Verification of ARMA identification for modelling temporal correlations of GNSS observations using the ARMASA toolbox
Verification of ARMA identification for modelling temporal correlations of GNSS observations using the ARMASA toolbox
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DOI：
10.1007/s11200-011-0033-2
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发表时间：
2011-08
影响因子：
0.9
通讯作者：
Xiaoguang Luo;M. Mayer;B. Heck
中科院分区：
文献类型：
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作者：
Xiaoguang Luo;M. Mayer;B. Heck
经典的最小二乘（LS）算法在全球卫星导航系统（GNSS）观测数据处理中得到了广泛的应用。然而，这种方法提供了可靠的估计未知参数和现实的准确性措施，只有当功能和随机模型都适当指定。在许多现有的全球导航卫星系统软件产品中实施的随机模型的一个基本缺陷在于忽略了全球导航卫星系统观测的时间相关性。通过对LS估计得到的观测残差时间序列的分析，利用自回归滑动平均（阿尔马）过程可以有效地描述GNSS观测值的时间相关性。对于给定的噪声实现，可以使用MATLAB® Central中免费提供的ARMASA工具箱自动估计和识别拟合良好的阿尔马模型。在将ARMASA工具箱应用于GNSS观测的时间相关性的基于残差的建模的初始阶段，本文利用大量具有代表性的模拟噪声时间序列，对自动阿尔马估计工具的性能进行了实证分析。与GNSS残差相当的时间相关特性。结果表明，无偏模型估计率随着数据长度的增加而增加，随着模型复杂度的增加而减少。对于大样本，超过80%的识别阿尔马模型是无偏的。此外，模型误差表示真实数据生成过程和模型估计值之间的偏差，对于相对于相关长度足够大的样本量，模型误差快速收敛到相关的渐近值。
The classical least-squares (LS) algorithm is widely applied in practice of processing observations from Global Satellite Navigation Systems (GNSS). However, this approach provides reliable estimates of unknown parameters and realistic accuracy measures only if both the functional and stochastic models are appropriately specified. One essential deficiency of the stochastic model implemented in many available GNSS software products consists in neglecting temporal correlations of GNSS observations. Analysing time series of observation residuals resulting from the LS evaluation, the temporal correlation behaviour of GNSS measurements can be efficiently described by means of socalled autoregressive moving average (ARMA) processes. For a given noise realisation, a well-fitting ARMA model can be automatically estimated and identified using the ARMASA toolbox available free of charge in MATLAB® Central.In the preliminary stage of applying the ARMASA toolbox to residual-based modelling of temporal correlations of GNSS observations, this paper presents an empirical performance analysis of the automatic ARMA estimation tool using a large amount of simulated noise time series with representative temporal correlation properties comparable to the GNSS residuals. The results show that the rate of unbiased model estimates increases with data length and decreases with model complexity. For large samples, more than 80% of the identified ARMA models are unbiased. Additionally, the model error representing the deviation between the true data-generating process and the model estimate converges rapidly to the associated asymptotical value for a sufficiently large sample size with respect to the correlation length.