基于不完全量测下离散线性滤波的修正Riccati方程

在量测数据丢失下滤波方程和Riccati方程出现一些新的性质变化．探测概率小于1的不完全量测条件下,利用正定矩阵性质和Lyapunov不等式, 研究了离散系统修正Riccati差分方程(MRDE)与数据丢失位置之间的关系．结果表明在一定条件下MRDE解与丢失数据位置满足单调递减的函数系．由于统计意义下的理论MRDE模型求解计算量随丢失/探测数量增加而呈指数型递增, 本文最后给出了一组便于工程应用的期望状态误差协方差上下界算法, 算法复杂度为O(k²).     

不完全量测下随机有偏离散系统的Cramér-Rao下界

针对含有不完全随机有偏测量序列的状态估计问题, 给出了统计意义下的修正递推估计误差方差Cramér-Rao下界(CRLB)求解算法. 首先建立了不完全随机有偏量测离散系统的数学模型, 进而推导了枚举的CRLB和统计意义的CRLB计算式, 该统计意义的CRLB为枚举CRLB的下界, 其计算量远小于枚举CRLB求解的计算量. 最后, 以给定探测概率和偏差发生率下的一类光电跟踪系统为例, 进行了数字仿真.     

多天线协同接收PSK载波参数估计的CRLB

针对利用多个独立天线对同一信号进行协同接收的问题,推导了数据辅助（DA）和非数据辅助（NDA）方式BPSK/QPSK信号频率及相位估计的Cramer-Rao下界（CRLB）,并与传统单个天线接收时的CRLB进行了比较。结果表明,在DA方式下,多天线协同接收PSK信号频率及相位估计的CRLB与传统单天线接收的CRLB相同;在NDA方式下,多天线协同接收的CRLB则要低于传统单天线接收的CRLB。     

不完全量测下基于事件触发机制的面目标跟踪系统CRLB

面目标跟踪系统状态估计问题中,附加的强非线性面目标扩展测量会增加系统的通信量和估计中心的计算量.为此,基于工程应用,提出一种不完全量测下的事件触发机制来控制面目标测量传输.从理论上推导了事件触发机制下面目标跟踪系统的理想（枚举）克拉美罗下界（Cramer-Rao lower bound,CRLB）和统计意义下的CRLB,该统计意义CRLB为理想CRLB的下界,计算复杂度远小于理想CRLB,便于工程应用.典型测试航路下的仿真结果表明:不完全量测下,面目标跟踪系统CRLB明显小于传统质点目标跟踪系统CRLB;同时,利用所提事件触发机制,可在大幅减少面目标跟踪系统通信量的同时保证系统的最优估计性能.     

通道参数对MIMO雷达估计性能的影响效果分析

为在目标参数估计中正确处理MIMO雷达收发通道网的未知系数,提出并建立了3种通道参数模型,分别推导了各模型下的目标估计和克拉美罗界(Cramer-Rao lower bound,CRLB),比较了各模型下的参数估计性能,研究了通道参数的不同处理方法对MIMO雷达估计性能的影响效果。理论分析表明,在目标估计时如果将通道系数作为未知参量与目标参数联合估计,可比将其作为随机参量求期望获得更高的参数估计精度,而且随着信噪比的降低两者的参数估计性能差异会随之扩大。仿真实验也验证了上述结论的正确性。     

基于多目标CRLB的分布式相干MIMO雷达阵列优化

根据分布式相干MIMO雷达的工作原理和空间多目标信号模型,在目标位置估计的基础上,推导证明了多目标位置估计的克拉美罗下界(Cramer-Rao lower bound,CRLB)。在对比单目标条件下阵列优化的前提下,提出了基于多目标空间分集增益和目标互扰模型的优化布阵准则,同时分析论证了多目标条件下优化布阵存在的必然性,给出了均匀非对称水平布型为优化布阵的结论。仿真实验验证了理论分析的正确性。     

多无源传感器的在线配准

为估计无源传感器的角度偏差,在只有角度测量信息的前提下,提出了多无源传感器的在线配准方法.该方法运用几何知识,由传感器测量的多个角度数据得到目标的估计距离,通过估计距离进行在线滤波器的初始化,进而实时估计传感器的角度偏差;并给出了配准模型的Cramer-Rao下限(CRLB).Monte-Carlo仿真表明:该方法能有效地估计无源传感器的角度偏差,同时得到目标航迹.     

全相位FFT测相方差及其Cramer- Rao下限

为揭示全相位FFT(All-phase FFT,apFFT)相位测量法相比于现有方法精度提高的内在原因,在前人基础上,结合谱泄漏分布特征及其参数估计理论,推导出了适用于apFFT测相的两未知参数估计模型的克拉罗下限(Cramer-Rao lower bound,CRLB),以及apFFT测相误差与频偏分布的关系.指出该理论下限比传统三参数的CRLB低12 dB,基于此总结出一系列在不同信噪比和不同频偏情况下的apFFT测相性能结论.仿真结果表明:在不同的信噪比环境和不同的频偏情况下,apFFT的测相方差都能被CRLB2所界定,验证了上述结论及其新的CRLB正确性.     

