一种新的综合Kalman滤波及其在星载GPS 低轨卫星定轨中的应用

针对将Kalman滤波方法应用到星载GPS定轨时，由于动态噪声和观测噪声确定不准而造成滤波的发散、污染观测值造成Kalman滤波估值的扭曲及计算舍入误差可能带来协方差阵的不正定性等缺陷，提出了一种新的综合Kalman滤波方法。该方法用拟准检定法准确地探测和修正量测方程中存在的粗差；用UD分解算法克服了数值的不稳定性，改进了计算精度；用Sage自适应滤波器克服滤波器的发散。算例结果表明，这种综合卡尔曼滤波方法具有数值稳定性好、较强的自适应性和较好地削弱粗差影响等优点。     

自适应渐消卡尔曼滤波及其在SINS初始对准中的应用

卡尔曼滤波常常被用于惯性导航系统初始对准算法,其使用前提是对系统状态进行建模,从而得到比较准确的系统噪声和观测噪声统计特性。在模型失配和观测噪声干扰的情况下,常规卡尔曼滤波会出现精度下降甚至发散,从而影响初始对准精度。针对这一问题,提出了一种新型渐消卡尔曼滤波算法,引入了多重渐消因子对预测误差协方差阵进行调整,设计了基于新息向量统计特性的滤波状态χ2检验条件,使渐消因子的引入时机更加合理,算法的自适应性得到增强。将改进的卡尔曼滤波算法应用到惯性导航系统的初始对准问题中,仿真试验和实测数据试验结果表明,与常规渐消因子滤波算法相比,新算法可以有效提高滤波精度及鲁棒性。     

Adaptive GPS/INS integration for relative navigation

Relative navigation based on GPS receivers and inertial measurement units is required in many applications including formation flying, collision avoidance, cooperative positioning, and accident monitoring. Since sensors are mounted on different vehicles which are moving independently, sensor errors are more variable in relative navigation than in single-vehicle navigation due to different vehicle dynamics and signal environments. In order to improve the robustness against sensor error variability in relative navigation, we present an efficient adaptive GPS/INS integration method. In the proposed method, the covariances of GPS and inertial measurements are estimated separately by the innovations of two fundamentally different filters. One is the position-domain carrier-smoothed-code filter and the other is the velocity-aided Kalman filter. By the proposed two-filter adaptive estimation method, the covariance estimation of the two sensors can be isolated effectively since each filter estimates its own measurement noise. Simulation and experimental results demonstrate that the proposed method improves relative navigation accuracy by appropriate noise covariance estimation.     

基于渐消因子的改进Kalman滤波时间尺度估计算法

Kalman滤波时间尺度算法是一种实时的原子钟状态估计方法,在守时实验室具有重要实用价值。由于原子钟状态模型误差估计存在偏差,Kalman滤波时间尺度算法中状态估计可能出现相应异常扰动,应当对状态模型误差进行实时控制。对此,引入基于渐消因子的改进Kalman滤波时间尺度算法。对状态预测协方差矩阵引入渐消因子,利用统计量实时计算渐消因子的量值,控制状态预测协方差阵的增长,降低了原子钟状态估计的扰动。实验结果表明,相比于标准Kalman滤波时间尺度算法和基于预测残差构造自适应因子的Kalman滤波算法,基于渐消因子的改进Kalman滤波时间尺度算法能够提高原子钟状态估计的准确度,改进时间尺度的稳定度。     

Adaptive estimation of multiple fading factors in Kalman filter for navigation applications

