scholarly journals Simultaneous Estimation of Microphysical Parameters and the Atmospheric State Using Simulated Polarimetric Radar Data and an Ensemble Kalman Filter in the Presence of an Observation Operator Error

2010 ◽  
Vol 138 (2) ◽  
pp. 539-562 ◽  
Author(s):  
Youngsun Jung ◽  
Ming Xue ◽  
Guifu Zhang
Keyword(s):  
Parameter Estimation ◽  
Kalman Filter ◽  
State Estimation ◽  
Radar Data ◽  
The State ◽  
Polarimetric Radar ◽  
Observation Operator ◽  
Operator Error ◽  
Microphysical Parameters ◽  
Positive Impacts

Abstract The impacts of polarimetric radar data on the estimation of uncertain microphysical parameters are investigated through observing system simulation experiments when the effects of uncertain parameters on the observation operators are also considered. Five fundamental microphysical parameters (i.e., the intercept parameters of rain, snow, and hail and the bulk densities of snow and hail) are estimated individually or collectively using the ensemble square root Kalman filter. The differential reflectivity ZDR, specific differential phase KDP, and radar reflectivity at horizontal polarization ZH are used individually or in combinations for the parameter estimation while the radial velocity and ZH are used for the state estimation. In the process, the parameter values estimated in the previous analysis cycles are used in the forecast model and in observation operators in the ensuing assimilation cycle. Analyses are first performed that examine the sensitivity of various observations to the microphysical parameters with and without observation operator error. The results are used to help interpret the filter behaviors in parameter estimation. The experiments in which either a single or all five parameters contain initial errors reveal difficulties in estimating certain parameters using ZH alone when observation operator error is involved. Additional polarimetric measurements are found to be beneficial for both parameter and state estimation in general. It is found that the polarimetric data are more helpful when the parameter estimation is not very successful with ZH alone. Between ZDR and KDP, KDP is found to produce larger positive impacts on parameter estimation in general while ZDR is more useful in the estimation of the intercept parameter of hail. In the experiments that attempt to correct errors in all five parameters, the filter fails to correctly estimate the snow intercept parameter and the density with or without polarimetric data, seemingly due to the small sensitivity of the observations to these parameters and complications involving the observation operator error. When these two snow parameters are not corrected during the estimation process, the estimations of the other three parameters and of all of the state variables are significantly improved and the positive impacts of polarimetric data are larger than that of a five-parameter estimation. These results reveal the significant complexity of the estimation problem for a highly nonlinear system and the need for careful sensitivity analysis. The problem is potentially more challenging with real-data cases when unknown sources of model errors are inevitable.

scholarly journals Simultaneous Estimation of Microphysical Parameters and Atmospheric State with Simulated Radar Data and Ensemble Square Root Kalman Filter. Part II: Parameter Estimation Experiments

2008 ◽  
Vol 136 (5) ◽  
pp. 1649-1668 ◽  
Author(s):  
Mingjing Tong ◽  
Ming Xue
Keyword(s):  
Parameter Estimation ◽  
Kalman Filter ◽  
Radar Data ◽  
Filter Method ◽  
Simultaneous Estimation ◽  
Observation Data ◽  
Square Root ◽  
Model Errors ◽  
Microphysical Parameters

Abstract The ensemble Kalman filter method is applied to correct errors in five fundamental microphysical parameters that are closely involved in the definition of drop/particle size distributions of microphysical species in a commonly used single-moment ice microphysics scheme, for a model-simulated supercell storm, using radar data. The five parameters include the intercept parameters for rain, snow, and hail/graupel and the bulk densities of hail/graupel and snow. The ensemble square root Kalman filter (EnSRF) is employed for simultaneous state and parameter estimation. The five microphysical parameters are estimated individually or in different combinations starting from different initial guesses. A data selection procedure based on correlation information is introduced, which combined with variance inflation, effectively avoids the collapse of the spread of parameter ensemble, hence filter divergence. Parameter estimation results demonstrate, for the first time, that the ensemble-based method can be used to correct model errors in microphysical parameters through simultaneous state and parameter estimation, using radar reflectivity observations. When error exists in only one of the microphysical parameters, the parameter can be successfully estimated without exception. The estimation of multiple parameters is less reliable, mainly because the identifiability of the parameters becomes weaker and the problem might have no unique solution. The parameter estimation results are found to be very sensitive to the realization of the initial parameter ensemble, which is mainly related to the use of relatively small ensemble sizes. Increasing ensemble size generally improves the parameter estimation. The quality of parameter estimation also depends on the quality of observation data. It is also found that the results of state estimation are generally improved when simultaneous parameter estimation is performed, even when the estimated parameter values are not very accurate.

