SINS/GNSS integrated navigation system based on maximum versoria filter

In the missile-borne Strapdown Inertial Navigation System/Global Navigation Satellite System (SINS/GNSS) integrated navigation system, due to the factors such as the high dynamics, the signal blocking by obstacles, the signal intefereces, etc., there always exist pulse interferences or measurement information interruptions in the satellite receiver, which make nonstationary measurement process. The traditional Kalman Filter (KF) can tackle the state estimation problem under Gaussian white noise, but its performance will be significantly reduced under non-Gaussian noises. In order to deal with the non-Gaussian conditions in the actual missile-borne SINS/GNSS integrated navigation systems, a Maximum Versoria Criterion Extended Kalman Filter (MVC-EKF) algorithm is proposed based on the MVC and the idea of M-estimation, which assigns a smaller weight to the anomalous measurements so as to suppress the influence of anomalous measurements on the state estimation while maintaining a relatively low calculation cost. Finally, the integrated navigation simulation experiments prove the effectiveness and robustness of the proposed algorithm.     

Adaptive Gaussian sum squared-root cubature Kalman filter with split-merge scheme for state estimation

The paper deals with state estimation problem of nonlinear non-Gaussian discrete dynamic systems for improvement of accuracy and consistency. An efficient new algorithm called the adaptive Gaussian-sum square-root cubature Kalman filter（AGSSCKF） with a split-merge scheme is proposed. It is developed based on the squared-root extension of newly introduced cubature Kalman filter（SCKF） and is built within a Gaussian-sum framework. Based on the condition that the probability density functions of process noises and initial state are denoted by a Gaussian sum using optimization method, a bank of SCKF are used as the sub-filters to estimate state of system with the corresponding weights respectively, which is adaptively updated. The new algorithm consists of an adaptive splitting and merging procedure according to a proposed split-decision model based on the nonlinearity degree of measurement. The results of two simulation scenarios（one-dimensional state estimation and bearings-only tracking） show that the proposed filter demonstrates comparable performance to the particle filter with significantly reduced computational cost.     

Optimal robust non-fragile Kalman-type recursive filtering with finite-step autocorrelated noises and multiple packet dropouts

In this paper, the optimal robust non-fragile Kalman-type recursive filtering problem is studied for a class of uncertain systems with finite-step autocorrelated measurement noises and multiple packet dropouts. The system state, measurement output and filter parameters are all subject to stochastic uncertainties or multiplicative noises, where the measurement noises are finite-step autocorrelated. When there exist multiple packet dropouts in the system output, the original system is converted into an auxiliary stochastic uncertain system by the augmentation of system states and measurements. The process noises and measurement noises of the auxiliary system are shown to be finite-step autocorrelated and cross-correlated. Then, a robust non-fragile Kalman-type recursive filter is designed that is optimal in the minimum-variance sense. The proposed filter is not only robust against the uncertainties in the system model and measurement model, but also non-fragile against the implementation error with the filter parameters. Simulation results are employed to demonstrate the effectiveness of the proposed method.     

Optimal filtering for systems with finite-step autocorrelated noises and multiple packet dropouts

This paper addresses the optimal filtering problem for a class of uncertain dynamical systems with multiple packet dropouts and finite-step correlated observation noises. By rearranging the stochastic terms in the transmission and measurement matrices of the dynamical system into the noises directly, the process noises and observation noises in resulted system depend on the state as well as the stochastic uncertain perturbations, and are not only autocorrelated respectively but also cross-correlated. For this complicated dynamical system, instead of designing a Kalman-type filter, a globally optimal filtering in the minimum mean square error sense is developed by exploiting sufficiently the statistical properties of correlated noises. Numerical simulation is provided to demonstrate the performance of the proposed filter.     

