Stability and performance analysis of the compressed Kalman filter algorithm for sparse stochastic systems

This paper considers the problem of estimating unknown sparse time-varying signals for stochastic dynamic systems.To deal with the challenges of extensive sparsity,we resort to the compressed sensing method and propose a compressed Kalman filter(KF)algorithm.Our algorithm first compresses the original high-dimensional sparse regression vector via the sensing matrix and then obtains a KF estimate in the compressed low-dimensional space.Subsequently,the original high-dimensional sparse signals can be well recovered by a reconstruction technique.To ensure stability and establish upper bounds on the estimation errors,we introduce a compressed excitation condition without imposing independence or stationarity on the system signal,and therefore suitable for feedback systems.We further present the performance of the compressed KF algorithm.Specifically,we show that the mean square compressed tracking error matrix can be approximately calculated by a linear deterministic difference matrix equation,which can be readily evaluated,analyzed,and optimized.Finally,a numerical example demonstrates that our algorithm outperforms the standard uncompressed KF algorithm and other compressed algorithms for estimating high-dimensional sparse signals.

Research on Kalman Filtering Algorithmfor Deformation Information Series ofSimilar Single-Difference Model

Using similar single-difference methodology(SSDM) to solve the deformation values of the monitoring points, there is unstability of the deformation information series, at sometimes.In order to overcome this shortcoming, Kalman filtering algorithm for this series is established,and its correctness and validity are verified with the test data obtained on the movable platform in plane. The results show that Kalman filtering can improve the correctness, reliability and stability of the deformation information series.

Multi-sensor Hybrid Fusion Algorithm Based on Adaptive Square-root Cubature Kalman Filter

处于正常操作条件，一个常规方形根的求容积法 Kalman 过滤器(SRCKF ) 给足够地好的评价结果。然而，如果大小不是可靠的， SRCKF 可以给不精密的结果并且到时间分叉。这研究与过滤器获得修正介绍一个适应 SRCKF 算法因为测量的盒子失灵。由建议一个切换的标准，一个最佳的过滤器根据测量质量从适应、常规的 SRCKF 被选择。一个分系统软差错察觉算法与过滤器剩余被造。利用一个清楚的分系统差错系数，有缺点的分系统由于系统重建被孤立。以便改进多传感器系统的性能，一个混合熔化算法基于适应 SRCKF 被介绍。状态和错误协变性矩阵被 priori 熔化估计也预言，并且被分系统的预言并且估计的信息更新。建议算法被用于容器动态放系统模拟。他们与正常 SRCKF 和本地评价相比是加权的熔化算法。模拟结果证明介绍适应 SRCKF 改进分系统过滤的坚韧性，并且混合熔化算法有更好的表演。模拟验证建议算法的有效性。

TEC and Instrumental Bias Estimation of GAGAN Station Using Kalman Filter and SCORE Algorithm

The standalone Global Positioning System (GPS) does not meet the higher accuracy requirements needed for approach and landing phase of an aircraft. To meet the Category-I Precision Approach (CAT-I PA) requirements of civil aviation, satellite based augmentation system (SBAS) has been planned by various countries including USA, Europe, Japan and India. The Indian SBAS is named as GPS Aided Geo Augmented Navigation (GAGAN). The GAGAN network consists of several dual frequency GPS receivers located at various airports around the Indian subcontinent. The ionospheric delay, which is a function of the total electron content (TEC), is one of the main sources of error affecting GPS/SBAS accuracy. A dual frequency GPS receiver can be used to estimate the TEC. However, line-of-sight TEC derived from dual frequency GPS data is corrupted by the instrumental biases of the GPS receiver and satellites. The estimation of receiver instrumental bias is particularly important for obtaining accurate estimates of ionospheric delay. In this paper, two prominent techniques based on Kalman filter and Self-Calibration Of pseudo Range Error (SCORE) algorithm are used for estimation of instrumental biases. The estimated instrumental bias and TEC results for the GPS Aided Geo Augmented Navigation (GAGAN) station at Hyderabad (78.47°E, 17.45°N), India are presented.

