Recursive Motion and Structure Estimation with Complete Error Characterization

We present an algorithm that perfom recursive estimation of ego-motion andambient structure from a stream of monocular Perspective images of a number of feature points. The algorithm is based on an Extended Kalman Filter (EKF) that integrates over time the instantaneous motion and structure measurements computed by a 2-perspective-views step. Key features of our filter are (I) global observability of the model, (2) complete on-line characterization of the uncertainty of the measurements provided by the two-views step. The filter is thus guaranteed to be well-behaved regardless of the particular motion undergone by the observel: Regions of motion space that do not allow recovery of structure (e.g. pure rotation) may be crossed while maintaining good estimates of structure and motion; whenever reliable measurements are available they are exploited. The algorithm works well for arbitrary motions with minimal smoothness assumptions and no ad hoc tuning. Simulations are presented that illustrate these characteristics

Progress on the realization of innovative low cost disposable hail sensing probes

Detailed studies and researches about hail characterization are considered to play a key role both in weather prediction and potentially also in damage assessment after a strong hail event occurred. Most monitoring instruments perform indirect monitoring operations, sensing the parameters from a remote position and not being directly inside a hailstorm. Since 2015 the CINFAI (Italian National Consortium for the Physic of Atmospheres and Hydrospheres) with its local operative research unit at the DET (Department of Electronic and Telecommunications) of Politecnico di Torino, Italy, realized a first preliminary study concerning the realization of artificial disposable sensing probes to study and monitor hail (conducted within a project called HaSP, founded by Regione Piemonte, Italy) [1]. The study was continued in cooperation with EST (Envisens Technologies s.r.l.), a small Italian engineering company, in order to realize the first small prototypes. Introducing the appropriate modifications, a similar version of the probes can be also suitable for monitoring atmospheric parameters [2]. Aim of this work is to present the progress on the realization of low cost disposable hail sensing probes for remote sensing and the study of the properties of hail. The probes are designed as artificial hailstones in order to study both the physical properties of the portion of atmosphere where the formation of hail occurs and the modification of atmospheric conditions while the hailstones are falling to the ground. For this reason, the probes and the hailstones should have the most similar as possible fluid-dynamic properties. The artificial probes can be dropped by a plane, or potentially by a UAV (Unmanned Aircraft Vehicle) if permitted by specific legislation, which fly above and through the clouds where the hail formation occurs. Each probe is equipped with different sensors and during their falling to the ground, they directly measure different physical parameters (e.g humidity, temperature, pressure, acceleration…). All data are sent to a receiver located on the ground exploiting a specific communication link realized at a frequency not affected by the presence of hail and water in the atmosphere. The hail sensing probes can be used for efficient monitoring operations and studies of hail formation dynamics and conditions, thus increasing the set of instruments used for monitoring, remotely sensing and study the physical properties of hail, and possibly also to improve the hail forecasting models

Real Time Monitoring of Extreme Rainfall Events with Simple X-Band Mini Weather Radar

Real time rainfall events monitoring is very important for a large number of reasons: Civil Protection, hydrogeological risk management, hydroelectric power purposes, road and traffic regulation, and tourism. Efficient monitoring operations need continuous, high-resolution and large-coverage data. To monitor and observe extreme rainfall events, often much localized over small basins of interest, and that could frequently causing flash floods, an unrealistic extremely dense rain gauge network should be needed. On the other hand, common large C-band or S-band long range radars do not provide the necessary spatial and temporal resolution. Simple short-range X-band mini weather radar can be a valid compromise solution. The present work shows how a single polarization, non-Doppler and non-coherent, simple and low cost X-band radar allowed monitoring three very intense rainfall events occurred near Turin during July 2014. The events, which caused damages and floods, are detected and monitored in real time with a sample rate of 1 minute and a radial spatial resolution of 60 m, thus allowing to describe the intensity of the precipitation on each small portion of territory. This information could be very useful if used by authorities in charge of Civil Protection in order to avoid inconvenience to people and to monitor dangerous situations

