【作者】 陈宇；

【导师】 许录平；

【作者基本信息】 西安电子科技大学 ， 导航、制导与控制， 2022， 博士

【摘要】 随着新技术的发展,目标的机动性越来越强,系统模型展现出更强的非线性非高斯特征,给传统的目标状态估计带来了严峻的挑战。现有的线性与非线性滤波方法越来越难以满足实际应用的需求,平滑变结构滤波器作为一种新型的鲁棒滤波器,更适宜于实际应用中的模型不确定系统,受到了广泛的关注。虽然平滑变结构滤波器理论逐渐完善,但其依旧存在一些未解决的问题,迫切需要提出一些新的理论和方法对其进行改进和优化,使其更具理论意义和实际应用价值。本文围绕线性与非线性系统、高斯与非高斯噪声系统、实时处理与非实时处理、单模型与多模型、状态突变系统等方面展开研究,基于平滑变结构滤波器提出一系列的方法,力求所研究内容能够形成一个较为完整的理论体系,适应复杂的环境需求。本文的主要研究工作包括以下几个方面:(1)针对线性系统,现有平滑变结构滤波器主要应用于状态与量测一一对应关系的系统,对于没有量测值对应的状态需要构建伪量测或者构建低阶的观测器,这些方法容易受到噪声的影响,估计精度不高,是次优的方法。本文提出了一种基于最小均方差理论的平滑变结构滤波器,理论上是最优方法。仿真结果表明所提方法在不存在模型误差时相比传统的平滑变结构滤波器估计精度更高。在存在模型误差时,与经典的卡尔曼滤波器相比,所提方法的精度高、鲁棒性更好。(2)针对非线性系统,现有平滑变结构滤波器一直没有解决在量测方程非线性情况下的状态估计问题,本文提出了扩展平滑变结构滤波器和无迹平滑变结构滤波器。两种滤波器通过对量测先滤波,然后分别利用非线性方程局部线性化和无迹变换确定性采样方法求得状态估计值。仿真结果表明,在不存在模型误差拥有相似精度时,所提方法与传统的扩展卡尔曼滤波器、无迹卡尔曼滤波器相比,在存在模型误差时目标跟踪精度更高稳定性更好。它克服了当前平滑变结构滤波器要求量测方程必须为线性的不足,使得平滑变结构滤波器可以用于各类非线性系统,大大扩展了其适用范围。(3)针对量测噪声呈现厚尾非高斯分布时,容易引起抖振现象导致状态估计精度下降的问题,提出了几种处理非高斯噪声的平滑变结构滤波方法。分析了平滑变结构滤波器中抖振现象产生的原因和切换函数作用,改进了线性的饱和函数,构造了两种新的非线性切换函数和一种分段饱和函数,基于这些函数提出的平滑变结构滤波方法能更好地处理线性和非线性系统中的厚尾非高斯分布噪声。理论分析和仿真结果表明,所提的这些滤波器能够抑制厚尾分布噪声和随机干扰引起的抖动,提高状态估计的精度。(4)针对非实时系统的状态估计问题,提出了基于非实时系统的的平滑变结构固定区间平滑器和平滑变结构固定滞后平滑器。基于平滑变结构滤波器的状态估计结果,利用更多的量测数据,通过两种平滑方法对估计的状态进行平滑进一步提高精度。实验仿真结果表明,两种平滑变结构平滑器相比平滑变结构滤波器均能提高状态估计精度。(5)针对机动目标跟踪中状态估计系统鲁棒性差的问题,提出了交互式多模型的平滑变结构滤波器和一种改进的平滑变结构滤波器。给出了两种滤波器在平滑变结构滤波方法基础上分别结合交互式多模型理论和贝叶斯滤波理论状态估计的推导过程。仿真结果表明,在机动目标跟踪中,所提的交互式多模型平滑变结构滤波器比传统的交互式卡尔曼滤波器在模型失配时鲁棒性更好。所提改进的平滑变结构滤波器在状态突变时相比现有平滑变结构滤波方法,能够稳定跟踪目标。更多还原

