适用处理非高斯观测噪声的强跟踪卡尔曼滤波器

在高斯噪声条件下,卡尔曼滤波器(KF)能够获得系统状态的一致最小方差线性无偏估计.但当噪声非高斯,KF性能将严重下降.观测噪声非高斯现象在深空探测自主导航中经常遇到,然而现有模型可能存在着精度不高、稳定性不强或者计算复杂度较高的缺点.针对这种现状,本文在传统强跟踪卡尔曼滤波器(STKF)中新息正交原则的基础上,推导了适用处理非高斯观测噪声的强跟踪卡尔曼滤波器(STKFNO),并将其嵌入到无迹卡尔曼滤波(UKF)框架下形成适用处理非线性系统非高斯观测噪声的强跟踪无迹卡尔曼滤波器(STUKFNO).所提出的算法被应用到深空光学自主导航系统中,仿真结果表明所提出的算法能够较好地应对观测噪声的非高斯性.     

Humanoid state estimation using a moving horizon estimator

In this research, a new state estimator based on moving horizon estimation theory is suggested for the humanoid robot state estimation. So far, there are almost no studies on the moving horizon estimator (MHE)-based humanoid state estimator. Instead, a large number of humanoid state estimators based on the Kalman filter (KF) have been proposed. However, such estimators cannot guarantee optimality when the system model is nonlinear or when there is a non-Gaussian modeling error. In addition, with KF, it is difficult to incorporate inequality constraints. Since a humanoid is a complex system, its mathematical model is normally nonlinear, and is limited in its ability to characterize the system accurately. Therefore, KF-based humanoid state estimation has unavoidable limitations. To overcome these limitations, we propose a new approach to humanoid state estimation by using a MHE. It can accommodate not only nonlinear systems and constraints, but also it can partially cope with non-Gaussian modeling error. The proposed estimator framework facilitates the use of a simple model, even in the presence of a large modeling error. In addition, it can estimate the humanoid state more accurately than a KF-based estimator. The performance of the proposed approach was verified experimentally.     

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 General Probabilistic Framework for uncertainty and global sensitivity analysis of deterministic models: A hydrological case study

The present study proposes a General Probabilistic Framework (GPF) for uncertainty and global sensitivity analysis of deterministic models in which, in addition to scalar inputs, non-scalar and correlated inputs can be considered as well. The analysis is conducted with the variance-based approach of Sobol/Saltelli where first and total sensitivity indices are estimated. The results of the framework can be used in a loop for model improvement, parameter estimation or model simplification. The framework is applied to SWAP, a 1D hydrological model for the transport of water, solutes and heat in unsaturated and saturated soils. The sources of uncertainty are grouped in five main classes: model structure (soil discretization), input (weather data), time-varying (crop) parameters, scalar parameters (soil properties) and observations (measured soil moisture). For each source of uncertainty, different realizations are created based on direct monitoring activities. Uncertainty of evapotranspiration, soil moisture in the root zone and bottom fluxes below the root zone are considered in the analysis. The results show that the sources of uncertainty are different for each output considered and it is necessary to consider multiple output variables for a proper assessment of the model. Improvements on the performance of the model can be achieved reducing the uncertainty in the observations, in the soil parameters and in the weather data. Overall, the study shows the capability of the GPF to quantify the relative contribution of the different sources of uncertainty and to identify the priorities required to improve the performance of the model. The proposed framework can be extended to a wide variety of modelling applications, also when direct measurements of model output are not available.     

A new real-time suboptimum filtering and prediction scheme for general nonlinear discrete dynamic systems with Gaussian or non-Gaussian noise

A new suboptimum state filtering and prediction scheme is proposed for nonlinear discrete dynamic systems with Gaussian or non-Gaussian disturbance and observation noises. This scheme is an online estimation scheme for real-time applications. Furthermore, this scheme is very suitable for state estimation under either constraints imposed on estimates or missing observations. State and observation models can be any nonlinear functions of the states, disturbance and observation noises as long as noise samples are independent, and the density functions of noise samples and conditional density functions of the observations given the states are available. State models are used to calculate transition probabilities from gates to gates. If these transition probabilities are known or can be estimated, state models are not needed for estimation. The proposed scheme (PR) is based upon state quantisation and multiple hypothesis testing. Monte Carlo simulations have shown that the performance of the PR, sampling importance resampling (SIR) particle filter and extended Kalman (EK) filter are all model-dependent, and that the performance of the PR is better than both the SIR particle filter and EK filter for some nonlinear models, simulation results of three of which are given in this article.     

观测误差协方差估计下的集合鲁棒滤波数据同化方法

在数据同化方法中,观测误差协方差矩阵是相关的,且与时间和状态有一定的依赖性.针对这种相关特性,将鲁棒滤波方法与观测误差协方差估计方法相结合,得到随状态时间变化的观测误差协方差,提出一种带有观测误差估计的鲁棒数据同化新方法,更新观测误差协方差,改善估计效果.从分析误差协方差,转移矩阵特征值放大等角度优化同化方法.利用非线...     

