Computation of the circular error probability integral

The author describes a simplified derivation of the representation of the circular error probability (CEP) integral, which is the integral over a disk centered at the origin of a zero mean two-dimensional Gaussian random variable, as a one-dimensional integral. In addition, two series are presented which can be used to compute efficiently the CEP integral. The domain of applicability of the series and methods for acceleration of the convergence of these series are discussed. The integral occurs in the evaluation of communication and radar signals, and in other statistical applications.<>     

A Comparison of Ground Level Event e/p and Fe/O Ratios with Associated Solar Flare and CME Characteristics

Solar energetic particle (SEP) events reaching rigidities >1 GV are observed at 1?AU as ground-level events (GLEs). They are considered to be extreme cases of gradual SEP events, produced by shocks driven by wide and fast CMEs that are usually associated with long-duration (>1 hour) soft X-ray (SXR) flares. However, some large gradual SEP events, including GLEs, are associated with flares of short-duration (<1 hour) timescales comparable to those of flares seen with impulsive, low-energy SEP events with enhanced charge states, heavy-element abundances, and e/p ratios. The association of some GLEs with short-duration SXR events challenges us to understand the GLE event-to-event variation with SXR durations and whether it truly reflects the nature of the particle acceleration processes or simply the characteristics of the solar regions from which large, fast CMEs arise. We examine statistically the associated flare, active region (AR), and CME characteristics of ～40?GLEs observed since 1976 to determine how the GLE e/p and Fe/O ratios, each measured in two energy ranges, depend on those characteristics. The abundance ratios trend weakly to lower, more coronal, and less scattered values with increasing flare timescales, thermal and nonthermal peak fluxes, and measures of source AR sizes. These results and the wide range of solar longitude connections for GLEs with high abundance ratios argue against a significant role for flare effects in the GLEs. We suggest that GLE SEPs are accelerated predominately in CME-driven shocks and that a coupling of flare size and timescales with CME properties could explain the SEP abundance correlations with flare properties.     

Energy Spectra, Composition, and Other Properties of Ground-Level Events During Solar Cycle 23

We report spacecraft measurements of the energy spectra of solar protons and other solar energetic particle properties during the 16 Ground Level Events (GLEs) of Solar Cycle 23. The measurements were made by eight instruments on the ACE, GOES, SAMPEX, and STEREO spacecraft and extend from ～0.1 to ～500–700?MeV. All of the proton spectra exhibit spectral breaks at energies ranging from ～2 to ～46?MeV and all are well fit by a double power-law shape. A comparison of GLE events with a larger sample of other solar energetic particle (SEP) events shows that the typical spectral indices are harder in GLE events, with a mean slope of ?3.18 at >40?MeV/nuc. In the energy range 45 to 80?MeV/nucleon about ～50?% of GLE events have properties in common with impulsive ³He-rich SEP events, including enrichments in Ne/O, Fe/O, ²²Ne/²⁰Ne, and elevated mean charge states of Fe. These ³He-rich events contribute to the seed population accelerated by CME-driven shocks. An analysis is presented of whether highly-ionized Fe ions observed in five events could be due to electron stripping during shock acceleration in the low corona. Making use of stripping calculations by others and a coronal density model, we can account for events with mean Fe charge states of 〈Q _Fe〉≈+20 if the acceleration starts at ～1.24–1.6 solar radii, consistent with recent comparisons of CME trajectories and type-II radio bursts. In addition, we suggest that gradual stripping of remnant ions from earlier large SEP events may also contribute a highly-ionized suprathermal seed population. We also discuss how observed SEP spectral slopes relate to the energetics of particle acceleration in GLE and other large SEP events.     

离港航空器滑出时间的BP神经网络预测模型

准确地预测离港航空器滑出时间可有效提升机场场面运行效率,降低运行成本。构建基于BP 神经网络的离港航空器滑出时间预测模型,分析影响离港航空器滑出时间的可量化因素,并对其相关性进行检验;通过我国中南某机场2 周实际运行数据对模型进行验证,并以均方根误差、平均绝对误差和平均绝对误差百分比检验预测结果的准确性。结果表明：同时...     

