The effect of stochastic gravity models in airborne vector gravimetry

Geophysics ◽  
2002 ◽  
Vol 67 (3) ◽  
pp. 770-776 ◽  
Author(s):  
Jay Hyoun Kwon ◽  
Christopher Jekeli
Keyword(s):  
Stochastic Model ◽  
Traditional Approach ◽  
A Priori ◽  
Vertical Component ◽  
Optimal Estimation ◽  
Gravity Models ◽  
Gravity Vector ◽  
Gravity Disturbance ◽  
Gravitational Vector ◽  
Vector Gravimetry

Measurements of specific force using inertial measurement units (IMU) combined with Global Positioning System (GPS) accelerometry can be used on an airborne platform to determine the total gravitational vector. Traditional methods, originating with inertial surveying systems and based on Kalman filtering, rely on choosing an appropriate stochastic model for the gravity disturbance components included in the set of system error states. An alternative procedure that uses no a priori stochastic model has proven to be as effective, or moreso, in extracting the gravity vector from airborne IMU/GPS data. This method is based on inspecting acceleration residuals from a Kalman filter that estimates only sensor biases. Using actual data collected over the Canadian Rocky Mountains, this method was compared to the traditional approach adapted for different types of stochastic models for the gravity disturbance vector. In all test cases, the estimation filter without a gravitational model yielded better results—up to 50%. This implies that accurate gravity vector determination from airborne IMU/GPS need not rely on an a priori stochastic model of the field, even though the theory of optimal estimation requests it. However, no filter was able to remove all systematic errors from the data; these remaining errors could only be reduced by elementary methods such as endpoint matching and correlative processing of adjacent passes of the system over the gravity field. The final, best gravity estimates had standard deviations with respect to control data of 6 mGal in the horizontal components and 3–4 mGal in the vertical component.

Using spherical scaling functions in scalar and vector airborne gravimetry

2020 ◽  
Author(s):  
Vadim Vyazmin ◽  
Yuri Bolotin
Keyword(s):  
Gravity Model ◽  
Kalman Filtering ◽  
A Priori ◽  
Systematic Errors ◽  
Airborne Gravimetry ◽  
Survey Area ◽  
Gravity Disturbance ◽  
Airborne Measurements ◽  
Disturbance Vector ◽  
Vector Gravimetry

<p>Airborne gravimetry is capable to provide Earth’s gravity data of high accuracy and spatial resolution for any area of interest, in particular for hard-to-reach areas. An airborne gravimetry measuring system consists of a stable-platform or strapdown gravimeter, and GNSS receivers. In traditional (scalar) airborne gravimetry, the vertical component of the gravity disturbance vector is measured. In actively developing vector gravimetry, all three components of the gravity disturbance vector are measured.</p><p>In this research, we aim at developing new postprocessing algorithms for estimating gravity from airborne data taking into account a priori information about spatial behavior of the gravity field in the survey area. We propose two algorithms for solving the following two problems:</p><p>1) <em>In scalar gravimetry:</em>  Mapping gravity at the flight height using the gravity disturbances estimated along the flight lines (via low-pass or Kalman filtering), taking into account spatial correlation of the gravity field in the survey area and statistical information on the along-line gravity estimate errors.</p><p>2) <em>In vector gravimetry:</em>  Simultaneous determination of three components of the gravity disturbance vector from airborne measurements at the flight path.</p><p>Both developed algorithms use an a priori spatial gravity model based on parameterizing the disturbing potential in the survey area by three-dimensional harmonic spherical scaling functions (SSFs). The algorithm developed for solving Problem 1 provides estimates of the unknown coefficients of the a priori gravity model using a least squares technique. Due to the assumption that the along-line gravity estimate errors at any two lines are not correlated, the algorithm has a recursive (line-by-line) implementation. At the last step of the recursion, regularization is applied due to ill-conditioning of the least squares problem. Numerical results of processing the GT-2A airborne gravimeter data are presented and discussed.</p><p>To solve Problem 2, one need to separate the gravity horizontal component estimates from systematic errors of the inertial navigation system (INS) of a gravimeter (attitude errors, inertial sensor bias). The standard method of gravity estimation based on gravity modelling over time is not capable to provide accurate results, and additional corrections should be applied. The developed algorithm uses a spatial gravity model based on the SSFs. The coefficients of the gravity model and the INS systematic errors are estimated simultaneously from airborne measurements at the flight path via Kalman filtering with regularization at the last time moment. Results of simulation tests show a significant increase in accuracy of gravity vector estimation compared to the standard method.</p><p>This research was supported by RFBR (grant number 19-01-00179).</p>

scholarly journals Ozone profile smoothness as a priori information in the inversion of limb measurements