Assimilation of Remote Sensing and Crop Model for LAI Estimation Based on Ensemble Kalman Filter

Data assimilation in agricultural remote sensing research is of great significance to integrate with remote sensing observations and model simulations for parameters estimation. The present investigation not only designed and realized the Ensemble Kalman Filtering algorithm （EnKF） assimilation by combing the crop growth model （CERES-Wheat） with remote sensing data, but also optimized and updated the key parameters （LAI） of winter wheat by using remote sensing data. Results showed that the assimilation LAI and the observation ones agreed with each other, and the R2 reached 0.8315. So assimilation remote sensing and crop model could provide reference data for the agricultural production.

Chan-Kalman算法在井下定位中的应用研究

针对井下环境存在的非视距误差而导致超宽带定位技术精度降低的问题,对可抑制定位误差的Chan-Kalman算法进行了研究。该算法基于TOA定位模型,通过Chan算法对标签位置坐标进行初步解算,再采用卡尔曼滤波算法对初步解算结果进行优化,最终得出较为精确的标签位置坐标。实验结果表明,该算法明显提高了超宽带定位系统的定位精度。

基于改进Kalman滤波与Camshift结合的嵌入式跟踪系统设计

针对传统Camshift算法难以在运动目标受遮挡的情况下有效跟踪的问题,提出一种基于改进Kalman滤波与Camshift相结合的目标跟踪算法,通过对Kalman滤波器的状态变量Xk增加高维特征宽高比a与高度h参数,并将P0、Q、R与窗口高度h相关联,同时在受遮挡时自适应改变Xk参数,使Kalman滤波器能够代替Camshift算法输出足够大的跟踪框标注受遮挡目标位置。实验表明,改进算法在有效帧率方面提高了42.6%,且平均BH距离降低了0.27,显著提高了跟踪的准确性和鲁棒性。

基于Kalman-Chan算法的5G毫米波室内定位试验

卫星定位系统因其能够提供高精度、全天候的定位服务而深受人们的欢迎,但是在室内环境中,由于建筑物的遮挡,卫星定位系统无法在室内提供高精度定位服务。随着万物互联时代的到来,人们对室内定位技术展开了研究。近年来,室内定位技术层出不穷,例如蓝牙定位、UWB定位等。目前,随着5G技术的成熟以及5G基站的密集化部署,促进了基于5G技术的室内定位的发展。影响室内定位精度的难点之一就是非视距传播(NLOS)和多径效应引起的误差,而毫米波通信作为5G关键技术之一,因其具有高频带和高带宽的特性,有利于提高多径分辨率,可提高到达时间差(TDOA)测量的精度。为抑制NLOS和多径效应引起的误差,本文对基于5G室内定位的Kalman-Chan融合算法展开了研究,即先利用卡尔曼算法对观测量进行距离重构,再结合Chan算法对用户位置进行估算,经过大量试验验证证明,该融合算法可使二维平面上的定位精度达到0.31 m。

Real-time localization estimator of mobile node in wireless sensor networks based on extended Kalman filter

Localization of the sensor nodes is a key supporting technology in wireless sensor networks （WSNs）. In this paper, a real-time localization estimator of mobile node in WSNs based on extended Kalman filter （KF） is proposed. Mobile node movement model is analyzed and online sequential iterative method is used to compute location result. The detailed steps of mobile sensor node self-localization adopting extended Kalman filter （EKF） is designed. The simulation results show that the accuracy of the localization estimator scheme designed is better than those of maximum likelihood estimation （MLE） and traditional KF algorithm.

基于Kalman滤波的原子时算法研究

守时系统的目标在于建立和保持一个稳定可靠的时间尺度,时间尺度算法正是基于此目标计算出一个频率稳定度、准确度、可靠性更高的时间尺度,时间尺度的算法本质就是综合守时系统内的原子钟,通过各原子钟与主钟的N-1组观测钟差对N台原子钟的权重和预测值进行估计;传统的加权平均算法会忽略发挥主要影响的噪声过程,更注重权重的合理分配来提高综合原子时的稳定度,缺少对噪声的关注,针对守时系统实时性的需求,对原子钟噪声模型进行了研究,在频率预测过程中研究了Kalman滤波和频率跳变检测的应用,并与传统加权平均算法进行了对比,仿真实验表明改进的算法提升了综合原子时的中长期稳定度,其中100天稳达到了5×10-14数量级,既保留了AT1时间尺度连续、实时的良好特性,又避免了Kalman算法发散性的问题,经实际测试可应用于小型守时实验室的守时系统构建。

