non-Gaussian State Estimation Research Articles

A new nonparametric degradation modeling method for truncated degradation signals by axis rotation

Nonparametric degradation modeling can automatically formulate the principal degradation pattern of condition monitoring signals. It performs higher flexibility than parametric modeling in describing complicated degradation processes of machinery. Functional principal component analysis (FPCA) is a commonly used nonparametric modeling technique. A basic requirement of FPCA is that different units must share the same scale in X-axis. A FPCA-based degradation modeling method has been specially designed for truncated degradation signals whose amplitudes are truncated at the failure threshold. This method formulates the degradation time as a function of state level by axis rotation. Since the degradation signals of different units are truncated at the same failure threshold level, the axis rotation strategy ensures the same scale in X-axis. However, in cases of noisy signals, one state level may correspond to multiple time points, which means that the time function depending on state level does not exist. In addition, this method assumes that the noise term as well as the functional principal component (FPC) scores follow the Gaussian distribution, which restricts the flexibility in real practice. Aiming at the above two issues, this paper develops a new degradation modeling method based on the FPCA by axis rotation. The proposed method formulates the degradation model on the definition of first pass time (FPT), which ensures the existence of the time function depending on state level. The noise term and the FPC scores are not restricted to the Gaussian distribution. A particle filtering based updating algorithm is developed to deal with the non-Gaussian state estimation issue of the FPC scores. The effectiveness of the proposed method is verified using an experiment of milling cutter wear.

Improved Particle Filter for Non-Gaussian Forecasting-aided State Estimation

Improved Particle Filter for Non-Gaussian Forecasting-aided State Estimation

The Megopolis resampler: Memory coalesced resampling on GPUs

The resampling process employed in widely used methods such as Importance Sampling (IS), with its adaptive extension (AIS), are used to solve challenging problems requiring approximate inference; for example, non-linear, non-Gaussian state estimation problems. However, the re-sampling process can be computationally prohibitive for practical problems with real-time requirements. We consider the problem of developing highly parallelisable resampling algorithms for massively parallel hardware architectures of modern graphics processing units (GPUs) to accomplish real-time performance. We develop a new variant of the Metropolis algorithm—Megopolis—that improves performance without requiring a tuning parameter or reducing resampling quality. The Megopolis algorithm is built upon exploiting the memory access patterns of modern GPU units to reduce the number of memory transactions without the need for tuning parameters. Extensive numerical experiments on GPU hardware demonstrate that the proposed Megopolis algorithm is numerically stable and outperforms the original Metropolis algorithm and its variants—Metropolis-C1 and Metropolis-C2–in speed and quality metrics. Further, given the absence of open tools in this domain and facilitating fair comparisons in the future and supporting the signal processing community, we also open source the complete project, including a repository of source code with Megopolis and all other comparison methods.

Pipeline Gaussian Particle Filter and Hardware Design for Attitude Estimation with UAV

This paper based on the Gaussian particle filter (GPF) deals with the attitude estimation of UAV. GPF algorithm has better estimation accuracy than the general nonlinear non-Gaussian state estimation and is usually used to improve the system’s real-time performance whose noise is specific such as Gaussian noise during the mini UAV positioning and navigation. The attitude estimation algorithm is implemented on FPGA to verify the effectiveness of the Gaussian particle filter. Simulation results have illustrated that the GPF algorithm is effective and has better real-time performance than that of the particle filter.

Two-stage particle filtering for non-Gaussian state estimation with fading measurements

In this paper, the filtering problem for systems with fading measurements is considered. Taking advantage of the cascaded structure of the system, the original filtering problem is decomposed into two subproblems: 1) recovery of the original measurements from the faded ones, and 2) state estimation based on the recovered signals. A two-stage particle filtering (PF) algorithm is proposed to achieve simultaneous measurement recovery and state estimation. In our scheme, the second-stage resampling procedure can be implemented concurrently, resulting in a significant reduction of execution time. Two examples are provided to demonstrate the effectiveness of our algorithm. A benchmark problem for nonlinear filtering is tackled in the first example and, in the second example, the proposed algorithm is applied to the object tracking problem where the measured signal is distorted by the communication channel. Simulation results show that, compared with the brute force PF, the two-stage PF can strike better balance between tracking accuracy and execution time.

