Kalman Filter and Time Series

Author(s):  
Kateřina Frončková ◽  
Pavel Pražák
Keyword(s):  
2011 ◽  
Vol 11 (4) ◽  
pp. 1099-1108 ◽  
Author(s):  
M. R. Saradjian ◽  
M. Akhoondzadeh

Abstract. Thermal anomaly is known as a significant precursor of strong earthquakes, therefore Land Surface Temperature (LST) time series have been analyzed in this study to locate relevant anomalous variations prior to the Bam (26 December 2003), Zarand (22 February 2005) and Borujerd (31 March 2006) earthquakes. The duration of the three datasets which are comprised of MODIS LST images is 44, 28 and 46 days for the Bam, Zarand and Borujerd earthquakes, respectively. In order to exclude variations of LST from temperature seasonal effects, Air Temperature (AT) data derived from the meteorological stations close to the earthquakes epicenters have been taken into account. The detection of thermal anomalies has been assessed using interquartile, wavelet transform and Kalman filter methods, each presenting its own independent property in anomaly detection. The interquartile method has been used to construct the higher and lower bounds in LST data to detect disturbed states outside the bounds which might be associated with impending earthquakes. The wavelet transform method has been used to locate local maxima within each time series of LST data for identifying earthquake anomalies by a predefined threshold. Also, the prediction property of the Kalman filter has been used in the detection process of prominent LST anomalies. The results concerning the methodology indicate that the interquartile method is capable of detecting the highest intensity anomaly values, the wavelet transform is sensitive to sudden changes, and the Kalman filter method significantly detects the highest unpredictable variations of LST. The three methods detected anomalous occurrences during 1 to 20 days prior to the earthquakes showing close agreement in results found between the different applied methods on LST data in the detection of pre-seismic anomalies. The proposed method for anomaly detection was also applied on regions irrelevant to earthquakes for which no anomaly was detected, indicating that the anomalous behaviors can be related to impending earthquakes. The proposed method receives its credibility from the overall capabilities of the three integrated methods.


2021 ◽  
Author(s):  
Mohit Mishra ◽  
Gildas Besançon ◽  
Guillaume Chambon ◽  
Laurent Baillet ◽  
Arnaud Watlet ◽  
...  

<p><span>Landslides display heterogeneity in movement types and rates, ranging from creeping motion to catastrophic acceleration. In most of the catastrophic events, rocks, debris, or soil can travel at several tens of meters per year speed, causing significant cost in life losses, infrastructure, economy, and ecosystem of the region. In contrast, slow-moving landslides display typical velocities scaling from few centimeters to several meters per year. Although slow-moving landslides rarely claim life losses, they can still cause considerable damage to public and private infrastructure. Sometimes these slow, persistent landslides eventually lead to catastrophic acceleration, e.g., clayey landslides are prone to these transitions. Such events need to be detected by Early Warning Systems (EWS) in advance to take timely actions to reduce life and economic losses. Several approaches are proposed to forecast the time of failure; still, there is a need to improve prediction strategies and EWS’s. </span></p><p><span>Here we present state and parameter estimation for a simplified viscoplastic sliding model of a landslide using a Kalman filter approach, which is termed as an observer problem in control theory. The model under investigation is based on underlying mechanics (physics-based model) that portray a landslide behavior. In this model, a slide block is assumed to be placed on an inclined surface, where landslide (slide block) motion is regulated by basal pore fluid pressure and opposed by sliding resistance governed by friction, cohesion, and viscosity. This model is described by an Ordinary Differential Equation (ODE) with displacement as a state and landslide material and geometrical properties as parameters. In this approach, known parameter values (landslide geometrical parameters and some material properties) and water table height time-series are provided as input. Finally, two illustrative examples validate the presented approach: i) a synthetic case study and ii) Hollin hill landslide (Uhlemann et al., 2016) field data. </span></p><p><span>In both examples, displacement, friction angle, and viscosity are well estimated from known parameter values, water table height time-series, and displacement measurements. In the simulation results for the Hollin Hill field data, it is observed that friction angle almost remains constant while viscosity varies significantly through time.</span></p><p> </p><p><span>Uhlemann, S., Smith, A., Chambers, J., Dixon, N., Dijkstra, T., Haslam, E., Meldrum P., Merritt, A., Gunn, D., and Mackay, J., (2016). Assessment of ground-based monitoring techniques applied to landslide investigations. </span><em><span>Geomorphology</span></em><span>, 253, 438-451. doi:10.1016/j.geomorph.2015.10.027.</span></p>


2019 ◽  
Vol 11 (11) ◽  
pp. 1266 ◽  
Author(s):  
Mingzheng Zhang ◽  
Dehai Zhu ◽  
Wei Su ◽  
Jianxi Huang ◽  
Xiaodong Zhang ◽  
...  

Continuous monitoring of crop growth status using time-series remote sensing image is essential for crop management and yield prediction. The growing season of summer corn in the North China Plain with the period of rain and hot, which makes the acquisition of cloud-free satellite imagery very difficult. Therefore, we focused on developing image datasets with both a high temporal resolution and medium spatial resolution by harmonizing the time-series of MOD09GA Normalized Difference Vegetation Index (NDVI) images and 30-m-resolution GF-1 WFV images using the improved Kalman filter model. The harmonized images, GF-1 images, and Landsat 8 images were then combined and used to monitor the summer corn growth from 5th June to 6th October, 2014, in three counties of Hebei Province, China, in conjunction with meteorological data and MODIS Evapotranspiration Data Set. The prediction residuals ( Δ P R K ) in NDVI between the GF-1 observations and the harmonized images was in the range of −0.2 to 0.2 with Gauss distribution. Moreover, the obtained phenological curves manifested distinctive growth features for summer corn at field scales. Changes in NDVI over time were more effectively evaluated and represented corn growth trends, when considered in conjunction with meteorological data and MODIS Evapotranspiration Data Set. We observed that the NDVI of summer corn showed a process of first decreasing and then rising in the early growing stage and discuss how the temperature and moisture of the environment changed with the growth stage. The study demonstrated that the synthesized dataset constructed using this methodology was highly accurate, with high temporal resolution and medium spatial resolution and it was possible to harmonize multi-source remote sensing imagery by the improved Kalman filter for long-term field monitoring.


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