Two-Dimensional Monte Carlo Filter for a Non-Gaussian Environment

In a non-Gaussian environment, the accuracy of a Kalman filter might be reduced. In this paper, a two- dimensional Monte Carlo Filter is proposed to overcome the challenge of the non-Gaussian environment for filtering. The two-dimensional Monte Carlo (TMC) method is first proposed to improve the efficacy of the sampling. Then, the TMC filter (TMCF) algorithm is proposed to solve the non-Gaussian filter problem based on the TMC. In the TMCF, particles are deployed in the confidence interval uniformly in terms of the sampling interval, and their weights are calculated based on Bayesian inference. Then, the posterior distribution is described more accurately with less particles and their weights. Different from the PF, the TMCF completes the transfer of the distribution using a series of calculations of weights and uses particles to occupy the state space in the confidence interval. Numerical simulations demonstrated that, the accuracy of the TMCF approximates the Kalman filter (KF) (the error is about 10−6) in a two-dimensional linear/ Gaussian environment. In a two-dimensional linear/non-Gaussian system, the accuracy of the TMCF is improved by 0.01, and the computation time reduced to 0.067 s from 0.20 s, compared with the particle filter.

Entropy production in continuously measured Gaussian quantum systems

The entropy production rate is a key quantity in nonequilibrium thermodynamics of both classical and quantum processes. No universal theory of entropy production is available to date, which hinders progress toward its full grasping. By using a phase space-based approach, here we take the current framework for the assessment of thermodynamic irreversibility all the way to quantum regimes by characterizing entropy production—and its rate—resulting from the continuous monitoring of a Gaussian system. This allows us to formulate a sharpened second law of thermodynamics that accounts for the measurement back action and information gain from a continuously monitored system. We illustrate our framework in a series of physically relevant examples.

Crystal growth, structural, nonlinear optical and theoretical investigations of Benzilic acid crystals

Organic single crystals of Benzilic Acid (BA) were grown by slow solvent evaporating method by using acetone as solvent. The unit cell parameter values and the crystal system are recognized by using single crystal XRD technique. The optical assessment of BA molecules is observed by with UV-Vis spectral analysis as the ultraviolet range between 200 and 400 nm and the visible region between 400 and 800 nm. The nonlinear optical (NLO) properties such as second harmonic efficiency nature of BA crystal were analyzed using Nd:YAG laser. The laser-induced damage threshold assessment of BA crystal is measured as 2.76 GW/cm2. From the Density Functional Theory (DFT), the molecular structural feature and vibrational frequencies were defined by using the Gaussian system along with comparisons of experimental frequencies. Using the DFT method, the derived vibrational frequency values showed an admirable accord with experimental frequencies. The charge interactions within the BA molecules are confirmed by HOMO and LUMO energy value. The first-order molecular hyperpolarizabilities, dipole moment, polarizability and Mulliken charge analysis of the BA molecule are also evaluated.

A Nonlinear Double Model for Multisensor-Integrated Navigation Using the Federated EKF Algorithm for Small UAVs

Aimed at improving upon the disadvantages of the single centralized Kalman filter for integrated navigation, including its fragile robustness and low solution accuracy, a nonlinear double model based on the improved decentralized federated extended Kalman filter (EKF) for integrated navigation is proposed. The multisensor error model is established and simplified in this paper according to the near-ground short distance navigation applications of small unmanned aerial vehicles (UAVs). In order to overcome the centralized Kalman filter that is used in the linear Gaussian system, the improved federated EKF is designed for multisensor-integrated navigation. Subsequently, because of the navigation requirements of UAVs, especially for the attitude solution accuracy, this paper presents a nonlinear double model that consists of the nonlinear attitude heading reference system (AHRS) model and nonlinear strapdown inertial navigation system (SINS)/GPS-integrated navigation model. Moreover, the common state parameters of the nonlinear double model are optimized by the federated filter to obtain a better attitude. The proposed algorithm is compared with multisensor complementary filtering (MSCF) and multisensor EKF (MSEKF) using collected flight sensors data. The simulation and experimental tests demonstrate that the proposed algorithm has a good robustness and state estimation solution accuracy.

Optimal control for networked control systems with multiple delays and packet dropouts

This article focuses on the problem of optimal linear quadratic Gaussian control for networked control systems with multiple delays and packet dropouts. The main contributions are twofold. Firstly, based on the introduced maximum principle for linear quadratic Gaussian system with multiple input delays and packet dropouts, a nonhomogeneous relationship between the state and costate is obtained, which is the key technical tool to solve the problem. Secondly, a necessary and sufficient condition for the optimal networked control problem is given in virtue of the coupled Riccati equations, and the explicit expression of the optimal controller is presented. Numerical examples are shown to illustrate the proposed algorithm.

