一种新型高精度非线性滤波算法研究

针对非线性、非高斯系统状态的在线估计问题,提出了一种新的高精度粒子滤波算法。该算法通过引入积分修正因子,对积分卡尔曼滤波器的积分点进行在线修正,并采用修正后的积分卡尔曼滤波产生优选的建议分布函数,由于高精度地融入最新量测信息,一定程度上克服了权值退化问题。仿真实验表明,新算法具有较高的滤波精度,是一种有效的非线性滤波算法。     

高斯渐进贝叶斯滤波器

渐进贝叶斯方法将先验分布到后验分布的演化描述为一阶动态系统,通过在伪时间上连续地引入观测信息实现后验状态估计.该方法的一般形式解,即动态系统的时间导数,是难以得到的.本文提出一种高斯型渐进贝叶斯滤波器.首先在线性高斯条件下推导了时间导数的解析解;然后证明了在该条件下,由该解析解确定的一阶动态系统与常量状态估计的Kalman-Bucy滤波器是一致的,且由此导出的高斯渐进贝叶斯滤波器与卡尔曼滤波器是一致的.最后利用一阶Taylor展开推导了滤波器在非线性高斯条件下的近似解表达式,并采用Monte Carlo方法给出了具体实现方法.通过若干仿真算例表明,新滤波器具有较高的精度,且在一定精度条件下的时间复杂度低于一般粒子滤波器.     

非线性交互粒子滤波算法

在非线性非高斯系统状态估计问题中,后验概率密度函数的解析形式难以获得,标准粒子滤波算法采用状态转移概率函数代替后验概率作为重要性采样概率密度函数,而未考虑当前观测数据的影响．针对该问题,首先提出了非线性交互多模型算法;然后应用该算法产生重要性采样概率密度函数,设计了新的非线性交互粒子滤波器．新的概率密度函数融入最新观测数据,更接近系统状态后验概率．比较实验表明了所提出算法的有效性．     

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.     

多传感器分布式信息融合粒子滤波器

针对非线性非Gaussian系统的状态估计问题,提出一种基于信息融合的多传感器分布式粒子滤波算法。该算法首先利用粒子滤波方法分别计算局部传感器的状态估值,再应用分布式标量加权融合准则对状态估值进行信息融合。仿真结果表明和单传感器情形相比可提高滤波的精度。     

模式转换未知的一类混杂系统的状态估计

Since the state of hybrid systems is determined by interacting continuous and discrete dynamics, the state estimation of hybrid systems becomes a challenging problem. It is more complicated when the discrete mode transition information is not available, and the modes of hybrid systems are nonlinear stochastic dynamic systems. To address this problem, this paper proposes a novel hybrid strong tracking filter (HSTF) for state estimation of a class of hybrid nonlinear stochastic systems with unknown mode transition, the method for designing HSTF is presented. The HSTF can estimate the continuous state and discrete mode accurately with unknown mode transition information, and the estimation of hybrid states is robust against the initial state. Simulation results illustrate the effectiveness of the proposed approach.     

A particle filter via constrained sampling for nonlinear dynamic systems

This article is concentrated on the particle filtering problem for nonlinear systems with nonlinear equality constraints. Considering the constraint information incorporated into filters can improve the state estimation accuracy, we propose an adaptive constrained particle filter via constrained sampling. First, in order to obtain particles drawn from the constrained important density function, we construct and solve a general optimization function theoretically fusing equality constraints and the importance density function. Furthermore, to reduce the computation time caused by the number of particles, the constrained Kullback‐Leiler distance sampling method is given to online adapt the number of particles needed for state estimation. A simulation study in the context of road‐confined vehicle tracking demonstrates that the proposed filter outperforms the typical constrained ones for equality constrained dynamic systems.     

基于粒子滤波的机动目标跟踪算法仿真研究

针对非线性多目标模型,应用粒子滤波算法,这种方法不受模型线性和Gauss假设的约束,是一种处理非线性非高斯动态系统状态递推估计的有效算法。在粒子滤波的基础上融合扩展卡尔曼滤波算法和无迹卡尔曼滤波算法。融合后的新算法在计算提议概率密度分布时,粒子的产生充分考虑当前时刻的量测,使得粒子的分布更加接近状态的后验概率分布,再用平滑算法处理滤波的结果。仿真结果表明,算法有较好的跟踪效果。     

Robust unscented Kalman filter with adaptation of process and measurement noise covariances