scholarly journals On Robust State Estimation of Gene Networks

2010 ◽  
Vol 2 ◽  
pp. 117959721000200 ◽  
Author(s):  
Chia-Hua Chuang ◽  
Chun-Liang Lin
Keyword(s):  
Parameter Estimation ◽  
Kalman Filter ◽  
Quantitative Analysis ◽  
State Estimation ◽  
Gene Networks ◽  
Gene Network ◽  
Biological Systems ◽  
Uncertain Process ◽  
Network Systems ◽  
Internal States

Gene networks in biological systems are not only nonlinear but also stochastic due to noise corruption. How to accurately estimate the internal states of the noisy gene networks is an attractive issue to researchers. However, the internal states of biological systems are mostly inaccessible by direct measurement. This paper intends to develop a robust extended Kalman filter for state and parameter estimation of a class of gene network systems with uncertain process noises. Quantitative analysis of the estimation performance is conducted and some representative examples are provided for demonstration.

The Analysis and Prediction of Microphysical States and Polarimetric Radar Variables in a Mesoscale Convective System Using Double-Moment Microphysics, Multinetwork Radar Data, and the Ensemble Kalman Filter

2014 ◽  
Vol 142 (1) ◽  
pp. 141-162 ◽  
Author(s):  
Bryan J. Putnam ◽  
Ming Xue ◽  
Youngsun Jung ◽  
Nathan Snook ◽  
Guifu Zhang
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Mesoscale Convective System ◽  
Radar Data ◽  
Cold Pool ◽  
Convective System ◽  
Polarimetric Radar ◽  
Microphysics Scheme ◽  
Mesoscale Convective ◽  
Double Moment

Abstract Doppler radar data are assimilated with an ensemble Kalman Filter (EnKF) in combination with a double-moment (DM) microphysics scheme in order to improve the analysis and forecast of microphysical states and precipitation structures within a mesoscale convective system (MCS) that passed over western Oklahoma on 8–9 May 2007. Reflectivity and radial velocity data from five operational Weather Surveillance Radar-1988 Doppler (WSR-88D) S-band radars as well as four experimental Collaborative and Adaptive Sensing of the Atmosphere (CASA) X-band radars are assimilated over a 1-h period using either single-moment (SM) or DM microphysics schemes within the forecast ensemble. Three-hour deterministic forecasts are initialized from the final ensemble mean analyses using a SM or DM scheme, respectively. Polarimetric radar variables are simulated from the analyses and compared with polarimetric WSR-88D observations for verification. EnKF assimilation of radar data using a multimoment microphysics scheme for an MCS case has not previously been documented in the literature. The use of DM microphysics during data assimilation improves simulated polarimetric variables through differentiation of particle size distributions (PSDs) within the stratiform and convective regions. The DM forecast initiated from the DM analysis shows significant qualitative improvement over the assimilation and forecast using SM microphysics in terms of the location and structure of the MCS precipitation. Quantitative precipitation forecasting skills are also improved in the DM forecast. Better handling of the PSDs by the DM scheme is believed to be responsible for the improved prediction of the surface cold pool, a stronger leading convective line, and improved areal extent of stratiform precipitation.

scholarly journals A Strong Tracking Mixed-Degree Cubature Kalman Filter Method and Its Application in a Quadruped Robot

Sensors ◽  
2020 ◽  
Vol 20 (8) ◽  
pp. 2251 ◽  
Author(s):  
Jikai Liu ◽  
Pengfei Wang ◽  
Fusheng Zha ◽  
Wei Guo ◽  
Zhenyu Jiang ◽  
...  
Keyword(s):  
Kalman Filter ◽  
State Estimation ◽  
Real Time ◽  
Quadruped Robot ◽  
The State ◽  
Estimation Accuracy ◽  
Robot System ◽  
Calculation Time ◽  
Motion State ◽  
Cubature Kalman Filter

