Additional results on `reducing geometric dilution of precisionusing ridge regression'

R.J. Kelly (1990) presented preliminary results on the feasibility of using ridge regression to reduce the effects of geometric dilution of precision (GDOP) error inflation in position-fix navigation systems. Results indicate that the ridge technique will not reduce bias inflation due to the effects of GDOP in applications where bias-like measurement errors persist for time periods which greatly exceed the response time of an aircraft's guidance loop. This conclusion will preclude the use of ridge regression on navigation systems whose dominant error sources are bias-like. This applies in particular to the Global Positioning System (GPS) selective availability error source. All the simulation results given in Kelly's work are, however, valid for the conditions defined. Although ridge regression has not yielded a satisfactory solution to the general GDOP problem, it has illuminated the role that multicollinearity plays in navigation signal processors such as the Kalman filter. After a background discussion, bias inflation, initial position guess errors, ridge parameter selection methodology, and the recursive ridge filter, are discussed     

Solution and performance analysis of geolocation by TDOA

One method of geolocation is based on measuring the time difference of arrivals (TDOAs) of a signal received by three or four geostationary satellites. The received signals are cross-correlated to determine the TDOAs and a set of nonlinear equations are solved to produce the location estimate. An exact solution for the transmitter position is derived for the three or four receiver cases. Extension of the solution method to more receivers is straightforward. An analysis of the performance of the system is given, together with expressions for predicting the localization mean-square errors (MSEs) and bias, and the Cramer-Rao bound. Both precision in TDOA measurements and the relative geometry between receivers and transmitter affect the localization accuracy. The geometric factors act as multipliers to the TDOA variance in the bias and MSE formulae. A study of the dependency of the geometric factors on transmitter position and satellite spacings are provided, as well as simulation results     

Novel Nonlinear Filtering & Prediction Method for Maneuvering Target Tracking

A new nonlinear filtering and prediction (NFP) algorithm with input es?imation is proposed for maneuvering target tracking. In the proposed method, the acceleration level is determined by a decision process, where a least squares (LS) estimator plays a major role in detecting target maneuvering within a sliding window. We first illustrate that the optimal solution to minimize the mean squared error (MSE) must consider a trade-off between the bias and error variance. For the application of target tracking, we then derive the MSE of target positions in a closed form by using orthogonal space decompositions. Then we discuss the NFP estimator, and evaluate how well the approach potentially works in the case of a set of given system parameters. Comparing with the traditional unbiased minimum variance filter (UMVF), Kalman filter, and interactive multiple model (IMM) algorithms, numerical results show that the newly proposed NFP method performs comparable or better in all scenarios with significantly less computational requirements.     

SINS/BDS紧组合系统中自适应 两阶段扩展卡尔曼滤波

在实际应用中，以伪距/伪距率为观测量的SINS/BDS紧组合导航系统，存在量测噪声的统计特性与实际不相符的情况，传统扩展卡尔曼滤波（EKF）方法无法有效解决这一问题，从而引起滤波误差增大。提出了一种SINS/BDS紧组合导航系统的GDOP估算及在线估计量测噪声的自适应两阶段EKF（ATEKF）方法，该方法使用经过紧组合修正后的SINS输出的位置，并结合星历数据中提供的卫星位置求解GDOP。在此基础上，利用GDOP值以及新息，实现了紧组合导航系统的量测噪声方差阵（Rk）的在线实时估计，从而达到自适应滤波的效果，改善导航精度。     

基于鲁棒扩展卡尔曼滤波的双目视觉测量相对导航技术研究

针对非合作目标相对导航问题,为提高相对导航的精度和可靠性,采用双目视觉测量方法实现追踪器与目标器之间相对状态的测量,并基于鲁棒扩展卡尔曼滤波方法,提出了一种鲁棒相对导航滤波方法。仿真结果表明,该方法对相对导航系统模型中的不确定性具有良好的鲁棒性,且滤波精度较高。     

GPS/惯性组合方式讨论与导航精度分析

 本文讨论GPS/惯性组合两种方式的优缺点。并以GPS伪距和伪距率与惯导组合为例,按GPS测量误差的不同,以及使用差分机等情况,仿真计算了机载使用的组合导航性能,进行了详细的精度分析。结果表明,这种组合的导航精度比GPS和惯导各自的导航精度高。在采用差分GPS机与惯导组合后,位置误差将进一步减少,使组合导航具有开辟例如飞机进场着陆等新的使用领域的可能性。     

Euler angle dilution of precision in GPS attitude determination

The geometric dilution of precision (GDOP) is a useful parameter that indicates the effectiveness of the GPS satellite geometry on the positional navigation performance. In this work, the concept of the dilution of precision is extended to the attitude navigation solution. A new set of parameters, referred to as the Euler angle dilution of precision (EADOP), is defined. The validity and the usefulness of the new parameters are verified through simulations. Two scenarios involving a stationary platform and a moving platform are investigated. The results show that the EADOP is a good indication of the expected accuracy of the Euler angle estimates     