Unscented Kalman filter (UKF) has been extensively used for state estimation of nonlinear stochastic systems, which suffers from performance degradation and even divergence when the noise distribution used in the UKF and the truth in a real system are mismatched. For state estimation of nonlinear stochastic systems with non-Gaussian measurement noise, the Masreliez–Martin extended Kalman filter (EKF) gives better state estimates in relation to the standard EKF. However, the process noise and the measurement noise covariance matrices should be known, which is impractical in applications. This paper presents a robust Masreliez–Martin UKF which can provide reliable state estimates in the presence of both unknown process noise and measurement noise covariance matrices. Two numerical examples involving relative navigation of spacecrafts demonstrate that the proposed filter can provide improved state estimation performance over existing robust filtering approaches. Vision-aided robot arm tracking experiments are also provided to show the effectiveness of the proposed approach.     

交互式容积卡尔曼滤波及其应用 交互式容积卡尔曼滤波及其应用

针对非线性系统模型参数未知情况下的状态估计问题, 提出一种融合极大后验估计的交互式容积卡尔曼滤波算法(InCKF). 该算法利用二阶斯特林插值公式和无迹变换对非线性函数的近似思想, 实现对模型未知参数的确定, 从而使滤波算法摆脱对模型参数精确已知的依赖, 并通过容积卡尔曼滤波算法完成状态估计和量测更新. 仿真结果表明, 相比于经典的参数扩维方法, InCKF 算法具有更高的精度和更强的数值稳定性.

     

State Estimation of a Class of Hybrid Systems in the Presence of Unknown Mode Transitions

Since the state of hybrid systems is determined by interacting continuous and discrete dynamics,the state estimation of hybrid systems becomes a challenging problem.It is more com- plicated when the discrete mode transition information is not available,and the modes of hybrid systems are nonlinear stochastic dynamic systems.To address this problem,this paper proposes a novel hybrid strong tracking filter (HSTF) for state estimation of a class of hybrid nonlinear stochas- tic systems with unknown mode transition,the method for designing HSTF is presented.The HSTF can estimate the continuous state and discrete mode accurately with unknown mode transition in- formation,and the estimation of hybrid states is robust against the initial state.Simulation results illustrate the effectiveness of the proposed approach.     

基于均差滤波与高斯和的非线性非高斯系统滤波算法

针对一类非线性非高斯系统的滤波问题,在分析均差滤波算法和高斯和滤波算法的基础上,提出一种基于均差滤波的高斯和滤波算法,适于处理非线性非高斯系统的滤波问题.对于似然密度位于条件转移概率密度拖尾处的情况,与传统的粒子滤波算法相比,所提算法能提高滤波的精度和实时性.仿真实验验证了新算法的有效性.     

递推更新高斯粒子滤波器

传统高斯粒子滤波算法(Gaussian particle Filter,GPF)中,粒子的重要性密度函数是由高斯滤波器结合当前最新量测来构建的.由于传统高斯滤波器在量测更新阶段直接利用量测对状态进行线性更新,在某些条件下会导致所构建的重要性密度函数并不能很好地近似状态真实分布.为了解决这一问题,结合递推更新的思想,本文推导出了递推更新高斯滤波器(recursive update Gaussian filter,RUGF)的一般结构.并在此基础上,选用RUGF来构建粒子滤波的重要性密度函数,从而提出了基于递推更新的高斯粒子滤波算法(recursive update gaussian particle filter,RUGPF).仿真表明,在非线性系统状态估计问题中,递推更新可以很好的利用量测信息,相比于传统的GPF,本文所提出的RUGPF滤波算法可以提供更高精度的估计结果.     

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.     

A skewed unscented Kalman filter

State estimation of nonlinear systems is a challenging task, especially when the Gaussian approximation fails. The unscented Kalman filter was proposed to deal with state estimation of nonlinear systems. We modify the traditional unscented Kalman filter to capture the third-order moment (skewness) of the state vector. Methods are also proposed to reduce the computation time of the suggested approach, and showing that the proposed algorithm is as fast as the unscented Kalman filter. Simulation results confirm that the method is better than, or at least as good as, the unscented Kalman filter.     