基于定位误差修正的运动目标TDOA/FDOA无源定位方法

针对时差(TDOA)、频差(FDOA)无源定位的两步加权最小二乘(TSWLS)方法定位均方根误差(RMSE)和定位偏差适应测量噪声能力差的问题,在分析了影响两步法定位性能的因素基础上提出一种基于一阶泰勒级数展开的定位误差修正方法。该方法的第1步和两步法相同;其第2步避免了两步法第2步中引入估计偏差的平方运算,利用一阶泰勒级数展开得到第1步定位误差的线性最小均方估计,修正第1步定位结果得到目标位置和速度的最终估计,从理论上证明了该方法可以达到定位的克拉美罗下限(CRLB)。计算机仿真对比了新方法和TSWLS方法、基于泰勒级数(TS)展开的迭代极大似然(ML)方法以及约束总体最小二乘(CTLS)方法的定位性能,新算法复杂度和两步法相当,且均方误差和定位偏差低于两步法、泰勒级数法和CTLS方法。     

Optimum Steady-State Position and Velocity Estimation Using Noisy Sampled Position Data

The Kalman filtering technique is used to obtain analytical expressions for the optimum position and velocity accuracy that can be achieved in a navigation system that measures position at uniform sampling intervals of T seconds through random noise with an rms value of ?x. A one-dimensional dynamic model, with piecewise-constant acceleration assumed, is used in the analysis, in which analytic expressions for position and velocity accuracy (mean square), before and after observations, are obtained. The errors are maximum immediately before position measurements are made. The maximum position error, however, can be bounded by the inherent sensor error by use of a sufficiently high sampling rate, which depends on the sensor accuracy and acceleration level. The steady-state Kalman filter for realizing the optimum estimates consists of a double integrator, the initial conditions of which are reset at each observation.     

Gravity modeling in aerospace applications

The science of inertial navigation has evolved to the point that the traditional gravity model is a principal error source in advanced, precise systems. Specifically, the unmodeled vertical deflections of the earth's gravitational field are a major contributor to CEP (circular error probable) divergence in precise terrestrial inertial navigation systems (INS). Over the years, several studies have been undertaken to the development of advanced techniques for accurate, real-time compensation of gravity disturbance vectors. More complex on-board gravity models which compute vertical deflection components will reduce the CEP divergence rate, but imperfect modeling due to on-board processing limitations will still cause residual vertical deflection errors. In order to eliminate or reduce gravity-induced errors in the INS requires measurement of gravity disturbance values and in-flight compensation to the inertial navigator. It is assumed in this paper that gravity disturbance values have been measured prior to the airborne mission and various techniques for compensation are to be considered. As part of a screening process in this study, several gravity compensation techniques (both deterministic and stochastic models) were investigated. The screening process involved identification of gravity models and algorithms, and developments of selection criteria for subsequent screening of the candidates.     

Evaluation of estimation algorithms part I: incomprehensive measures of performance

Practical metrics for performance evaluation of estimation algorithms are discussed. A variety of metrics useful for evaluating various aspects of the performance of an estimation algorithm is introduced and justified. They can be classified in two different ways: 1) absolute error measures (without a reference), relative error measures (with a reference), or frequency counts (of some events), and 2) optimistic (i.e., how good the performance is), pessimistic (i.e., how bad the performance is), or balanced (neither optimistic nor pessimistic). Pros and cons of these metrics and the widely-used RMS error are explained. The paper advocates replacing the RMS error in many cases by a measure called average Euclidean error     

增量粒子滤波方法

提出增量粒子滤波的概念,建立增量粒子滤波模型及其分析方法,给出其算法.对于工程实际中存在的由未知系统误差的影响而无法精确建立量测似然函数的这一问题,提出增量粒子滤波方法,通过对带有未知系统误差的量测数据进行校正,获得精确的量测似然函数,建立精确的增量粒子滤波模型,从而消除这种未知系统误差的影响,减少重采样的次数,较好地保存了粒子的多样性,提高非线性滤波的精度.模拟仿真中,重采样的次数减少41.7%,滤波误差均值和均方根误差分别降低了45.3%和70.1%,有效地改善了滤波的效果.      

