Robust Student's t based Stochastic Cubature Filter for Nonlinear Systems with Heavy-tailed Process and Measurement Noises

In this paper, a new robust Student's t based stochastic cubature filter (RSTSCF) is proposed for nonlinear state-space model with heavy-tailed process and measurement noises. The heart of the RSTSCF is a stochastic Student's t spherical radial cubature rule (SSTSRCR), which is derived based on the third-degree unbiased spherical rule and the proposed third-degree unbiased radial rule. The existing stochastic integration rule is a special case of the proposed SSTSRCR when the degrees of freedom parameter tends to infinity. The proposed filter is applied to a manoeuvring bearings-only tracking example, where an agile target is tracked and the bearing is observed in clutter. Simulation results show that the proposed RSTSCF can achieve higher estimation accuracy than the existing Gaussian approximate filter, Gaussian sum filter, Huber-based nonlinear Kalman filter, maximum correntropy criterion based Kalman filter, and robust Student's t based nonlinear filters, and is computationally much more efficient than the existing particle filter.Comment: 9 pages, 2 figure

Estimation of Parameters in Avian Movement Models

The knowledge of the movement of animals is important and necessary for ecologists to do further analysis such as exploring the animal migration route. A novel method which is based on the state space modeling has been proposed to track the bird, where the VHF transmitter is attached to the bird to emit the signal and several towers with antenna arrays installed on its top are built to receive the signal. The method consists of two parts, the first one is called movement model which accounts for prediction of the dynamic movement of the target, and the second part is the measurement model which links the target's state variables to the available measurements data, the measurement includes the time when the signal was detected, the ID of the antenna array which detected the signal and integers between 0 and 255, the integers are proportional to the strength of received signal. The extended Kalman filter is then applied to estimate the location of the target with combing the movement model and measurement model. In the movement model, several parameters with positive values are deployed to define the change of the state variables with time, these parameters reflect the relationship of the state variables at current time and next time. In this paper, a method based on the maximum likelihood estimation is proposed to estimate the appropriate values for these unknown constant variables with given measurement data, and a kite is applied to demonstrate the validity of the proposed method. Furthermore, the unscented transformation is applied in Kalman filter to achieve more accurate estimation of the target's states

Sigma-Point Filtering and Smoothing Based Parameter Estimation in Nonlinear Dynamic Systems

We consider approximate maximum likelihood parameter estimation in nonlinear state-space models. We discuss both direct optimization of the likelihood and expectation--maximization (EM). For EM, we also give closed-form expressions for the maximization step in a class of models that are linear in parameters and have additive noise. To obtain approximations to the filtering and smoothing distributions needed in the likelihood-maximization methods, we focus on using Gaussian filtering and smoothing algorithms that employ sigma-points to approximate the required integrals. We discuss different sigma-point schemes based on the third, fifth, seventh, and ninth order unscented transforms and the Gauss--Hermite quadrature rule. We compare the performance of the methods in two simulated experiments: a univariate nonlinear growth model as well as tracking of a maneuvering target. In the experiments, we also compare against approximate likelihood estimates obtained by particle filtering and extended Kalman filtering based methods. The experiments suggest that the higher-order unscented transforms may in some cases provide more accurate estimatesComment: Revised version. 14 pages, 11 figures. Submitted to Journal of Advances in Information Fusio

Progressive Gaussian Filtering

In this paper, we propose a progressive Bayesian procedure, where the measurement information is continuously included into the given prior estimate (although we perform observations at discrete time steps). The key idea is to derive a system of ordinary first-order differential equations (ODE) by employing a new coupled density representation comprising a Gaussian density and its Dirac Mixture approximation. The ODE is used for continuously tracking the true non-Gaussian posterior by its best matching Gaussian approximation. The performance of the new filter is evaluated in comparison with state-of-the-art filters by means of a canonical benchmark example, the discrete-time cubic sensor problem

Observer-Side Parameter Estimation For Adaptive Control

In adaptive control, a controller is precisely designed for a certain model of the system, but that model's parameters are updated online by another mechanism called the adaptive update. This allows the controller to aim for the benefits of exact model knowledge while simultaneously remaining robust to model uncertainty. Like most nonlinear controllers, adaptive controllers are often designed and analyzed under the assumption of deterministic full state feedback. However, doing so inherently decouples the adaptive update mechanism from the probabilistic information provided by modern state observers. The simplest way to reconcile this is to let the observer produce both state estimates and model parameter estimates, so that all probabilistic information is shared within the framework of the observer. While this technique is becoming increasingly common, it is still not widely accepted due to a lack of general closed-loop stability proofs. In this thesis, we will investigate observer-side parameter estimation for adaptive control by precisely juxtaposing its mechanics against the current, widely accepted adaptive control designs. Additionally, we will propose a new technique that increases the robustness of observer-based adaptive control by following the same line of reasoning used for the popular concurrent learning method

Robust Power System Dynamic State Estimator with Non-Gaussian Measurement Noise: Part II--Implementation and Results

