Recursive estimation of 3D motion and surface structure from local affine flow parameters

A recursive structure from motion algorithm based on optical flow measurements taken from an image sequence is described. It provides estimates of surface normal in addition to 3D motion and depth. The measurements are affine motion parameters which approximate the local flow fields associated with near-planar surface patches in the scene. These are integrated over time to give estimates of the 3D parameters using an extended Kalman filter. This also estimates the camera focal length and, so, the 3D estimates are metric. The use of parametric measurements means that the algorithm is computationally less demanding than previous optical flow approaches and the recursive filter builds in a degree of noise robustness. Results of experiments on synthetic and real image sequences demonstrate that the algorithm performs well.     

Identification of process and measurement noise covariance for state and parameter estimation using extended Kalman filter

The performance of Bayesian state estimators, such as the extended Kalman filter (EKF), is dependent on the accurate characterisation of the uncertainties in the state dynamics and in the measurements. The parameters of the noise densities associated with these uncertainties are, however, often treated as ‘tuning parameters’ and adjusted in an ad hoc manner while carrying out state and parameter estimation. In this work, two approaches are developed for constructing the maximum likelihood estimates (MLE) of the state and measurement noise covariance matrices from operating input-output data when the states and/or parameters are estimated using the EKF. The unmeasured disturbances affecting the process are either modelled as unstructured noise affecting all the states or as structured noise entering the process predominantly through known, but unmeasured inputs. The first approach is based on direct optimisation of the ML objective function constructed by using the innovation sequence generated from the EKF. The second approach - the extended EM algorithm - is a derivative-free method, that uses the joint likelihood function of the complete data, i.e. states and measurements, to compute the next iterate of the decision variables for the optimisation problem. The efficacy of the proposed approaches is demonstrated on a benchmark continuous fermenter system. The simulation results reveal that both the proposed approaches generate fairly accurate estimates of the noise covariances. Experimental studies on a benchmark laboratory scale heater-mixer setup demonstrate a marked improvement in the predictions of the EKF that uses the covariance estimates obtained from the proposed approaches.     

Updating response sensitivity models of nonlinear vibrating structures using particle filters

The problem of updating response gradients with respect to chosen system parameters based on spatially sparse measurements is considered. The measurement noise and imperfections in mathematical modeling are treated as Gaussian white noise processes. The system states are augmented by response gradients with respect to system parameters and an extended set of equations in the state space is formulated. These equations are cast in the form of Ito’s stochastic differential equations and measured data are assimilated into this model using Monte Carlo based Bayesian filtering tools. Illustrative examples include a few low dimensional dynamical systems with cubic and hereditary nonlinearities.     

Weight assignment for adaptive image restoration by neural networks

This paper presents a scheme for adaptively training the weights, in terms of varying the regularization parameter, in a neural network for the restoration of digital images. The flexibility of neural-network-based image restoration algorithms easily allow the variation of restoration parameters such as blur statistics and regularization value spatially and temporally within the image. This paper focuses on spatial variation of the regularization parameter. We first show that the previously proposed neural-network method based on gradient descent can only find suboptimal solutions, and then introduce a regional processing approach based on local statistics. A method is presented to vary the regularization parameter spatially. This method is applied to a number of images degraded by various levels of noise, and the results are examined. The method is also applied to an image degraded by spatially variant blur. In all cases, the proposed method provides visually satisfactory results in an efficient way.     

Despeckling SAR-type multiplicative noise

Despeckling multiplicative noise is important in processing coherent radar images. Assuming that measurements are corrupted by multiplicative noise and that a priori values are contaminated by either multiplicative or additive noise, we have obtained Bayesian, maximum likelihood and weighted least-squares (LS) estimators, based on gamma and normal distributions. These estimators have been shown to be biased if the noise in measurements is multiplicative. A technique of bias-correction to remove biases from the estimated parameters is proposed. The bias-correction technique requires no distributions about the measurements and the a priori mean, and can be applied to eliminate bias from Bayesian, maximum likelihood and weighted LS estimators in multiplicative noise models. It theoretically provides a solid foundation for, and thus justifies some of current practice in, despeckling multiplicative noise, such as Lee's local statistics and Kuan's adaptive smoothing filter. Some despeckling measures are also proposed and simulated experiment results are reported.     

