Seismic data deconvolution using Kalman filter based on a new system model

Geophysics ◽  
2016 ◽  
Vol 81 (1) ◽  
pp. V31-V42
Author(s):  
Xiaoying Deng ◽  
Zhengjun Zhang ◽  
Dinghui Yang
Keyword(s):  
Kalman Filter ◽  
Wiener Filter ◽  
System Model ◽  
Filter Model ◽  
New Model ◽  
Nonstationary Signals ◽  
Seismic Wavelet ◽  
Seismic Resolution ◽  
Resolution Improvement ◽  
Reflectivity Function

Seismic resolution plays an important role in geologic interpretation and reservoir prediction. To improve the vertical resolution of a seismic image, we have developed a new Kalman filter system model for seismic deconvolution. Similar to the conventional Kalman filter model for seismic deconvolution, our new Kalman model is also based on the common viewpoint that a reflected seismic record can be regarded as a convolution of a seismic wavelet with a reflection coefficient series. The new model uses a reversed seismic wavelet to slide across a reflectivity function to achieve the convolution result, instead of using a reversed reflectivity function to slide across a seismic wavelet in the conventional Kalman filter model. A simpler state equation for the new model is achieved, and the number of parameters to select is fewer than the conventional. Furthermore, the number of parameters can be reduced to only one by a theoretical demonstration for stationary noisy signals, which decreases the requirement for multiple parameters selection in the conventional model. The practical selection for this parameter should be a compromise between resolution improvement and noise amplification. Experimental results in the time and frequency domains on synthetic and field seismic records revealed that the Kalman filter based on the new model has the advantages of a higher resolution and peak signal-to-noise ratio (PS/N) than the conventional Kalman filter for stationary and nonstationary signals, and it works similarly to the Wiener filter for stationary signals, and it is superior to the Wiener filter in resolution and PS/N for nonstationary signals. The Kalman filter based on the new model can be applied to seismic resolution improvement.

A KALMAN FILTER APPROACH TO THE DECONVOLUTION OF SEISMIC SIGNALS

Geophysics ◽  
1974 ◽  
Vol 39 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Norman D. Crump
Keyword(s):  
Kalman Filter ◽  
Wiener Filter ◽  
Seismic Signal ◽  
Seismic Signals ◽  
Discrete State ◽  
Seismic Wavelet ◽  
State Variable ◽  
Deconvolution Technique ◽  
Reflectivity Function ◽  
Filter Approach

It is common practice to model a reflection seismogram as a convolution of the reflectivity function of the earth and an energy waveform referred to as the seismic wavelet. The objective of the deconvolution technique described here is to extract the reflectivity function from the reflection seismogram. The most common approach to deconvolution has been the design of inverse filters based on Wiener filter theory. Some of the disadvantages of the inverse filter approach may be overcome by using a state variable representation of the earth’s reflectivity function and the seismic signal generating process. The problem is formulated in discrete state variable form to facilitate digital computer processing of digitized seismic signals. The discrete form of the Kalman filter is then used to generate an estimate of the reflectivity function. The principal advantages of this technique are its capability for handling continually time‐varying models, its adaptability to a large class of models, its suitability for either single or multi‐channel processing, and its potentially high‐resolution capabilities. Examples based on both synthetic and field seismic data illustrate the feasibility of the method.

scholarly journals Sistem Navigasi Quadrotor Berbasis IMU dengan Kalman Filter

ELKHA ◽  
2019 ◽  
Vol 11 (1) ◽  
pp. 39
Author(s):  
Lasmadi Lasmadi
Keyword(s):  
Kalman Filter ◽  
Navigation System ◽  
Measurement Accuracy ◽  
State Space Model ◽  
System Model ◽  
Test Results ◽  
Position Measurement ◽  
Filter Model ◽  
Space Model ◽  
Navigation Data

The navigation system on quadrotor is important to maintain stability and determine its own position when flying autonomously. The GPS can provide the position measurement, but it has limitations in the specific environments and cannot provide the orientation information. This study aims to design the navigation system for quadrotor based on IMU sensor with Kalman filters using the state space model. The system model was developed using Matlab software. Kalman filter is designed to estimate the navigation data and eliminate noise on the sensor so that it can improve the measurement accuracy. The test results showed that the system model can provide orientation estimation and translation estimation of the quadrotor, while the Kalman filter model is acceptable to reduce noise on the sensor's raw data. When tested indoors, the system can provide the measurement accuracy above 90%.