A modified Gaussian sum approach to estimation of non-Gaussiansignals

A Gaussian sum estimation algorithm has previously been developed to deal with noise processes that are non-Gaussian. Inherent in this algorithm is a serious growing memory problem that causes the number of terms in the Gaussian sum to increase exponentially at each iteration. A modified Gaussian sum estimation algorithm using an adaptive filter is developed that avoids the growing memory problem of the previous algorithm while providing effective state estimation. The adaptive filter is comprised of a fixed set of estimators operating in parallel with each individual estimate possessing its own corresponding weighting term. A simulation example illustrates the new non-Gaussian estimation technique     

考虑非高斯相关噪声的视线角速率提取算法

针对捷联导引头敏感信息存在非高斯噪声且状态噪声与观测噪声相关的问题,提出了修正球面坐标系下带有相关噪声解耦的扩展椭球集员滤波（ESMF）算法。首先,通过对弹目相对距离及其变化率的规范化处理,得到修正球面坐标系下的视线角速率提取模型;然后,利用相关噪声解耦方法去除观测方程中耦合的状态噪声项,基于泰勒级数展开推导了相关噪声解耦后的模型线性化表达式,得到包含线性化误差的虚拟噪声椭球集合,并根据最小迹和最小化尺度因子上界的优化方法得到状态更新与观测更新椭球,形成非高斯相关噪声解耦的扩展椭球集员滤波算法。仿真结果表明,所提算法能够在考虑非高斯相关噪声的情况下,实现捷联导引头视线角速率的高精度提取。     

非线性非高斯模型的高斯和PHD滤波算法(英文)

A new multi-target filtering algorithm, termed as the Gaussian sum probability hypothesis density （GSPHD） filter, is proposed for nonlinear non-Gaussian tracking models. Provided that the initial prior intensity of the states is Gaussian or can be identified as a Gaussian sum, the analytical results of the algorithm show that the posterior intensity at any subsequent time step remains a Gaussian sum under the assumption that the state noise, the measurement noise, target spawn intensity, new target birth intensity, target survival probability, and detection probability are all Gaussian sums. The analysis also shows that the existing Gaussian mixture probability hypothesis density （GMPHD） filter, which is unsuitable for handling the non-Gaussian noise cases, is no more than a special case of the proposed algorithm, which fills the shortage of incapability of treating non-Gaussian noise. The multi-target tracking simulation results verify the effectiveness of the proposed GSPHD.     

飞机的随机变结构最优控制方法

 <正> 一、引言 系统的变结构控制(VSC——Variable Structure Control)方法,最初是由苏联学者Utkin等人提出来的,近二十年来发展非常迅速,并越来越多地应用于各个工业领域,其中包括航空部门。变结构系统(VSS——Variable Structure System)的主要特征是存在滑动模态。处于滑动模态时,系统的运动等价于一个低阶系统。研究表明,VSS比传统的控制系统有更好的优点:快速性,对参数变化及外加扰动有强鲁棒性以及实现简单等。然而,VSC的不足之处在于需要获得全部状态变量,这是很难保证的。     

导航精度的评估与检验

 在Poor估计算法的基础上，研究了导航系统的位置误差模型，对Poor假设进行了修改和补充，将随机过程的各态历经性推广到多元随机过程的各态历经性，提出了Poor估计算法必须建立在多元随机过程的各态历经性上才能实现，并给出了实现的充分条件。讨论了导航精度的假设检验问题，提出通过对不同导航系统之间的相对误差进行多元统计分析，来研究各导航系统的精度问题。     

Almost instant time inference for hybrid partially dynamic Bayesian networks

A Bayesian network (BN) is a compact representation for probabilistic models and inference. They have been used successfully for many military and civilian applications. It is well known that, in general, the inference algorithms to compute the exact a posterior probability of a target node given observed evidence are either computationally infeasible for dense networks or impossible for general hybrid networks. In those cases, one either computes the approximate results using stochastic simulation methods or approximates the model using discretization or a Gaussian mixture model before applying an exact inference algorithm. This paper combines the concept of simulation and model approximation to propose an efficient algorithm for those cases. The main contribution here is a unified treatment of arbitrary (nonlinear non-Gaussian) hybrid (discrete and continuous) BN inference having both computation and accuracy scalability. The key idea is to precompile the high-dimensional hybrid distribution using a hypercube representation and apply it for both static and dynamic BN inference. Since the inference process essentially becomes a combination of table look-up and some simple operations, the method is shown to be extremely efficient. It can also he scaled to achieve any desirable accuracy given sufficient preprocessing time and memory for the cases where exact inference is not possible     

