We introduce a radar system capable of tracking a 5 mm spherical target continuously in three dimensions. The 10 GHz (X-band) radar system has a transmission power of 1 W and operates in the near field of the horn antennae. By comparing the phase shift of the electromagnetic wave traveling through the free space with an IQ-mixer, we obtain the relative movement of the target with respect to the antennae. From the azimuth and inclination angles of the receiving antennae obtained in the calibration, we reconstruct the target trajectory in a three-dimensional Cartesian system. Finally, we test the tracking algorithm with target moving in circular as well as in pendulum motions and discuss the capability of the radar system.

1.
H. R. H.
Heinrich Hertz
,
Electric Waves: Being Researches on the Propagation of Electric Action with Finite Velocity through Space
(
Macmillan
,
1893
).
2.
M. I.
Skolnik
,
Introduction to Radar Systems
, 3rd ed. (
McGraw Hill
,
Boston
,
2001
).
3.
Radar Handbook
, edited by
M. I.
Skolnik
, 3rd ed. (
McGraw-Hill Education
,
New York
,
2008
).
4.
M. E.
O’Neal
,
D. A.
Landis
,
E.
Rothwell
,
L.
Kempel
, and
D.
Reinhard
,
Am. Entomol.
50
,
212
(
2004
).
5.
V. A.
Drake
and
D. R.
Reynolds
,
Radar Entomology: Observing Insect Flight and Migration
(
CABI
,
2012
).
6.
D.
Atlas
,
Radar in Meteorology: Battan Memorial and 40th Anniversary Radar Meteorology Conference
(
American Meteorological Society
,
1990
).
7.
R. J.
Sullivan
,
Radar Foundations for Imaging and Advanced Concepts
(
SciTech Publishing
,
Raleigh, NC
,
2004
).
8.
H. M.
Jaeger
,
S. R.
Nagel
, and
R. P.
Behringer
,
Rev. Mod. Phys.
68
,
1259
(
1996
).
9.
J.
Duran
,
Sands, Powders and Grains: An Introduction to the Physics of Granular Materials
, 1st ed. (
Springer-Verlag
,
New York
,
2000
).
10.
A.
Yu
, ed.,
AIP Conf. Proc.
1542
(
2013
), available at http://aip.scitation.org/toc/apc/1542/1?expanded=1542.
11.
A.
Fortini
and
K.
Huang
,
Phys. Rev. E
91
,
032206
(
2015
).
12.
K.
Huang
,
M.
Brinkmann
, and
S.
Herminghaus
,
Soft Matter
8
,
11939
(
2012
).
13.
M.
Nakagawa
,
S. A.
Altobelli
,
A.
Caprihan
,
E.
Fukushima
, and
E.-K.
Jeong
,
Exp. Fluids
16
,
54
(
1993
).
14.
E. E.
Ehrichs
,
H. M.
Jaeger
,
G. S.
Karczmar
,
J. B.
Knight
,
V. Y.
Kuperman
, and
S. R.
Nagel
,
Science
267
,
1632
(
1995
).
15.
M.
Neudecker
,
S.
Ulrich
,
S.
Herminghaus
, and
M.
Schröter
,
Phys. Rev. Lett.
111
,
028001
(
2013
).
16.
A. G.
Athanassiadis
,
P. J.
La Rivière
,
E.
Sidky
,
C.
Pelizzari
,
X.
Pan
, and
H. M.
Jaeger
,
Rev. Sci. Instrum.
85
,
083708
(
2014
).
17.
M.
Toiya
,
J.
Hettinga
, and
W.
Losert
,
Granular Matter
9
,
323
(
2007
).
18.
J. A.
Dijksman
,
F.
Rietz
,
K. A.
Lorincz
,
M. v.
Hecke
, and
W.
Losert
,
Rev. Sci. Instrum.
83
,
011301
(
2012
).
19.
E. R.
Weeks
,
J. C.
Crocker
,
A. C.
Levitt
,
A.
Schofield
, and
D. A.
Weitz
,
Science
287
,
627
(
2000
).
20.
J. R.
Royer
,
E. I.
Corwin
,
A.
Flior
,
M.-L.
Cordero
,
M. L.
Rivers
,
P. J.
Eng
, and
H. M.
Jaeger
,
Nat. Phys.
1
,
164
(
2005
).
21.
R. D.
Maladen
,
Y.
Ding
,
C.
Li
, and
D. I.
Goldman
,
Science
325
,
314
(
2009
).
22.
N.
Menon
and
D. J.
Durian
,
Science
275
,
1920
(
1997
).
23.
P.
Dixon
and
D.
Durian
,
Phys. Rev. Lett.
90
,
184302
(
2003
).
24.
A.
Fingerle
,
K.
Roeller
,
K.
Huang
, and
S.
Herminghaus
,
New J. Phys.
10
,
053020
(
2008
).
25.
K.
Huang
and
I.
Rehberg
,
Phys. Rev. Lett.
107
,
028001
(
2011
).
26.
D. J.
Parker
,
C. J.
Broadbent
,
P.
Fowles
,
M. R.
Hawkesworth
, and
P.
McNeil
,
Nucl. Instrum. Methods Phys. Res., Sect. A
326
,
592
(
1993
).
27.
D. J.
Parker
,
A. E.
Dijkstra
,
T. W.
Martin
, and
J. P. K.
Seville
,
Chem. Eng. Sci.
52
,
2011
(
1997
).
28.
K. M.
Hill
,
Y.
Fan
,
J.
Zhang
,
C. V.
Niekerk
,
E.
Zastrow
,
S. C.
Hagness
, and
J. T.
Bernhard
,
Granular Matter
12
,
201
(
2010
).
29.
S.
Sabah
and
R.
Lorenz
, in
EPAC
(
IOP Publishing
,
Bristol, UK and Philadelphia, PA
1998
), Vol. 98, p.
1589
.
30.

Note that the influence from the fluctuations of k is relatively small because of the square root dependency.

31.
J. J.
Carr
,
Practical Antenna Handbook
(
McGraw-Hill
,
New York
,
2001
).
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