Derivation of Z-R equation using Mie approach for a 77 GHz radar

The ETSI (European Telecommunications Standards Institute) defines the frequency band around 77 GHz as dedicated to automatic cruise control long-range radars. This work aims to demonstrate that, with specific assumption and the right theoretical background it is also possible to use a 77 GHz as a mini weather radar and/or a microwave rain gauge. To study the behavior of a 77 GHz meteorological radar, since the raindrop size are comparable to the wavelength, it is necessary to use the general Mie scattering theory. According to the Mie formulation, the radar reflectivity factor Z is defined as a function of the wavelength on the opposite of Rayleigh approximation in which is frequency independent. Different operative frequencies commonly used in radar meteorology are considered with both the Rayleigh and Mie scattering theory formulation. Comparing them it is shown that with the increasing of the radar working frequency the use of Rayleigh approximation lead to an always larger underestimation of rain. At 77 GHz such underestimation is up to 20 dB which can be avoided with the full Mie theory. The crucial derivation of the most suited relation between the radar reflectivity factor Z and rainfall rate R (Z-R equation) is necessary to achieve the best Quantitative Precipitation Estimation (QPE) possible. Making the use of Mie scattering formulation from the classical electromagnetic theory and considering different radar working frequencies, the backscattering efficiency and the radar reflectivity factor have been derived from a wide range of rain rate using specific numerical routines. Knowing the rain rate and the corresponding reflectivity factor it was possible to derive the coefficients of the Z-R equation for each frequency with the least square method and to obtain the best coefficients for each frequency. The coefficients are then compared with the ones coming from the scientific literature. The coefficients of a 77 GHz weather radar are then obtained. A sensitivity analysis of a 77 GHz weather radar using such Z-R relation is also studied. The work shows that the right knowledge of Z-R equation is absolutely essential to use such a specific radar for the estimation of rainfall. The use Mie scattering theory is absolutely necessary for a 77 GHz radar in order to avoid the heavy underestimation of rainfall

High resolution KE-maps with X-band mini weather radar

The erosion of the terrain starts with the process of soil detachment by raindrop impact. The Kinetic Energy (KE)of a single raindrop can represent the basic and most commonly used unit of raindrop erosivity. KE is functions of the drop size, drop shape and its terminal velocity. It can be expressed as the rain kinetic energy per unit area and per unit time (KEtime, time-specific kinetic energy) or, alternatively, as the amount of rain kinetic energy per unit volume of rain (KEmm volume-specific kinetic energy). The total KE of rainfall is evaluated by summing up the individual kinetic energies of all the raindrops. Therefore, KE can be calculated directly for any rainfall event by knowing its intensity (I) and by using one of the so-called KE–I relationships, which are present in large number in the scientific landscape, relations that in turn derive from an assumed Drop Size Distribution (DSD). Alternatively, it would be more pertinent to relate KE with data obtained by a disdrometer: however, such instruments are costly, complex (and therefore critics to use) and, consequently not generally available. Short-range X band weather radars are a good alternative solution to estimate KE. They can provide measure of radar reflectivity factor (Z) taking into account that indeed Z is related to the drops kinetic energy than the rain intensity itself. By using the weather radar, it is possible to measure KE exploiting the KE-Z relationships. In this work, we consider a pulsed X-band radar, non-coherent, non-Doppler, with vertical polarization, acquiring reflectivity maps each minute with radial resolution of 60 meters, up to a maximum range of 30 km. By using the high temporal and spatial resolution radar maps it is possible to realize high-resolution KE maps exploiting one of the KE-Z relations available in the literature, in particular the one by Yu et. al. in 2012. Starting from the maps acquired by the radar in the form of digital number, the radar reflectivity maps are obtained exploiting signal processing algorithms and the consequent KE maps are evaluated. A significant correlation between a strong rain event and some landslides in the nearby hills is presented. The high-resolution KE maps can put in evidence the spatial and temporal variability of the kinetic energy of rainfall. Used in conjunction with GIS layers concerning topography, soil properties and land use, such KE maps have a strong potential for geosciences applications

Refined upper bounds on the coarsening rate of discrete, ill-posed diffusion equations

"We study coarsening phenomena observed in discrete, ill-posed diffusion equations that arise in a variety of applications, including computer vision, population dynamics and granular flow. Our results provide rigorous upper bounds on the coarsening rate in any dimension. Heuristic arguments and the numerical experiments we perform indicate that the bounds are in agreement with the actual rate of coarsening."http://deepblue.lib.umich.edu/bitstream/2027.42/64211/1/non8_12_002.pd