结构随机跳变系统的自举滤波方法

针对在结构随机跳变系统的滤波中存在的“基础结构失真”问题,提出了一种对系统结构的非线性、系统状态和噪声的分布形式不再限制的滤波新方法。并就该方法的性能同目前广泛应用的滤波方法做了仿真比较,仿真结果证实了该方法的有效性及其优良性能。     

非线性非高斯秩滤波方法

基于秩滤波原理,提出一种非线性非高斯秩滤波方法,给出其递推过程.目前常用的非线性滤波方法有无迹Kalman滤波和粒子滤波,无迹Kalman滤波只适用于高斯分布的情况,粒子滤波方法却存在粒子退化及重采样引起的粒子贫化问题.而非线性非高斯秩滤波方法不仅适用于常见的多元t分布、多元极值分布等非高斯分布的非线性滤波,并且计算简单、工作量小,便于工程应用.从仿真算例可以看到,该方法的滤波精度与无迹Kalman滤波和粒子滤波方法相比提高了500%以上.      

基于模糊系统的径向高斯网络的自适应状态观测器

利用模糊系统的径向高斯函数网络对一类非线性时变系统的状态进行了估计。给出了一种递阶自组织在线学习算法,提出了非线性时变系统的自适应状态观测器,并对其结构及特征进行了讨论,仿真结果表明这种自适应状态观测器能很好地观测系统的状态。     

K-Nearest Neighbor Particle Filters for Dynamic Hybrid Bayesian Networks

In state estimation of dynamic systems, Kalman filters and HMM filters have been applied to linear-Gaussian models and models with finite state spaces. However, they do not work well in most practical problems with nonlinear and non-Gaussian models. Even when the state space is finite, the dynamic Bayesian networks describing the HMM model could be too complicated to manage. Sequential Monte Carlo methods, also known as particle filters (PFs), have been introduced to deal with these real-world problems. They allow us to treat any type of probability distribution, nonlinearity and nonstationarity although they usually suffer major drawbacks of sample degeneracy and inefficiency in high-dimensional cases. We show how we can exploit the structure of partially dynamic hybrid Bayesian networks (PD-HBN) to reduce ``sample depletion' and increase the efficiency of particle filtering by combining the well-known K-nearest neighbor (KNN) majority voting strategy and the concept of evolution algorithm. Essentially, the novel method resamples the dynamic variables and randomly combines them with the existing samples of static variables to produce new particles. As new observations become available, the algorithm allows the particles to incorporate the latest information so that the fittest particles associated with a proposed objective rule will be kept for resampling. We also conduct a theoretical analysis on the proposed KNN-PF algorithm, and demonstrate the accuracy of the performance prediction with extensive simulations. Performance analysis and numerical results show that this new approach has a superior estimation/classification performance compared to other related algorithms.     

Reliability estimation of mechanical seals based on bivariate dependence analysis and considering model uncertainty

The reliability estimation of mechanical seals is of crucial importance due to their wide applications in pumps in various mechanical systems. Failure of mechanical seals might cause leakage, and might lead to system failure and other relevant consequences. In this study, the reliability estimation for mechanical seals based on bivariate dependence analysis and considering model uncertainty is proposed. The friction torque and leakage rate are two degradation performance indicators of mechanical seals that can be described by the Wiener process, Gamma process, and inverse Gaussian process. The dependence between the two indicators can be described by different copula functions. Then the model uncertainty is considered in the reliability estimation using the Bayesian Model Average (BMA) method, while the unknown parameters in the model are estimated by Bayesian Markov Chain Monte Carlo (MCMC) method. A numerical simulation study and fatigue crack study are conducted to demonstrate the effectiveness of the BMA method to capture model uncertainty. A degradation test of mechanical seals is conducted to verify the proposed model. The optimal stochastic process models for two performance indicators and copula function are determined based on the degradation data. The results show the necessity of using the BMA method in degradation modeling.     

