Interacting multiple model fixed-lag smoothing algorithm forMarkovian switching systems

We investigate a suboptimal approach to the fixed-lag smoothing problem for Markovian switching systems. A fixed-lag smoothing algorithm is developed by applying the basic Interacting Multiple Model (IMM) approach to a state-augmented system. The computational load is roughly d (the fixed lag) times beyond that of filtering for the original system. In addition, an algorithm that approximates the “fixed-lag” mode probabilities given measurements up to current time is proposed. The algorithm is illustrated via a target tracking simulation example where a significant improvement over the filtering algorithm is achieved at the cost of a time delay (i.e., data up to time k are used to produce the smoothed state estimate at time k-d where the fixed large d>0). the IMM fixed-lag smoothing performance for the given example is comparable to that of an existing IMM fixed-interval smoother. Compared with fixed-interval smoothers, the fixed-lag smoothers can be implemented in real-time with a small delay     

卡尔曼平滑的自校准技术

介绍了卡尔曼平滑技术的固定区间平滑方法，推导了非线性时变模型的固定区间平滑公式，并将之应用到轨道约束自校准技术中，且导出了相应公式。     

晃动环境下组合导航系统精度事后评估算法研究

海风、波浪、海流等因素会产生舰船的摇摆晃动,从而给舰船导航系统精度带来严重干扰.固定区间平滑滤波处理算法能够利用观测时间间隔内全部观测信息得到状态的最小方差估计,对导航精度进行事后评估.在研究晃动环境下的SINS/GP S组合导航应用平滑滤波算法的相关原理的基础上,首先利用Kalman滤波器进行组合导航,存储相关信息后按时间逆序利用固定区间平滑滤波算法进行事后分析.该方法可以针对不同的海况以及不同的海上作业需求,有效地为组合导航系统精度提供检验标准,考核各种海洋环境下的导航系统精度.     

Variable structure multiple model fixed-interval smoothing

This paper focuses on fixed-interval smoothing for stochastic hybrid systems. When the truth-mode mismatch is encountered, existing smoothing methods based on fixed structure of model-set have significant performance degradation and are inapplicable. We develop a fixed-interval smoothing method based on forward- and backward-filtering in the Variable Structure Multiple Model (VSMM) framework in this paper. We propose to use the Simplified Equivalent model Interacting Multiple Model (SEIMM) in the forward and the backward filters to handle the difficulty of different mode-sets used in both filters, and design a re-filtering procedure in the model-switching stage to enhance the estimation performance. To improve the computational efficiency, we make the basic model-set adaptive by the Likely-Model Set (LMS) algorithm. It turns out that the smoothing performance is further improved by the LMS due to less competition among models. Simulation results are provided to demonstrate the better performance and the computational efficiency of our proposed smoothing algorithms.     

Detection and Estimation with Fixed Lag for Abruptly Changing Systems

The problem of state estimation and system structure detection for discrete-time stochastic systems with parameters which may switch among a finite set of values is considered. The switchings are modeled by a semi-Markov, or Markov, chain with known transition statistics. A fixed time delay (lag) is allowed in estimation (smoothing) and detection. The optimal solutions require geometrically increasing computations and storage with time. Suboptimal solutions are proposed to alleviate this problem and simulation results are presented to illustrate the effectiveness of the proposed algorithms and the advantages of introducing a delay in processing of the observations.     

基于SVD的R-T-S最优平滑在机载SAR运动补偿POS系统中的应用

 机载合成孔径雷达（SAR）运动补偿用位置姿态系统（POS）的导航精度直接影响SAR成像的效果。为进一步提高POS的导航精度和数值稳定性,提出将基于奇异值分解（SVD）的Rauch-Tung-Striebel（R-T-S）最优固定区间平滑应用于POS后处理中。在基于SVD的前向卡尔曼滤波（KF）的基础上,进行了基于SVD的后向R-T-S最优固定区间平滑,获得位置、速度和姿态的最优估计。该方法将原算法中均方误差阵进行奇异值分解,不仅具有很好的数值稳定性和鲁棒性,而且避免了矩阵的求逆。半物理仿真结果表明,该方法在导航精度和数据平滑度上明显优于目前工程中应用的KF,是一种有效的事后处理方法。     

A New Approach to Estimation of Initial Conditions and Smoothing Problems

A unified approach utilizing the Kalman-Bucy filtering technique istaken to solve the estimation problem of initial conditions and thesmoothing problem in linear dynamic systems. The equivalencebetween the forward integration method and the backward integrationmethod of the smoothing solution is proved. Complete analyticalsolutions of filtering and smoothing problems of rectilinear motion ofa randomly accelerated spacecraft are derived when the vehicle istracked by the ranging system at the ground station.     