This paper is the second of a two-part series that discusses the implementation issues and test results of a robust Unscented Kalman Filter (UKF) for power system dynamic state estimation with non-Gaussian synchrophasor measurement noise. The tuning of the parameters of our Generalized Maximum-Likelihood-type robust UKF (GM-UKF) is presented and discussed in a systematic way. Using simulations carried out on the IEEE 39-bus system, its performance is evaluated under different scenarios, including i) the occurrence of two different types of noises following thick-tailed distributions, namely the Laplace or Cauchy probability distributions for real and reactive power measurements; ii) the occurrence of observation and innovation outliers; iii) the occurrence of PMU measurement losses due to communication failures; iv) cyber attacks; and v) strong system nonlinearities. It is also compared to the UKF and the Generalized Maximum-Likelihood-type robust iterated EKF (GM-IEKF). Simulation results reveal that the GM-UKF outperforms the GM-IEKF and the UKF in all scenarios considered. In particular, when the system is operating under stressed conditions, inducing system nonlinearities, the GM-IEKF and the UKF diverge while our GM-UKF does converge. In addition, when the power measurement noises obey a Cauchy distribution, our GM-UKF converges to a state estimate vector that exhibits a much higher statistical efficiency than that of the GM-IEKF; by contrast, the UKF fails to converge. Finally, potential applications and future work of the proposed GM-UKF are discussed in concluding remarks section.Comment: Submitted to IEEE Transactions on Power System

State Estimation-Based Robust Optimal Control of Influenza Epidemics in an Interactive Human Society

This paper presents a state estimation-based robust optimal control strategy for influenza epidemics in an interactive human society in the presence of modeling uncertainties. Interactive society is influenced by the random entrance of individuals from other human societies whose effects can be modeled as a non-Gaussian noise. Since only the number of exposed and infected humans can be measured, states of the influenza epidemics are first estimated by an extended maximum correntropy Kalman filter (EMCKF) to provide a robust state estimation in the presence of the non-Gaussian noise. An online quadratic program (QP) optimization is then synthesized subject to a robust control Lyapunov function (RCLF) to minimize susceptible and infected humans, while minimizing and bounding the rates of vaccination and antiviral treatment. The joint QP-RCLF-EMCKF meets multiple design specifications such as state estimation, tracking, pointwise control optimality, and robustness to parameter uncertainty and state estimation errors that have not been achieved simultaneously in previous studies. The uniform ultimate boundedness (UUB)/convergence of error trajectories is guaranteed using a Lyapunov stability argument. The soundness of the proposed approach is validated on the influenza epidemics of an interactive human society with a population of 16000. Simulation results show that the QP-RCLF-EMCKF achieves appropriate tracking and state estimation performance. The robustness of the proposed controller is finally illustrated in the presence of modeling error and non-Gaussian noise

Mobile Localization in Non-Line-of-Sight Using Constrained Square-Root Unscented Kalman Filter

Localization and tracking of a mobile node (MN) in non-line-of-sight (NLOS) scenarios, based on time of arrival (TOA) measurements, is considered in this work. To this end, we develop a constrained form of square root unscented Kalman filter (SRUKF), where the sigma points of the unscented transformation are projected onto the feasible region by solving constrained optimization problems. The feasible region is the intersection of several discs formed by the NLOS measurements. We show how we can reduce the size of the optimization problem and formulate it as a convex quadratically constrained quadratic program (QCQP), which depends on the Cholesky factor of the \textit{a posteriori} error covariance matrix of SRUKF. As a result of these modifications, the proposed constrained SRUKF (CSRUKF) is more efficient and has better numerical stability compared to the constrained UKF. Through simulations, we also show that the CSRUKF achieves a smaller localization error compared to other techniques and that its performance is robust under different NLOS conditions.Comment: Under review by IEEE Trans. on Vehicular Technolog

Map matching when the map is wrong: Efficient vehicle tracking on- and off-road for map learning

Given a sequence of possibly sparse and noisy GPS traces and a map of the road network, map matching algorithms can infer the most accurate trajectory on the road network. However, if the road network is wrong (for example due to missing or incorrectly mapped roads, missing parking lots, misdirected turn restrictions or misdirected one-way streets) standard map matching algorithms fail to reconstruct the correct trajectory. In this paper, an algorithm to tracking vehicles able to move both on and off the known road network is formulated. It efficiently unifies existing hidden Markov model (HMM) approaches for map matching and standard free-space tracking methods (e.g. Kalman smoothing) in a principled way. The algorithm is a form of interacting multiple model (IMM) filter subject to an additional assumption on the type of model interaction permitted, termed here as semi-interacting multiple model (sIMM) filter. A forward filter (suitable for real-time tracking) and backward MAP sampling step (suitable for MAP trajectory inference and map matching) are described. The framework set out here is agnostic to the specific tracking models used, and makes clear how to replace these components with others of a similar type. In addition to avoiding generating misleading map matching trajectories, this algorithm can be applied to learn map features by detecting unmapped or incorrectly mapped roads and parking lots, incorrectly mapped turn restrictions and road directions

Inertia Sensor Aided Alignment for Burst Pipeline in Low Light Conditions

Merging short-exposure frames can provide an image with reduced noise in low light conditions. However, how best to align images before merging is an open problem. To improve the performance of alignment, we propose an inertia-sensor aided algorithm for smartphone burst photography, which takes rotation and out-plane relative movement into account. To calculate homography between frames, a three by three rotation matrix is calculated from gyro data recorded by smartphone inertia sensor and three-dimensional translation vector are estimated by matched feature points detected from two frames. The rotation matrix and translations are combined to form the initial guess of homography. An unscented Kalman filter is utilized to provide a more accurate homography estimation. We have tested the algorithm on a variety of different scenes with different camera relative motions. We compare the proposed method to benchmark single-image and multi-image denoising methods with favorable results.Comment: 5 pages, 2 figures, 2018 25th IEEE International Conference on Image Processing (ICIP