2004 ◽  
Vol 22 (10) ◽  
pp. 3411-3420 ◽  
Author(s):  
V. F. Sofieva ◽  
J. Tamminen ◽  
H. Haario ◽  
E. Kyrölä ◽  
M. Lehtinen
Keyword(s):  
A Priori ◽  
Optimal Estimation ◽  
Maximum A Posteriori ◽  
A Posteriori ◽  
A Priori Information ◽  
Ozone Profile ◽  
Stellar Occultation ◽  
Atmospheric Profiles ◽  
Priori Information ◽  
Typical Measurement

Abstract. In this work we discuss inclusion of a priori information about the smoothness of atmospheric profiles in inversion algorithms. The smoothness requirement can be formulated in the form of Tikhonov-type regularization, where the smoothness of atmospheric profiles is considered as a constraint or in the form of Bayesian optimal estimation (maximum a posteriori method, MAP), where the smoothness of profiles can be included as a priori information. We develop further two recently proposed retrieval methods. One of them - Tikhonov-type regularization according to the target resolution - develops the classical Tikhonov regularization. The second method - maximum a posteriori method with smoothness a priori - effectively combines the ideas of the classical MAP method and Tikhonov-type regularization. We discuss a grid-independent formulation for the proposed inversion methods, thus isolating the choice of calculation grid from the question of how strong the smoothing should be. The discussed approaches are applied to the problem of ozone profile retrieval from stellar occultation measurements by the GOMOS instrument on board the Envisat satellite. Realistic simulations for the typical measurement conditions with smoothness a priori information created from 10-years analysis of ozone sounding at Sodankylä and analysis of the total retrieval error illustrate the advantages of the proposed methods. The proposed methods are equally applicable to other profile retrieval problems from remote sensing measurements.

scholarly journals A practical information-centered technique to remove a priori information from lidar optimal-estimation-method retrievals

2019 ◽  
Vol 12 (7) ◽  
pp. 3943-3961 ◽  
Author(s):  
Ali Jalali ◽  
Shannon Hicks-Jalali ◽  
Robert J. Sica ◽  
Alexander Haefele ◽  
Thomas von Clarmann
Keyword(s):  
Water Vapor ◽  
A Priori ◽  
Estimation Method ◽  
Optimal Estimation ◽  
Mixing Ratio ◽  
A Priori Information ◽  
Fine Grid ◽  
Large Power ◽  
Priori Information ◽  
Water Vapor Mixing Ratio

Abstract. Lidar retrievals of atmospheric temperature and water vapor mixing ratio profiles using the optimal estimation method (OEM) typically use a retrieval grid with a number of points larger than the number of pieces of independent information obtainable from the measurements. Consequently, retrieved geophysical quantities contain some information from their respective a priori values or profiles, which can affect the results in the higher altitudes of the temperature and water vapor profiles due to decreasing signal-to-noise ratios. The extent of this influence can be estimated using the retrieval's averaging kernels. The removal of formal a priori information from the retrieved profiles in the regions of prevailing a priori effects is desirable, particularly when these greatest heights are of interest for scientific studies. We demonstrate here that removal of a priori information from OEM retrievals is possible by repeating the retrieval on a coarser grid where the retrieval is stable even without the use of formal prior information. The averaging kernels of the fine-grid OEM retrieval are used to optimize the coarse retrieval grid. We demonstrate the adequacy of this method for the case of a large power-aperture Rayleigh scatter lidar nighttime temperature retrieval and for a Raman scatter lidar water vapor mixing ratio retrieval during both day and night.

scholarly journals Synergy of stereo cloud top height and ORAC optimal estimation cloud retrieval: evaluation and application to AATSR

2016 ◽  
Vol 9 (3) ◽  
pp. 909-928 ◽  
Author(s):  
Daniel Fisher ◽  
Caroline A. Poulsen ◽  
Gareth E. Thomas ◽  
Jan-Peter Muller
Keyword(s):  
A Priori ◽  
Single Layer ◽  
Optimal Estimation ◽  
Open Water ◽  
A Priori Information ◽  
Cloud Parameters ◽  
Cloud Properties ◽  
Priori Information ◽  
Cloud Parameter ◽  
The Impact

