有色量测噪声下的改进求容积卡尔曼滤波器

为解决标准求容积卡尔曼滤波器在有色量测噪声条件下滤波精度退化的问题,提出改进求容积卡尔曼滤波器及其平方根形式.首先利用一阶马尔科夫模型白化非线性离散随机系统中有色量测噪声,将有色量测噪声下非线性离散随机系统转化为白噪声下非线性时滞系统.然后根据所得非线性时滞系统推导其高斯域的贝叶斯滤波框架,最后基于3度Spherical-Radial规则将该滤波框架近似为改进的求容积卡尔曼滤波器和其平方根形式.机动目标跟踪仿真试验结果表明两种改进求容积卡尔曼滤波算法在标准白噪声条件下与标准求容积卡尔曼滤波算法的估计精度相同,而在有色量测噪声背景下滤波精度和鲁棒性更优.     

基于不确定模型误差系统的变分贝叶斯STCKF

强跟踪容积卡尔曼滤波器在对含有模型误差和时变噪声的非线性系统进行滤波时, 容易出现性能降低甚至发散. 鉴于此, 提出一种基于变分贝叶斯的强跟踪容积卡尔曼滤波算法. 该算法运用虚拟噪声法补偿模型误差, 假设虚拟噪声均值非零, 且满足高斯分布, 虚拟噪声方差服从逆gamma分布, 在强跟踪容积卡尔曼滤波器估计状态的同时, 采用变分贝叶斯推理估计虚拟噪声参数. 仿真结果表明, 所提出算法对含模型误差与时变噪声的非线性系统具有较好的估计精度, 相比于自适应算法具有更强的鲁棒性.     

Distributed adaptive Kalman filter based on variational Bayesian technique

In this paper, distributed Kalman filter design is studied for linear dynamics with unknown measurement noise variance, which modeled by Wishart distribution. To solve the problem in a multi-agent network, a distributed adaptive Kalman filter is proposed with the help of variational Bayesian, where the posterior distribution of joint state and noise variance is approximated by a free-form distribution. The convergence of the proposed algorithm is proved in two main steps: noise statistics is estimated, where each agent only use its local information in variational Bayesian expectation (VB-E) step, and state is estimated by a consensus algorithm in variational Bayesian maximum (VB-M) step. Finally, a distributed target tracking problem is investigated with simulations for illustration.     

有色量测噪声下的HCKF及其应用

针对高阶容积卡尔曼滤波（HCKF）算法在有色量测噪声条件下滤波精度下降的问题,提出了有色量测噪声下的HCKF算法。通过一阶马尔科夫模型将有色量测噪声进行白化,将带有色量测噪声的非线性离散随机系统转化为白噪声下的非线性时滞系统,并给出高斯域内针对非线性时滞系统的贝叶斯滤波框架。利用高阶容积准则对该滤波框架进行近似计算,进而得到有色量测噪声下的HCKF算法。将所提算法应用到机动目标跟踪系统中,仿真实验结果表明,量测噪声为白噪声时,所提算法与标准HCKF算法具有相同的估计性能;在量测噪声为有色噪声时,所提算法相比于标准HCKF具有更优的估计精度和鲁棒性。     

基于SRCKF 的自适应高斯和状态滤波算法

针对非线性非高斯离散动态系统中的状态估计问题,基于高斯和递推关系,提出一种高斯和状态估计算法GSSRCKF.首先将状态噪声、观测噪声及滤波初值均表示为高斯和的形式,以平方根容积卡尔曼滤波为子滤波器分别估计各高斯子项对应的系统状态;然后结合各子项对应的权值实现全局估计;最后设计高斯子项对应权值的自适应策略,并采用约简控制法降低计算复杂度.仿真结果验证了所提出的算法在滤波稳定性方面的优越性.     

An algorithmic approach to adaptive state filtering using recurrentneural networks

Practical algorithms are presented for adaptive state filtering in nonlinear dynamic systems when the state equations are unknown. The state equations are constructively approximated using neural networks. The algorithms presented are based on the two-step prediction-update approach of the Kalman filter. The proposed algorithms make minimal assumptions regarding the underlying nonlinear dynamics and their noise statistics. Non-adaptive and adaptive state filtering algorithms are presented with both off-line and online learning stages. The algorithms are implemented using feedforward and recurrent neural network and comparisons are presented. Furthermore, extended Kalman filters (EKFs) are developed and compared to the filter algorithms proposed. For one of the case studies, the EKF converges but results in higher state estimation errors that the equivalent neural filters. For another, more complex case study with unknown system dynamics and noise statistics, the developed EKFs do not converge. The off-line trained neural state filters converge quite rapidly and exhibit acceptable performance. Online training further enhances the estimation accuracy of the developed adaptive filters, effectively decoupling the eventual filter accuracy from the accuracy of the process model.     