测向交叉定位系统中的最优交会角研究

研究了测向交叉定位系统中的最优交会角问题。在目标到两部被动传感器基线之间的垂直距离不同的情况下和最小圆概率误差（CEP）准则下,得出了一些有意义的结论。研究表明,最优交会角跟目标到两部传感器基线的垂直距离与基线长度的比值l有关。当l≥√3/6时,只存在一个最优交会角且此时目标与两部被动传感器呈等腰三角形,并在此情况下分析了l的变化对圆概率误差的影响。当l＜√3/6时,存在两个相等的最优交会角。得出的结论在多个被动传感器的优化配置进而提高目标定位精度方面具有一定的理论和实际意义。     

混合线性/非线性状态空间模型的边缘Rao-Blackwellized粒子滤波法(英文)

本文提出了边缘 Rao-Blackwellized 粒子滤波器(marginal Rao-Blackwellized particle filter, MRBPF)算法,算法融合了 Rao-Blackwellized 粒子滤波器(Rao-Blackwellized particle filter , RBPF)算法和边缘粒子滤波器(marginal particle filter, MPF)算法。算法中状态被分为线形和非线性两部分,分别用 MPF 和卡尔曼滤波器(Kalman Filter)进行估计。地形辅助导航(terrain aided navigation, TAN)的仿真结果表明,与 RBPF 相比,提出算法的非线性状态估计的误差均方根(root mean square error, RMSE)和误差方差分别降低了约 29%和 96%,独立粒子数提高了约80%,获得了更好的收敛结果。分析表明,现有RBPF是MRBPF的一个特例。     

A Procedure for Directly Calculating CEP in DF Fixing

The cumulative probability for a circular error probability (CEP) radius can be developed as a power series which converges efficiently for cases of practical interest and is suitable for numerical solution with simple iteration methods. The procedure can be applied with equal facility to circles of arbitrary probability level.     

The Marginal Rao-Blackwellized Particle Filter for Mixed Linear/Nonlinear State Space Models

In this paper, the marginal Rao-Blackwellized particle filter （MRBPF）, which fuses the Rao-Blackwellized particle filter （RBPF） algorithm and the marginal particle filter （MPF） algorithm, is presented. The state space is divided into linear and non-linear parts, which can be estimated separately by the MPF and the optional Kalman filter. Through simulation in the terrain aided navigation （TAN） domain, it is demonstrated that, compared with the RBPF, the root mean square errors （RMSE） and the error variance of the nonlinear state estimations by the proposed MRBPF are respectively reduced by 29% and 96%, while the unique particle count is increased by 80%. It is also found that the MRBPF has better convergence properties, and analysis has shown that the existing RBPF is nothing more than a special case of the MRBPF.     

Installation error calibration for MEMS angular measurement system in hypersonic wind tunnel

The accuracy of model attitude measurement has an important impact on wind tunnel test results. Microelectromechanical System Inertial Measurement Unit (MEMS IMU) provides a feasible way to measure model attitudes with high accuracy. However, the installation error between MEMS IMU coordinate system and the body coordinate system of test models can make the accuracy of the model attitude measurement decrease. In wind tunnel tests, the installation error depends on the relationship between the IMU and the model mechanism before tests. Therefore, in-field calibration in wind tunnel tests is necessary to reduce installation errors. To improve attitude measurement accuracy, the least squares quaternion calibration method based on MEMS IMU and six-position calibration procedure are proposed. High-precision three-axis turntable tests are performed. The pitch accuracy after calibration is higher than that before calibration in the angle of attack sweeping tests. The Root-Mean-Square Errors (RMSE) in the roll and yaw are within 0.01°, which are smaller than those before calibration. In the roll sweeping tests, RMSE of three attitude angles decrease significantly. In hypersonic wind tunnel tests, the pitch errors before and after calibration are within 0.05° and 0.02° in the angle of attack sweeping tests without wind. In five angle of attack sweeping tests with wind, the deviation between the mean of the pitch and the pitch after the elastic angle correction is within 0.03° and the standard deviation of five tests is within 0.01°. The proposed method is confirmed to enhance the accuracy of attitude measurement effectively, which is convenient for engineering applications.     

