By Xiaoguang Luo
Global Navigation satellite tv for pc structures (GNSS), reminiscent of GPS, became a good, trustworthy and conventional device for quite a lot of purposes. although, while processing GNSS information, 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 should be successfully defined through autoregressive relocating ordinary (ARMA) techniques. moreover, this paintings comprises an up to date assessment of the GNSS errors results and a entire description of assorted mathematical tools.
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Additional info for GPS Stochastic Modelling: Signal Quality Measures and ARMA Processes
Examining Fig. 3b, the frequencies that have not been considered in the course of harmonic regression illustrate significant noise amplitude spectra. Furthermore, the advantages of the empirical averaging over the harmonic regression are clearly visible at the frequencies of twice and six times per year. In addition to the annual and sub-annual periodicities, the first significant peak in Fig. 7 years) indicates a long-periodic signal, which may be attributed to an artefact without a realistic background (Fischer et al.
Two methods are briefly described in the following text. The first one solves a set of homogenous linear difference equations (Brockwell and Davis 2002, p. 90), while the second determines the ACVF of an ARMA process as a convolution of the separate autocovariances of the AR and MA components (Broersen 2006, p. 74). First Method. 2 Time Series Analysis 21 ∞ j where ∞ j=0 ψj < ∞ and (r) = j=0 ψj r (Brockwell and Davis 2002, p. 85). Regarding Eqs. 49), ψj can be determined based on the relation (r) = Bq (r)/Ap (r), or equivalently by the identity (1 + a1 r + · · · + ap r p )(ψ0 + ψ1 r + · · · ) = 1 + b1 r + · · · + bq r q .
2005, Chap. 4). The Cox-Stuart (CT) test relies upon the simple principle that a data series exhibits an upward (downward) trend if the earlier observations tend to be smaller (larger) than the later ones (Cox and Stuart 1955). The test statistic TCT is defined as the number of positive differences yi , given by yi = xi+m − xi , i = 1, . . , m m = n/2, if n is even, 1, . . , m − 1 m = (n + 1)/2, if n is odd. 74) In fact, TCT follows a binomial distribution TCT ∼ Bin(L, p) with p = 1/2, where L denotes the number of non-zero yi .