Limited constraint, robust Kalman filtering for GNSS troposphere tomography

Rohm, Witold; Zhang, Kefei; Bosy, Jarosław

doi:10.5194/amt-7-1475-2014

Cited by 62 publications

(66 citation statements)

References 29 publications

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“…In this case, the covariance of fitted parameters is estimated with equation (5) and the error of each individual ZTD sample is the only one that influences the results. Then, a combination of power-law (PL) and white (WH) noise process is implemented for which a covariance matrix of observations C is computed as: (10) where a and b are the amplitudes of the WH and PL noise processes, while I and J k are the covariance matrices of white and 30 colored noise, respectively (Williams et al, 2003). We completed our analysis with autoregressive fractionally integrated moving average noise model (ARFIMA) of varying orders: p, d and q of AR, FI and MA, respectively.…”

Section: Noise Analysis Of Ztdmentioning

confidence: 99%

Noise characteristics in Zenith Total Delay from homogeneously reprocessed GPS time series

Kłos

Hunegnaw

Teferle

et al. 2016

Preprint

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Abstract. Zenith Total Delay (ZTD) time series, derived from the re-processing of Global Positioning System (GPS) data, provide valuable information for the evaluation of global atmospheric reanalysis products such as ERA-Interim. Identifying 10 the correct noise characteristics in the ZTD time series is an important step to assess the 'true' magnitude of ZTD trend uncertainties. The ZTD residual time series for 1995-2015 are generated from our homogeneously re-processed and homogenized GPS time series from over 700 globally distributed stations classified into five major climate zones. The annual peak of ZTD data ranges between 10 and 150 mm with the smallest values for the polar and Alpine zone. The amplitudes of daily curve fall between 0 and 12 mm with the greatest variations for the dry zone. The autoregressive process 15 of fourth order plus white noise model were found to be optimal for ZTD series. The tropical zone has the largest amplitude of autoregressive noise (9.59 mm) and the greatest amplitudes of white noise (13.00 mm). All climate zones have similar median coefficients of AR(1) (0.80±0.05) with a minimum for polar and Alpine, which has the highest coefficients of AR (2) (0.27±0.01) and AR(3) (0.11±0.01) and clearly different from the other zones considered. We show that 53 of 120 examined trends became insignificant, when the optimum noise model was employed, compared to 11 insignificant trends for pure 20 white noise. The uncertainty of the ZTD trends may be underestimated by a factor of 3 to 12 compared to the white noise only assumption.

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Section: Noise Analysis Of Ztdmentioning

confidence: 99%

Noise characteristics in Zenith Total Delay from homogeneously reprocessed GPS time series

Kłos

Hunegnaw

Teferle

et al. 2016

Preprint

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“…The problem becomes worse when the GNSS network is flat [21]. To solve this problem, additional constraints or a priori information are usually used [9,16,17,21,28]. Three kinds of constraints are usually added:…”

Section: General Methods and Existing Problemsmentioning

confidence: 99%

“…The GNSS meteorological data include only surface temperature, humidity and pressure. We first used the Wexler formulations [34,35] to calculate vapor pressure from radiosonde and GNSS meteorological data and then calculated the WR according to Equation (16). We used the derived wet refractivity to establish a priori information equations according to Equation (8).…”

Section: Comparisons Between Adaptive Smoothing and Constant Smoothingmentioning

confidence: 99%

“…Flores et al proposed using horizontal smoothing, vertical smoothing and boundary conditions to solve the ill-posed problem and use the singular value decomposition to solve the inversion problem [9]. This method has been developed by many other scientists for troposphere tomography [12][13][14][15][16][17]. Other approaches to retrieve the 3D WV include algebraic reconstruction techniques [18,19] and estimating WV directly from raw GPS phase observations [20].…”

Section: Introductionmentioning

confidence: 99%

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An Improved Tomography Approach Based on Adaptive Smoothing and Ground Meteorological Observations

et al. 2017

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Using the Global Navigation Satellite System (GNSS) to sense three-dimensional water vapor (WV) has been intensively investigated. However, this technique still heavily relies on the a priori information. In this study, we propose an improved tomography approach based on adaptive Laplacian smoothing (ALS) and ground meteorological observations. By using the proposed approach, the troposphere tomography is less dependent on a priori information and the ALS constraints match better with the actual situation than the constant constraints. Tomography experiments in Hong Kong during a heavy rainy period and a rainless period show that the ALS method gets superior results compared with the constant Laplacian smoothing (CLS) method. By validation with radiosonde and European Centre for Medium-Range Weather Forecasts (ECMWF) data, we found that the introduction of ground meteorological observations into tomography can solve the perennial problem of resolving the wet refractivity in the lower troposphere and thus significantly improve the tomography results. However, bad data quality and incompatibility of the ground meteorological observations may introduce errors into tomography results.

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“…However, some limitations in the tomographic technique still have not been resolved (Bender et al, 2009;Bender and Raabe, 2007;Rohm et al, 2014). In the tomographic approach, the probed space is usually discretized into a number of 3-D closed voxels.…”

Section: Introductionmentioning

confidence: 99%

Assessing the performance of troposphere tomographic modeling using multi-source water vapor data during Hong Kong's rainy season from May to October 2013

Chen

Liu

2016

Atmos. Meas. Tech.

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Abstract. Acquiring accurate atmospheric water vapor spatial information remains one of the most challenging tasks in meteorology. The tomographic technique is a powerful tool for modeling atmospheric water vapor and monitoring the water vapor spatial and temporal distribution/variation information. This paper presents a study on the monitoring of water vapor variations using tomographic techniques based on multi-source water vapor data, including GPS (Global Positioning System), radiosonde, WVR (water vapor radiometer), NWP (numerical weather prediction), AERONET (AErosol RObotic NETwork) sun photometer and synoptic station measurements. An extensive investigation has been carried out using multi-source data collected from May to October 2013 in Hong Kong. With the use of radiosonde observed profiles, five different vertical a priori information schemes were designed and examined. Analysis results revealed that the best vertical constraint is to employ the average radiosonde profiles over the 3 days prior to the tomographic time and that the assimilation of multi-source data can increase the tomography modeling accuracy. Based on the best vertical a priori information scheme, comparisons of slant wet delay (SWD) measurements between GPS data and multi-observational tomography showed that the root mean square error (RMSE) of their differences is 10.85 mm. Multi-observational tomography achieved an accuracy of 7.13 mm km −1 when compared with radiosonde wet refractivity observations. The vertical layer tomographic modeling accuracy was also assessed using radiosonde water vapor profiles. An accuracy of 11.44 mm km −1 at the lowest layer (0-0.4 km) and an RMSE of 3.30 mm km −1 at the uppermost layer (7.5-8.5 km) were yielded. At last, a test of the tomographic modeling in a torrential storm occurring on 21-22 May 2013 in Hong Kong demonstrated that the tomographic modeling is very robust, even during severe precipitation conditions.

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Limited constraint, robust Kalman filtering for GNSS troposphere tomography

Cited by 62 publications

References 29 publications

Noise characteristics in Zenith Total Delay from homogeneously reprocessed GPS time series

Noise characteristics in Zenith Total Delay from homogeneously reprocessed GPS time series

An Improved Tomography Approach Based on Adaptive Smoothing and Ground Meteorological Observations

Assessing the performance of troposphere tomographic modeling using multi-source water vapor data during Hong Kong's rainy season from May to October 2013

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