A Novel Smooth Variable Structure Smoother for Robust Estimation

The smooth variable structure filter (SVSF) is a new-type filter based on the sliding-mode concepts and has good stability and robustness in overcoming the modeling uncertainties and errors. However, SVSF is insufficient to suppress Gaussian noise. A novel smooth variable structure smoother (SVSS) based on SVSF is presented here, which mainly focuses on this drawback and improves the SVSF estimation accuracy of the system. The estimation of the linear Gaussian system state based on SVSS is divided into two steps: Firstly, the SVSF state estimate and covariance are computed during the forward pass in time. Then, the smoothed state estimate is computed during the backward pass by using the innovation of the measured values and covariance estimate matrix. According to the simulation results with respect to the maneuvering target tracking, SVSS has a better performance compared with another smoother based on SVSF and the Kalman smoother in different tracking scenarios. Therefore, the SVSS proposed in this paper could be widely applied in the field of state estimation in dynamic system.

Analysis of approximations of GUM supplement 2 based non-Gaussian PDFs of measurement models with Rosenblatt Gaussian transformation mappings

In scientific metrology practise the application of Monte Carlo simulations with the aid of the GUM Supplement 2 (GS2) technique for performing multivariate uncertainty analyses is now more prevalent, however a key remaining challenge for metrologists in many laboratories is the implicit assumption of Gaussian characteristics for summarizing and analysing measurement model results. Whilst non-Gaussian probability density functions (PDFs) may result from Monte Carlo simulations when the GS2 is applied for more complex non-linear measurement models, in practice results are typically only reported in terms of multivariate expected and covariance values. Due to this limitation the measurement model PDF summary is implicitly restricted to a multivariate Gaussian PDF in the absence of additional higher order statistics (HOS) information. In this paper an earlier classical theoretical result by Rosenblatt that allows for an arbitrary multivariate joint distribution function to be transformed into an equivalent system of Gaussian distributions with mapped variables is revisited. Numerical simulations are performed in order to analyse and compare the accuracy of the equivalent Gaussian system of mapped random variables for approximating a measurement model’s PDF with that of an exact non-Gaussian PDF that is obtained with a GS2 Monte Carlo statistical simulation. Results obtained from the investigation indicate that a Rosenblatt transformation offers a convenient mechanism to utilize just the joint PDF obtained from the GS2 data in order to both sample points from a non-Gaussian distribution, and also in addition which allows for a simple two-dimensional approach to estimate coupled uncertainties of random variables residing in higher dimensions using conditional densities without the need for determining parametric based copulas.

Robust filtering with randomly delayed measurements and its application to ballistic target tracking in boost phase

Motivated by the performance degradation of High-degree Cubature Kalman Filtering (HCKF) in coping with randomly delayed measurements in non-Gaussian system, a novel robust filtering named as Randomly Delayed High-degree Cubature Huber-based Filtering (RD-HCHF) is proposed in this paper. At first, the system model is re-written by the Bernoulli random variables to describe the randomly delayed measurements. Then, the Randomly Delayed HCKF (RD-HCKF) is derived based on the rewritten system model and 5th-degree spherical-radial cubature (SRC) rule. In order to enhance the robustness of the filter in glint noise case, the measurement update of RD-HCKF is modified by the Huber technique, which is essentially an M-estimator. Therefore, the proposed RD-HCHF is not only robust to the randomly delayed measurements, but also robust to the glint noise. In addition, the RD-HCHF is applied to the ballistic target tracking in boost phase, and the Gravity-Turn (GT) model is taken as the target model. Finally, the simulation is conducted and the tracking performance of RD-HCHF is compared with that of HCKF, RD-HCKF and High-degree Cubature Huber-based Filtering (HCHF). The results clearly confirm the superiority of the RD-HCHF.

Linear or Nonlinear Modeling for ENSO Dynamics?

The observed ENSO statistics exhibits a non-Gaussian behavior, which is indicative of the presence of nonlinear processes. In this paper, we use the Recharge Oscillator Model (ROM), a largely used Low-Order Model (LOM) of ENSO, as well as methodologies borrowed from the field of statistical mechanics to identify which aspects of the system may give rise to nonlinearities that are consistent with the observed ENSO statistics. In particular, we are interested in understanding whether the nonlinearities reside in the system dynamics or in the fast atmospheric forcing. Our results indicate that one important dynamical nonlinearity often introduced in the ROM cannot justify a non-Gaussian system behavior, while the nonlinearity in the atmospheric forcing can instead produce a statistics similar to the observed. The implications of the non-Gaussian character of ENSO statistics for the frequency of extreme El Niño events is then examined.