Cubature Kalman Filter Under Minimum Error Entropy With Fiducial Points for INS/GPS Integration

Traditional cubature Kalman filter(CKF)is a preferable tool for the inertial navigation system(INS)/global positioning system(GPS)integration under Gaussian noises.The CKF,however,may provide a significantly biased estimate when the INS/GPS system suffers from complex non-Gaussian disturbances.To address this issue,a robust nonlinear Kalman filter referred to as cubature Kalman filter under minimum error entropy with fiducial points(MEEF-CKF)is proposed.The MEEF-CKF behaves a strong robustness against complex nonGaussian noises by operating several major steps,i.e.,regression model construction,robust state estimation and free parameters optimization.More concretely,a regression model is constructed with the consideration of residual error caused by linearizing a nonlinear function at the first step.The MEEF-CKF is then developed by solving an optimization problem based on minimum error entropy with fiducial points(MEEF)under the framework of the regression model.In the MEEF-CKF,a novel optimization approach is provided for the purpose of determining free parameters adaptively.In addition,the computational complexity and convergence analyses of the MEEF-CKF are conducted for demonstrating the calculational burden and convergence characteristic.The enhanced robustness of the MEEF-CKF is demonstrated by Monte Carlo simulations on the application of a target tracking with INS/GPS integration under complex nonGaussian noises.     

基于双EnKF的土壤水分与土壤属性参数同时估计

为提高土壤水分数据同化结果的精度,将基于双集合卡尔曼滤波(Dual Ensemble Kalman Filter,DEnKF)的状态-参数估计方案与简单生物圈模型(simple biosphere model 2,SiB2)相结合,同时更新土壤水分和优化模型参数(土壤属性参数)。选用2008年6月1日~10月29日黑河上游阿柔冻融观测站为参考站,开展了同化表层土壤水分观测数据的实验。研究结果表明:DEnKF可同时优化土壤属性参数和改进土壤水分估计,该方法对表层土壤水分估计的精度0.04高于EnKF算法的精度0.05。当观测数据稀少时,DEnKF算法仍然可以得到较高精度的土壤水分估计,3层土壤水分的估计精度在0.02~0.05之间。     

基于高斯–广义双曲混合分布的非线性卡尔曼滤波

本文研究带非平稳厚尾非高斯量测噪声的非线性系统状态估计问题.考虑到广义双曲分布包含多种常见厚尾分布特例,且其混合分布为共轭的广义逆高斯分布,选用广义双曲分布建模厚尾噪声;进而引入伯努利变量构建高斯–广义双曲混合分布来建模非平稳厚尾噪声,并利用该分布的高斯分层结构得到系统的概率模型.随后采用变分贝叶斯方法实现对系统状态以及噪声参数的后验估计,得到针对此类噪声系统的卡尔曼滤波(Kalman filter, KF)框架,现有的几种鲁棒滤波算法均是本文算法的特例.机器人跟踪仿真实验表明,所提算法与同类算法相比具有更好的估计精度和数值稳定性,且对于初始参数具有较好的鲁棒性.     

Cooperative multi-robot belief space planning for autonomous navigation in unknown environments

We investigate the problem of cooperative multi-robot planning in unknown environments, which is important in numerous applications in robotics. The research community has been actively developing belief space planning approaches that account for the different sources of uncertainty within planning, recently also considering uncertainty in the environment observed by planning time. We further advance the state of the art by reasoning about future observations of environments that are unknown at planning time. The key idea is to incorporate within the belief indirect multi-robot constraints that correspond to these future observations. Such a formulation facilitates a framework for active collaborative state estimation while operating in unknown environments. In particular, it can be used to identify best robot actions or trajectories among given candidates generated by existing motion planning approaches, or to refine nominal trajectories into locally optimal paths using direct trajectory optimization techniques. We demonstrate our approach in a multi-robot autonomous navigation scenario and consider its applicability for autonomous navigation in unknown obstacle-free and obstacle-populated environments. Results indicate that modeling future multi-robot interaction within the belief allows to determine robot actions (paths) that yield significantly improved estimation accuracy.     