A closed-form solution for moving source localization using LBI changing rate of phase difference only

Due to the deficiencies in the conventional multiple-receiver localization systems based on direction of arrival(DOA) such as system complexity of interferometer or array and amplitude/phase unbalance between multiple receiving channels and constraint on antenna configuration,a new radiated source localization method using the changing rate of phase difference(CRPD)measured by a long baseline interferometer(LBI) only is studied. To solve the strictly nonlinear problem, a two-stage closed-form solution is proposed. In the first stage, the DOA and its changing rate are estimated from the CRPD of each observer by the pseudolinear least square(PLS) method,and then in the second stage, the source position and velocity are found by another PLS minimization. The bias of the algorithm caused by the correlation between the measurement matrix and the noise in the second stage is analyzed. To reduce this bias, an instrumental variable(IV) method is derived. A weighted IV estimator is given in order to reduce the estimation variance. The proposed method does not need any initial guess and the computation is small. The Cramer–Rao lower bound(CRLB) and mean square error(MSE) are also analyzed. Simulation results show that the proposed method can be close to the CRLB with moderate Gaussian measurement noise.     

微小型飞行器惯性组合姿态确定与航路导航研究

构建了微小型飞行器(MAV)导航、制导与控制(GNC)系统。研究了微惯性导航测量单元零偏的温度建模及非正交误差的多位置标定补偿方法,提出微小型飞行器导航、制导与控制系统闭环条件下,利用导航、制导与控制回路的飞行状态特征信息的微惯性组合导航系统滤波算法,根据微小型飞行器飞行状态实时调整卡尔曼滤波器的观测噪声方差,有效提高了动态过程中姿态测量精度和微小型飞行器的飞行平稳度。完成了组合导航系统滤波算法验证飞行试验及自主姿态稳定和航路飞行试验。飞行试验表明:微小型飞行器实现了自主姿态稳定与长距离超视距航路点导航飞行,航路点导航误差小于30 m,惯性组合姿态确定与航路导航系统及算法满足微小型飞行器自主飞行对导航系统的需求。     

单轴旋转惯导系统误差特性分析

旋转调制技术能够抑制陀螺和加速度计的误差,提高惯性导航系统的导航精度。从捷联惯导系统的误差方程出发,推到出了单轴旋转惯导系统的误差传播方程,在此基础上分析了旋转调制的基本原理。分别对陀螺和加速度计常值偏差、标度因数误差、安装误差和转台安装误差等在旋转调制下的影响进行了研究,仿真分析了旋转调制提高系统导航精度的作用,最后在实验室条件下做静止导航实验进行了验证。研究的结果能为单轴旋转惯导系统的研究和开发提供一定的理论参考。     

一种对GPS/INS组合导航的曳引式拉偏干扰

为解决GPS/INS组合导航对抗难题,提出一种针对GPS/INS组合导航的曳引式拉偏干扰方法。通过干扰设备产生欺骗干扰信号,使GPS/INS组合中的GPS接收机输出与其实际位置逐渐偏离的导航定位数据,当偏离误差无法被组合导航纠正时发生曳引式拉偏干扰。文中给出干扰方法的定义、信号形式、简化形式,通过半实物仿真实验证明其有效性并对其干扰效果进行了分析。     

十二表冗余捷联惯导系统数据融合技术研究

针对采用正十二面体冗余仪表构型的十二表冗余捷联惯性导航系统,通过仿真和样机试验,开展了基于最小二乘估计的数据融合算法研究。对不同故障模式下的系统精度进行了分析,并通过Monte Carlo仿真验证了数据融合算法对提高系统导航精度的有效性。设计开展了样机静态导航试验,试验结果表明,理论最优的马尔柯夫估计并不完全适用于脉冲输出形式仪表的数据融合。最后通过优化改进加权系数、构造加权矩阵,显著提升了样机的静态导航精度,使样机位置误差和姿态误差与三表直接解算相比分别降低了78.6%和77.9%。     

Geolocation of a known altitude object from TDOA and FDOA measurements

Most satellite systems for locating an object on Earth use only time difference of arrival (TDOA) measurements. When there are relative motions between an emitter and receivers, frequency difference of arrival (FDOA) measurements can be used as well. Often, the altitude of an object is known (it is zero, for example) or can be measured with an altimeter. Two sets of geolocation solutions are proposed which exploit the altitude constraint to improve the localization accuracy. One is for TDOAs alone and the other for the combination of TDOA and FDOA measurements. The additional complexity by imposing the constraint is a one-dimensional Newton's search and the rooting of a polynomial. The covariance matrices of the new estimators are derived under a small measurement noise assumption and shown to attain the constrained Cramer-Rao lower bound (CRLB). When there is a bias error in the assumed altitude, using the altitude constraint will introduce a bias to the solution. Since applying the constraint decreases the variance, there is a tradeoff between variance and bias in the mean square error (MSE). The maximum allowable altitude error such that the constraint solution will remain superior to the unconstraint is given. Simulation results are included to corroborate the theoretical development.     

