The Composite Covariance of a Kalman Filter Estimation

A Kalman filter estimation of the state of a system is merely a random vector that has a normal, also called Gaussian, distribution. Elementary statistics teaches any Gaussian distribution is completely and uniquely characterized by its mean and covariance (variance if univariate). Such characterization is required for statistical inference problems on a Gaussian random vector. This mean and composite covariance of a Kalman filter estimate of a system state will be derived here. The derived covariance is in recursive form. One must not confuse it with the “error covariance” output of a Kalman filter. Potential applications, including geological ones, of the derivation are described and illustrated with a simple example.

Study of Flash Flood in the Rishiganga and Dhauliganga Catchment in Chamoli District of Uttarakhand, India

The present study is an attempt to investigate a flash flood that occurred on the morning of 7th February 2021 in the Rishiganga and Dhauliganga Catchments in Chamoli District of Uttarakhand. A catastrophic flood was triggered due to a massive rock-cum-snow avalanche caused by Antecedent Snow falls in the region. A huge flash flood was generated as a tremendous quantity of rockslide, comprising deposited ice and snowmelt, rolled down the Ronthi Glacier and flowed downstream into the glacier valley. This massive flash flood hit the NTPC's Tapovan-Vishnugad hydel project and the Rishiganga Hydel Project, bridges, roads, and communities in and around Raini, Tapovan and Joshimath regions in the Chamoli district of Uttarakhand. The mud and slush-inducing elements resulted in the development of a dammed lake, which momentarily blocked one of the Rishiganga's tributaries. Temporal satellite image has been used to access the information of disaster damage assessment in the region. The high-resolution satellite image clearly showing flash flood watermarks in the region and on the avalanches site rock outcrops reaching up to 50–130m height on the way to Raini Gaon. As part of our analysis, we have also looked at the valley's slope profile, which clearly shows the valley's height following the destruction. It is estimated that more than Rs 4,000 crore infrastructures loss due to this flash flood in the region. Besides, two bridges have also been lost. Hydometeriological analysis was also carried out in order to obtain the trend of rapid increase in temperature in the valley where disaster occurred. Using remote sensing (RS) and Geographic Information System (GIS) techniques, thematic layers were generated for obtaining information on the flash flood.

Perception of and Preference for Rural Built Environment of Rural Residents: Evidence from Sichuan

Rural areas are undergoing tremendous changes due to rapid urbanization and new construction. However, few studies have investigated the perspectives of local residents on the changing landscape. This study investigates the aforementioned phenomenon via field surveys conducted in seven villages and townships in Sichuan Province. Factor analysis was performed on 352 valid questionnaires to analyze the perceptions of and preferences for the built environment of rural residents. Each analysis extracted 5 factors from 20 variables. The comparative analysis identified three common factors, namely, convenient transportation, public environment and roads, which influenced the perceptions on and preferences for the rural built environment. However, the importance of each factor differed in terms of perception and preference. Results of the analysis and comparison highlight areas that can be improved and promoted in new rural construction. Suggestions for development and construction are provided to promote the progress of new countryside regions.

Exploration of Measurement Methods of 3D In-Situ Stresses in Rock Masses

This paper gives an overview of the measurement methods for the 3D in-situ stresses. Rock masses in the Earth’s crust are stressed in a natural stress state, which has six components in three dimensions. They are called “in-situ stresses” or “field stresses” with three principal stress components. Reliable estimate of the in-situ stresses in the rock mass is essential and vital for proper planning and design, underground excavation, mineral resource exploitation and ground stability control in geotechnical, mining and petroleum engineering. The basic principles of the measurement methods, including overcoring, hydraulic fracturing, back analysis, borehole slotting, flat jack, geophysical, and borehole breakout, are introduced. The advantages and limitations are discussed and compared. Methods that measure borehole deformation and strains during overcoring appear most common and are the only methods for the complete 3D stresses. Other measurement methods generally provide results of the orientations and/or magnitudes of some components of the in-situ stresses, mostly the maximum and the minimum stresses in the plane perpendicular to the borehole. In some methods the vertical stress is assumed as a principal stress.