反舰导弹命中精度评估方法

研究了基于Bayes方法的反舰导弹命中精度评估方法,提出了导弹命中点系统误差评估方法、Bayes检验方案和CEP评估方法。     

基于DS算法的混胺燃料近红外光谱分析模型传递

对混胺燃料的近红外光谱分析模型的传递方法进行研究。采用 K/S(Kennard/Stone)算法选择转换集样品,采摘用直接校正(Direct Standardization,DS)算法对从仪器采集的光谱进行校正。通过光谱平均差异(ARMS)比较奇异值分解(Singular Value Decomposition,SVD)算法和偏最小二乘法(Partial Least Squares,PLS)对光谱校正的效果。当 PLS算法的最佳主因子数为 3时,DS-PLS算法的光谱校正率可达到 97.5%,优于 DS-SVD算法。混胺样品的分析模型经过 DS-PLS算法传递后,对从仪器的混胺样品各项指标的预测标准偏差(SEP)明显好于传递前,与主仪器预测效果接近,说明采用 K/S算法选择合适的转换集样品后,通过 DS-PLS模型传递算法可有效降低仪器间的光谱差异,实现近红外光谱分析模型在各台光谱仪之间共享。     

A Note on Bounds for Target Tracking with pd>1

Recently several new results for Cramer-Rao lower bounds (CRLBs) in dynamical systems have been developed. Several different approaches and approximations have been presented. For the general case of target tracking with a detection probability smaller than one and possibly in the presence of false measurements, two main approaches have been presented. The first approach is the information reduction factor (IRF) approach. The second approach is the enumeration (ENUM) approach, also referred to as the conditioning approach. It has been found that the ENUM approach leads to a strictly larger covariance matrix than the IRF approach, however, still providing a lower bound on the attainable error covariance. Thus, the ENUM approach provides a strictly tighter bound on the attainable performance. It has been conjectured that these bounds converge to one another in the limit or equivalently after an initial transition stage. We demonstrate, using some recent results from the modified Riccati equation (MRE) and by means of counter examples, that this conjecture does not hold true in general. We also demonstrate that the conjecture does hold true in the special case of deterministic target motion, or equivalently in the absence of process noise. Furthermore, we show that the detection probability has an influence on the limiting behaviors of the bounds. Moreover, we show that the MRE approximation provides a very good and computationally efficient approximation of the ENUM bound. The various results are illustrated by means of representative examples.     

电离层顶部电子含量对GNSS电离层层析的影响分析

卫星信号射线上的总电子含量(slant total electron content, STEC)是像素基全球卫星导航系统电离层层析(computerized ionospheric tomography, CIT)建模的必要数据来源，但电离层层析通常忽略1 000 km以上的顶部电子含量，为弄清这部分电子含量对层析结果的影响，利用NeQuick2模型计算站星视线上的STEC与其在电离层区域内的STEC比值来改正原始数据，并分别利用改正前后的STEC进行电离层层析。结果显示，电离层顶部电子含量占比约为10%，白天占比略大于黑夜，与测高仪站的数据相比，改正后的均方根值比改正前提高了20%以上；与Swarm卫星提供的电子剖面数据对比，改正后的层析结果精度较改正前提升了19.6%左右，且该方法受地磁扰动影响较为明显。总的来说，利用CIT进行小尺度电离层探测，可较直观地看出，顶部电子含量对层析结果的影响较大，需要采取相应手段予以剔除。     

Dimension reduction for array processing with robust interference cancellation

We present a robust solution for data reduction in array processing. The purpose is to reduce the computation and improve the performance of applied signal processing algorithms by mapping the data into a lower dimension beamspace (BS) through a transformation. Nulls steering to interference are incorporated into a transformation using the subspace projection technique, and the BS spatial spectrum estimation accuracy is evaluated and maximized with a measure. The derived transformation tries to preserve the full-dimension Cramer-Rao bounds (CRBs) for the parameters of interest while rejecting undesired signals effectively. When compared with an optimal method and an adaptive approach, simulation results show that significant improvements are obtained in terms of BS direction-of-arrival (DOA) estimation root-mean-squared error (RMSE), bias, and resolution probability.