Recursive Particle Filter-Based RBF Network on Time Series Prediction of Measurement Data

Most physical phenomena in nature are chaotic or close to chaos. An irregular time series can be generated or measured with a purely deterministic equation of motion in nonlinear and chaotic systems. This paper presents an adaptive state-space particle filtering (PF)-based trained radial basis function (RBF) network for chaotic and nonstationary observation–prediction. The recursive Bayesian filtering algorithm, which uses the particle representation of density function, is adopted to accomplish nonlinear and non-Gaussian state estimation and achieve improved convergence rate and quality of solution. Four sampling importance resampling approaches, namely, multinomial, systematic, stratified, and residual resampling methods, are considered to resolve weight degeneracy. The effectiveness of our proposed methods is investigated using two chaotic time series and three measurement datasets, including the Mackey–Glass time series, Rossler time series, monthly Lake Erie levels, monthly water usage series, and SML2010 data set. The performances are evaluated through an extensive simulation by computing the average mean square error, mean absolute percentage error, and average relative variance metrics. Simulation results show that the proposed PF-based RBF structure can provide more effective and accurate prediction performances compared with the conventional gradient descent, extended Kalman filter (EKF), and decoupled EKF algorithms (DEKF).

Bayesian parameter estimation and model selection for strongly nonlinear dynamical systems

The Bayesian model selection and parameter estimation framework developed by Khalil et al. (J Sound Vib 332(15):3670–3691, 2013, Bayesian inference for complex and large-scale engineering systems. Ph.D. thesis, Carleton University, 2013) and Sandhu et al. (J Comput Methods Appl Mech Eng 282:161–183, 2014, Bayesian model selection and parameter estimation for a nonlinear fluid–structure interaction problem. Master’s thesis, Carleton University, 2012, 54th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference, 2013) is extended to handle strongly nonlinear systems. The evidence required to estimate the posterior probability of each proposed model is computed using the Chib–Jeliazkov method. The posterior parameter samples generated using Metropolis–Hastings (M–H) Markov Chain Monte Carlo (MCMC) simulations are required by this method. The M–H MCMC-based parameter estimation procedure is complemented by an efficient particle filter and an ensemble Kalman filter for the strongly non-Gaussian state estimation problem. A strongly nonlinear system having multiple fixed (equilibrium) points is analyzed to demonstrate the efficacy of the algorithm.

An improved particle filter algorithm based on Markov Random Field modeling in stationary wavelet domain for SAR image despeckling

Particle filter (PF) is an effective approach to nonlinear and non-Gaussian Bayesian state estimation and has been successfully applied to wavelet-based synthetic aperture radar (SAR) image despeckling. In this paper, we propose an improved PF despeckling algorithm based on Markov Random Field (MRF) model that can preserve the edge, textural information and structural features of SAR images well. First, we show that the wavelet coefficients of SAR images which exhibit significantly non-Gaussian statistics can be described accurately by generalized Gaussian distribution (GGD) in stationary wavelet domain. Secondly, to amend the weight deviation, MRF model parameters are introduced to redefine the importance weight of the particles. At last, region-divided processing is implemented for the real time application of the proposed algorithm. The effectiveness of the proposed algorithm is demonstrated by application to simulated images and real SAR images.

Novel algorithm for geomagnetic navigation

To solve the highly nonlinear and non-Gaussian recursive state estimation problem in geomagnetic navigation, the unscented particle filter (UPF) was introduced to navigation system. The simulation indicates that geomagnetic navigation using UPF could complete the position estimation with large initial horizontal position errors. However, this navigation system could only provide the position information. To provide all the kinematics states estimation of aircraft, a novel autonomous navigation algorithm, named unscented particle and Kalman hybrid navigation algorithm (UPKHNA), was proposed for geomagnetic navigation. The UPKHNA used the output of UPF and barometric altimeter as position measurement, and employed the Kalman filter to estimate the kinematics states of aircraft. The simulation shows that geomagnetic navigation using UPKHNA could provide all the kinematics states estimation of aircraft continuously, and the horizontal positioning performance is better than that only using the UPF.

Constrained Bayesian state estimation – A comparative study and a new particle filter based approach

This paper investigates constrained Bayesian state estimation problems by using a Particle Filter (PF) approach. Constrained systems with nonlinear model and non-Gaussian uncertainty are commonly encountered in practice. However, most of the existing Bayesian methods are unable to take constraints into account and require some simplifications. In this paper, a novel constrained PF algorithm based on acceptance/rejection and optimization strategies is proposed. The proposed method retains the ability of PF in nonlinear and non-Gaussian state estimation, while take advantage of optimization techniques in constraints handling. The performance of the proposed method is compared with other accepted Bayesian estimators. Extensive simulation results from three examples show the efficacy of the proposed method in constraints handling and its robustness against poor prior information.

A Survey of Sample Size Adaptation Techniques for Particle Filters

The paper deals with the particle filter in discrete-time nonlinear non-Gaussian system state estimation. One of the key parameters affecting estimate quality of the particle filter is the sample size. In the literature, there is a number of techniques coming from various ideas that aim at adapting the sample size while keeping quality in some sense fixed. The goal of the paper is to provide a survey of sample size adaptation techniques, to classify them and to discuss various aspects concerning the techniques.