Nonlinear non-Gaussian Models Research Articles

Extended Drones Tracking From ISAR Images With Doppler Effect and Orientation Based Robust Sub-Random Matrices Algorithm

The simultaneous imaging and tracking of drones and small UAVs is one of the most challenging problems in inverse synthetic aperture radar (ISAR) signal processing and has received significant attention recently. Wide-angle ISAR imaging may offer better resolution and richer geometrical features. Aiming at this issue, we propose a new algorithm for multiple extended drone targets (EDTs) detection and tracking from wide-angle ISAR images. Since a conventional tracking algorithm using a random matrices model (RMM) is not accurate enough to reconstruct a drone's extension by one ellipse, an appropriate technique needs to be developed for ISAR imaging and tracking of EDTs. This paper models the EDT's extension as multiple ellipses with a time-varying orientation angle and solves the resulting interference problem involving data association between the nonlinear measurements and sub-ellipses. Recently, the multi-Bernoulli (MB) filter for extended targets has been proposed with the RMM approach for linear ellipsoidal target tracking by additional state variables. However, the implementation of the MB-RMM filter for nonlinear non-Gaussian models and the Doppler effect has not been presented, especially for ISAR images. We consider linearizing the nonlinear observations to solve the nonlinearity due to the Doppler effect, target motion, and wide-angle ISAR images. We presented a new robust Sub-RMM-MB-TBD filter to obtain the estimated orientation of EDT's shape after using the range-only motion compensation that uses both range and Doppler information. Moreover, the authors applied the k-space algorithm to generate ISAR image. Simulation results demonstrate this remarkable performance.

Algorithm of Gaussian Sum Filter Based on SGQF for Nonlinear Non-Gaussian Models

Algorithm of Gaussian Sum Filter Based on SGQF for Nonlinear Non-Gaussian Models

On infinite horizon active fault diagnosis for a class of non-linear non-Gaussian systems

Abstract The paper considers the problem of active fault diagnosis for discrete-time stochastic systems over an infinite time horizon. It is assumed that the switching between a fault-free and finitely many faulty conditions can be modelled by a finite-state Markov chain and the continuous dynamics of the observed system can be described for the fault-free and each faulty condition by non-linear non-Gaussian models with a fully observed continuous state. The design of an optimal active fault detector that generates decisions and inputs improving the quality of detection is formulated as a dynamic optimization problem. As the optimal solution obtained by dynamic programming requires solving the Bellman functional equation, approximate techniques are employed to obtain a suboptimal active fault detector.

Computational aspects of sequential Monte Carlo filter and smoother

Progress in information technologies has enabled to apply computer- intensive methods to statistical analysis. In time series modeling, sequential Monte Carlo method was developed for general nonlinear non-Gaussian state-space models and it enables to consider very complex nonlinear non-Gaussian models for real-world problems. In this paper, we consider several computational problems associated with sequential Monte Carlo filter and smoother, such as the use of a huge number of parti- cles, two-filter formula for smoothing, and parallel computation. The posterior mean smoother and the Gaussian-sum smoother are also considered.

Convolution kernels implementation of cardinalized probability hypothesis density filter

The probability hypothesis density (PHD) propagates the posterior intensity in place of the posterior probability density of the multi-target state. The cardinalized PHD (CPHD) recursion is a generalization of PHD recursion, which jointly propagates the posterior intensity function and posterior cardinality distribution. A number of sequential Monte Carlo (SMC) implementations of PHD and CPHD filters (also known as SMCPHD and SMC-CPHD filters, respectively) for general non-linear non-Gaussian models have been proposed. However, these approaches encounter the limitations when the observation variable is analytically unknown or the observation noise is null or too small. In this paper, we propose a convolution kernel approach in the SMC-CPHD filter. The simulation results show the performance of the proposed filter on several simulated case studies when compared to the SMC-CPHD filter.