Multi-day flow forecasting using the Kalman filter

1991 ◽  
Vol 18 (2) ◽  
pp. 320-327 ◽  
Author(s):  
Murray A. Fitch ◽  
Edward A. McBean
Keyword(s):  
Kalman Filter ◽  
Prediction Model ◽  
Linear Prediction ◽  
Measured Data ◽  
System Model ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Forecasting Performance ◽  
Optimal Forecasting ◽  
Linear Prediction Model

A model is developed for the prediction of river flows resulting from combined snowmelt and precipitation. The model employs a Kalman filter to reflect uncertainty both in the measured data and in the system model parameters. The forecasting algorithm is used to develop multi-day forecasts for the Sturgeon River, Ontario. The algorithm is shown to develop good 1-day and 2-day ahead forecasts, but the linear prediction model is found inadequate for longer-term forecasts. Good initial parameter estimates are shown to be essential for optimal forecasting performance. Key words: Kalman filter, streamflow forecast, multi-day, streamflow, Sturgeon River, MISP algorithm.

Maximum Correntropy Criterion Constrained Kalman Filter

2017 ◽  
Author(s):  
Seyed Fakoorian ◽  
Mahmoud Moosavi ◽  
Reza Izanloo ◽  
Vahid Azimi ◽  
Dan Simon
Keyword(s):  
Kalman Filter ◽  
Gaussian Noise ◽  
State Constraints ◽  
Statistical Information ◽  
Second Order ◽  
System Model ◽  
Error Covariance ◽  
Inequality State ◽  
Maximum Correntropy Criterion ◽  
Non Gaussian

Non-Gaussian noise may degrade the performance of the Kalman filter because the Kalman filter uses only second-order statistical information, so it is not optimal in non-Gaussian noise environments. Also, many systems include equality or inequality state constraints that are not directly included in the system model, and thus are not incorporated in the Kalman filter. To address these combined issues, we propose a robust Kalman-type filter in the presence of non-Gaussian noise that uses information from state constraints. The proposed filter, called the maximum correntropy criterion constrained Kalman filter (MCC-CKF), uses a correntropy metric to quantify not only second-order information but also higher-order moments of the non-Gaussian process and measurement noise, and also enforces constraints on the state estimates. We analytically prove that our newly derived MCC-CKF is an unbiased estimator and has a smaller error covariance than the standard Kalman filter under certain conditions. Simulation results show the superiority of the MCC-CKF compared with other estimators when the system measurement is disturbed by non-Gaussian noise and when the states are constrained.

Online Dynamic Response Reconstruction in the Presence of Observation Outliers

2021 ◽  
Author(s):  
Chaodong Zhang ◽  
Jian’an Li ◽  
Youlin Xu
Keyword(s):  
Kalman Filter ◽  
Dynamic Response ◽  
Numerical Study ◽  
Frame Structure ◽  
System Model ◽  
Measurement Information ◽  
Model Errors ◽  
Process Noise ◽  
Robust Kalman Filter ◽  
Response Reconstruction

Previous studies show that Kalman filter (KF)-based dynamic response reconstruction of a structure has distinct advantages in the aspects of combining the system model with limited measurement information and dealing with system model errors and measurement Gaussian noises. However, because the recursive KF aims to achieve a least-squares estimate of state vector by minimizing a quadratic criterion, observation outliers could dramatically deteriorate the estimator’s performance and considerably reduce the response reconstruction accuracy. This study addresses the KF-based online response reconstruction of a structure in the presence of observation outliers. The outlier-robust Kalman filter (OKF), in which the outlier is discerned and reweighted iteratively to achieve the generalized maximum likelihood (ML) estimate, is used instead of KF for online dynamic response reconstruction. The influences of process noise and outlier duration to response reconstruction are investigated in the numerical study of a simple 5-story frame structure. The experimental work on a simply-supported overhanging steel beam is conducted to testify the effectiveness of the proposed method. The results demonstrate that compared with the KF-based response reconstruction, the proposed OKF-based method is capable of dealing with the observation outliers and producing more accurate response construction in presence of observation outliers.

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