一种基于灰色预测理论和抗差自适应Kalman滤波的滑坡监测算法

针对当前的山体滑坡监测技术监测精度低、实时性差、自动化程度低的问题,提出了一种基于灰色预测理论和抗差自适应Kalman滤波的滑坡监测技术。该技术使用抗差自适应Kalman滤波技术,对包括实时动态(RTK)载波相位差分定位数据、无人机摄影测量数据、土工带传感器数据在内的多源数据进行融合分析,将滑坡形变监测精度提高到了mm级。RTK技术和土工带传感器的使用克服了天气状况、植被覆盖对滑坡监测的影响。使用灰色预测理论对山体滑坡监测点进行形变预测,结合蠕变切线角判据,该技术实现了对山体滑坡预警等级的划分。仿真实验结果显示,该山体滑坡监测技术能够成功实现山体滑坡预测预警功能。

Kalman滤波算法在海洋钻机中控制信号的优化

海洋钻机由于其应用的特殊性,对控制信号的稳定程度及控制精度有更高的要求。针对海洋钻机电控系统中信号受噪声干扰大的情况,提出一种基于Kalman滤波算法的PID控制信号优化方式,控制过程中信号是多维且非平稳输出,利用Matlab/Simulink软件仿真PID传递函数并整定参数,利用传递控制信号的输出作为Kalman滤波算法线性观测方程的输入,运行正态分布融合模型,建立海洋钻机控制信号的干扰高斯白噪声的模型,对稳定信号及噪声观测值进行加权平均更新迭代计算,以便于获取最小方差估计值,从而得到降噪的信号。实验仿真表明,与传统的PID信号输出相比较,系统具备更强的抗干扰能力和更好的鲁棒性。

基于ARIMA-Kalman滤波混合算法的铁路进站客流预测方法

轨道交通车站客流预测,是优化车站客运组织、提高运营安全和运输效率的有效途径。针对传统ARIMA模型对客流量预测性能较差的问题,提出一种基于ARIMA-Kalman滤波混合预测方法。具体通过建立ARIMA模型训练实验样本,结合Kalman滤波器,建立预测递推方程,最终利用Kalman滤波预测方法对客流量进行预测。基于江门东站进站客流数据的仿真实验结果表明,相较于单一ARIMA模型,所提出的ARIMA-Kalman滤波混合算法预测结果的均方根误差降低了257.106,平均绝对误差降低了145.675,平均绝对百分比误差下降了5.655%,证明了所提出的混合算法预测精度更高。

卫星时滞系统的强跟踪鲁棒扩展Kalman滤波

针对具有状态时滞和未知不确定性的卫星姿态控制系统,提出一种强跟踪鲁棒扩展Kalman滤波器,以实现执行器和传感器的并发故障估计。首先,考虑系统噪声,视故障为系统的辅助变量,建立增广时滞非线性系统。然后,提出鲁棒扩展Kalman滤波器,引入鲁棒上界以减少线性化误差。进一步,针对系统过程不确定性导致预测协方差精度较低的问题,引入基于多重次优渐消因子的强跟踪算法,以降低不确定性对滤波精度的影响。最后,给出仿真算例,将所提出方法与鲁棒扩展Kalman算法和扩展Kalman算法进行对比仿真。仿真结果表明,相较于其他两种算法,所提出方法的状态估计和故障估计均方根误差的平均值分别降低了69.2%、60.6%和88.1%、78.9%,仿真结果验证了设计方案的有效性。

低速旋转GNSS卫星导航双天线加权kalman定位测速方法

GNSS常用于载体的定位测速。设想在旋转载体两侧对向各安装一个GNSS接收机天线,使得在任一历元下均能稳定接收GNSS信号。但当载体滚转时,GNSS观测量测量误差将使得传统kalman滤波器定位测速结果出现跳变。本文以低速旋转的用户模型为例,提出一种加权Kalman滤波算法。应用该方法的过程中,利用观测量残余与测量均方差的比值,调整超限观测量的方差,减小其滤波增益,达到弱化超限观测值的权重的目的,实现所有可见卫星均参与滤波,使得定位结果不会发生跳变。通过半实物仿真对本文所提出算法进行性能验证。从仿真实验结果可知,与传统的Kalman算法相比,本文算法的定位结果可用率(三维定位误差小于30 m)从89%提升至99%,三维测速误差(1σ)从0.19 m/s提升至0.11 m/s。