A Local Brightness Normalization (LBN) algorithm for destriping Hyperion images

A hybrid algorithm based on global moments matching and local brightness normalization is proposed for correcting vertical stripes in Hyperion images. Two types of vertical stripes are identified: (1) global stripes comprising entire columns of dark pixels with brightness values lower than the global brightness, and (2) local stripes comprising intermittent segments of pixels within a specific column that have lower brightness values compared with the local neighbourhood brightness. The proposed algorithm operates in four steps. First, a minimum noise fraction-transformation-based filtering is used to minimize spatially decorrelated noise. Then no-data pixels values are corrected. Next, global stripes are demarcated and corrected. Finally, local stripes are flagged and corrected. Applications of the proposed algorithm to two Hyperion datasets show significant reduction in vertical stripes.     

基于自适应密度估计的系统参数辨识

针对噪声分布未知的ARMAX系统,提出了一种自适应非参数噪声密度估计方法,由估计误差动态调整高斯核函数的全局带宽和局部带宽,实现了未知噪声分布密度的自适应估计;通过极小化似然函数,给出了基于噪声密度估计的参数辨识迭代算法,分析了算法的收敛性并给出了算法收敛的充分条件.仿真结果表明本文提出的算法在系统噪声未知时具有较强的抗噪能力和良好的收敛性.     

On-line state and parameter estimation of EPDM polymerization reactors using a hierarchical extended Kalman filter

A hierarchical extended Kalman filter (EKF) design is proposed to estimate unmeasured state variables and key kinetic parameters in a first principles model of a continuous ethylene–propylene–diene polymer (EPDM) reactor. The estimator design is based on decomposing the dynamic model into two subsystems by exploiting the triangular model structure and the different sampling frequencies of on-line and laboratory measurements directly related to the state variables of each subsystem. The state variables of the first subsystem are reactant concentrations and zeroth-order moments of the molecular weight distribution (MWD). Unmeasured state variables and four kinetic parameters systematically chosen to reduce bias are estimated from frequent and undelayed on-line measurements of the ethylene, propylene, diene and total polymer concentrations. The state variables of the second subsystem are first-order moments of the MWD. Given state and parameters estimates from the first subsystem EKF, the first-order moments and three non-stationary parameters added to the model for bias reduction are estimated from infrequent and delayed laboratory measurements of the ethylene and diene contents and number average molecular weight of the polymer. Simulation tests show that the hierarchical EKF generates satisfactory estimates even in the presence of measurement noise and plant/model mismatch.     

On-line estimation for process control and optimization applications

Design of Kalman filter type and moving horizon estimators for on-line estimation applications based on first principles models is reviewed. Important design issues are discussed, such as: model development; choice of process noise model and selection of model parameters for on-line estimation; use of asynchronous and delayed measurements; and off-line estimation of fixed but uncertain model parameters. The main conclusion, which is substantiated through application examples, is that robust and reliable estimation applications based on first principles models of considerable complexity, can be designed and implemented for use in an industrial environment.     

Spatially recursive algorithms for adaptive estimation of two-dimensional non-causal and non-stationary simultaneous autoregressive model parameters

Using the shift-invariance properties (Zhao and He 1988), two fast spatially recursive algorithms for adaptive estimation of two-dimensional (2D) non-causal and non-stationary simultaneous autoregressive (SAR)model parameters are presented. One is based on the conventional least-squares (LS) criterion, and the other producing unbiased estimates of the parameters is based on a modified LS criterion. The multiplicative operation numbers of the algorithms are 15m^3/2 + 16m and 16m^3/2 + 21m PR (per recursion) respectively, where m is the number of the estimated parameters. This makes a considerable reduction in the computational burden in contrast with the algorithms now in existence. The tracking performances of the algorithms are evaluated by computer simulations which show that both the algorithms track the variations of the parameters, but the unbiased one possesses much high estimation accuracy as expected.     