基于高斯似然近似的自适应球面径向积分滤波算法

针对量测噪声较小的环境下传统滤波算法容易出现偏差增大的实际问题, 基于高斯近似原理, 提出一种基于高斯似然近似的球面径向积分滤波(SRGLAF) 算法. 为进一步解决量测未知环境下的状态估计问题, 充分结合CKF 等确定性采样型滤波算法和SRGLAF 的优势, 设计一种基于高斯似然近似的自适应球面径向积分滤波(ASRGLAF) 算法. 仿真结果表明: SRGLAF 能够提高量测噪声较小环境下的估计精度, 而在量测噪声未知环境中, ASRGLAF 能够有效地进行状态估计, 具有明显的滤波优势.

     

An enhanced adaptive Kalman filtering for linear systems with inaccurate noise statistics

This paper investigates the simultaneous state and noise covariance estimation for linear systems with inaccurate noise statistics. An enhanced adaptive Kalman filtering (EAKF) based on dynamic recursive nominal covariance estimation (DNRCE) and modified variational Bayesian (VB) inference is presented. The EAKF realizes the concurrently estimation of state and noise covariance matrices by introducing a nominal parameter in the traditional recursive covariance estimation and designing a new adaptive forgotten factor for the dynamic model of the estimated information propagation. The simulation of a target tracking example shows that, compared with the existing filters, the proposed filter has good adaptive performance for inaccurate and time-varying noise covariance matrices.     

Marginalized adaptive particle filtering for nonlinear models with unknown time-varying noise parameters

Knowledge of the noise distribution is typically crucial for the state estimation of general state-space models. However, properties of the noise process are often unknown in the majority of practical applications. The distribution of the noise may also be non-stationary or state dependent and that prevents the use of off-line tuning methods. For linear Gaussian models, Adaptive Kalman filters (AKF) estimate unknown parameters in the noise distributions jointly with the state. For nonlinear models, we provide a Bayesian solution for the estimation of the noise distributions in the exponential family, leading to a marginalized adaptive particle filter (MAPF) where the noise parameters are updated using finite dimensional sufficient statistics for each particle. The time evolution model for the noise parameters is defined implicitly as a Kullback–Leibler norm constraint on the time variability, leading to an exponential forgetting mechanism operating on the sufficient statistics. Many existing methods are based on the standard approach of augmenting the state with the unknown variables and attempting to solve the resulting filtering problem. The MAPF is significantly more computationally efficient than a comparable particle filter that runs on the full augmented state. Further, the MAPF can handle sensor and actuator offsets as unknown means in the noise distributions, avoiding the standard approach of augmenting the state with such offsets. We illustrate the MAPF on first a standard example, and then on a tire radius estimation problem on real data.     

基于MCC的鲁棒高阶CKF在组合导航中的应用

针对高阶容积卡尔曼滤波器在非高斯噪声情况下滤波精度下降的问题,提出了一种新的基于Maximum Correntropy Criterion（MCC）的鲁棒高阶容积卡尔曼滤波算法。考虑到高阶容积规则可以较好地解决非线性问题,在高阶容积滤波的基础上,结合统计线性回归模型对量测更新过程进行重构,利用MCC估计算法实现状态的量测更新,同时解决了系统的非线性和非高斯问题。将所提算法应用到SINS/GPS组合导航系统中,仿真结果表明,核宽的选取对算法的滤波性能有较大的影响,在高斯混合噪声条件下,所提算法相比传统高阶容积卡尔曼滤波算法具有更强的鲁棒性和更高的滤波精度。     

An adaptive unscented Kalman filter approach to secure state estimation for wireless sensor networks

Wireless sensor networks are vulnerable to false data injection attacks, which may mislead the state estimation. To solve this problem, this paper presents a chi-square test-based adaptive secure state estimation (CTASSE) algorithm for state estimation and attack detection. Taking advantage of Kalman filters, attack signal together with process noise or measurement noise are described as total white Gaussian noise with uncertain covariance matrix. The chi-square test method is used in the adaptation of the total noise covariance and attack detection. Then, a standard adaptive unscented Kalman filter (UKF) is used for the state estimation. Finally, simulation results show that the proposed CTASSE algorithm performs better than other UKFs in state estimation and is also effective in real-time attack detection.     

