Doppler Spectrum Estimation by Ramanujan Fourier Transforms

The Doppler spectrum estimation of a weather radar signal in a classic way can be made by two methods, temporal one based in the autocorrelation of the successful signals, whereas the other one uses the estimation of the power spectral density PSD by using Fourier transforms. We introduces a new tool of signal processing based on Ramanujan sums cq(n), adapted to the analysis of arithmetical sequences with several resonances p/q. These sums are almost periodic according to time n of resonances and aperiodic according to the order q of resonances. New results will be supplied by the use of Ramanujan Fourier Transform (RFT) for the estimation of the Doppler spectrum for the weather radar signal

A Network of Portable, Low-Cost, X-Band Radars

Radar is a unique tool to get an overview on the weather situation, given its high spatio- temporal resolution. Over 60 years, researchers have been investigating ways for obtaining the best use of radar. As a result we often find assurances on how much radar is a useful tool, and it is! After this initial statement, however, regularly comes a long list on how to increase the accuracy of radar or in what direction to move for improving it. Perhaps we should rather ask: is the resulting data good enough for our application? The answers are often more complicated than desired. At first, some people expect miracles. Then, when their wishes are disappointed, they discard radar as a tool: both attitudes are wrong; radar is a unique tool to obtain an excellent overview on what is happening: when and where it is happening. At short ranges, we may even get good quantitative data. But at longer ranges it may be impossible to obtain the desired precision, e.g. the precision needed to alert people living in small catchments in mountainous terrain. We would have to set the critical limit for an alert so low that this limit would lead to an unacceptable rate of false alarm

Doppler W-band polarization diversity space-borne radar simulator for wind studies

CloudSat observations are used in combination with collocated European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis to simulate spaceborne W-band Doppler observations from slant-looking radars. The simulator also includes cross-polarization effects which are relevant if the Doppler velocities are derived from polarization diversity pulse pair correlation. A specific conically scanning radar configuration (WIVERN), recently proposed to the ESA-Earth Explorer 10 call that aims to provide global in-cloud winds for data assimilation, is analysed in detail in this study. One hundred granules of CloudSat data are exploited to investigate the impact on Doppler velocity estimates from three specific effects: (1) non-uniform beam filling, (2) wind shear and (3) crosstalk between orthogonal polarization channels induced by hydrometeors and surface targets. Errors associated with non-uniform beam filling constitute the most important source of error and can account for almost 1 m s−1 standard deviation, but this can be reduced effectively to less than 0.5 m s−1 by adopting corrections based on estimates of vertical reflectivity gradients. Wind-shear-induced errors are generally much smaller (∼ 0.2 m s−1 ). A methodology for correcting these errors has been developed based on estimates of the vertical wind shear and the reflectivity gradient. Low signal-to-noise ratios lead to higher random errors (especially in winds) and therefore the correction (particularly the one related to the wind-shear-induced error) is less effective at low signal-to-noise ratio. Both errors can be underestimated in our model because the CloudSat data do not fully sample the spatial variability of the reflectivity fields, whereas the ECMWF reanalysis may have smoother velocity fields than in reality (e.g. they underestimate vertical wind shear). The simulator allows for quantification of the average number of accurate measurements that could be gathered by the Doppler radar for each polar orbit, which is strongly impacted by the selection of the polarization diversity H − V pulse separation, Thv. For WIVERN a selection close to 20 µs (with a corresponding folding velocity equal to 40 m s−1 ) seems to achieve the right balance between maximizing the number of accurate wind measurements (exceeding 10 % of the time at any particular level in the mid-troposphere) and minimizing aliasing effects in the presence of high winds. The study lays the foundation for future studies towards a thorough assessment of the performance of polar orbiting wide-swath W-band Doppler radars on a global scale. The next generation of scanning cloud radar systems and reanalyses with improved resolution will enable a full capture of the spatial variability of the cloud reflectivity and the in-cloud wind fields, thus refining the results of this study

Observability analysis and optimal sensor placement in stereo radar odometry

© 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.Localization is the key perceptual process closing the loop of autonomous navigation, allowing self-driving vehicles to operate in a deliberate way. To ensure robust localization, autonomous vehicles have to implement redundant estimation processes, ideally independent in terms of the underlying physics behind sensing principles. This paper presents a stereo radar odometry system, which can be used as such a redundant system, complementary to other odometry estimation processes, providing robustness for long-term operability. The presented work is novel with respect to previously published methods in that it contains: (i) a detailed formulation of the Doppler error and its associated uncertainty; (ii) an observability analysis that gives the minimal conditions to infer a 2D twist from radar readings; and (iii) a numerical analysis for optimal vehicle sensor placement. Experimental results are also detailed that validate the theoretical insights.Peer ReviewedPostprint (author's final draft

Implementation of polarization diversity pulse-pair technique using airborne W-band radar

This work describes the implementation of polarization diversity on the National Research Council Canada W-band Doppler radar and presents the first-ever airborne Doppler measurements derived via polarization diversity pulse-pair processing. The polarization diversity pulse-pair measurements are interleaved with standard pulse-pair measurements with staggered pulse repetition frequency, this allows a better understanding of the strengths and drawbacks of polarization diversity, a methodology that has been recently proposed for wind-focused Doppler radar space missions. Polarization diversity has the clear advantage of making possible Doppler observations of very fast decorrelating media (as expected when deploying Doppler radars on fast-moving satellites) and of widening the Nyquist interval, thus enabling the observation of very high Doppler velocities (up to more than 100 m s−1 in the present work). Crosstalk between the two polarizations, mainly caused by depolarization at backscattering, deteriorated the quality of the observations by introducing ghost echoes in the power signals and by increasing the noise level in the Doppler measurements. In the different cases analyzed during the field campaigns, the regions affected by crosstalk were generally associated with highly depolarized surface returns and depolarization of backscatter from hydrometeors located at short ranges from the aircraft. The variance of the Doppler velocity estimates can be well predicted from theory and were also estimated directly from the observed correlation between the H-polarized and V-polarized successive pulses. The study represents a key milestone towards the implementation of polarization diversity in Doppler space-borne radars