一种基于无线信号辅助的室内无死角定位算法

针对传统惯性导航系统定位误差随时间积累的问题,提出了一种基于无线信号辅助定位的室内无死角定位算法。该算法首先利用加速度计、陀螺仪、磁力计和气压计等传感器数据实现三维定位,然后利用无线信号对惯导定位中的位置偏差进行实时校正,再通过航向最优估计算法对航向误差进行修正,在位置和航向上增强惯导系统的实用性。利用实验室自主研发的微惯性测量单元固定在腰部脊椎位置进行实验验证,结果显示基于无线信号辅助的室内无死角定位算法精度达到1%以内,与纯惯导技术相比,能够提供更持久和准确的三维位置信息。     

伪距解除相关法在GPS/SINS紧组合系统中的应用研究

介绍了伪距解除相关法的原理 ,设计了一种加权平均跟踪误差估计器 ,用以估计 GPS接收机码环跟踪误差。研究结果表明 ,与未对伪距测量值进行修正时相比 ,应用伪距解除相关技术可以减小组合系统的导航误差 ,提高系统的导航精度     

地形辅助制导系统

本文叙述一种地形辅助制导系统,用来修正惯性系统或其它导航系统的误差,以提高飞行器的制导精度。这种辅助系统含有一个卡尔曼滤波器,它将飞行器所飞过的实际地形信息与预存的地图进行比较和处理,从而估计出导航系统的误差。对于一般的丘陵地形,辅助制导后的精度可达到数十米的范围。它适用于飞机、巡航导弹、弹道导弹和其它武器运载系统,而且所需的设备简单,易于实现。     

基于两步最小二乘定位的偏差改进算法

针对传统最小二乘(LS)定位算法在噪声较大时会出现有偏估计的问题。首先详细推导了传统两步最小二乘算法在时差角度联合定位场景下的理论偏差,给出了出现偏差的原因;其次对误差均值加入二次约束条件,提出一种基于时差角度联合定位的改进算法,并详细推导新算法的理论偏差以及均方误差。相比于其他加限制条件的方法,新算法能有效降低估计偏差,另外由于其不需要进行特征值分解且能得到闭式解,计算复杂度较小。仿真结果表明,新算法在保持原有均方误差(MSE)的前提下能显著降低估计偏差,其定位偏差与最大似然估计器相当。     

平流层飞艇升降阶段BPNN惯性导航算法

软式平流层飞艇艇体在上升和下降时经常呈堆叠状态,GPS信号会被艇体间歇性遮挡,因而只能采用惯性导航。为保证在飞艇上升和下降过程中,INS/GPS组合导航系统在被艇体遮挡GPS时仍能够提供满足精度要求的导航信息,设计了一种改进的反向传播神经网络(Back Propagation Neural Network, BPNN）惯性导航算法。采用神经网络,根据惯性导航系统在1s内的速度均值和姿态变化量,预估其在1s末的位置误差和速度误差,并对惯性导航结果进行修正。仿真实验和跑车试验结果表明,在GPS失效的30s内,新算法使得位置误差低于15m,速度误差低于0.7m/s,误差相比纯惯性导航降低了85%。     

GPS小波去噪的误差方差建模技术与试验

如何消除GPS观测数据的噪声以提高定位精度并估算消噪信号的误差方差对工程测量具有重要意义。在介绍小波多尺度分析的基础上,推导了在小波多尺度分析巾平滑信号误差的理论方差模型。并通过实际的GPS单点静态定位试验给予验证。试验结果表明,该方法在有效消除噪声的同时,计算得到的各尺度平滑信号的误差方差与理论方差模型基本一致。     

一种鲁棒Sigma-point滤波算法及其在相对导航中的应用

研究了一种鲁棒Sigma-point滤波方法在无人机编队相对导航问题上的应用。该方法采用Huber估计方法,将Sigma-point滤波量测更新转化为求解线性回归问题,新的Sigma-point滤波方法是一种混合L1、L2范数最小估计,当量测噪声为受污染的高斯白噪声时,该方法具有一定的鲁棒性。给出了编队无人机相对惯导方程和相对视线矢量测量原理,应用鲁棒Sigma-point滤波方法融合相对惯导信息和相对视线矢量信息,估计出无人机之间的相对姿态、相对速度和相对位置。仿真结果表明,与扩展卡尔曼滤波和常规Sigma-point滤波相比,鲁棒Sigma-point滤波可以获得更高的估计精度。