Cubature Kalman Filters

In this paper, we present a new nonlinear filter for high-dimensional state estimation, which we have named the cubature Kalman filter (CKF). The heart of the CKF is a spherical-radial cubature rule, which makes it possible to numerically compute multivariate moment integrals encountered in the nonlinear Bayesian filter. Specifically, we derive a third-degree spherical-radial cubature rule that provides a set of cubature points scaling linearly with the state-vector dimension. The CKF may therefore provide a systematic solution for high-dimensional nonlinear filtering problems. The paper also includes the derivation of a square-root version of the CKF for improved numerical stability. The CKF is tested experimentally in two nonlinear state estimation problems. In the first problem, the proposed cubature rule is used to compute the second-order statistics of a nonlinearly transformed Gaussian random variable. The second problem addresses the use of the CKF for tracking a maneuvering aircraft. The results of both experiments demonstrate the improved performance of the CKF over conventional nonlinear filters.      

A parallel processing solution to the adaptive Kalman filtering problem with vector measurements

The adaptive Kalman filtering problem with vector measurements is considered. A computational algorithm is derived which gives estimates of the state of a linear dynamic system driven by additive white Gaussian noise with unknown covariance Q and observed by a linear function of the state contaminated by additive white Gaussian noise with unknown covariance R. The computational algorithm is inherently parallel in nature and it is noted that the algorithm should be implemented in a special purpose parallel processing digital computer made up of a number of filters similar to steady state Kalman filters each with a different gain. It is shown that the estimates of the state and the estimates of the unknown covariances Q and R can be made arbitrarily close to the optimal nonlinear Bayesian estimates by an appropriate choice for the number of parallel paths in the computer. When the filtering algorithm is implemented in a parallel processing computer the total processing time for state estimation in the unknown noise environment is only slightly increased over that required for a steady state Kalman filter. A numerical example with a five dimensional state and two dimensional measurement vector is presented.     

A mixture-of-experts framework for adaptive Kalman filtering

This paper proposes a modular and flexible approach to adaptive Kalman filtering using the framework of a mixture-of-experts regulated by a gating network. Each expert is a Kalman filter modeled with a different realization of the unknown system parameters such as process and measurement noise. The gating network performs on-line adaptation of the weights given to individual filter estimates based on performance. This scheme compares very favorably with the classical Magill filter bank, which is based on a Bayesian technique, in terms of: estimation accuracy; quicker response to changing environments; and numerical stability and computational demands. The proposed filter bank is further enhanced by periodically using a search algorithm in a feedback loop. Two search algorithms are considered. The first algorithm uses a recursive quadratic programming approach which extremizes a modified maximum likelihood function to update the parameters of the best performing filter in the bank. This particular approach to parameter adaptation allows a real-time implementation. The second algorithm uses a genetic algorithm to search for the parameter vector and is suited for post-processed data type applications. The workings and power of the overall filter bank and the suggested adaptation schemes are illustrated by a number of examples.     

State estimation of nonlinear dynamic systems using weighted variance-based adaptive particle swarm optimization

New heuristic filters are proposed for state estimation of nonlinear dynamic systems based on particle swarm optimization (PSO) and differential evolution (DE). The methodology converts state estimation problem into dynamic optimization to find the best estimate recursively. In the proposed strategy the particle number is adaptively set based on the weighted variance of the particles. To have a filter with minimal parameter settings, PSO with exponential distribution (PSO-E) is selected in conjunction with jDE to self-adapt the other control parameters. The performance of the proposed adaptive evolutionary algorithms i.e. adaptive PSO-E, adaptive DE and adaptive jDE is studied through a comparative study on a suite of well-known uni- and multi-modal benchmark functions. The results indicate an improved performance of the adaptive algorithms relative to original simple versions. Further, the performance of the proposed heuristic filters generally called adaptive particle swarm filters (APSF) or adaptive differential evolution filters (ADEF) are evaluated using different linear (nonlinear)/Gaussian (non-Gaussian) test systems. Comparison of the results to those of the extended Kalman filter, unscented Kalman filter, and particle filter indicate that the adopted strategy fulfills the essential requirements of accuracy for nonlinear state estimation.     