Kalman filter is the most frequently used algorithm in navigation applications. A conventional Kalman filter (CKF) assumes that the statistics of the system noise are given. As long as the noise characteristics are correctly known, the filter will produce optimal estimates for system states. However, the system noise characteristics are not always exactly known, leading to degradation in filter performance. Under some extreme conditions, incorrectly specified system noise characteristics may even cause instability and divergence. Many researchers have proposed to introduce a fading factor into the Kalman filtering to keep the filter stable. Accordingly various adaptive Kalman filters are developed to estimate the fading factor. However, the estimation of multiple fading factors is a very complicated, and yet still open problem. A new approach to adaptive estimation of multiple fading factors in the Kalman filter for navigation applications is presented in this paper. The proposed approach is based on the assumption that, under optimal estimation conditions, the residuals of the Kalman filter are Gaussian white noises with a zero mean. The fading factors are computed and then applied to the predicted covariance matrix, along with the statistical evaluation of the filter residuals using a Chi-square test. The approach is tested using both GPS standalone and integrated GPS/INS navigation systems. The results show that the proposed approach can significantly improve the filter performance and has the ability to restrain the filtering divergence even when system noise attributes are inaccurate.     

Application of unscented Kalman filter in satellite orbit simulation

IntroductionAs is well known,the Kal manfilter(KF) is al-ways usedto deal withthe system whose dynam-ics and observation models are linear , and theextended Kal manfilter(EKF) is the most widelyused esti mator for nonlinear systems . In theEKFthe kal man …     

Application of unscented Kalman filter in satellite orbit simulation

A new estimate method is proposed, which takes advantage of the unscented transform method, thus the true mean and covariance are approximated more accurately. The new method can be applied to nonlinear systems without the linearization process necessary for the EKF, and it does not demand a Gaussian distribution of noise and what's more, its ease of implementation and more accurate estimation features enables it to demonstrate its good performance in the experiment of satellite orbit simulation. Numerical experiments show that the application of the unscented Kalman filter is more effective than the EKF.     

Robust adaptive filter for shipborne kinematic positioning and velocity determination during the Baltic Sea experiment

Information on trajectory and attitude is essential for analyzing gravimetric data collected on kinematic platforms. Usually, a Kalman filter is used to obtain high-accuracy positional and velocity information. However, this can be affected by measurement outliers and by state disturbances that occur frequently under a fast-changing environment. To overcome these problems, a robust adaptive Kalman filtering algorithm is applied for state estimates, which introduces an equivalent weight to resist measurement outliers and an optimal adaptive factor to balance the contributions of the kinematic model information and the measurements. In addition to the conventional robust estimator, an improved Current Statistical (CS) model is proposed. The improved CS model adopts a variance adaptive learning algorithm, and it can perform self-adaptation of acceleration variance with the innovation information; thus, it can overcome the shortcoming of lower tracking accuracy and avoid setting the maximum acceleration. Following a gravimetry campaign on the Baltic Sea, it is shown in theory and in practice that the robust adaptive Kalman filter is not only simple in its calculation but also more reliable in controlling the colored observation noise and kinematic state disturbance compared with the classical Kalman filter. The improved CS model performs best, especially when analyzing the positioning errors at the turns due to the target maneuvering. Compared to the CS model, the RMS values of the positional estimates derived from the improved CS model decrease by almost 30% in the horizontal direction, and no significant improvement in the vertical direction is found.     

附加原子钟物理模型的PPP时间传递算法

传统精密单点定位(PPP)时间传递算法通常把接收机钟差当作相互独立的白噪声逐历元进行估计,而忽略了钟差参数历元间的相关性。针对这一问题,本文提出了一种附加原子钟物理模型的PPP时间传递算法。该算法通过利用Kalman滤波对高稳定度的原子钟钟差进行建模,拓展传统PPP时间传递模型中的接收机钟差参数,并给出了Kalman滤波过程噪声协方差和初始状态向量的确定方法。试验结果表明:该算法可以有效避免传统算法时间传递结果需要一定收敛时间的问题,使解算结果更加符合原子钟的物理特性,能够显著提高时间传递结果的精度和稳定性,可将单站时间传递精度平均提高58%,站间时间传递精度平均提高51%。     