Abstract. In this paper we evaluate the impact on the cloud parameter retrievals of the ORAC (Optimal Retrieval of Aerosol and Cloud) algorithm following the inclusion of stereo-derived cloud top heights as a priori information. This is performed in a mathematically rigorous way using the ORAC optimal estimation retrieval framework, which includes the facility to use such independent a priori information. Key to the use of a priori information is a characterisation of their associated uncertainty. This paper demonstrates the improvements that are possible using this approach and also considers their impact on the microphysical cloud parameters retrieved. The Along-Track Scanning Radiometer (AATSR) instrument has two views and three thermal channels, so it is well placed to demonstrate the synergy of the two techniques. The stereo retrieval is able to improve the accuracy of the retrieved cloud top height when compared to collocated Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO), particularly in the presence of boundary layer inversions and high clouds. The impact of the stereo a priori information on the microphysical cloud properties of cloud optical thickness (COT) and effective radius (RE) was evaluated and generally found to be very small for single-layer clouds conditions over open water (mean RE differences of 2.2 (±5.9) microns and mean COD differences of 0.5 (±1.8) for single-layer ice clouds over open water at elevations of above 9 km, which are most strongly affected by the inclusion of the a priori).

scholarly journals A Model of Gravity Vector Measurement Noise for Estimating Accelerometer Bias in Gravity Disturbance Compensation

Sensors ◽  
2018 ◽  
Vol 18 (3) ◽  
pp. 883 ◽  
Author(s):  
Junbo Tie ◽  
Juliang Cao ◽  
Lubing Chang ◽  
Shaokun Cai ◽  
Meiping Wu ◽  
...  
Keyword(s):  
Measurement Noise ◽  
Gravity Vector ◽  
Disturbance Compensation ◽  
Gravity Disturbance ◽  
Vector Measurement

scholarly journals Retrieval of temperature and water vapor profiles from radio occultation refractivity and bending angle measurements using an Optimal Estimation approach: a simulation study

2005 ◽  
Vol 5 (6) ◽  
pp. 1665-1677 ◽  
Author(s):  
A. von Engeln ◽  
G. Nedoluha
Keyword(s):  
Water Vapor ◽  
Radio Occultation ◽  
A Priori ◽  
Estimation Method ◽  
Lower Troposphere ◽  
Optimal Estimation ◽  
Pronounced Difference ◽  
Bending Angle ◽  
Advantages And Disadvantages ◽  
The Impact

Abstract. The Optimal Estimation Method is used to retrieve temperature and water vapor profiles from simulated radio occultation measurements in order to assess how different retrieval schemes may affect the assimilation of this data. High resolution ECMWF global fields are used by a state-of-the-art radio occultation simulator to provide quasi-realistic bending angle and refractivity profiles. Both types of profiles are used in the retrieval process to assess their advantages and disadvantages. The impact of the GPS measurement is expressed as an improvement over the a priori knowledge (taken from a 24h old analysis). Large improvements are found for temperature in the upper troposphere and lower stratosphere. Only very small improvements are found in the lower troposphere, where water vapor is present. Water vapor improvements are only significant between about 1 km to 7 km. No pronounced difference is found between retrievals based upon bending angles or refractivity. Results are compared to idealized retrievals, where the atmosphere is spherically symmetric and instrument noise is not included. Comparing idealized to quasi-realistic calculations shows that the main impact of a ray tracing algorithm can be expected for low latitude water vapor, where the horizontal variability is high. We also address the effect of altitude correlations in the temperature and water vapor. Overall, we find that water vapor and temperature retrievals using bending angle profiles are more CPU intensive than refractivity profiles, but that they do not provide significantly better results.

scholarly journals A method for improved SCIAMACHY CO2 retrieval in the presence of optically thin clouds

2010 ◽  
Vol 3 (1) ◽  
pp. 209-232 ◽  
Author(s):  
M. Reuter ◽  
M. Buchwitz ◽  
O. Schneising ◽  
J. Heymann ◽  
H. Bovensmann ◽  
...  
Keyword(s):  
Absorption Band ◽  
Near Infrared ◽  
A Priori ◽  
Optimal Estimation ◽  
Surface Flux ◽  
Co2 Absorption ◽  
Retrieval Scheme ◽  
Priori Information ◽  
Transfer Of Information