载波相位平滑伪距在GPS/SINS紧组合导航系统中的应用

针对GPS/SINS紧组合导航系统中伪距噪声大从而引起组合导航系统精度低的问题,提出了将载波相位平滑伪距方法引入到组合导航系统中,利用具有较高精度的载波相位对低精度伪距进行平滑滤波,在建立观测方程的同时,为了减小Kalman滤波器计算量,选用最佳4颗卫星的伪距与伪距率作为观测值,并提出了一种四面体选星法,该方法不需要进行矩阵求逆运算,减小了运算量。利用光纤陀螺捷联惯导系统与GPS接收机搭建了实验验证系统,通过车载实验对所提出的方法进行了验证,实验结果表明,经过载波相位平滑后的伪距噪声得到了降低,从而能够进一步提高GPS/SINS组合导航系统的定位精度,其位置误差均方根值相比无载波相位平滑减小近40%。     

GNSS最优载波相位平滑伪距研究

平滑常数是影响载波相位平滑伪距精度的关键参数,实际数据处理时主要依据经验设定平滑常数。这种主观设定过程缺乏理论依据,无法达到最优平滑效果。针对此问题,以适用于实时GNSS载波相位平滑伪距的经典Hatch递推滤波算法为基础,在连续时间域上分析了载波相位平滑伪距误差的主要构成,给出了总误差估算公式,分析了平滑常数对平滑精度的影响传导机制。进一步,采用令平滑总误差最小为目标的极值法推导给出了最优载波相位平滑常数的计算公式,给出了最优载波相位平滑伪距的完整处理步骤。最优平滑常数算法在数学意义上最优,大幅压缩了伪距测量误差,又不会引入过大的电离层发散误差。通过两个实际算例,证明了算法有效性。     

基于数字滤波的低频时码秒脉冲抖动平滑方法研究

低频时码授时信号在接收时,由于环境等因素的影响会导致解调得到的低频时码秒脉冲出现抖动。为减小该抖动现象对低频时码定时精度的影响,基于我国低频时码授时系统(BPC),研究并设计基于数字滤波的秒脉冲抖动平滑方法,通过仿真实验,验证分析了最小均方误差(LMS)自适应滤波算法和卡尔曼滤波算法的有效性和抖动平滑性能。结果表明,低频时码秒脉冲的抖动现象可以通过BPC 1PPS (one pulse per second)和本地1PPS之间的相位差波动情况反映;LMS自适应滤波算法和卡尔曼滤波算法对BPC 1PPS的抖动平滑处理均有明显效果,卡尔曼滤波算法的抖动平滑效果更优,但存在一定的收敛时间,LMS自适应滤波算法的滤波结果响应速度快,但抖动平滑性能受滤波器阶数的影响。所以,在实际应用中,应根据实际需求选择合适的滤波器及相关参数。     

Suboptimal Algorithms for Nonlinear Smoothing

This paper presents second-order algorithms for fixed- point and fixed-lag smoothing problems for nonlinear systems. The algorithms are obtained on the basis of the state augmentation approach, used earlier by the authors, for dealing with linear smoothing problems. Both discrete-and continuous-time forms of solutions are presented and the results are illustrated by considering a radar tracking problem. Some of the advantages of the proposed smoothing solutions compared to existing ones are also discussed.     

用于非线性跟踪问题的一种新的粒子滤波器

机动目标跟踪系统通常是非线性而且不完全观测的 ,所以问题的关键在于每一时刻的目标机动性都是高度不确定的。提出了一种新的平滑粒子滤波算法 ,该算法在粒子滤波器中加入了对系统模型的概率分布密度的平滑处理 ,从而很好的解决了目标的机动性估计问题。在仿真研究中 ,与辅助粒子滤波器的比较验证了本文算法处理非线性跟踪问题的优越性     

A comparison of smoothing approaches for angle measurement

For high-resolution active direction finding of completely correlated targets, one can use two approaches, i.e. frequency-domain smoothing and non-frequency-domain smoothing, such as spatial smoothing, or a multidimensional search of signal-subspace. A performance comparison of the two approaches is presented for the fluctuating target cases under an equal transmitted-energy constraint. both theoretical analysis and simulations are used to study the performance of the detection (determination of number of targets) and angle estimation. It is found that the frequency-domain smoothing can significantly outperform the non-frequency-domain smoothing under the equal transmitted-energy constraint     

局域增强系统级联双频平滑技术研究(英文)

针对电离层误差时间梯度和空间梯度对局域增强系统的不利影响,提出使用级联双频平滤波方法解决此问题。级联双频平滤波先使用一个双频平滑滤波器精确估计电离层误差,利用得到的估计值修正码伪距观测量中的电离层误差,再使用一个双频平滑滤波器削弱噪声。这样,电离层误差被完全从平滑过程中移出,由L2码观测量引入的附加的噪声也被压制。基于中国民航新航行系统实验室的局域增强系统测试平台所采集的数据对级联双频平滤波的有效性和基于级联双频平滤波的局域增强系统的精度进行了分析。结果表明级联双频平滤波技术可以同时消除电离层误差时间梯度和空间梯度导致的平滑滤波残差和差分校正残差,并具有较低的滤波噪声。     