Design of weak current measurement system and research on temperature impact

A dedicated weak current measurement system was designed to measure the weak currents generated by the neutron ionization chamber.This system incorporates a second-order low-pass filter circuit and the Kalman filtering algorithm to effectively filter out noise and minimize interference in the measurement results.Testing conducted under normal temperature conditions has demonstrated the system's high precision performance.However,it was observed that temperature variations can affect the measurement performance.Data were collected across temperatures ranging from -20 to 70℃,and a temperature correction model was established through linear regression fitting to address this issue.The feasibility of the temperature correction model was confirmed at temperatures of -5 and 40℃,where relative errors remained below 0.1% after applying the temperature correction.The research indicates that the designed measurement system exhibits excellent temperature adaptability and high precision,making it particularly suitable for measuring weak currents.

基于观测方程重构滤波算法的锂离子电池荷电状态估计

滤波算法中观测方程的准确性在电池状态评估中起着决定性作用。然而,该文通过试验发现,由于温度、工作电流和荷电状态(SOC)的影响,即使使用精度较高的电池模型,扩展卡尔曼滤波(EKF)算法中观测方程的输出值与实际电压之间仍会存在较大误差,即产生了较大的新息。该文提出一种基于观测方程重组的增强型扩展卡尔曼滤波(E-EKF)算法。该算法的核心思想是利用具有温度、SOC和电流自适应能力的误差修正策略对观测方程进行重组,实现算法中新息的降低,进而提高SOC估计的准确性。使用两种不同温度下的典型工况试验对E-EKF算法的性能进行了验证。试验结果表明,该算法能够适应不同的温度和工况,并具有较高的SOC估计精度。

基于EM-KF算法的微地震信号去噪方法

针对微地震信号能量较弱,噪声较强,使微地震弱信号难以提取问题,提出了一种基于EM-KF(Expectation Maximization Kalman Filter)的微地震信号去噪方法。通过建立一个符合微地震信号规律的状态空间模型,并利用EM(Expectation Maximization)算法获取卡尔曼滤波的参数最优解,结合卡尔曼滤波,可以有效地提升微地震信号的信噪比,同时保留有效信号。通过合成和真实数据实验结果表明,与传统的小波滤波和卡尔曼滤波相比,该方法具有更高的效率和更好的精度。

基于分数阶模型多新息无迹卡尔曼滤波算法的超级电容SOC估计

对超级电容的SOC估计展开了研究。首先,搭建了超级电容测试平台,用于超级电容的参数辨识,并对超级电容进行了常规性能测试;其次,在不同的环境温度和动态工况下采用多种算法进行超级电容SOC估计。结果表明,采用分数阶模型多新息无迹卡尔曼滤波(FOMIUKF)算法对超级电容SOC的估计精度最高,对超级电容的路端电压跟随情况最好,估计结果的均方根误差和平均绝对误差的最大值分别约为1.8%和1.73%。

基于GA-LSTM自适应卡尔曼滤波的路面不平度识别

准确、快速地识别出车辆当前行驶的路面激励信息,是实现智能底盘控制进而保证车辆平顺性的关键。针对传统路面不平度识别算法准确率低、自适应性差等问题,提出了基于遗传算法(genetic algorithm,GA)优化长短期记忆神经网络(long short-term memory networks,LSTM)自适应卡尔曼滤波的路面不平度识别算法。基于2自由度车辆悬架模型,通过灰色关联法选择LSTM神经网络的特征输入变量,并采用GA优化LSTM神经网络的模型参数以准确识别路面等级,并据此实时更新卡尔曼滤波器算法中的噪声矩阵,实现了在复杂路况下对路面不平度的自适应识别。仿真和试验研究表明,所提出的基于GA-LSTM自适应卡尔曼滤波算法能够快速准确的识别路面不平度与路面等级,与传统卡尔曼滤波算法相比,相关系数、均方根误差和最大绝对误差分别提高3.11%、37.5%和51.2%,表明所提算法对复杂工况具有很好的自适应能力。