On the determination of the atmospheric outer scale length of turbulence using GPS phase difference observations : The Seewinkel network

Microwave electromagnetic signals from the Global Navigation Satellite System (GNSS) are affected by their travel through the atmosphere: the troposphere, a non-dispersive medium, has an especial impact on the measurements. The long-term variations of the tropospheric refractive index delay the signals, whereas its random variations correlate with the phase measurements. The correlation structure of residuals from GNSS relative position estimation provides a unique opportunity to study specific properties of the turbulent atmosphere. Prior to such a study, the residuals have to be filtered from unwanted additional effects, such as multipath. In this contribution, we propose to investigate the property of the atmospheric noise by using a new methodology combining the empirical mode decomposition with the Hilbert–Huang transform. The chirurgical “designalling of the noise” aims to filter both the white noise and low-frequency noise to extract only the noise coming from tropospheric turbulence. Further analysis of the power spectrum of phase difference can be performed, including the study of the cut-off frequencies and the two slopes of the power spectrum of phase differences. The obtained values can be compared with theoretical expectations. In this contribution, we use Global Positioning System (GPS) phase observations from the Seewinkel network, specially designed to study the impact of atmospheric turbulence on GPS phase observations. We show that (i) a two-slope power spectrum can be found in the residuals and (ii) that the outer scale length can be taken to a constant value, close to the physically expected one and in relation with the size of the eddies at tropospheric height.[Figure not available: see fulltext.] © 2020, The Author(s)

Noise behavior in CGPS position time series : the eastern North America case study

We analyzed the noise characteristics of 112 continuously operating GPS stations in eastern North America using the Spectral Analysis and the Maximum Likelihood Estimation (MLE) methods. Results of both methods show that the combination ofwhite plus flicker noise is the best model for describing the stochastic part of the position time series. We explored this further using the MLE in the time domain by testing noise models of (a) powerlaw, (b)white, (c)white plus flicker, (d)white plus randomwalk, and (e) white plus flicker plus random-walk. The results show that amplitudes of all noise models are smallest in the north direction and largest in the vertical direction. While amplitudes of white noise model in (c–e) are almost equal across the study area, they are prevailed by the flicker and Random-walk noise for all directions. Assuming flicker noise model increases uncertainties of the estimated velocities by a factor of 5–38 compared to the white noise model

Extracting white noise statistics in GPS coordinate time series

The noise in GPS coordinate time series is known to follow a power-law noise model with different components (white noise, flicker noise, and random walk). This work proposes an algorithm to estimate the white noise statistics, through the decomposition of the GPS coordinate time series into a sequence of sub time series using the empirical mode decomposition algorithm. The proposed algorithm estimates the Hurst parameter for each sub time series and then selects the sub time series related to the white noise based on the Hurst parameter criterion. Both simulated GPS coordinate time series and real data are employed to test this new method; the results are compared to those of the standard (CATS software) maximum-likelihood (ML) estimator approach. The results demonstrate that this proposed algorithm has very low computational complexity and can be more than 100 times faster than the CATS ML method, at the cost of a moderate increase of the uncertainty (∼ 5%) of the white noise amplitude. Reliable white noise statistics are useful for a range of applications including improving the filtering of GPS time series, checking the validity of estimated coseismic offsets, and estimating unbiased uncertainties of site velocities. The low complexity and computational efficiency of the algorithm can greatly speed up the processing of geodetic time series

Análise das características de ruído em séries temporais GPS

Tese de mestrado em Engenharia Geográfica, apresentada à Universidade de Lisboa, através da Faculdade de Ciências, 2013A presença de ruído em séries temporais produz efeitos significativos sobre as incertezas das velocidades baseadas nessas séries e é, por isso, importante contabilizar o ruído existente numa série, de forma a avaliar a magnitude do seu efeito, relacionando as incertezas com as amplitudes de ruído. As séries temporais apresentam fontes de erros que evidenciam a presença de ruído branco juntamente com ruído colorido (temporalmente correlacionado). Este estudo avaliou as características do ruído de um conjunto de 55 séries temporais de posições semanais estimadas a partir de dados obtidos com o Sistema de Posicionamento Global (GPS - Global Positioning System), de estações localizadas em Portugal e Espanha. Para caracterizar o ruído presente nas séries temporais foram utilizados diversos modelos de ruído e combinações de modelos de ruído, que permitiram estudar e comparar os processos de ruído estocásticos em séries temporais contínuas, apontar qual o melhor modelo ou combinação que descreve o ruído presente nas séries observadas e simultaneamente determinar incertezas mais próximas da realidade para a velocidade da estação. As amplitudes de ruído das séries temporais obtidas para cada uma das componentes indicaram que a combinação de ruído branco com ruído rosa é a que melhor descreve o ruído presente na série, indicando que, em séries temporais de coordenadas GPS, o ruído branco não é dominante. Quando o índice espectral não é especificado, é necessário determinar o índice que minimiza o ruído para cada série. Verificou-se que os menores valores de ruído são estimados com os maiores índices espectrais e a média dos diversos índices espectrais calculados para as três componentes aponta o índice de -0.97 para alcançar o menor ruído. Correlacionando as incertezas de velocidade obtidas pelo modelo de ruído branco e pela combinação de modelos de ruído branco com ruído rosa, foi possível determinar um factor que permite relacionar as incertezas das velocidades entre esses modelos. Nesse sentido, conclui-se que as incertezas baseadas num modelo de ruído branco com ruído rosa são cerca de 3.3 vezes superiores às obtidas com base num modelo de ruído branco.The presence of noise in time series produces meaningful effects in the uncertainties of the velocities based on those series. Therefore, it is important to evaluate the noise in a series, in order to access the magnitude of its effect, and to relate the velocities uncertainties with the noise amplitudes. The time series presents error sources that show the presence of white noise with coloured noise (time correlated). In this dissertation, the noise characteristics of a set of 55 time series of weekly positions based on Global Positioning System (GPS) data for stations located in Portugal and in Spain are evaluated. To characterize the noise present in the time series were used several noise models and combinations of noise models that allowed to study and to compare the stochastic noise processes in continued time series, to indicate the best model or combination that describes the noise present in the observed series, and simultaneously to determinate the realistic uncertainties of the station velocity. The obtained noise amplitude of the time series for each of the components indicated that the combined white noise with flicker noise is the one that best describes the noise present in the series, indicating that the white noise is not dominant in GPS coordinate time series. When the spectral index is not specified, it is essential determinate the index that minimizes the noise for each time series. It was verified that lower values of noise are estimated with higher spectral index and the average of the several calculated spectral index to the three components, indicates the -0.97 rate to obtain the lower noise. Correlating the uncertainties of velocity obtained by the white noise and by the combined models of white noise and flicker noise, it was possible to establish a relation between the uncertainties of the velocity for the different models. Accordingly, it is concluded that the uncertainties of the velocities based on a combination of white noise and flicker noise are about 3.3 times higher than those based on white noise only