Sigma-point particle filter for parameter estimation in a multiplicative noise environment

A pre-requisite for the "optimal estimate'' by the ensemble-based Kalman filter (EnKF) is the Gaussian assumption for background and observation errors, which is often violated when the errors are multiplicative, even for a linear system. This study first explores the challenge of the multiplicative noise to the current EnKF schemes. Then, a Sigma Point Kalman Filter based Particle Filter (SPPF) is presented as an alternative to solve the issues associated with multiplicative noise. The classic Lorenz '63 model and a higher dimensional Lorenz '96 model are used as test beds for the data assimilation experiments. Performance of the SPPF algorithm is compared against a standard EnKF as well as an advanced square-root Sigma-Point Kalman Filters (SPKF). The results show that the SPPF outperforms the EnKF and the square-root SPKF in the presence of multiplicative noise. The super ensemble structure of the SPPF makes it computationally attractive compared to the standard Particle Filter (PF)

Space-Time Sampling for Network Observability

Designing sparse sampling strategies is one of the important components in having resilient estimation and control in networked systems as they make network design problems more cost-effective due to their reduced sampling requirements and less fragile to where and when samples are collected. It is shown that under what conditions taking coarse samples from a network will contain the same amount of information as a more finer set of samples. Our goal is to estimate initial condition of linear time-invariant networks using a set of noisy measurements. The observability condition is reformulated as the frame condition, where one can easily trace location and time stamps of each sample. We compare estimation quality of various sampling strategies using estimation measures, which depend on spectrum of the corresponding frame operators. Using properties of the minimal polynomial of the state matrix, deterministic and randomized methods are suggested to construct observability frames. Intrinsic tradeoffs assert that collecting samples from fewer subsystems dictates taking more samples (in average) per subsystem. Three scalable algorithms are developed to generate sparse space-time sampling strategies with explicit error bounds.Comment: Submitted to IEEE TAC (Revised Version

Continuous reservoir model updating by ensemble Kalman filter on Grid computing architectures

A reservoir engineering Grid computing toolkit, ResGrid and its extensions, were developed and applied to designed reservoir simulation studies and continuous reservoir model updating. The toolkit provides reservoir engineers with high performance computing capacity to complete their projects without requiring them to delve into Grid resource heterogeneity, security certification, or network protocols. Continuous and real-time reservoir model updating is an important component of closed-loop model-based reservoir management. The method must rapidly and continuously update reservoir models by assimilating production data, so that the performance predictions and the associated uncertainty are up-to-date for optimization. The ensemble Kalman filter (EnKF), a Bayesian approach for model updating, uses Monte Carlo statistics for fusing observation data with forecasts from simulations to estimate a range of plausible models. The ensemble of updated models can be used for uncertainty forecasting or optimization. Grid environments aggregate geographically distributed, heterogeneous resources. Their virtual architecture can handle many large parallel simulation runs, and is thus well suited to solving model-based reservoir management problems. In the study, the ResGrid workflow for Grid-based designed reservoir simulation and an adapted workflow provide tools for building prior model ensembles, task farming and execution, extracting simulator output results, implementing the EnKF, and using a web portal for invoking those scripts. The ResGrid workflow is demonstrated for a geostatistical study of 3-D displacements in heterogeneous reservoirs. A suite of 1920 simulations assesses the effects of geostatistical methods and model parameters. Multiple runs are simultaneously executed using parallel Grid computing. Flow response analyses indicate that efficient, widely-used sequential geostatistical simulation methods may overestimate flow response variability when compared to more rigorous but computationally costly direct methods. Although the EnKF has attracted great interest in reservoir engineering, some aspects of the EnKF remain poorly understood, and are explored in the dissertation. First, guidelines are offered to select data assimilation intervals. Second, an adaptive covariance inflation method is shown to be effective to stabilize the EnKF. Third, we show that simple truncation can correct negative effects of nonlinearity and non-Gaussianity as effectively as more complex and expensive reparameterization methods

Sigma-point Kalman filter data assimilation methods for strongly nonlinear dynamical models.