复杂运动状态的视频目标跟踪自适应切换算法

针对实际环境中运动目标的状态转移模型以及随机噪声分布存在的不确定性,提出了一种适用于复杂运动状态的视频目标跟踪算法。该算法同时结合了Kalman滤波(KF)实时性好的优点,以及粒子滤波(PF)能同时处理非线性、非高斯滤波问题的优点,通过对Kalman滤波性能进行分析,定义了评价滤波性能优劣的参数并作为判断条件,实现了不同运动状态下Kalman滤波和粒子滤波自适应切换。通过实验表明该方法在目标运动状态发生显著变化时仍能够实现稳定跟踪,同时具有较高的跟踪精度。     

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     

Hierarchical multispectral galaxy decomposition using a MCMC algorithm with multiple temperature simulated annealing

We present a new method for the parametric decomposition of barred spiral galaxies in multispectral observations. The observation is modelled with a realistic image formation model and the galaxy is composed of physically significant parametric structures. The model also includes a parametric filtering to remove non-desirable aspects of the observation. Both the model and the filter parameters are estimated by a robust Monte Carlo Markov chain (MCMC) algorithm. The algorithm is based on a Gibbs sampler combined with a novel strategy of simulated annealing in which several temperatures allow to manage efficiently the simulation effort. Besides, the overall decomposition is performed following an original framework: a hierarchy of models from a coarse model to the finest one is defined. At each step of the hierarchy the estimate of a coarse model is used to initialize the estimation of the finer model. This leads to an unsupervised decomposition scheme with a reduced computation time. We have validated the method on simulated and real 5-band images: the results showed the accuracy and the robustness of the proposed approach.     

A data-model-fusion prognostic framework for dynamic system state forecasting

A novel data-model-fusion prognostic framework is developed in this paper to improve the accuracy of system state long-horizon forecasting. This framework strategically integrates the strengths of the data-driven prognostic method and the model-based particle filtering approach in system state prediction while alleviating their limitations. In the proposed methodology, particle filtering is applied for system state estimation in parallel with parameter identification of the prediction model (with unknown parameters) based on Bayesian learning. Simultaneously, a data-driven predictor is employed to learn the system degradation pattern from history data so as to predict system evolution (or future measurements). An innovative feature of the proposed fusion prognostic framework is that the predicted measurements (with uncertainties) from the data-driven predictor will be properly managed and utilized by the particle filtering to further update the prediction model parameters, thereby enabling markedly better prognosis as well as improved forecasting transparency. As an application example, the developed fusion prognostic framework is employed to predict the remaining useful life of lithium ion batteries through electrochemical impedance spectroscopy tests. The investigation results demonstrate that the proposed fusion prognostic framework is an effective forecasting tool that can integrate the strengths of both the data-driven method and the particle filtering approach to achieve more accurate state forecasting.     

Hybrid method based on particle filter and NARX for real-time flow rate estimation in multi-product pipelines

Real-time flow estimation plays a vital role in multi-product pipeline operations, and the accuracy of real-time flow estimation is affected by noise interference and instrument accuracy and cannot be performed by direct observation of flow meter. Pipeline flow models based on the first principle method are established and employed as soft sensors of pipeline real-time flow rate. However, these models are validated by the controlled experimental pipeline, which may be ineffective regarding actual pipelines with uncertain physical parameters. In this paper, a novel approach integrating data-driven and model-driven method is proposed to estimate the flow rate of petroleum products on-line. The difference between the theoretical model and actual state of a pipeline is accounted for by the friction coefficient, and on-line calibration is achieved by solving multi-objective optimisation problems with asynchronous operation data. The flow state of the pipeline is obtained in real time by the particle filter when new pressure observations with noise become available. The estimation performance of local pressure mutation points is improved by adopting the recurrent nonlinear autoregressive neural network modelling blue of the data-driven method. The effectiveness of the proposed method is evaluated blue by examining actual data of the pipeline over a period of time. The prediction results of some other model-driven and data-driven methods are also compared to blue that of the proposed method. The results blue indicate that the proposed method improves the accuracy and reliability of the product flow rate estimations even under unforeseen operation conditions.     

Projected sequential Gaussian processes: A C++ tool for interpolation of large datasets with heterogeneous noise

Heterogeneous datasets arise naturally in most applications due to the use of a variety of sensors and measuring platforms. Such datasets can be heterogeneous in terms of the error characteristics and sensor models. Treating such data is most naturally accomplished using a Bayesian or model-based geostatistical approach; however, such methods generally scale rather badly with the size of dataset, and require computationally expensive Monte Carlo based inference. Recently within the machine learning and spatial statistics communities many papers have explored the potential of reduced rank representations of the covariance matrix, often referred to as projected or fixed rank approaches. In such methods the covariance function of the posterior process is represented by a reduced rank approximation which is chosen such that there is minimal information loss. In this paper a sequential Bayesian framework for inference in such projected processes is presented. The observations are considered one at a time which avoids the need for high dimensional integrals typically required in a Bayesian approach. A C++ library, gptk, which is part of the INTAMAP web service, is introduced which implements projected, sequential estimation and adds several novel features. In particular the library includes the ability to use a generic observation operator, or sensor model, to permit data fusion. It is also possible to cope with a range of observation error characteristics, including non-Gaussian observation errors. Inference for the covariance parameters is explored, including the impact of the projected process approximation on likelihood profiles. We illustrate the projected sequential method in application to synthetic and real datasets. Limitations and extensions are discussed.     

