non-Gaussian Observation Noise Research Articles

Gaussian-inverse gamma mixture distribution–based extended Kalman observer for dynamic positioning control system of offshore platform

Under different working conditions and control objectives, fuzzy model predictive control is used to optimize the control effect by adjusting the weight to achieve stable and accurate control for the dynamic positioning control of offshore platforms. Also, aiming at the situation where the measurement noise of dynamic positioning control may be time-varying and non-Gaussian and the statistics of the noise are not exact, this paper proposes a variational Bayesian extended Kalman filter observer. In order to model non-Gaussian noise more reasonably, the joint posterior distribution of non-Gaussian noise with state and time-varying covariance is described as the product of Gaussian and independent inverse gamma distributions. Then, the variational Bayesian (VB) method was used to simultaneously estimate the system state, the intermediate variable values of the new distribution, and the noise parameters through fixed-point iteration. The fuzzy algorithm is applied to the model predictive control, and the weight parameters of the model predictive control are adaptively changed to better adapt to the changing working conditions in the control process. The simulation results show that the variational Bayesian extended Kalman filter observer has better performance than the existing algorithms when dealing with the time-varying non-Gaussian observation noise, whose statistics are not exact. The variational Bayesian extended Kalman filter observer can significantly improve the accuracy of the control when it is used in fuzzy model predictive control.

Robust recursive sigma point Kalman filtering for Huber-based generalized M-estimation

For nonlinear state estimation driven by non-Gaussian noise, the estimator is required to be updated iteratively. Since the iterative update approximates a linear process, it fails to capture the nonlinearity of observation models, and this further degrades filtering accuracy and consistency. Given the flaws of nonlinear iteration, this work incorporates a recursive strategy into generalized M-estimation rather than the iterative strategy. The proposed algorithm extends nonlinear recursion to nonlinear systems using the statistical linear regression method. The recursion allows for the gradual release of observation information and consequently enables the update to proceed along the nonlinear direction. Considering the correlated state and observation noise induced by recursions, a separately reweighting strategy is adopted to build a robust nonlinear system. Analogous to the nonlinear recursion, a robust nonlinear recursive update strategy is proposed, where the associated covariances and the observation noise statistics are updated recursively to ensure the consistency of observation noise statistics, thereby completing the nonlinear solution of the robust system. Compared with the iterative update strategies under non-Gaussian observation noise, the recursive update strategy can facilitate the estimator to achieve higher filtering accuracy, stronger robustness, and better consistency. Therefore, the proposed strategy is more suitable for the robust nonlinear filtering framework.

Multi-Hypothesis Marginal Multi-Target Bayes Filter for a Heavy-Tailed Observation Noise

A multi-hypothesis marginal multi-target Bayes filter for heavy-tailed observation noise is proposed to track multiple targets in the presence of clutter, missed detection, and target appearing and disappearing. The proposed filter propagates the existence probabilities and probability density functions (PDFs) of targets in the filter recursion. It uses the Student’s t distribution to model the heavy-tailed non-Gaussian observation noise, and employs the variational Bayes technique to acquire the approximate distributions of individual targets. K-best hypotheses, obtained by minimizing the negative log-generalized-likelihood ratio, are used to establish the existence probabilities and PDFs of targets in the filter recursion. Experimental results indicate that the proposed filter achieves better tracking performance than other filters.

Certified dimension reduction in nonlinear Bayesian inverse problems

We propose a dimension reduction technique for Bayesian inverse problems with nonlinear forward operators, non-Gaussian priors, and non-Gaussian observation noise. The likelihood function is approximated by a ridge function, i.e., a map which depends nontrivially only on a few linear combinations of the parameters. We build this ridge approximation by minimizing an upper bound on the Kullback–Leibler divergence between the posterior distribution and its approximation. This bound, obtained via logarithmic Sobolev inequalities, allows one to certify the error of the posterior approximation. Computing the bound requires computing the second moment matrix of the gradient of the log-likelihood function. In practice, a sample-based approximation of the upper bound is then required. We provide an analysis that enables control of the posterior approximation error due to this sampling. Numerical and theoretical comparisons with existing methods illustrate the benefits of the proposed methodology.

Robust fading cubature Kalman filter and its application in initial alignment of SINS

Strapdown inertial navigation system (SINS) is a commonly used autonomous positioning instrument. As an integral calculating system, initial alignment is an essential work of SINS. Cubature Kalman filter (CKF) is a common algorithm for nonlinear initial alignment. Under the condition of inaccurate system model and non-Gaussian observation noise, the filter will appear to unstable or even divergence. In order to solve this problem, an anti-jamming improvement suitable for initial alignment is proposed in this paper. In which the prior covariance matrix and the observation noise covariance matrix are tuned by multiple fading factors. A Chi-square test method is designed to check the filter’s state, determining the introducing method of the fading factors autonomously. Experiment results show that, the proposed algorithm performs better in terms of robustness and adaptability even under the condition of inaccurate model and non-Gaussian observation noise.

An Improved Gaussian Mixture CKF Algorithm under Non-Gaussian Observation Noise

In order to solve the problems that the weight of Gaussian components of Gaussian mixture filter remains constant during the time update stage, an improved Gaussian Mixture Cubature Kalman Filter (IGMCKF) algorithm is designed by combining a Gaussian mixture density model with a CKF for target tracking. The algorithm adopts Gaussian mixture density function to approximately estimate the observation noise. The observation models based on Mini RadaScan for target tracking on offing are introduced, and the observation noise is modelled as glint noise. The Gaussian components are predicted and updated using CKF. A cost function is designed by integral square difference to update the weight of Gaussian components on the time update stage. Based on comparison experiments of constant angular velocity model and maneuver model with different algorithms, the proposed algorithm has the advantages of fast tracking response and high estimation precision, and the computation time should satisfy real-time target tracking requirements.