GNSS/INS紧组合最大熵卡尔曼滤波算法

针对实际环境中量测噪声易被野值污染而呈现非高斯分布,进而导致传统卡尔曼滤波(KF)算法性能降低的问题,提出了最大熵卡尔曼滤波(MCKF)算法. 该算法基于最大熵准则(MCC)和M估计的思想推导得到. 与KF相比,所提算法能够给异常量测值分配较小的权重以减轻其对于状态估计的影响,与基于Huber函数的卡尔曼滤波(HKF)算法相比,其能够更有效地利用量测信息,因此所提算法相比于KF和HKF而言更加鲁棒. 在全球卫星导航系统(GNSS)与惯性导航系统(INS)的紧组合模式下进行车载实测实验,由于GNSS的伪距与伪距率等原始量测信息质量不佳,因此KF和HKF的性能均受到影响,而所提MCKF算法能够有效地抑制异常量测值的影响,能够更快地收敛且得到更高的估计精度.      

应用Jones—TryonKalman滤波器对在轨GPSRb钟进行状态监测

针对用于石英钟和GPS主控站原子钟状态监测的Jones—TryonKalman滤波器,尝试把其引入到在轨GPSRb钟状态监测中去,结合哈达玛方差分析了其过程噪声和观测噪声协方差矩阵的确定方法,并讨论了滤波初值的选取,从而得到一个适合在轨GPSRb钟状态监测的滤波器。算例表明,这种Jones—TryonKal—man滤波器可以较好地监测在轨GPSRb钟的状态。     

Consideration of time-correlated errors in a Kalman filter applicable to GNSS

An algorithm for considering time-correlated errors in a Kalman filter is presented. The algorithm differs from previous implementations in that it does not suffer from numerical problems; does not contain inherent time latency or require reinterpretation of Kalman filter parameters, and gives full consideration to additive white noise that is often still present but ignored in previous implementations. Simulation results indicate that the application of the new algorithm yields more realistic and therefore useful state and covariance information than the standard implementation. Results from a field test of the algorithm applied to the problem of kinematic differential GPS demonstrate that the algorithm provides slightly pessimistic covariance estimates whereas the standard Kalman filter provides optimistic covariance estimates.     

Real-time estimation of satellite clock offset using adaptively robust Kalman filter with classified adaptive factors

In order to estimate the satellite clock offset in a real-time mode, a new algorithm of adaptively robust Kalman filter with classified adaptive factors for clock offset estimation is proposed. Compared with standard Kalman filter clock offset model, the new method can detect and control outliers and clock jumps automatically in real-time. Moreover, the clock model parameters, which contain the clock offset, clock speed and clock shift, are classified to decide the adaptive factors in the new model. Thus, clock jumps with different characteristics can be distinguished more effectively. Meanwhile, the dynamic noise characteristics of clock offset series are used for stochastic modeling. An actual numerical example is presented, which shows that the proposed filter can give a better performance than other commonly used filters.     

提高卫星导航精度的卡尔曼滤波算法应用研究

采用卫星导航对海上航行的船舶进行速度测量是目前最广泛应用的方法,但是卫星导航接收机由于受外界偶然因素的影响,其显示的速度往往包含噪声,且属于随机的高斯白噪声。针对此问题,提出一种基于卡尔曼滤波理论的计算模型,只考虑上一个时刻和当前时刻的关系,大大地减少数据冗余;应用迭代的方法来处理卡尔曼滤波,以更好地简化计算的过程,并根据深圳某航海公司的实际数据对此计算模型进行仿真验证。实验结果表明,对于数据跳跃十分大且明显的噪声数据,经过滤波后,这些数据变得更加平滑和准确。     

平方根 UKF及其在 GNSS多径估计中的应用

针对一般的加性高斯白噪声系统,结合平方根无迹卡尔曼滤波和加性噪声无迹卡尔曼滤波的优点,提出了无须增广变量的加性高斯白噪声系统的平方根无迹卡尔曼滤波方法,并给出了其详细算法.该算法较传统方法具有较小的运算负担,较高的精度,并能有效克服滤波的发散.该方法应用于卫星导航系统动态多径估计问题,能够高效准确地得到直射信号与多径信号的各个参数的估计,从而抑制多径的影响.仿真试验表明,该方法在诸多方面改进了已有方法,是一种高效准确的非线性滤波方法.     