基于误差状态卡尔曼滤波估计的旋翼无人机输入饱和控制

针对GPS（global positioning system）信号缺失环境下无人机自主飞行控制问题,设计了一种基于视觉与IMU（inertial measurement unit）融合的误差状态卡尔曼滤波（ESKF）框架,并在此基础上提出了一种新的输入饱和控制方法以进一步缓解视野约束以及运动模糊问题．不同于传统的扩展卡尔曼滤波（EKF）框架,本文设计的滤波框架是对误差状态进行更新与校正,而不是直接对系统状态进行估计．由于误差状态是小量,并且其线性程度较高,因此相对于系统状态局部线性化而言,误差状态的局部线性化的模型误差更小,进而可以提高状态估计的精度．基于ESKF框架得到的全状态估计,本文提出了一种新的线性与双曲正切混合的饱和函数,进而设计了输入饱和控制器并通过李亚普诺夫函数证明了闭环系统平衡点的渐近稳定性．最后,在旋翼无人机平台上的对比实验结果表明：本文ESKF方法得到的状态估计精度更高．另外,本文所提出的输入饱和控制方法有助于保证视觉特征在视野之内,并且比有界积分控制方法有更好的暂态以及稳态性能．     

Variational-Bayes Optical Flow

The Horn-Schunck (HS) optical flow method is widely employed to initialize many motion estimation algorithms. In this work, a variational Bayesian approach of the HS method is presented, where the motion vectors are considered to be spatially varying Student’s t-distributed unobserved random variables, i.e., the prior is a multivariate Student’s t-distribution, while the only observations available is the temporal and spatial image difference. The proposed model takes into account the residual resulting from the linearization of the brightness constancy constraint by Taylor series approximation, which is also assumed to be a spatially varying Student’s t-distributed observation noise. To infer the model variables and parameters we recur to variational inference methodology leading to an expectation-maximization (EM) framework with update equations analogous to the Horn-Schunck approach. This is accomplished in a principled probabilistic framework where all of the model parameters are estimated automatically from the data. Experimental results show the improvement obtained by the proposed model which may substitute the standard algorithm in the initialization of more sophisticated optical flow schemes.     

A novel real-time adaptive suboptimal recursive state estimation scheme for nonlinear discrete dynamic systems with non-Gaussian noise

A real-time state filtering and prediction scheme which is adaptive, recursive, and suboptimal is proposed for discrete time nonlinear dynamic systems with either Gaussian or non-Gaussian noise. The proposed scheme (PR) estimates states adaptively whenever both the observation is available and there exists a non-zero and finite number of real state roots of the observation model, otherwise the PR estimates states non-adaptively. The PR state transition and observation functions are as general as the state transition and observation functions for particle filters. The PR is based upon discrete noise approximation, state quantization, and a suboptimal implementation of multiple hypothesis testing. The PR first detects state estimate divergence points along the time axis, and then state estimate divergences are prevented by introducing new admissible state quantization levels; whereas the extended Kalman filter (EKF), sampling importance resampling (SIR) particle filter (bootstrap filter), and auxiliary sampling importance resampling (ASIR) particle filter produce diverging state estimates from actual state values for many dynamic models. The PR uses state transition functions in order to calculate transition probabilities from gates to gates. If these transition probabilities are somehow available, then state transition functions are not needed for state estimation with the PR; whereas state transition functions are necessary for state estimation with both particle filters and the EKF. The PR is very suitable for state estimation with either constraints imposed on state estimates or missing observations. The PR is more general than grid-based estimation approaches. Monte Carlo simulations have shown the effectiveness of the PR, that is, the PR performance is better than the performances of the EKF, SIR, and ASIR particle filters for many nonlinear models with white Gaussian noise, four examples of which are presented in the paper.     

Bayesian estimation via sequential Monte Carlo sampling—Constrained dynamic systems

Nonlinear and non-Gaussian processes with constraints are commonly encountered in dynamic estimation problems. Methods for solving such problems either ignore the constraints or rely on crude approximations of the model or probability distributions. Such approximations may reduce the accuracy of the estimates since they often fail to capture the variety of probability distributions encountered in constrained linear and nonlinear dynamic systems. This article describes a practical approach that overcomes these shortcomings via a novel extension of sequential Monte Carlo (SMC) sampling or particle filtering. Inequality constraints are imposed by accept/reject steps in the algorithm. The proposed approach provides samples representing the posterior distribution at each time point, and is shown to satisfy the same theoretical properties as unconstrained SMC. Illustrative examples show that results of the proposed approach are at least as accurate as moving horizon estimation, but computationally more efficient and in addition, the approach indicates the uncertainty associated with these estimates.