scholarly journals Cramér-Rao Bound Study of Multiple Scattering Effects in Target Separation Estimation

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Edwin A. Marengo ◽  
Paul Berestesky

The information about the distance of separation between two-point targets that is contained in scattering data is explored in the context of the scalar Helmholtz operator via the Fisher information and associated Cramér-Rao bound (CRB) relevant to unbiased target separation estimation. The CRB results are obtained for the exact multiple scattering model and, for reference, also for the single scattering or Born approximation model applicable to weak scatterers. The effects of the sensing configuration and the scattering parameters in target separation estimation are analyzed. Conditions under which the targets' separation cannot be estimated are discussed for both models. Conditions for multiple scattering to be useful or detrimental to target separation estimation are discussed and illustrated.

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Edwin A. Marengo ◽  
Maytee Zambrano-Nunez ◽  
Paul Berestesky

The target position information contained in scattering data is explored in the context of the scalar Helmholtz operator for the basic two-point scatterer system by means of the statistical estimation framework of the Fisher information and associated Cramér-Rao bound (CRB) relevant to unbiased position estimation. The CRB results are derived for the exact multiple scattering model and, for reference, also for the single scattering or first Born approximation model applicable to weak scatterers. The roles of the sensing configuration and the scattering parameters in target localization are analyzed. Blind spot conditions under which target localization is impossible are derived and discussed for both models. It is shown that the sets of sensing configuration and scattering parameters for which localization is impeded are different but equivalent (they have the same size) under the exact multiple scattering model and the Born approximation. Conditions for multiple scattering to be useful or detrimental to localization are derived.


2006 ◽  
Vol 6 (4) ◽  
pp. 8125-8154
Author(s):  
A. Battaglia ◽  
M. O. Ajewole ◽  
C. Simmer

Abstract. MonteCarlo simulations have been performed to evaluate the importance of multiple scattering effects in co- and cross-polar radar returns for 94GHz radars in Cloudsat and airborne configurations. Thousands of vertically structured profiles derived from some different cloud resolving models are used as a test-bed. Mie theory is used to derive the single scattering properties of the atmospheric hydrometeors. Multiple scattering effects in the cross polar channel (reflectivity enhancement) are particularly elusive, especially in airborne configuration. They can be quite consistent in satellite configurations, like Cloudsat, especially in regions of high attenuation and in the presence of highly forward scattering layers associated with snow and graupel particles. When the cross polar returns are analysed, high LDR values appear both in space and in airborne configurations. The LDR signatures are footprints of multiple scattering effects since they cannot be explained by single scattering computations, even including non-spherical particles. We see these signatures confirmed by some experimental data collected during the Wakasa Bay experiment. Multiple scattering effects can be important for Clousat applications like rainfall and snowfall retrievals since single scattering based algorithms will be otherwise burdened by positive biases.


2014 ◽  
Vol 53 (7) ◽  
pp. 1790-1808 ◽  
Author(s):  
Alessandro Battaglia ◽  
Simone Tanelli ◽  
Gerald M. Heymsfield ◽  
Lin Tian

AbstractDeep convective systems observed by the High Altitude Imaging Wind and Rain Airborne Profiler (HIWRAP) radar during the 2011 Midlatitude Continental Convective Clouds Experiment (MC3E) field campaign in Oklahoma provide the first evidence of multiple-scattering effects simultaneously at Ku and Ka band. One feature is novel and noteworthy: often, in correspondence to shafts with strong convection and when moving from the top of the cloud downward, the dual wavelength ratio (DWR) first increases as usual in Ku–Ka-band observations, but then it reaches a maximum and after that point it steadily decreases all the way to the surface, forming what will be hereinafter referred to as a knee. This DWR knee cannot be reproduced by single-scattering theory under almost any plausible cloud microphysical profile. On the other hand, it is explained straightforwardly with the help of multiple-scattering theory when simulations involving hail-bearing convective cores with large horizontal extents are performed. The DWR reduction in the lower troposphere (i.e., DWR increasing with altitude) is interpreted as the result of multiple-scattering pulse stretching caused by the highly diffusive hail layer positioned high up in the atmosphere, with Ka multiple scattering typically exceeding that occurring in the Ku channel. Since the effects of multiple scattering increase with increasing footprint size, if multiple-scattering effects are present in the aircraft measurements, they are likely to be more pronounced in the spaceborne dual-frequency Ku–Ka radar observations, envisaged for the NASA–Japan Aerospace Exploration Agency (JAXA) Global Precipitation Measurement (GPM) Mission, launched in February 2014. This notional study supports the idea that DWR knees will be observed by the GPM radar when overflying high-density ice shafts embedded in large convective systems and suggests that their explanation must not be sought in differential attenuation or differential Mie effects but via multiple-scattering effects.


2007 ◽  
Vol 7 (7) ◽  
pp. 1719-1730 ◽  
Author(s):  
A. Battaglia ◽  
M. O. Ajewole ◽  
C. Simmer

Abstract. MonteCarlo simulations have been performed to evaluate the importance of multiple scattering effects in co- and cross-polar radar returns for 94 GHz radars in Cloudsat and airborne configurations. Thousands of vertically structured profiles derived from some different cloud resolving models are used as a test-bed. Mie theory is used to derive the single scattering properties of the atmospheric hydrometeors. Multiple scattering effects in the co-polar channel (reflectivity enhancement) are particularly elusive, especially in airborne configuration. They can be quite consistent in satellite configurations, like CloudSat, especially in regions of high attenuation and in the presence of highly forward scattering layers associated with snow and graupel particles. When the cross polar returns are analysed [but note that CloudSat does not measure any linear depolarization ratio (LDR hereafter)], high LDR values appear both in space and in airborne configurations. The LDR signatures are footprints of multiple scattering effects; although depolarization values as high as −5 dB can be generated including non-spherical particles in single scattering modelling, multiple scattering computations can produce values close to complete depolarization (i.e. LDR=0 dB). Our simulated LDR profiles from an air-borne platform well reproduce, in a simple frame, some experimental observations collected during the Wakasa Bay experiment. Since LDR instrumental uncertainties were not positively accounted for during that experiment, more focused campaigns with air-borne polarimetric radar are recommended. Multiple scattering effects can be important for CloudSat applications like rainfall and snowfall retrievals since single scattering based algorithms will be otherwise burdened by positive biases.


1986 ◽  
Vol 47 (C8) ◽  
pp. C8-589-C8-592
Author(s):  
N. BINSTED ◽  
S. L. COOK ◽  
J. EVANS ◽  
R. J. PRICE ◽  
G. N. GREAVES

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