稀疏高斯厄米特PHD机动多目标跟踪算法

针对基于概率假设密度（probability hypothesis density，PHD）的非线性机动多目标跟踪精度低、滤波发散、目标数目估计不准确等问题，提出一种基于交互式多模型的稀疏高斯厄米特PHD算法.该算法在PHD滤波器下，采用稀疏高斯厄米特方法对目标进行状态预测和量测更新，构造一种稀疏高斯厄米特PHD滤波器；然后将交互式多模型算法融入稀疏高斯厄米特PHD滤波框架中，解决了目标机动过程中运动模式不确定的问题.仿真结果表明该算法能对机动多目标进行有效的跟踪，相比交互式多模型不敏卡尔曼PHD等滤波方法具有更高的状态估计精度，且目标数目估计更准确.     

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.     

自适应各向异性SGHQF 及其在组合导航中的应用

针对稀疏高斯厄米特积分滤波(SGHQF)中积分点利用效率不高的问题,提出一种基于状态分量可观测度分析的自适应各向异性SGHQF (AASGHQF)。给出了利用状态分量可观测度和各向异性权重向量来控制各维通道积分精度等级的方法,进而对各变量通道的积分点数目进行合理分配。以CNS/SAR/SINS非线性组合导航为应用背景,对UKF、SGHQF和AASGHQF进行了仿真对比分析。仿真结果表明, AASGHQF与SGHQF的滤波估计精度相当,均高于UKF;AASGHQF比SGHQF需要更少的积分点,提高了计算效率。     

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。     

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.

     

Cubature卡尔曼滤波-卡尔曼滤波算法

针对条件线性高斯状态空间模型,提出cubature卡尔曼滤波-卡尔曼滤波算法(CKF-KF),分别应用CKF和KF估计模型中的非线性和线性状态.该算法对非线性与线性状态均进行cubature采样,并将两种样本通过线性方程和量测方程进行传播,以获得非线性状态估计.机动目标跟踪仿真结果表明,CKF-KF的估计精度比Rao-Blackwellized粒子滤波器(RBPF)略低,但算法运行时间不到其1％;与无迹卡尔曼滤波器(UKF-KF)相比,估计精度相当,但算法运行时间降低了22％,有效地提高了实时性.     

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.     

基于正则化的高斯粒子滤波算法

针对非线性系统的状态估计问题,提出一种改进的高斯粒子滤波算法。该算法是基于正则化粒子滤波(RPF),将重采样中离散的概率分布函数近似为连续分布,进而在高斯粒子滤波(GPF)中引入正则化粒子滤波算法得到的最新预测值,并利用这一观测值进行状态估计的更新。最后,对RGPF和GPF两种算法进行综合分析和实验仿真,结果表明,与标准GPF算法相比,RGPF具有较高的滤波精度。     

跳变约束下马尔可夫切换非线性系统滤波

针对系统状态演化多模不确定性和状态约束多样性,本文提出了跳变约束下马尔可夫切换非线性系统的交互式多假设估计方法.定义了包含跳变马尔可夫参数可能取值的假设集,根据最优贝叶斯滤波,推导出状态与假设的后验概率递推更新.基于统计线性回归线性化非线性函数,利用伪量测法,将线性化的约束扩维到真实量测中,给出了非线性系统滤波的近似解析最优解.最终给出所提算法的稀疏网格积分近似最优估计实现.在交叉道路机动目标跟踪仿真场景中,所提算法的滤波精度优于基于泰勒展开的交互式多模型算法,基于统计线性回归的交互式多模型算法,以及基于泰勒展开的非线性系统约束滤波算法.     

基于MCMC的改进粒子滤波算法

针对传统粒子滤波算法建议分布函数的选取问题和粒子退化现象,提出一种基于马尔可夫蒙特卡洛思想的改进粒子滤波算法.使用基于比例对称采样方法选取Sigma点的无迹卡尔曼滤波,产生粒子滤波并建议分布函数;将似然分布自适应权值调整策略应用于权值选取步骤;采用系统重采样方法,加入了用来保持粒子多样性的马尔科夫链蒙特卡洛步骤.仿真结果表明,该算法的估计状态能够更好地吻合真实轨迹,在非线性、非高斯场合的估计性能较优.     

平方根体积积分卡尔曼滤波

体积积分是一种新的具有较高代数精度的积分方法。为了提高非线性滤波算法的精度和数值稳定性,将体积积分规则和平方根分解引入卡尔曼滤波框架中,提出了平方根体积积分卡尔曼滤波算法（SRCQKF）。新算法采用球半径体积规则和高斯-拉盖尔积分规则计算积分点,利用矩阵的QR分解得到协方差矩阵的平方根并传播平方根。两个典型的非线性系统的实验结果表明,与体积卡尔曼滤波相比,新算法提高了非线性状态的估计精度,具有较高的数值稳定性。     