Particle flters for probability hypothesis density flter with the presence of unknown measurement noise covariance

In Bayesian multi-target fltering,knowledge of measurement noise variance is very important.Signifcant mismatches in noise parameters will result in biased estimates.In this paper,a new particle flter for a probability hypothesis density（PHD）flter handling unknown measurement noise variances is proposed.The approach is based on marginalizing the unknown parameters out of the posterior distribution by using variational Bayesian（VB）methods.Moreover,the sequential Monte Carlo method is used to approximate the posterior intensity considering non-linear and non-Gaussian conditions.Unlike other particle flters for this challenging class of PHD flters,the proposed method can adaptively learn the unknown and time-varying noise variances while fltering.Simulation results show that the proposed method improves estimation accuracy in terms of both the number of targets and their states.     

A novel optimal data fusion algorithm and its application for the integrated navigation system of missile

For Inertial Navigation System(INS)/Celestial Navigation System(CNS)/Global Navigation Satellite System(GNSS) integrated navigation system of the missile, the performance of data fusion algorithms based on the Cubature Kalman Filter(CKF) is seriously degraded when there are non-Gaussian noise and process-modeling errors in the system model. Therefore, a novel method is proposed, which is called Optimal Data Fusion algorithm based on the Adaptive Fading maximum Correntropy generalized high-degree...     

混合高斯测量噪声下的多模型滤波

就带有混合高斯测量噪声的离散时间系统 ,提出了一种简化的多模型滤波。理论分析证明该滤波方法用较少的计算量得到了与交互多模型滤波相同的估计性能。为满足应用要求 ,给出了该滤波器的数值鲁棒实现方法。一个关于仅有方位测量的制导例子验证了该滤波算法的有效性。     

Radar Measurement Noise Variance Estimation with Several Targets of Opportunity

A number of methods exist to track a target's uncertain motion through space using inherently inaccurate sensor measurements. A powerful method of adaptive estimation is the interacting multiple model (IMM) estimator. In order to carry out state estimation from the noisy measurements of a sensor, however, the filter should have knowledge of the statistical characteristics of the noise associated with that sensor. The statistical characteristics (accuracies) of real sensors, however, are not always available, in particular for legacy sensors. A method is presented of determining the measurement noise variances of a sensor, assumed to be constant, by using multiple IMM estimators while tracking targets whose motion is not known---targets of opportunity. Combining techniques outlined in [2] and [6], the likelihood functions are obtained for a number of IMM estimators, each with different assumptions on the measurement noise variances. Then a search is carried out over a varying grid of IMMs to bracket the variances of the sensor measurement noises. The end result consists of estimates of the measurement noise variances of the sensor in question.     

带异步相关噪声的战斗机蛇形机动跟踪算法

针对异步相关噪声背景下战斗机蛇形机动模式转弯角速度辨识问题,考虑到目标状态与转弯角速度之间相互耦合的特性,从联合优化的解决思路出发,基于期望最大化（EM）算法框架,提出了一种带异步相关噪声的联合估计与辨识算法。首先采用"去相关框架"解除过程噪声与量测噪声之间的相关性,从而将异步相关噪声背景下的转弯角速度辨识问题转换成具有一步状态延迟的转弯角速度辨识问题,其次通过解除目标状态与转弯角速度之间的非线性耦合关系,基于期望最大化算法实现了战斗机蛇形机动目标状态与转弯角速度的联合估计与辨识,从而获得转弯角速度闭环形式的解析解：在E-step,通过利用异步相关噪声背景下的高阶容积卡尔曼平滑器（HCKS）,获得目标状态的后验估计;在M-step,通过极大化条件似然函数,获得转弯角速度的解析解。最后通过仿真验证了所提算法的目标状态估计与角速度辨识的精度均优越于传统的扩维法。