Recursive Noise Adaptive Kalman Filtering by Variational Bayesian Approximations

This article considers the application of variational Bayesian methods to joint recursive estimation of the dynamic state and the time-varying measurement noise parameters in linear state space models. The proposed adaptive Kalman filtering method is based on forming a separable variational approximation to the joint posterior distribution of states and noise parameters on each time step separately. The result is a recursive algorithm, where on each step the state is estimated with Kalman filter and the sufficient statistics of the noise variances are estimated with a fixed-point iteration. The performance of the algorithm is demonstrated with simulated data.      

Effective cubature FastSLAM: SLAM with Rao-Blackwellized particle filter and cubature rule for Gaussian weighted integral

Simultaneous localization and mapping (SLAM) is a key technology for mobile robot autonomous navigation in unknown environments. While FastSLAM algorithm is a popular solution to the large-scale SLAM problem, it suffers from two major drawbacks: one is particle set degeneracy due to lack of measurements in proposal distribution of particle filter; the other is errors accumulation caused by inaccurate linearization of the nonlinear robot motion model and the environment measurement model. To overcome the problems, a new Jacobian-free cubature FastSLAM (CFastSLAM) algorithm is proposed in this paper. The main contribution of the algorithm lies in the utilization of third-degree cubature rule, which calculates the nonlinear transition density of Gaussian prior more accurately, to design an optimal proposal distribution of the particle filter and to estimate the Gaussian densities of the feature landmarks. On the basis of Rao-Blackwellized particle filter, the proposed algorithm is comprised by two main parts: in the first part, a cubature particle filter (CPF) is derived to localize the robot; in the second part, a set of cubature Kalman filters is used to estimate environment landmarks. The performance of the proposed algorithm is investigated and compared with that of FastSLAM2.0 and UFastSLAM in simulations and experiments. Results verify that the CFastSLAM improves the SLAM performance.     

具有噪声信息与状态模型不确定系统的IMM自适应滤波

卡尔曼滤波器广泛用于解决线性高斯系统的状态估计问题.然而,在实际应用中过程噪声和系统模型参数先验信息未知,且量测受到异常值干扰,给准确估计系统状态带来极大困难.针对具有噪声信息和状态模型不确定的动态系统,提出一种广义交互式多模型自适应滤波算法.该算法设计多个模型并行的方式对系统不确定进行处理,对于每个模型,建立Skew-T分布非对称重尾噪声表示模型,为了解决过程噪声与系统协方差相互耦合难以求解的问题,利用逆威沙特分布对系统预测协方差矩阵进行描述,并通过变分贝叶斯推理递归计算系统状态的后验分布.仿真结果和实验验证表明,在噪声信息和状态模型不确定条件下,所提出算法具有较高的估计精度.     

Cubature Kalman smoothers

The cubature Kalman filter (CKF) is a relatively new addition to derivative-free approximate Bayesian filters built under the Gaussian assumption. This paper extends the CKF theory to address nonlinear smoothing problems; the resulting state estimator is named the fixed-interval cubature Kalman smoother (FI-CKS). Moreover, the FI-CKS is reformulated to propagate the square-root error covariances. Although algebraically equivalent to the FI-CKS, the square-root variant ensures reliable implementation when committed to embedded systems with fixed precision or when the inference problem itself is ill-conditioned. Finally, to validate the formulation, the square-root FI-CKS is applied to track a ballistic target on reentry.     

带有色厚尾量测噪声的鲁棒高斯近似滤波器和平滑器

为了解决带有色厚尾量测噪声的非线性状态估计问题,本文提出了新的鲁棒高斯近似（Gaussian approximate,GA）滤波器和平滑器.首先,基于状态扩展方法将量测差分后带一步延迟状态和白色厚尾量测噪声的非线性状态估计问题,转化成带厚尾量测噪声的标准非线性状态估计问题.其次,针对量测差分后模型中的噪声尺度矩阵和自由度（Degrees of freedom,DOF）参数未知问题,设计了新的高斯近似滤波器和平滑器,通过建立未知参数和待估计状态的共轭先验分布,并利用变分贝叶斯方法同时估计未知的状态、尺度矩阵、自由度参数.最后,利用目标跟踪仿真验证了本文提出的带有色厚尾量测噪声的鲁棒高斯近似滤波器和平滑器的有效性以及与现有方法相比的优越性.