Abstract. An optimal estimation based retrieval scheme for satellite based retrievals of XCO2 (the dry air column averaged mixing ratio of atmospheric CO2) is presented enabling accurate retrievals also in the presence of thin clouds. The proposed method is designed to analyze near-infrared nadir measurements of the SCIAMACHY instrument in the CO2 absorption band at 1580 nm and in the O2-A absorption band at around 760 nm. The algorithm accounts for scattering in an optically thin cirrus cloud layer and at aerosols of a default profile. The scattering information is mainly obtained from the O2-A band and a merged fit windows approach enables the transfer of information between the O2-A and the CO2 band. Via the optimal estimation technique, the algorithm is able to account for a priori information to further constrain the inversion. Test scenarios of simulated SCIAMACHY sun-normalized radiance measurements are analyzed in order to specify the quality of the proposed method. In contrast to existing algorithms for SCIAMACHY retrievals, the systematic errors due to cirrus clouds with optical thicknesses up to 1.0 are reduced to values below 4 ppm for most of the analyzed scenarios. This shows that the proposed method has the potential to reduce uncertainties of SCIAMACHY retrieved XCO2 making this data product potentially useful for surface flux inverse modeling.

scholarly journals The GRAPE aerosol retrieval algorithm

2009 ◽  
Vol 2 (2) ◽  
pp. 679-701 ◽  
Author(s):  
G. E. Thomas ◽  
C. A. Poulsen ◽  
A. M. Sayer ◽  
S. H. Marsh ◽  
S. M. Dean ◽  
...  
Keyword(s):  
A Priori ◽  
Optimal Estimation ◽  
Effective Radius ◽  
Retrieval Algorithm ◽  
Surface Reflectance ◽  
Data Set ◽  
Cloud Parameters ◽  
Aerosol Retrieval ◽  
Retrieval Scheme ◽  
Theoretical Performance

Abstract. The aerosol component of the Oxford-Rutherford Aerosol and Cloud (ORAC) combined cloud and aerosol retrieval scheme is described and the theoretical performance of the algorithm is analysed. ORAC is an optimal estimation retrieval scheme for deriving cloud and aerosol properties from measurements made by imaging satellite radiometers and, when applied to cloud free radiances, provides estimates of aerosol optical depth at a wavelength of 550 nm, aerosol effective radius and surface reflectance at 550 nm. The aerosol retrieval component of ORAC has several incarnations – this paper addresses the version which operates in conjunction with the cloud retrieval component of ORAC (described by Watts et al., 1998), as applied in producing the Global Retrieval of ATSR Cloud Parameters and Evaluation (GRAPE) data-set. The algorithm is described in detail and its performance examined. This includes a discussion of errors resulting from the formulation of the forward model, sensitivity of the retrieval to the measurements and a priori constraints, and errors resulting from assumptions made about the atmospheric/surface state.

scholarly journals Use of a Maximum Entropy Method as a Regularization Technique during the Retrieval of Trace Gas Profiles from Limb Sounding Measurements

2006 ◽  
Vol 23 (12) ◽  
pp. 1657-1667 ◽  
Author(s):  
J. Steinwagner ◽  
G. Schwarz ◽  
S. Hilgers
Keyword(s):  
Maximum Entropy ◽  
Random Noise ◽  
A Priori ◽  
Michelson Interferometer ◽  
Simulated Data ◽  
Optimal Estimation ◽  
Initial Guess ◽  
Entropy Method ◽  
Trace Gas ◽  
Regularization Techniques

Abstract The retrieval of trace gas profiles from radiance measurements of limb sounding instruments represents an inverse problem: vertical profiles of mixing ratios have to be extracted from sequences of horizontally measured radiances recorded by a spectrometer. Typically, these retrievals are plagued by random noise and systematic errors, necessitating the use of regularization techniques during inversion calculations. In the following, the use of selected maximum entropy operators as a regularization tool is discussed and their performance with conventional optimal estimation and Tikhonov-type regularization techniques is compared. The main gain with the proposed maximum entropy operators is that no a priori knowledge is needed; a reasonable initial guess profile is fully sufficient. The approach is verified by using simulated data of the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) instrument, an infrared Fourier transform spectrometer flown on the European Envisat mission.

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