Image recovery under nonlinear and non-Gaussian degradations

A new two-dimensional recursive filter for recovering degraded images is proposed that is based on particle-filter theory. The main contribution of this work lies in evolving a framework that has the potential to recover images suffering from a general class of degradations such as system nonlinearity and non-Gaussian observation noise. Samples of the prior probability distribution of the original image are obtained by propagating the samples through an appropriate state model. Given the measurement model and the degraded image, the weights of the samples are computed. The samples and their corresponding weights are used to calculate the conditional mean that yields an estimate of the original image. The proposed method is validated by demonstrating its effectiveness in recovering images degraded by film-grain noise. Synthetic as well as real examples are considered for this purpose. Performance is also compared with that of an existing scheme.

計測雑音の確率的な性質を考慮した連続時間線形時不変システムの同定

In this paper, we discuss the identification of continuous linear time invariant systems with non-Gaussian observation noise. First we analyze the stochastic property of actual observation noise in terms of mixture distribution. Then we consider the method of data processing that converts the stochastic distribution of the noise in the actual observation to Gaussian distribution and propose a new identification method based on this data processing. Finally, we demonstrate the proposed identification method in both simulation and experiment.

Learning and classification of complex dynamics

Standard, exact techniques based on likelihood maximization are available for learning auto-regressive process models of dynamical processes. The uncertainty of observations obtained from real sensors means that dynamics can be observed only approximately. Learning can still be achieved via "EM-K"-expectation-maximization (EM) based on Kalman filtering. This cannot handle more complex dynamics, however, involving multiple classes of motion. A problem arises also in the case of dynamical processes observed visually: background clutter arising for example, in camouflage, produces non-Gaussian observation noise. Even with a single dynamical class, non-Gaussian observations put the learning problem beyond the scope of EM-K. For those cases, we show here how "EM-C"-based on the CONDENSATION algorithm which propagates random "particle-sets," can solve the learning problem. Here, learning in clutter is studied experimentally using visual observations of a hand moving over a desktop. The resulting learned dynamical model is shown to have considerable predictive value: when used as a prior for estimation of motion, the burden of computation in visual observation is significantly reduced. Multiclass dynamics are studied via visually observed juggling; plausible dynamical models have been found to emerge from the learning process, and accurate classification of motion has resulted. In practice, EM-C learning is computationally burdensome and the paper concludes with some discussion of computational complexity.

Narrow-band interference suppression in spread-spectrum CDMA communications using pipelined recurrent neural networks

This paper investigates the application of pipelined recurrent neural networks (PRNN's) to the narrow-band interference (NBI) suppression over spread-spectrum (SS) code-division multiple-access (CDMA) channels in the presence of additive white Gaussian noise (AWGN) plus non-Gaussian observation noise. Optimal detectors and receivers for such channels are no longer linear. A PRNN that consists of a number of simpler small-scale recurrent neural network (RNN) modules with less computational complexity is conducted to introduce best nonlinear approximation capability into the minimum mean-squared error nonlinear predictor model in order to accurately predict the NBI signal based on adaptive learning for each module from previous non-Gaussian observations. Once the prediction of the NBI signal is obtained, a resulting signal is computed by subtracting the estimate from the received signal. Thus, the effect of the NBI can be reduced. Moreover, since those modules of a PRNN can be performed simultaneously in a pipelined parallelism fashion, this would lead to a significant improvement in its total computational efficiency. Simulation results show that PRNN-based NBI rejection provides a superior signal-to-noise ratio (SNR) improvement relative to the conventional adaptive nonlinear approximate conditional mean (ACM) filters, especially when the channel statistics and exact number of CDMA users are not known to those receivers.

On exact filters for continuous signals with discrete observations

Many filtering applications have continuous state dynamics X/sub t/=/spl int//sub 0//sup t/m(X/sub s/)ds+/spl sigma/W/sub t/+/spl rho/, discrete observations Y/sub j/=Y(t/sub j/), and nonadditive or non-Gaussian observation noise. One wants to calculate the conditional probability Pr{Xt/spl isin/dz|Y/sub j/, 0/spl les/t/sub j//spl les/t} economically. In this paper we show that a combination of convolution, scaling, and substitutions efficiently solves this problem under certain conditions. Our method is easy to use and assumes nothing about the observations other than the ability to construct p(Y/sub j/)|X(t/sub j/), the conditional density of the jth observation given the current state.

Robust locally optimal filters: Kalman and Bayesian estimation theory

This paper presents a unified approach to local optimality, robustness, and Bayesian estimation theory concepts in deriving Kalman filtering equations in the case of non-Gaussian observation noise. In most of these derivations, an approximation criterion proposed by Masreliez is used: the prediction error density is approximately Gaussian. It is shown that locally optimal Kalman filters are equivalent to one-step MAP iterative procedures. The introduction of nonlinear iterative techniques adds a new dimension to the analysis of recursive non-Gaussian estimation. Moreover, to estimate the parameters of the Kalman model, a direct solution of MAP equations is obtained through an m-interval piecewise linear approximation (MIPLA) of the locally optimal nonlinearity (score function). Robustness is achieved by proper modification and approximation of the score function. Finally, the performance of the filters in question are tested under intensive Monte Carlo simulations. Satisfactory results are obtained even in the case of extremely impulsive observation noise (Cauchy contaminated Gaussian).