Robust unscented Kalman filter for nanosat attitude estimation

A robust unscented Kalman filter based on a multiplicative quaternion-error approach is proposed for nanosat estimation in the presence of measurement faults. The global attitude parameterization is given by a quaternion, while the local attitude error is defined using a generalized three-dimensional attitude representation. The proposed algorithm uses a statistical function including measurement residuals to detect measurement faults and then uses an adaptation scheme based on multiple measurement scale factor for filter robustness against faulty measurements. The proposed algorithm is demonstrated for the attitude estimation of a nanosat with an on-board three-axis magnetometer and rate-integrating gyros in the presence of measurement faults as well as satellite orbit errors. To compare the estimation performance of the proposed algorithm, the robust unscented Kalman filter with single measurement noise scale factor, the standard extended Kalman filter and the unscented Kalman filter are also implemented under the same simulation conditions.     

Consensus based overlapping decentralized estimation with missing observations and communication faults

In this paper a new algorithm for discrete-time overlapping decentralized state estimation of large scale systems is proposed in the form of a multi-agent network based on a combination of local estimators of Kalman filtering type and a dynamic consensus strategy, assuming intermittent observations and communication faults. Under general conditions concerning the agent resources and the network topology, conditions are derived for the convergence to zero of the estimation error mean and for the mean-square estimation error boundedness. A centralized strategy based on minimization of the steady-state mean-square estimation error is proposed for selection of the consensus gains; these gains can also be adjusted by local adaptation schemes. It is also demonstrated that there exists a connection between the network complexity and efficiency of denoising, i.e., of suppression of the measurement noise influence. Several numerical examples serve to illustrate characteristic properties of the proposed algorithm and to demonstrate its applicability to real problems.     

An alternative Kalman innovation filter approach for receiver position estimation based on GPS measurements

This article presents an alternative Kalman innovation filter approach for receiver position estimation, based on pseudorange measurements of the global positioning system. First, a dynamic pseudorange model is represented as an ARMAX model and a pseudorange state-space innovation model suitable for both parameter identification and state estimation. The Kalman gain in the pseudorange coordinates is directly calculated from the identified parameters without prior knowledge of the noise properties and the receiver parameters. Then, the pseudorange state-space innovation model is transformed into the receiver state-space innovation model for optimal estimation of the receiver position. Hence, the proposed approach overcomes the drawbacks of the classical Kalman filter approach since it does not require prior knowledge of the noise properties, and the receiver's dynamic model to calculate the Kalman gain. In addition, due to its simplicity, it can be easily implemented in any receiver. To demonstrate the effectiveness of the approach, it is utilized to estimate the position of a stationary receiver and its performance is compared against two versions of the classical Kalman filter approach. The results show that the proposed approach yields consistently good estimation of the receiver position and outperforms the other methods.     

Wavelet-based image denoising with the normal inverse Gaussian prior and linear MMSE estimator

A new spatially adaptive wavelet-based method is introduced for reducing noise in images corrupted by additive white Gaussian noise. It is shown that a symmetric normal inverse Gaussian distribution is highly suitable for modelling the wavelet coefficients. In order to estimate the parameters of the distribution, a maximumlikelihood- based technique is proposed, wherein the Gauss?Hermite quadrature approximation is exploited to perform the maximisation in a computationally efficient way. A Bayesian minimum mean-squared error (MMSE) estimator is developed utilising the proposed distribution. The variances corresponding to the noisefree coefficients are obtained from the Bayesian estimates using a local neighbourhood. A modified linear MMSE estimator that incorporates both intra-scale and inter-scale dependencies is proposed. The performance of the proposed method is studied using typical noise-free images corrupted with simulated noise and compared with that of the other state-of-the-art methods. It is shown that the proposed method gives higher values of the peak signal-to-noise ratio compared with most of the other denoising techniques and provides images of good visual quality. Also, the performance of the proposed method is quite close to that of the state-of-the-art Gaussian scale mixture (GSM) method, but with much less complexity.     

