This paper deals with the retrieval of snow depth (SD) and snow water equivalent (SWE) using dual-polarization (HH-VV) synthetic aperture radar (SAR) data. The effect of different snowpack conditions on the SD and SWE inversion accuracy was demonstrated by using three TerraSAR-X acquisitions. The algorithm is based on the relationship between the SD, the co-polar phase difference (CPD), and particle anisotropy. The Dhundi observatory in the Indian Himalaya was selected as a validation test site where a field campaign was conducted for ground truth measurements in January 2016. Using the field measured values of the snow parameters, the particle anisotropy has been optimized and provided as an input to the SD retrieval algorithm. A spatially variable snow density ( ${\rho }_s$ ) was used for the estimation of the SWE, and a temporal resolution of 90 m was achieved in the inversion process. When the retrieval accuracy was tested for different snowpack conditions, it was found that the proposed algorithm shows good accuracy for recrystallized dry snowpack without distinct layering and low wetness (w). The statistical indices, namely, the root mean square error (RMSE), the mean absolute difference (MAD), and percentage error (PE), were used for the accuracy assessment. The algorithm was able to retrieve SD with an average MAE and RMSE of 6.83 cm and 7.88 cm, respectively. The average MAE and RMSE values for SWE were 17.32 mm and 21.41 mm, respectively. The best case PE in the SD and the SWE retrieval were 8.22 cm and 18.85 mm, respectively.

Monitoring the dynamics of snow and glaciers in the Indian Himalaya has always attracted the attention of the remote sensing community. The snow water equivalent (SWE) represents the amount of water contained in the snowpack, and it is a product of snow depth (SD) and snow density ( ${\rho }_s$). The estimation of SD at high spatial and temporal resolution is still a challenge, especially in rugged mountainous terrain, like the Himalayas. In this paper, bistatic TerraSAR-X quad-polarization data is used to retrieve the SD using the Polarimetric SAR Interferometry (PolInSAR) coherences. The PolInSAR coherence at hv polarization shows a linear relationship with SD, which is verified with the field data. This relationship is utilized for the retrieval of SD using the proposed algorithm. Spatially variable ${\rho }_s$ is used to retrieve the SWE. The coefficient of determination ( $R^2$) values of the retrieved SD on 8 January 2016 and 19 January 2016 are 0.62 and 0.80, respectively. Likewise, it is 0.61 and 0.72 for retrieved SWE. The root mean square error (RMSE) in SD on 8 January 2016 and 19 January 2016 are 7.00 cm and 5.48 cm, respectively; for SWE, it is 2.02 cm and 1.48 cm, respectively.

In this article, an algorithm for snow depth (SD) and snow water equivalent (SWE) retrieval is proposed based on a polarimetric synthetic aperture radar (SAR) decomposition model and field measured snow data. The field campaigns were conducted at the Dhundi observatory (in the Indian Himalaya) in January 2016 and 2018. The field-measured data are used here to build a linear regression between wetness (w) and the imaginary part of the snow permittivity (ε′′), and the validation of retrieved SD and SWE. The snow density (ρs) and w are calculated with a generalized volume parameter derived using a theoretical model and SAR data (coherency matrix). These snow parameters and the field-based regression relating w and ε′′ are eventually used for the SD and SWE retrieval. Three TerraSAR-X scenes of the quad-polarization X-band data acquired in January 2016 are used to study the effect of the snow conditions on the accuracy of the proposed algorithm. The mean absolute error (MAE), root-mean-square error (RMSE), and index of agreement (IOA) for SD are 4.84 cm, 5.12 cm, and 0.71, respectively. On the other hand, for SWE, it is 1.42 cm, 1.53 cm, and 0.71, respectively.

The aim of this paper is to get a controlled joint angle plot for a biped robot leg having three links and four degrees of freedom. Biped robots have better mobility than conventional wheeled robots, but the mathematical modeling are complicated than other kind of robots. To design a complete stable walking robot the first necessary thing is to give complete mathematical modeling of a biped robot. In this paper we are considering a part of biped robot and giving formalism to model and control it using basic PID controllers. The Mathematical modeling of this model are done by using DH convention and Lagrange Euler equation. PID controller is applied to each joint separately to control the joint angle. All calculation to find equation of motion performed in MATLAB.

The highly dynamic nature of snow requires frequent observations to study its various properties. Keeping this in mind, the present investigation presents results from the analysis of fully polarimetric synthetic aperture radar (POLSAR) parameters for the development of a snow depth (SD) inversion model for SD retrieval. Snow depth retrieved using ground penetrating radar (GPR) at 500 MHz over Austre Grønfjordbreen in the Svalbard region was used to understand the behaviour of certain polarimetric parameters. A significant correlation was found between field-measured SD and POLSAR parameters, namely coherence and normalized volume scattering power (R² = 0.84 and R² = 0.73, respectively.) Using the POLSAR scattering powers obtained from the six-component model-based decomposition (6SD), the heterogeneity and anisotropic behaviour in the firn areas are also explained. Further, based on the analyses shown in this work, a polarimetric parameter-based SD inversion algorithm have been proposed and validated. The univariate model with co-polarization coherence has the highest correlation (R² = 0.84, Root Mean Square Error (RMSE) = 0.18). We have even tested several multivariate models for the same, to conclude that a combination of coherence, normalized volume and double-bounce scattering have a high correlation with SD (R² = 0.84, RMSE = 0.18). Additionally, temporal and spatial variability in SD was also observed from three polarimetric SAR images acquired between 4 April 2015 and 15 May 2015 over the Western Nordenskiöld Land region. Increase in snow depth corresponding to snow precipitation events were also detected using the POLSAR data.