The motion state of a quadruped robot in operation changes constantly. Due to the drift caused by the accumulative error, the function of the inertial measurement unit (IMU) will be limited. Even though multi-sensor fusion technology is adopted, the quadruped robot will lose its ability to respond to state changes after a while because the gain tends to be constant. To solve this problem, this paper proposes a strong tracking mixed-degree cubature Kalman filter (STMCKF) method. According to system characteristics of the quadruped robot, this method makes fusion estimation of forward kinematics and IMU track. The combination mode of traditional strong tracking cubature Kalman filter (TSTCKF) and strong tracking is improved through demonstration. A new method for calculating fading factor matrix is proposed, which reduces sampling times from three to one, saving significantly calculation time. At the same time, the state estimation accuracy is improved from the third-degree accuracy of Taylor series expansion to fifth-degree accuracy. The proposed algorithm can automatically switch the working mode according to real-time supervision of the motion state and greatly improve the state estimation performance of quadruped robot system, exhibiting strong robustness and excellent real-time performance. Finally, a comparative study of STMCKF and the extended Kalman filter (EKF) that is commonly used in quadruped robot system is carried out. Results show that the method of STMCKF has high estimation accuracy and reliable ability to cope with sudden changes, without significantly increasing the calculation time, indicating the correctness of the algorithm and its great application value in quadruped robot system.

scholarly journals Sensitivities of Quantitative Precipitation Forecasts for Typhoon Soudelor (2015) near Landfall to Polarimetric Radar Data Assimilation

2020 ◽  
Vol 12 (22) ◽  
pp. 3711
Author(s):  
Chih-Chien Tsai ◽  
Kao-Shen Chung
Keyword(s):  
Data Assimilation ◽  
Radar Data ◽  
Convective Precipitation ◽  
Polarimetric Radar ◽  
Differential Phase ◽  
Observation Operator ◽  
Quantitative Precipitation Forecasts ◽  
Series Of Experiments ◽  
Differential Reflectivity ◽  
Radar Data Assimilation

Based on the preciousness and uniqueness of polarimetric radar observations collected near the landfall of Typhoon Soudelor (2015), this study investigates the sensitivities of very short-range quantitative precipitation forecasts (QPFs) for this typhoon to polarimetric radar data assimilation. A series of experiments assimilating various combinations of radar variables are carried out for the purpose of improving a 6 h deterministic forecast for the most intense period. The results of the control simulation expose three sources of the observation operator errors, including the raindrop shape-size relation, the limitations for ice-phase hydrometeors, and the melting ice model. Nevertheless, polarimetric radar data assimilation with the unadjusted observation operator can still improve the analyses, especially rainwater, and consequent QPFs for this typhoon case. The different impacts of assimilating reflectivity, differential reflectivity, and specific differential phase are only distinguishable at the lower levels of convective precipitation areas where specific differential phase is found most helpful. The positive effect of radar data assimilation on QPFs can last three hours in this study, and further improvement can be expected by optimizing the observation operator in the future

Simultaneous and Iterative Estimation of Vehicle Ride Model States and Parameters

2019 ◽  
Author(s):  
Lakshmi Sampathraghavan ◽  
Krishnakumar Ramarathnam
Keyword(s):  
Parameter Estimation ◽  
State Estimation ◽  
Optimal Solution ◽  
Simulated Data ◽  
The State ◽  
Average Error ◽  
Iterative Estimation ◽  
Vehicle Systems ◽  
Safety Systems ◽  
Parameter Estimators

Abstract With advancements in vehicle electronics and growing focus on vehicle safety systems, state and parameter estimation has become a remarkable sphere of research. In this study, the vehicle vertical dynamics states and parameters were estimated simultaneously and iteratively with relevant vehicle responses. This was achieved through vehicle tests, designed to excite the corresponding vehicle states. A linear Kalman filter was used for state estimation. Vehicle parameters were obtained as a optimal solution using an optimization algorithm. With the help of multi-DOF vehicle ride model along with real vehicle measurements, the state and parameter estimators work concurrently to obtain the results. A cleat test was performed for a Sports Utility Vehicle (SUV) in IPG CarMaker® and in reality, for evaluation of the proposed framework. The state estimation results showed upto 93% correlation from simulated data and upto 81% correlation from real time measurements. Parameter estimation produced an average error of only 9.1%. This demonstrated the efficacy of the algorithm for use in vehicle systems.

scholarly journals Ellipsoidal and Gaussian Kalman Filter Model for Discrete-Time Nonlinear Systems

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1168 ◽  
Author(s):  
Ligang Sun ◽  
Hamza Alkhatib ◽  
Boris Kargoll ◽  
Vladik Kreinovich ◽  
Ingo Neumann
Keyword(s):  
Kalman Filter ◽  
Nonlinear Systems ◽  
State Estimation ◽  
Discrete Time ◽  
Probability Distributions ◽  
Nonlinear Problems ◽  
The State ◽  
Filter Model ◽  
Highly Nonlinear ◽  
Correction Step