A genetic algorithm approach to the spectral estimation of time series with noise and missed observations

This study considers the problem of estimating the autoregressive moving average (ARMA) power spectral density when measurements are corrupted by noise and by missed observations. The missed observations model is based on a probabilistic structure. Unlike conventional cases of missed observation in parameter estimation problems, the variance of noise is unavailable, that is the time points of missed observations are unknown, and the probability of missing data needs to be estimated. In this situation, spectral estimation is more difficult to solve and becomes a highly nonlinear optimization problem with many local minima. In this paper, we use the genetic algorithm (GA) method to achieve a global optimal solution with a fast convergence rate for this spectral estimation problem. From the simulation results, we have determined that the performance is significantly improved if the probability of data loss is considered in the spectral estimation problem.     

结构可调的支持向量回归估计

针对定义域各分区间内样本数据的噪声强度不同，以及在局部范围内数据变化急剧等复杂情况，提出了结构可调的支持向量回归估计(AS-SVR)方法，包括采用不同的损失函数，对各样本点自适应地选用不同的参数等。推导了求解公式，给出了调整算法。实例测试表明，AS-SVR方法的楚模效果优于常规方法。     

COM motion estimation of a biped robot based on kinodynamics and torque equilibrium

A novel technique to estimate motion of the center of mass (COM) for a biped robot is proposed. A Kalman filter is synthesized where the time evolution of COM is predicted from the external force and corrected based on kinematic estimation and torque equilibrium. They complementarily work to compensate the initial estimation offset, the error accumulation, and errors in modeled mass properties. It makes use of the authors’ previous method to estimate the translational and rotational motion of the base body from inertial information and joint angle measurements. The information about torque equilibrium helps to reduce an uncertainty of the height of COM and to improve the estimation accuracy of it by utilizing an interference of the horizontal and vertical motion of COM. The parameters are tuned based on error analyses in mass properties and sensor signals. A comparative study showed a better performance of the proposed method than other methods through dynamics simulations.     

Gaussian mixture parameter estimation with known means and unknown class-dependent variances

This paper develops a recursive, convergent estimator for some parameters of Gaussian mixtures. The M class conditional (component) densities of the mixture random variable are Gaussian with known and distinct means and unknown and possibly different variances. A joint estimator of M prior (mixing) probabilities and M class conditional variances is derived. Sufficient conditions on the data and control parameters are derived for the estimator to converge. Convergence of the estimator follows from the use of a stochastic approximation theorem. Techniques to extend the estimators for the case of successive class labels forming a Markov chain are mentioned. The estimator has applications in blind parameter estimation in digital communication with symbol dependent noise variance and in image compression.     

A continuous-time framework for least squares parameter estimation

This paper proposes a continuous-time framework for the least-squares parameter estimation method through evolution equations. Nonlinear systems in the standard state space representation that are linear in the unknown, constant parameters are investigated. Two estimators are studied. The first one consists of a linear evolution equation while the second one consists of an impulsive linear evolution equation. The paper discusses some theoretical aspects related to the proposed estimators: uniqueness of a solution and an attractive equilibrium point which solves for the unknown parameters. A deterministic framework for the estimation under noisy measurements is proposed using a Sobolev space with negative index to model the noise. The noise can be of large magnitude. Concrete signals issued from an electronic device are used to discuss numerical aspects.     

Analysis of multispectral fields of satellite IR measurements: Using statistics of second spatial differential of spectral fields for measurement characterization

An approach using spatial analysis of satellite IR spectral measurements for quality assessment is presented. The second spatial differential is used as a model of measurement noise for spatially smooth radiative fields. Spatial differentiation significantly magnifies the noise contribution and reduces the physical signal amplitude because of differences in spatial distributions of instrument noise and atmospheric thermal fields. The second spatial differential represents a convenient and effective tool for numerical analysis of satellite IR measurements. This paper demonstrates that statistics of the second spatial differential are informative predictors for data‐quality characterization. Statistics of the second spatial differential are used for identifying anomalies in spectral channel data caused by detector noise, sensitivity loss to spatial shortwave thermal variations, and spatially (temporally) correlated noise.