改进最小二乘法在制导精度分析中的应用

在大型线性回归分析中,由于设计矩阵的病态使得经典的最小二乘法失去了优良性。本文针对其存在的问题提出了几点改进措施。采用了改进的最小二乘方法,此方法具有公式简单、运算方便的优点,减少了计算误差,提高了计算置信度,理论模拟和实际飞行数据计算表明:估值精度比最小二乘法有较大提高,与主成分等有偏估计的结果具有相近的水平。     

回归方程中待估参数有效数字位的选取准则

用实验方法确定经验公式时,回归方程中用最小二乘方法求得的待估参数的估计值往往是一个很长的数。用这个很长的数来表达经验公式显得冗长而不实用。如果估计值位数取得过少,则会影响回归方程的精度。本文根据误差理论和有效数字运算规则,在保证回归精度的条件下,提出估计值最少有效数字位的选取准则。     

多套测试系统比对试验中标准差处理方法

针对全组合测量的数据，根据最小二乘法原理，提出了一种特殊的多套测试系统精度比对实验中标准差的最小二乘平差处理方法，当比对套数ｍ＞３时，利用此方法可分解开究竟哪一台仪器（或哪一套测试系统）的标准差最小，哪一台其次，从而评定参与比对各仪器精度的优劣，并以五套测速比对系统为例进行分析、论证。     

A CONCISE M-METRIC LEAST SQUARE FORMULA FOR POLYNOMIAL ANALOGY

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Retrieval of vegetation equivalent water thickness from reflectance using genetic algorithm (GA)-partial least squares (PLS) regression

This study aimed to investigate the performance of genetic algorithms coupled with partial least squares (GA-PLS) modeling of spectral reflectance in retrieving equivalent water thickness (EWT) at leaf and canopy level. A genetic algorithm was used to identify a subset of spectral bands sensitive to the variation in EWT, and PLS was then applied to relate the identified bands to EWT values. GA-PLS was applied to leaf level reflectance available from LOPEX dataset, and canopy data includes reflectance simulated by a leaf radiative transfer model PROSPECT and a canopy radiative transfer model SAILH and acquired by airborne visible/infrared imaging spectrometer (AVIRIS). The results indicate that GA-PLS has the capability of retrieving EWT from leaf and canopy reflectance, and achieved good estimation accuracy, i.e. low root mean square errors (RMSE) and high squared correlation coefficients (R²). For the retrieval at leaf level, the estimation accuracy can be as good as RMSE = 0.0019 g/cm² and R² = 0.939 or better. For the retrieval at canopy level, the model accuracy is RMSE = 0.0061 g/cm² and R² = 0.966 or better when PROSPECT-SAILH simulated reflectance was used; when AVIRIS image spectra were used, the model accuracy is RMSE = 0.0094 g/cm² and R² = 0.8734 for the calibration, and RMSE = 0.0132 g/cm² and R² = 0.7756 for the validation. These results from GA-PLS modeling support the conclusion that GA-PLS has the potential to be applied to AVIRIS, Hyperion and HyMap imagery for retrieving EWT. The selected bands for the AVIRIS datasets differ from those for the LOPEX and PROSPECT-SAILH simulated datasets, and this inconsistence of the selected bands for different datasets indicates that the GA-PLS method has the advantage of tuning the optimum bands for PLS regression and accommodating the effects of confounding factors.     

非稳定动态过程非定常气动力建模

现有的大迎角非定常气动力建模方法，通常是以一个或多个频率的稳定振动试验数据来预测稳定滞环。然而，飞机快速机动如过失速机动的过程，不可能是持续的稳定振动，而是一个非稳定的动态过程。因此，这个过程中的气动力不会达到稳定滞环，而是始终处于进入滞环的初始非稳定过程中。基于振动理论分析得出，非定常气动力的动态响应过程存在非稳定和稳定两个阶段，传统建模方法着眼于稳定阶段，而飞机的真实机动过程在非稳定阶段。设计了一种适于非线性系统辨识的激励输入，并以最小二乘支持向量机（LS-SVM）方法为例，实现了在大迎角区幅值和频率范围内任意运动的非定常气动力建模。模型训练完成后，用来预测某机翼在不同基准状态下大迎角范围内做俯仰运动时的升力系数、阻力系数和俯仰力矩系数。结果表明，不仅稳定滞环实现了准确预测，进入滞环的初始非稳定过程也得到了准确预测；此外，基准状态对气动力在初始非稳定过程中的特性存在明显影响。进一步的验证还表明，基于稳定滞环数据只能预测到稳定滞环，无法预测进入滞环的非稳定过程。     