【Abstract】 With the development of new technology,the maneuvering performance of target is getting higher and higher and the system model is strongly nonlinear and non-Gaussian characteristics,which brings serious challenges to the traditional state estimation technology,the traditional linear and nonlinear filtering methods are difficult to meet the requirements of practical applications.As a new type of robust filter,being more suitable for model uncertainty system in practical application,SVSF has received extensive attention.Although the theory of SVSF is becoming more and more adequate,there are still some unsolved problems in its development process.It is urgent to propose some new theories and methods to improve and optimize it,so that the SVSF is of more theoretical and practical value.Starting from linear and nonlinear systems,Gaussian and non-Gaussian systems,real-time processing and non-real-time processing,single model and multi-model,stationary system and state abrupt system,a series of solutions are proposed based on SVSF.Strive for the proposed theoretical methods to form a relatively complete theoretical system to meet the needs of complex environmental scenarios.The main contributions of this dissertation include the following aspects:1.For linear systems,the existing SVSF is mainly used in systems in which states have to be measured.When the states without corresponding measurements,pseudo-measurements or low-order observers need to be constructed.These methods are easily affected by noise,the state estimation accuracy is not high,and these methods are sub-optimal methods.A new linear SVSF based on the minimum mean square error theory is proposed,which is the optimal method in theory.Simulations show that the proposed method is more accurate than the traditional SVSF.Compared with the classical Kalman filter,the proposed method has higher accuracy and better robustness to modeling errors.2.For nonlinear systems,the existing SVSF has not solved the state estimation problem of nonlinear measurement equations.The extended SVSF and unscented SVSF are proposed.Firstly,the measurenments are filterd and then two methods use the local linearization of nonlinear equations and the deterministic sampling method of unscented transformation to estimate states respectively.The simulation results show that when all methods have similar accuracy in no modeling errors,the proposed methods have higher tracking accuracy and better stability than the traditional extended Kalman filter and unscented Kalman filter.It overcomes the limitation that the measurement equation of SVSF must be linear,so that the SVSF can be used in various nonlinear systems and greatly expand its scope of application.3.Chattering phenomenon is easy to cause when heavy-tailed non-Gaussian measurement noises are present,and the performance of the conventional SVSF may break down,several non Gaussian SVSFs are proposed to solve the filtering problem in linear or nonliear systems with heavy-tailed measurement noises.The reason of chattering phenomenon and the effect of switching function in SVSF are analyzed,two new nonlinear switching functions and a piecewise saturation function are constructed.The proposed SVSFs can better handle the heavy-tailed measurement noises in linear and nonlinear systems.Theoretical analysis and simulation results show that the proposed filters can suppress chattering caused by heavytailed measurement noises and random interference,and improve the accuracy of state estimation.4.For the state estimation problem of non-real-time systems,a smooth variable structure fixed interval smoother and a smooth variable structure fixed lag smoother based on nonreal time systems are proposed.Based on the state estimation result of the SVSF,using more measurements,the estimated state is smoothed by two smoothers to further improve the accuracy.The simulation results show that the two smooth variable structure smoothers can improve the state estimation accuracy compared with SVSF.5.An interactive-multiple-model SVSF and an improved SVSF are proposed to improve robustness of state estimation system in maneuvering target tracking.The derivation process of the state estimation of the two filters based on the smooth variable structure filtering method combined with the interactive-multiple-model theory and the Bayesian filter theory are given respectively.Simulation results show that the proposed interactive multi-model SVSF is more robust than the traditional interactive-multiple-model Kalman filter in the case of model uncertainty in maneuvering target tracking.Compared with the existing smooth variable structure filtering methods,the improved SVSF can track the target stably when the state is abruptly changed.更多还原