基于修正积分卡尔曼粒子滤波的自适应目标跟踪算法

针对当前粒子滤波权值退化问题以及精度与时耗的矛盾,提出了一种新的高精度自适应粒子滤波算法。该算法综合考虑优选建议分布函数和重采样两种并行改进滤波性能的方法:首先,在积分卡尔曼滤波(QKF)的基础上引入修正因子,通过修正的积分卡尔曼滤波(PQKF)产生优选的建议分布函数,较好地克服了粒子退化现象,在提高滤波精度的同时降低了运算量;在重采样阶段,通过引入系统估计和预测提供的新息差值在线自适应调整采样粒子数,较好地保证了粒子采样的高效性和算法的实时性。实验表明,新算法具有高精度、低时耗的优点,是一种高精度自适应粒子滤波算法。     

Robust Ensemble Kalman Filter Based on Exponential Cost Function

This paper provides an alternative point of view to the robust estimation technique for nonlinear non Gaussian systems based on exponential quadratic cost function. The proposed method, named the risk sensitive ensemble Kalman filter (RSEnKF), is based on the ensemble Kalman filter (EnKF) which may be thought of as a Monte Carlo implementation of the Kalman filter for nonlinear estimation problems. The theory and formulation of the RSEnKF are presented in this paper. The proposed method is superior to the extended risk sensitive filter (ERSF) and the quadrature based risk sensitive filters in terms of estimation accuracy, and is faster than the risk sensitive particle filter (RSPF).     

Algorithm of Gaussian Sum Filter Based on SGQF for Nonlinear Non-Gaussian Models

To improve the filtering effect of the sparse grid quadrature filter (SGQF) under non-Gaussian conditions, the Gaussian sum technique is introduced, and the Gaussian sum sparse grid quadrature filter (GSSGQF) is developed. We present a systematic formulation of the SGQF and extend it to the discrete-time nonlinear system with the non-Gaussian noise. The proposed algorithm approximates the non-Gaussian probability densities by a finite number of weighted sums of Gaussian densities, and takes the SGQF as the Gaussian sub-filter to conduct the time and measurement update for each Gaussian component. An application in the discrete-time nonlinear system with the non-Gaussian noise has been shown to demonstrate the accuracy of the GSSGQF. It outperforms the unscented Kalman filter (UKF), the cubature Kalman filter (CKF) and the SGQF. Theoretical analysis and simulation results prove that the GSSGQF provides significant performance improvement in the calculation accuracy for nonlinear non-Gaussian filtering problems.

     

Generalized spline nonlinear adaptive filters

A new nonlinear filter, which employs an adaptive spline function as the basis function is designed in this paper. The input signal to this filter is used to generate suitable parameters to update the control points in a spline function. The update rule for updating the control points have been derived and a mean square analysis has been carried out. The output of the spline functions are suitably combined together to obtain the filter response. This filter is called the generalized spline nonlinear adaptive filter (GSNAF). The proposed GSNAF is similar to a functional link artificial neural network (FLANN), considering a functional expansion using spline basis functions. GSNAF has been shown to offer improved accuracy in benchmark classification scenarios and provide enhanced modeling accuracy in single input single output as well as in multiple input multiple output dynamic system identification cases.     

A new perspective on Gaussian sigma-point Kalman filters

There are a variety of Gaussian sigma-point Kalman filters (GSPKF) existing in the literature which are based on different quadrature rules. Their performances are always compared with each other on accuracy and robustness from the numerical-integration perspective, where the number of the sigma points and their corresponding weights are the main reasons resulting in the different accuracy. A new perspective on the GSPKF is proposed in this paper, which is the Mahalanobis distance ellipsoid (MDE). From the MDE perspective, GSPKFs differ from each other on accuracy and robustness mainly because they enclose different probability concentrations. This characteristic is evident when using the high-degree GSPKFs to filter the low-dimensional nonlinear systems. Two classical nonlinear system examples are used to demonstrate the proposed point of this paper. Moreover, some suggestions are given on how to select an appropriate GSPKF for a given nonlinear system.     

Adaptive Gaussian filters for nonlinear state estimation with one-step randomly delayed measurements

This paper proposes new algorithms of adaptive Gaussian filters for nonlinear state estimation with maximum one-step randomly delayed measurements. The unknown random delay is modeled as a Bernoulli random variable with the latency probability known a priori. However, a contingent situation has been considered in this work when the measurement noise statistics remain partially unknown. Due to unavailability of the complete knowledge of measurement noise statistics, the unknown measurement noise covariance matrix is estimated along with states following: (i) variational Bayesian approach, (ii) maximum likelihood estimation. The adaptation algorithms are mathematically derived following both of the above approaches. Subsequently, a general framework for adaptive Gaussian filter is presented with which variants of adaptive nonlinear filters can be formulated using different rules of numerical approximation for Gaussian integrals. This paper presents a few of such filters, viz., adaptive cubature Kalman filter, adaptive cubature quadrature Kalman filter with their higher degree variants, adaptive unscented Kalman filter, and adaptive Gauss–Hermite filter, and demonstrates the comparative performance analysis with the help of a nontrivial Bearing only tracking problem in simulation. Additionally, the paper carries out relative performance comparison between maximum likelihood estimation and variational Bayesian approaches for adaptation using Monte Carlo simulation. The proposed algorithms are also validated with the help of an off-line harmonics estimation problem with real data.