Quantifying lunar soil composition with partial least squares modeling of reflectance

Retrieval of lunar soil composition is commonly achieved through optical remote sensing in which spectral characteristics of returned lunar samples are related to their constituents. Partial least squares (PLS) and principal component regression (PCR) were applied to the dataset characterized by the Lunar Soil Characterization Consortium (LSCC) to estimate the content of FeO, Al₂O₃ and TiO₂ in the soils. The goal of this study was to test whether the conversion of reflectance to single scattering albedo (SSA) via Hapke’s radiative transfer model is able to improve the performance of PLS and PCR. Results from PLS and PCR modeling of SSA spectra indicate that the conversion does not necessarily improve the performance of PLS and PCR, and this depends on the chemical considered, the way to select the number of optimal factors, and how the data were pretreated. The conversion failed to accommodate the large deviation of highland samples with low FeO, TiO₂ and high Al₂O₃.     

MC-CDMA中的RLS-DRMTA算法

多载波码分多址(MC-CDMA)系统是将OFDM技术与CDMA技术结合起来的一种综合技术.MC-CDMA系统中同信道干扰仍然是影响系统性能的主要因素,这就需要使用智能天线来提高系统的性能.介绍一种适用于MC-CDMA系统的自适应阵的盲算法递推最小二乘解扩重扩多目标阵列(RLS-DRMTA)算法,利用扩频码的信息进行波束形成,不需要训练序列,节约了频谱资源;与LS-DRMTA算法相比,RLS-DRMTA算法节省了运算时间;另外仿真表明在正交频分复用(OFDM)解调后进行波束形成,提高了系统的性能;为了降低系统的复杂度,还用到了载波分组技术,但分组技术又会降低系统的性能,所以分组时考虑了系统性能和运算速度的折衷.仿真结果表明RLS-DRMTA算法能使方向图的主波束对准信号方向,而在干扰方向形成零陷,从而达到抑制干扰的目的.      

时频信号的非参数加窗稀疏协方差迭代分析法

针对多分量非平稳时频信号的分析，提出了一种非参数加窗稀疏协方差迭代分析（Sparse Iterative Covariance-based Estimation，SPICE）法。该方法通过引入局部化的窗函数，并在窗内对信号建立非参数化的时频模型，以获取非平稳信号的局部时频特性。分析表明：给出的非参数时频模型，可通过加权最小二乘（Weighted Least Square，WLS）进行求解。当将WLS的加权矩阵的构建问题转换为广义噪声协方差矩阵时，提出的模型也可借助于加窗SPICE方法来进行求解。分析和仿真均表明：与传统方法相比，提出方法具有噪声抑制能力强、能量集中度高和对于载频差异较小信号的分离效果佳等优点。     

一种遥测缓变参数自动判读的新方法

针对遥测参数中缓变参数的自动判读问题，提出一种基于历史数据统计特性的遥测缓变参数自动判读新方法。首先，设计了一种以参数目标数据时标为基准的时间间隔递推算法和线性插值方法，使历史数据与目标数据的时标得到有效统一。其次，基于方向和距离函数构造了双因子等价权函数，并利用抗差最小二乘估计算法得到了参数的估值和标准差。最后，根据参数的估值和标准差对目标数据进行统计分析，依据目标数据的概率分布判断参数是否存在异常，进而实现参数的自动判读。仿真校验结果表明，该方法能有效辨识缓变参数中的异常参数，且具有较强的抑制随机噪声和抗差自适应能力。与传统以人工为主的判读方式相比，该方法能有效提高遥测参数判读的效率和准确性。