In this paper, we propose a new technique—called Ellipsoidal and Gaussian Kalman filter—for state estimation of discrete-time nonlinear systems in situations when for some parts of uncertainty, we know the probability distributions, while for other parts of uncertainty, we only know the bounds (but we do not know the corresponding probabilities). Similarly to the usual Kalman filter, our algorithm is iterative: on each iteration, we first predict the state at the next moment of time, and then we use measurement results to correct the corresponding estimates. On each correction step, we solve a convex optimization problem to find the optimal estimate for the system’s state (and the optimal ellipsoid for describing the systems’s uncertainty). Testing our algorithm on several highly nonlinear problems has shown that the new algorithm performs the extended Kalman filter technique better—the state estimation technique usually applied to such nonlinear problems.

scholarly journals Performance and stochastic stability of the adaptive fading extended Kalman filter with the matrix forgetting factor

2016 ◽  
Vol 14 (1) ◽  
pp. 934-945
Author(s):  
Cenker Biçer ◽  
Levent Özbek ◽  
Hasan Erbay
Keyword(s):  
Kalman Filter ◽  
State Estimation ◽  
Extended Kalman Filter ◽  
Stochastic Systems ◽  
Estimation Error ◽  
The State ◽  
Forgetting Factor ◽  
The Matrix ◽  
Stochastic Framework ◽  
Theoretical Results

AbstractIn this paper, the stability of the adaptive fading extended Kalman filter with the matrix forgetting factor when applied to the state estimation problem with noise terms in the non–linear discrete–time stochastic systems has been analysed. The analysis is conducted in a similar manner to the standard extended Kalman filter’s stability analysis based on stochastic framework. The theoretical results show that under certain conditions on the initial estimation error and the noise terms, the estimation error remains bounded and the state estimation is stable.The importance of the theoretical results and the contribution to estimation performance of the adaptation method are demonstrated interactively with the standard extended Kalman filter in the simulation part.

Assimilation of Simulated Polarimetric Radar Data for a Convective Storm Using the Ensemble Kalman Filter. Part II: Impact of Polarimetric Data on Storm Analysis

2008 ◽  
Vol 136 (6) ◽  
pp. 2246-2260 ◽  
Author(s):  
Youngsun Jung ◽  
Ming Xue ◽  
Guifu Zhang ◽  
Jerry M. Straka
Keyword(s):  
Kalman Filter ◽  
Positive Impact ◽  
Radar Data ◽  
Error Model ◽  
Horizontal Wind ◽  
Polarimetric Radar ◽  
Convective Storm ◽  
Mixing Ratios ◽  
Distribution Parameters ◽  
The Impact

Abstract A data assimilation system based on the ensemble square-root Kalman filter (EnSRF) is extended to include the additional capability of assimilating polarimetric radar variables. It is used to assess the impact of assimilating additional polarimetric observations on convective storm analysis in the Observing System Simulation Experiment (OSSE) framework. The polarimetric variables considered include differential reflectivity ZDR, reflectivity difference Zdp, and specific differential phase KDP. To simulate the observational data more realistically, a new error model is introduced for characterizing the errors of the nonpolarimetric and polarimetric radar variables. The error model includes both correlated and uncorrelated error components for reflectivities at horizontal and vertical polarizations (ZH and ZV, respectively). It is shown that the storm analysis is improved when polarimetric variables are assimilated in addition to ZH or in addition to both ZH and radial velocity Vr. Positive impact is largest when ZDR, Zdp, and KDP are assimilated all together. Improvement is generally larger in vertical velocity, water vapor, and rainwater mixing ratios. The rainwater field benefits the most while the impacts on horizontal wind components and snow mixing ratio are smaller. Improvement is found at all model levels even though the polarimetric data, after the application of thresholds, are mostly limited to the lower levels. Among ZDR, Zdp, and KDP, ZDR is found to produce the largest positive impact on the analysis. It is suggested that ZDR provides more independent information than the other variables. The impact of polarimetric data is also expected to be larger when they are used to retrieve drop size distribution parameters. The polarimetric radar data thresholding prior to assimilation is found to be necessary to minimize the impact of noise. This study is believed to be the first to directly assimilate (simulated) polarimetric data into a numerical model.

Sign in / Sign up

Export Citation Format

Share Document