Performance of an advanced derivative-less, sigma-point Kalman filter (SPKF) data assimilation scheme in a strongly nonlinear dynamical model is investigated. The SPKF data assimilation scheme is compared against standard Kalman filters such as the extended Kalman filter (EKF) and the ensemble Kalman filter (EnKF) schemes. Three particular cases, namely the state estimation, parameter estimation, and joint estimation of states and parameters from a set of discontinuous noisy observations are studied. The problems associated with the use of the tangent linear model (TLM) or the Jacobian when using standard Kalman filters are eliminated when using SPKF data assimilation algorithms. Further, the constraints and issues of SPKF data assimilation in real ocean or atmospheric models are emphasized. A reduced sigma-point subspace approach is proposed and investigated for higher dimensional systems. A low dimensional Lorenz '63 model and a higher dimensional Lorenz '95 model are used as the test-bed for data assimilation experiments. The results of the SPKF data assimilation schemes are compared with those of the standard EKF and EnKF where a highly nonlinear chaotic case is studied. It is shown that the SPKF is capable of estimating the model state and parameters with better accuracy than EKF and EnKF. Numerical experiments show that in all cases, the SPKF can give consistent results with better assimilation skills than EnKF and EKF, and can overcome the drawbacks associated with the use of EKF and EnKF. --P.iii-iv.The original print copy of this thesis may be available here: http://wizard.unbc.ca/record=b151781

Underwater Robots Part II: Existing Solutions and Open Issues

National audienceThis paper constitutes the second part of a general overview of underwater robotics. The first part is titled: Underwater Robots Part I: current systems and problem pose. The works referenced as (Name*, year) have been already cited on the first part of the paper, and the details of these references can be found in the section 7 of the paper titled Underwater Robots Part I: current systems and problem pose. The mathematical notation used in this paper is defined in section 4 of the paper Underwater Robots Part I: current systems and problem pose

Novel Computational Methods for State Space Filtering

The state-space formulation for time-dependent models has been long used invarious applications in science and engineering. While the classical Kalman filter(KF) provides optimal posterior estimation under linear Gaussian models, filteringin nonlinear and non-Gaussian environments remains challenging.Based on the Monte Carlo approximation, the classical particle filter (PF) can providemore precise estimation under nonlinear non-Gaussian models. However, it suffers fromparticle degeneracy. Drawing from optimal transport theory, the stochastic map filter(SMF) accommodates a solution to this problem, but its performance is influenced bythe limited flexibility of nonlinear map parameterisation. To account for these issues,a hybrid particle-stochastic map filter (PSMF) is first proposed in this thesis, wherethe two parts of the split likelihood are assimilated by the PF and SMF, respectively.Systematic resampling and smoothing are employed to alleviate the particle degeneracycaused by the PF. Furthermore, two PSMF variants based on the linear and nonlinearmaps (PSMF-L and PSMF-NL) are proposed, and their filtering performance is comparedwith various benchmark filters under different nonlinear non-Gaussian models.Although achieving accurate filtering results, the particle-based filters require expensive computations because of the large number of samples involved. Instead, robustKalman filters (RKFs) provide efficient solutions for the linear models with heavy-tailednoise, by adopting the recursive estimation framework of the KF. To exploit the stochasticcharacteristics of the noise, the use of heavy-tailed distributions which can fit variouspractical noises constitutes a viable solution. Hence, this thesis also introduces a novelRKF framework, RKF-SGαS, where the signal noise is assumed to be Gaussian and theheavy-tailed measurement noise is modelled by the sub-Gaussian α-stable (SGαS) distribution. The corresponding joint posterior distribution of the state vector and auxiliaryrandom variables is estimated by the variational Bayesian (VB) approach. Four differentminimum mean square error (MMSE) estimators of the scale function are presented.Besides, the RKF-SGαS is compared with the state-of-the-art RKFs under three kinds ofheavy-tailed measurement noises, and the simulation results demonstrate its estimationaccuracy and efficiency.One notable limitation of the proposed RKF-SGαS is its reliance on precise modelparameters, and substantial model errors can potentially impede its filtering performance. Therefore, this thesis also introduces a data-driven RKF method, referred to asRKFnet, which combines the conventional RKF framework with a deep learning technique. An unsupervised scheduled sampling technique (USS) is proposed to improve theistability of the training process. Furthermore, the advantages of the proposed RKFnetare quantified with respect to various traditional RKFs

Vehicle model-based filtering for spacecraft attitude determination

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1998.Includes bibliographical references (p. 166-170) and index.This thesis investigates the use of vehicle model-based filtering for spacecraft attitude determination. Whereas traditional navigation filters typically rely only on the kinematic relations between body rate and attitude in their filter designs, the state estimator presented here expands the plant model to include rigid body effects and disturbance torques. When rate sensing gyroscope measurement error components are large, as is anticipated in the new generation of micromechanical inertial sensors, the model-based approach provides superior performance to the standard kinematic designs. The estimation performance gains, which include enhanced attitude tracking of several tenths of a degree and closed-loop control stabilization, are most apparent when external attitude data becomes sparse. Even if the gyroscope measurement quality were to improve, for some satellite missions the possibility of an external measurement outage still necessitates vehicle dynamic modeling for greater gyro bias observability. The thesis also gives insight into robustness measures to compensate for model uncertainty, disturbance torque estimation, and GPS multipath error mitigation.by Christopher W. Dever.S.M