A New Optimal Hatch Filter to Minimize the Effects of Ionosphere Gradients for GBAS

At present, the main problem faced by ground-based augment system （GBAS） is that though carder smoothing filter and local differential global positioning system （LDGPS） improve the accuracy of the pseudorange by reducing the noise in it and eliminating almost all the common errors between the user and the reference station, they also cause extra errors on account of the effects of the ionosphere temporal and spatial gradients. Based on the analysis of these errors as well as the smoothing noise, this article suggests a new algorithm to design the optimal Hatch filter, whose smoothing window width varies real-time with the satellite elevation, ionosphere variation, and distance from the user to the reference station. By conducting the positioning process in the GBAS emulation platform for several hours and after its comparison with the performances of traditional Hatch filters, it is found that the errors in the differential correction become smaller and the positioning accuracy gets heightened with this new method.     

A simple fixed-lag algorithm for tracking frequency rate-of-change

A family of simple fixed-lag frequency smoothing algorithms which provide good estimates of both frequency and frequency rate-of-change is reported. The smoothers were developed from a fixed-gain αβ tracker by replacing the recursive derivative estimator with a finite-impulse-response (FIR) differentiator. Simulation results are presented which show that the smoothing algorithms provide frequency estimates with a similar variance to those produced by the αβ filter but with greatly improved frequency-rate estimates. The smoothing algorithms and the αβ filter are also compared on the basis of the bias and delay introduced in the frequency-rate estimates. Although the results presented are for frequency estimation, the smoothing algorithms can be used in any single-input tracking application where some lag in the estimates is allowable     

一种新型颤振激励系统的特性研究

在非结构网格的基础上，以欧拉方程为流场的主控方程，采用格心格式空间离散的有限体积法和四步Runge—Kutta显式时间推进的方法．对一种新型颤振激励系统的流场进行了数值研究。研究了该系统的工作原理和激励力特性。研究结果表明，该系统能很好地激励飞机结构。     

Carrier Tracking by Smoothing Filter Improves Symbol SNR

The potential benefit of using a smoothing filter to estimate a carrier phase over use of phase-locked loops (PLL) is determined. Numerical results are presented for the performance of three possible configurations of an all-digital coherent demodulation receiver. These are residual carrier PLL, sideband-aided residual carrier PLL, and finally sideband aided with Kalman smoother. The average symbol SNR after losses due to carrier phase estimation is computed for different total power SNRs, symbol rates, and symbol SNRs. It is found that smoothing is most beneficial for low symbol SNRs and low symbol rates. Smoothing gains up to 0.7 dB over sideband-aided residual carrier PLL, and the combined benefit of smoothing and sideband aiding relative to residual carrier loop is often in excess of 1 dB.     

双星预警系统弹道参数估计及一些问题分析

主要讨论由2颗地球同步轨道卫星组成的卫星预警系统(简称双星预警系统)中弹道导弹参数的估计问题。阐述了主动段运动的建模问题和弹道数据处理方法,考虑到微分求速的重要性,采用了带光滑约束的样条拟合方法。结合预警系统对弹道导弹预警的具体情况,分别讨论了预警系统下的发射原点估计、射向估计、关机时刻估计、关机点弹道参数估计、落点估计等问题。还讨论了系统中存在的两个问题的分析与解决。模型及分析方法均经过理论和仿真的验证,可应用于双星预警系统下的实际预警的研究。     

Remaining useful life prediction of aircraft lithium-ion batteries based on F-distribution particle filter and kernel smoothing algorithm

As an emergency and auxiliary power source for aircraft, lithium (Li)-ion batteries are important components of aerospace power systems. The Remaining Useful Life (RUL) prediction of Li-ion batteries is a key technology to ensure the reliable operation of aviation power systems. Particle Filter (PF) is an effective method to predict the RUL of Li-ion batteries because of its uncertainty representation and management ability. However, there are problems that particle weights cannot be updated in the prediction stage and particles degradation. To settle these issues, an innovative technique of F-distribution PF and Kernel Smoothing (FPFKS) algorithm is proposed. In the prediction stage, the weights of the particles are dynamically updated by the F kernel instead of being fixed all the time. Meanwhile, a first-order independent Markov capacity degradation model is established. Moreover, the kernel smoothing algorithm is integrated into PF, so that the variance of the parameters of capacity degradation model keeps invariant. Experiments based on NASA battery data sets show that FPFKS can be excellently applied to RUL prediction of Li-ion batteries.