An evaluation of the nonlinear/non-Gaussian filters for the sequential data assimilation

This paper aims to investigate several new nonlinear/non-Gaussian filters in the context of the sequential data assimilation. The unscented Kalman filter (UKF), the ensemble Kalman filter (EnKF), the sampling importance resampling particle filter (SIR-PF) and the unscented particle filter (UPF) are described in the state-space model framework in the Bayesian filtering background. We first evaluated those methods with a simple highly nonlinear Lorenz model and a scalar nonlinear non-Gaussian model to investigate the filter stability and the error sensitivity, and then their abilities in the one-dimensional estimation of the soil moisture content with the synthetic microwave brightness temperature assimilation experiment in the land surface model VIC-3L. All the results are compared with the EnKF. The advantages and disadvantages of each filter are discussed. The results in the Lorenz model showed that the particle filters are suitable for the large measurement interval assimilation and that the Kalman filters were suitable for the frequent measurement assimilation as well as small measurement uncertainties. The EnKF also showed its feasibility for the non-Gaussian noise. The performance of the SIR-PF was actually not as good as that of the UKF or the EnKF regarding a very small observation noise level compared with the uncertainties in the system. In the one-dimensional brightness temperature assimilation experiment, the UKF, the EnKF and the SIR-PF all proved to be flexible and reliable nonlinear filter algorithms for the low dimensional sequential land data assimilation application. For the high dimensional land surface system that takes the horizontal error correlations into account, the UKF is restricted by its computational demand in the covariance propagation; we must use the EnKF, the SIR-PF and other covariance reduction algorithms. The large computational cost prevents the UPF from being applied in practice.

Statistical signal processing approaches to fault detection

The parity space approach to fault detection and isolation (FDI) has been developed during the last 20 years, and the focus here is to describe its application to stochastic systems. A mixed model with both stochastic inputs and deterministic disturbances and faults is formulated over a sliding window. Algorithms for detecting and isolating faults on-line and analyzing the probability for correct and incorrect decisions off-line are provided. A major part of the paper is devoted to discussing properties of this model-based approach and generalizations to cases of incomplete model knowledge, and non-linear non-Gaussian models. For this purpose, a simulation example is used throughout the paper for numerical illustrations, and real-life applications for motivations. The final section discusses the reverse problem: fault detection approaches to statistical signal processing. It is motivated by three applications that a simple CUSUM detector in feedback loop with an adaptive filter can mitigate the inherent trade-off between estimation accuracy and tracking speed in linear filters.

STATISTICAL SIGNAL PROCESSING APPROACHES TO FAULT DETECTION

The parity space approach to fault detection and isolation (FDI) has been developed during the last twenty years, and the focus here is to describe its application to stochastic systems. A mixed model with both stochastic inputs and deterministic disturbances and faults is formulated over a sliding window. Algorithms for detecting and isolating faults on-line and analyzing the probability for correct and incorrect decisions off-line are provided. A major part of the paper is devoted to discussing properties of this model-based approach and generalizations to cases of incomplete model knowledge, and non-linear non-Gaussian models. For this purpose, a simulation example is used throughout the paper for numerical illustrations, and real-life applications for motivations. The final section discusses the reverse problem: fault detection approaches to statistical signal processing. It is motivated by three applications that a simple CUSUM detector in feedback loop with an adaptive filter can mitigate the inherent trade-off between estimation accuracy and tracking speed in linear filters.

Special Issue on Nonlinear Non-Gaussian Models and Related Filtering Methods

Special Issue on Nonlinear Non-Gaussian Models and Related Filtering Methods

Prediction via estimating functions

This paper is concerned with prediction methods for linear as well as non-linear non-Gaussian models. Recursive formulas are obtained by combining the information associated with the predictive functions. Nonlinear predictors are obtained for linear and nonlinear time series models. The innovation algorithm is shown to be a special case of the proposed algorithm for linear processes with known autocovariances. Least absolute deviation predictors are shown to be a special case as well. Recursive prediction incorporating the variability due to parameter estimation is also discussed in some detail.

A COMPUTATIONAL METHOD FOR ESTIMATING DENSITIES OF NON‐GAUSSIAN NONSTATIONARY UNIVARIATE TIME SERIES

Abstract. Kitagawa's (1987a) numerical integration formulae used to approximate the filtering, prediction and smoothing densities of nonlinear non‐Gaussian state‐space models are modified. The method involves integration by parts which permits the integration of the conditional system density and, possibly, the observational density prior to and independently of the computation of the filtering, prediction and smoothing densities. In addition to a substantial reduction in computing time and an increase in accuracy, this approach eliminates the necessity of incorporating dynamic adjustments to the filtering, prediction and smoothing processes to accommodate difficult noise densities.Three numerical examples are presented. One example replicates Kitagawa's non‐Gaussian state‐space model; the second is a linear Gaussian model; and the third is a nonlinear non‐Gaussian model. Comparisons of speed and accuracy between alternative methods and between three computers (personal computer, minicomputer and supercomputer) are made.