一种高精度声表面波标签无线测温算法

针对声表面波(Surface Acoustic Wave,SAW)标签无线测温时延估计精度不高的问题,提出了一种新算法;为降低对硬件转换速度和采样率的要求,采用频率步进连续波(Frequency stepped continuous wave,FSCW)作标签的询问信号,利用频率粗估计和相位精估计相结合的方法提取回波时延;推导出回波时延估计的Cramer-Rao下限(CRLB),分析了相关参数对其影响;在复加性高斯白噪声条件下,利用时延估计结果进行无线测温;当起始频率为902MHz,扫描带宽为26MHz时,仿真结果证明该算法测温误差仅为频率估计算法的1/60。     

光电跟踪系统临界探测概率研究

光电跟踪系统的估计性能随着探测概率的下降而降低,是否存在一个临界探测概率,当跟踪系统的实际探测概率高于临界探测概率时,跟踪系统统计意义下的估计误差协方差对任意估计初值均收敛是跟踪系统设计时的一个关键问题。本文证明了跟踪系统临界探测概率的存在性,并且给出了临界探测概率的一组上下界,其上界被描述成一个非线性矩阵不等式(NMI)的最优解,其下界仅与跟踪系统状态转移矩阵的特征值有关。进一步利用摄动线性化方法给出了求解临界探测概率上界的一种迭代线性矩阵不等式(ILMI)算法,并且对跟踪系统在三种标准测试场景中的临界探测概率上界进行了仿真求解,仿真结果表明:当跟踪系统的探测概率高于50%时,其统计意义下的估计误差协方差对任意估计初值均收敛,这为跟踪系统探测概率的设计提供了理论依据。     

Stabilisation for Markovian jump delta operator systems with time-varying delays and actuator saturation

In this paper, stochastic stabilisation is studied for Markovian jump delta operator systems with time-varying delays and actuator saturation. The transition probability rates in Markovian jump parameters are considered as partly known. Both lower and upper bounds are considered in the time-varying delays. Using Lyapunov–Krasovkii functional, a stochastic stabilisation condition is obtained for the closed-loop Markovian jump delta operator system with time-varying delays and actuator saturation. A numerical example is shown to illustrate the effectiveness and potential for the developed techniques.     

A robust stochastic stability analysis approach for power system considering wind speed prediction error based on Markov model

This paper proposes a robust stochastic stability analysis approach with partly unknown transition probability by considering the wind speed prediction error in power system. Firstly, taking this prediction error into account, based on Markov modeling theory, the stochastic dynamic model of wind power system with uncertain transition probability is developed. Secondly, according to the stochastic stability theory of Markov jump system, the transition probability of wind power system mode is divided into three cases: fully known, only known upper and lower bounds, and completely unknown. Then, by using linear matrix inequality (LMI) technology, a robust stochastic stability criterion with disturbance attenuation is obtained. Finally, test results show that the proposed analysis approach does not need to obtain the trajectory of the actual system operation parameters, and has the advantages of high computational efficiency.     

An improved method for bounding stationary measures of finite Markov processes

A new method to compute bounds on stationary results of finite Markov processes in discrete or continuous time is introduced. The method extends previously published approaches using polyhedra of eigenvectors for stochastic matrices with a known lower and upper bound of their elements. Known techniques compute bounds for the elements of the stationary vector with respect to the lower bounds of the matrix elements and another set of bounds with respect to the upper bounds of matrix elements. The resulting bounds are usually not sharp, if lower and upper bounds for the elements are known. The new approach combines lower and upper bounds resulting in sharp bounds which are often much tighter than bounds computed using only one bounding value for the matrix elements.     

Runtime analysis of the (mu+1) EA on simple Pseudo-Boolean functions

Although Evolutionary Algorithms (EAs) have been successfully applied to optimization in discrete search spaces, theoretical developments remain weak, in particular for population-based EAs. This paper presents a first rigorous analysis of the (mu+1) EA on pseudo-Boolean functions. Using three well-known example functions from the analysis of the (1+1) EA, we derive bounds on the expected runtime and success probability. For two of these functions, upper and lower bounds on the expected runtime are tight, and on all three functions, the (mu+1) EA is never more efficient than the (1+1) EA. Moreover, all lower bounds grow with mu. On a more complicated function, however, a small increase of mu probably decreases the expected runtime drastically.This paper develops a new proof technique that bounds the runtime of the (mu+1) EA. It investigates the stochastic process for creating family trees of individuals; the depth of these trees is bounded. Thereby, the progress of the population towards the optimum is captured. This new technique is general enough to be applied to other population-based EAs.     

Stochastic bounds for queueing systems with limited service schedules

Motivated by the study of cyclic service queue processor schedules and token ring local area networks, upper and lower stochastic bounds for a GI/G/1 vacation model with limited service are developed. The limited service vacation model is compared with the Bernoulli schedule vacation model. For the case of Poisson arrivals and infinitely divisible vacation durations simple, closed-form expressions are given for upper and lower bounds of the first two moments of the waiting time. Some upper and lower bounds are also derived for cyclic queues with limited service. The quality of the bounds is illustrated through numerical examples.     

Probabilistic cost estimation in advance of production in a computerized manufacturing system through stochastic geometric programming

A mathematical model for stochastic cost optimization has been developed. The model contains cost terms such as inventory cost, penalty cost for due date violation, and the machining cost. The probable range of cost has been estimated by a stochastic geometric program. If an exact solution is desired, a two stage stochastic geometric program has to be solved. This is mathematically tedious and requires great computational effort. However, managers are often concerned with a policy decision which can be based on the probable lower and upper bounds on the cost function. The probability level on the lower bound of cost has been calculated through the theory of error propagation. This approach is explained through an example.     

Markovian timed Petri nets for performance analysis ofsemiconductor manufacturing systems

A subclass of generalized stochastic Petri nets (GSPNs) with priorities, called Markovian timed Petri nets, are proposed to model semiconductor manufacturing systems that consider process priorities, routing priorities, resource re-entrance, and nonpreemptive operations. Uniformization technique is used to establish both lower and upper bounds of the performance of interest. These bounds are computable using linear programming. Numerical experiments have been conducted to evaluate the accuracy of the bounds using models adapted from real-world systems. The experiments show that the upper bounds are very close to the simulation results. Thus, performance measures can be accurately estimated using these bounds.