GPS Stochastic Modelling: Signal Quality Measures and ARMA by Xiaoguang Luo

By Xiaoguang Luo

Global Navigation satellite tv for pc structures (GNSS), corresponding to GPS, became an effective, trustworthy and traditional software for a variety of functions. even if, whilst processing GNSS info, the stochastic version characterising the precision of observations and the correlations among them is mostly simplified and incomplete, resulting in overly positive accuracy estimates.

This paintings extends the stochastic version utilizing signal-to-noise ratio (SNR) measurements and time sequence research of remark residuals. The proposed SNR-based remark weighting version considerably improves the result of GPS facts research, whereas the temporal correlation of GPS statement noise could be successfully defined through autoregressive relocating typical (ARMA) methods. additionally, this paintings contains an up to date assessment of the GNSS errors results and a accomplished description of assorted mathematical tools.

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14), the resulting covariance matrices of xˆ , ˆl and eˆ are Cxˆ xˆ = σ02 AT Q−1 ll A −1 , Cˆlˆl = P A Cll , Ceˆ eˆ = P ⊥ A Cll . 19) The minimum tr(Cxˆ xˆ ) indicates that the BLUE is a minimum variance linear unbiased estimator. This property is also independent of the distribution of l. Setting W equal to Q−1 ll in Eq. 11), the squared weighted norm of the errors becomes eˆ 2 Q−1 ll T −1 T −1 ˆ = l T Q−1 = eˆ T Q−1 ll e ll l − l Qll A A Qll A −1 AT Q−1 ll l. 20) In the weighted LS estimation, the weight matrix W plays the role of a metric tensor in a vector space.

For these purposes, the determination of an appropriate time series model from the given data plays an important role in time series analysis. This section describes the widely used classical decomposition model and the class of autoregressive moving average (ARMA) models which provide a general framework for studying stationary processes. In addition to the theoretical discussion, a practical example is presented to illustrate the approach followed in this thesis to time series modelling. A more detailed discussion of the algorithms introduced in this section can be found, for example, in Kendall and Ord (1990), Brockwell and Davis (2002), Broersen (2006) and Box et al.

34) = Cor(Xt+h , Xt ). γX (0) The ACF is symmetrical about the origin where it attains its maximum value of one. Most physical processes have an ACF decreasing in absolute value with an increasing lag. This means that the relation between Xt at a short temporal distance is stronger than that over a longer distance. Rapidly decaying ACF values as |h| increases indicate short-term dependency, while slowly decaying ACF values suggest the presence of long-term dependency. In practical problems, one may not start directly with a model, but with observed time series data {x1 , x2 , .

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