Distribution function tracking filter design using hybrid characteristic functions

A new tracking filtering algorithm for a class of multivariate dynamic stochastic systems is presented. The system is expressed by a set of time-varying discrete systems with non-Gaussian stochastic input and nonlinear output. A new concept, such as hybrid characteristic function, is introduced to describe the stochastic nature of the dynamic conditional estimation errors, where the key idea is to ensure the distribution of the conditional estimation error to follow a target distribution. For this purpose, the relationships between the hybrid characteristic functions of the multivariate stochastic input and the outputs, and the properties of the hybrid characteristic function, are established. A new performance index of the tracking filter is then constructed based on the form of the hybrid characteristic function of the conditional estimation error. An analytical solution, which guarantees the filter gain matrix to be an optimal one, is then obtained. A simulation case study is included to show the effectiveness of the proposed algorithm, and encouraging results have been obtained.     

Linear minimum mean square error filtering with stochastic linear equality constraints

Constrained filters, through utilising the prior state constraint information, are designed to obtain more accurate state estimates in applications, and most of them deal with the estimation problem of systems with deterministic constraints. In practice, complex environmental disturbance, incomplete information or uncooperative behaviour often brings out uncertainties of the constraints. This paper tackles the filtering problem of dynamic systems subject to the stochastic linear equality constraints expressed by random weighted basis matrices. The corresponding constrained dynamic model is constructed first and the linear-minimum-mean-square-error filter is derived based on the orthogonality principle. Due to the effect of constraint randomness, the resultant filter encounters the problem of nonlinear stochastic calculation of random parameters, which is solved by the Taylor-based and the UT-based schemes, respectively, and the computational complexity as well as the tractability of both schemes are analysed. Finally, a simulation study on a road-constrained vehicle tracking demonstrates that the proposed filter has better performance than the classical estimation projection method in terms of estimation accuracy and computational complexity.     

Joint state and parameter robust estimation of stochastic nonlinear systems

Successful implementation of many control strategies is mainly based on accurate knowledge of the system and its parameters. Besides the stochastic nature of the systems, nonlinearity is one more feature that may be found in almost all physical systems. The application of extended Kalman filter for the joint state and parameter estimation of stochastic nonlinear systems is well known and widely spread. It is a known fact that in measurements, there are inconsistent observations with the largest part of population of observations (outliers). The presence of outliers can significantly reduce the efficiency of linear estimation algorithms derived on the assumptions that observations have Gaussian distributions. Hence, synthesis of robust algorithms is very important. Because of increased practical value in robust filtering as well as the rate of convergence, the modified extended Masreliez–Martin filter presents the natural frame for realization of the joint state and parameter estimator of nonlinear stochastic systems. The strong consistency is proved using the methodology of an associated ODE system. The behaviour of the new approach to joint estimation of states and unknown parameters of nonlinear systems in the case when measurements have non‐Gaussian distributions is illustrated by intensive simulations. Copyright © 2015 John Wiley & Sons, Ltd.     

Robust fuzzy filter design for nonlinear systems with persistent bounded disturbances.

To date, nonlinear Linfinity-gain filtering problems have not been solved by conventional methods for nonlinear dynamic systems with persistent bounded disturbances. This study introduces a fuzzy filtering design to deal with the nonlinear Linfinity-gain filtering problem. First, the Takagi and Sugeno fuzzy model is employed to approximate the nonlinear dynamic system. Next, based on the fuzzy model, a fuzzy filter is developed to minimize the upper bound of Linfinity-gain of the estimation error under some linear matrix inequality (LMI) constraints. Therefore, the nonlinear Linfinity-gain filtering problem is transformed into a suboptimal filtering problem, i.e., to minimize the upper bound of the Linfinity-gain of the estimation error subject to some LMI constraints. In this situation, the nonlinear Linfinity-gain filtering problem can be easily solved by an LMI-based optimization method. The proposed methods, which efficiently attenuate the peak of estimation error due to persistent bounded disturbances, extend the Linfinity-gain filtering problems from linear dynamic systems to nonlinear dynamic systems.     

Stochastically resilient extended Kalman filtering for discrete-time nonlinear systems with sensor failures

Missing sensor data is a common problem, which severely influences the overall performance of modern data-intensive control and computing applications. In order to address this important issue, a novel resilient extended Kalman filter is proposed for discrete-time nonlinear stochastic systems with sensor failures and random observer gain perturbations. The failure mechanisms of multiple sensors are assumed to be independent of each other with different failure rates. The locally unbiased robust minimum mean square filter is designed for state estimation under these conditions. The performance of the proposed estimation method is verified by means of numerical Monte Carlo simulation of two different nonlinear stochastic systems, involving a sinusoidal system and a Lorenz oscillator system.