. It is well known, however, that significantly nonnormal noise, and particularly the presence of outliers, severely degrades the performance of the Kalman filter. This results in poor state estimates, nonwhite residuals and invalid inference. A first-order approximation is derived for the conditional prior distribution of the state of a discrete-time stochastic linear dynamic system in the presence of $\varepsilon$-contaminated normal observation noise. This distribution is then used to derive a first-order approximation of the conditional mean (minimum-variance) estimator. If the observation noise distribution can be represented as a member of the $\varepsilon$-contaminated normal neighborhood, then the conditional prior is also, to first order, an analogous perturbation from a normal distribution whose first two moments are given by the Kalman filter. Moreover, the perturbation is itself of a special form, combining distributions whose parameters are given by banks of parallel Kalman filters and optimal smoothers.

To evaluate the impact of data quality on the localization of brain activation in functional magnetic resonance imaging (fMRI) and to explore whether the temporal contrast-to-noise-ratio (CNR) provides a quantitative parameter to estimate fMRI quality. We investigated two methods for defining the CNR by comparing them on a single-run, single session, as well as on a group-wise basis. The CNRs of healthy subjects and a group of patients with brain lesions were calculated using two different strategies: one based on a general linear model (GLM) analysis (CNR_SPM), and one that acts as an adaptive low-pass filter and assumes that the high-frequency components contain the temporal noise (CNR_SG). Runs with low CNR were identified as outliers using a common exclusion criterion (2 x standard deviation (SD)). The results of the two CNR methods are highly correlated. Both between and within subjects and patients the CNR showed quite large variations, but the average CNR did not differ between a group of healthy subjects and a patient group. In total, seven of 213 runs (3.3% of all runs) had to be excluded when CNR_SG was used, and 14 of 213 (6.6%) runs had to be excluded when CNR_SPM was used. Calculating the CNR using an adaptive low-pass filter gives similar results to a GLM-based approach and could be advantageous for cases in which the hemodynamic response function (HRF) differs significantly from common assumptions. The CNR can be used to identify and exclude runs with suboptimal CNR, and to identify sessions with insufficient data quality. The CNR may serve as a quantitative and intuitive parameter to assess the performance and quality of clinical fMRI investigations, including information on both functional performance (contrast) and data quality (noise caused by the system and physiology).