动态EIV模型及其总体卡尔曼滤波方法

针对求解动态EIV模型时未考虑状态方程中状态转移矩阵误差的问题,本文建立了一种能够同时顾及状态方程和观测方程中各量误差的动态EIV模型。推导了针对该动态EIV模型的总体卡尔曼滤波方法及其近似精度评定公式。对比分析了本文总体卡尔曼滤波方法与已有总体卡尔曼滤波方法及总体最小二乘方法的异同。算例结果表明,本文方法统计上要优于标准卡尔曼滤波方法和已有的总体卡尔曼滤波方法。     

后向平滑与抗差估计融合的SRCKF滤波

将后向平滑平方根容积卡尔曼滤波用于GPS动态单点定位数据处理,并探讨了粗差对后向平滑滤波的影响。借鉴经典卡尔曼滤波抗差估计思想,给出平方根容积卡尔曼滤波的抗差算法以抵抗量测粗差,而当判断不含粗差时使用后向平滑算法,在有效提高滤波精度的同时避免了抗差滤波对每个历元都需进行迭代运算。实测GPS动态数据验证了算法的有效性。     

精密单点定位不等精度观测值的RKF研究

推导了精密单点定位含有粗差观测数据的M-LS滤波原理,对等价权阵采用三段降权函数实现抗差。从新息和残差的协方差关系出发,利用对粗差敏感的残差标准差作为抗差因子。通过迭代减弱卫星间载波残差及其抗差因子的相关性。针对载波和伪距观测值不等观测精度和不相关性,采用双抗差因子实现静态抗差卡尔曼滤波（robust Kalman filtering,RKF）。采用标准卡尔曼滤波、基于新息RKF、基于残差的增益矩阵双抗差因子RKF、基于残差的等价权阵双抗差因子RKF等4种模型,分别对一组实测数据解算分析。结果表明,基于新息RKF对精度较高的载波粗差不敏感;基于残差的增益矩阵RKF对载波较小的粗差抗差效果较差,且发生粗差历元时刻的状态参数与真值偏差较大;而基于残差构造的等价权阵双抗差因子RKF可以非常精确和高效地实现抗差,单个卫星粗差对测站位置参数影响小于1 mm。     

移动机器人视觉动态定位的稳健高斯混合模型

针对动态场景中运动路标点严重影响传统视觉自主定位算法精度,甚至产生定位失效的问题,提出一种顾及动态路标点的稳健高斯混合模型。在传统图优化视觉定位模型的基础上,增加“运动指数”描述图优化模型中路标点的运动概率,把传统图优化高斯模型增强为高斯混合模型,以约束运动路标点对图优化结果的影响;为增强模型对噪声的稳健性,采用方差膨胀模型约束残差方程;详细推导了该高斯混合模型的期望-最大化求解方法,把该问题转化为经典迭代最小二乘问题进行解算。仿真试验和真实数据试验表明：强动态场景中,提出的算法绝对精度指标和相对精度指标均优于传统优化算法;静态或弱动态场景中,提出的算法仍与传统优化算法定位性能相当。本文方法可有效减小场景中运动路标点对优化结果的影响,更适用于移动机器人的自主定位。     

基于EKF的北斗B1C信号数据/导频联合跟踪方法

针对北斗B1C信号在低载噪比情况下跟踪精度低的问题,提出一种基于扩展卡尔曼滤波（EKF）的北斗B1C信号数据/导频联合跟踪方法.通过构建数据/导频双通道联合跟踪模型,增加对B1C信号利用率,并在联合跟踪模型的基础上引入扩展卡尔曼滤波器,削弱传统跟踪环路中鉴别器和环路滤波器带来的跟踪误差,进一步提高跟踪环路对低载噪比信号的跟踪性能.仿真结果验证:在低载噪比情况下,相比于传统单导频通道跟踪、单导频扩展卡尔曼跟踪和联合跟踪,该方法可以有效提高跟踪精度.