Muzzle velocity measurement radar

32 Pages·2012·7.09 MB·English

AARMS TECHNOLOGY
Vol. 11, No. 2 (2012) 155–186
Muzzle velocity measurement radar
SÁNDOR (cid:31)SZ
National University of Public Service, Budapest, Hungary
The abundance of information provided by the Internet is characteristic nowadays but
knowledge transfer in high-tech issues/subjects is generally limited and only
concentrating on users/utilization. The researcher/producer companies are not
interested in deep knowledge sharing of equipment and thereby jeopardizing the
revenue and profits from production. Thus, the author does not rely on various
technical descriptions of these types of radars (unclassified description that could be
used as significant reference is not available).
The present article, however, conveys concrete information about the constructed radar
along with a theoretical survey which allows a system introduction and some know-how
transfer. (The know-how relating to FPGA’s circuit can not be included in this brief article
because of its complexity.)
The field of radar/DSP communication is widely known and used by several academic
publications. Several successfully used handbooks are mentioned in the reference list,
which indirectly contribute to theoretical knowledge and radar development. The most
generally used principles, e.g. radar receivers/transmitters, can be found in all the
handbooks, therefore choosing one of them as a reference for this article would be
arbitrary and unnecessary.
Introduction
This Doppler radar (from hereon referred to as MVMR) is the muzzle velocity (v )
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measuring system designed for artillery/research applications. This article is the
technical/theoretical overview of the existing radar and its principles, and is not focused
on detailed radar parameters. MVMR (created and installed in user’s country) can be
modified relatively easily with its electronic remote control feature, which allows
adjustments of the various parameters to FPGA/MCU. MVMR fulfils a secondary,
albeit educational goal, whereby radar’s components, data-processing, signal etc. can be
observed on the functioning processes for further research purposes. These educational
functions should have no implications for the normal use of the radar.
Received: November 22, 2010
Address for correspondence:
SÁNDOR (cid:31)SZ
E-mail: [email protected]
S. (cid:31)SZ:Muzzle velocity measurement radar
1. General survey
The following parameters/properties reflect the current user’s requirements; however,
MVMR may be configured with other specifications.
(cid:127) MVMR is triggered by X band Doppler radar (a trigger signal originated by shot’s
plasma state). Thereafter MVMR works at K band frequency as triggered CW.
(cid:127) The radar’s speed range is 180–1800 m/s.
(cid:127) Projectile diameter range is 20–200 mm.
(cid:127) Accuracy is ±0.03% (theoretically it is ±0.025%) – using FFT with 2048 points,
for generating a spectrograph.
(cid:127) The “speed-distance track” is displayed by military notebook, via Bluetooth
communication.
(cid:127) This radar features a multiplicity of functions as pre-selected by user.
Note: The MVMR performs FFT, which hereinafter will be considered as raw
incoming data for the next data processing.
The MVMR based on a spectrograph presenting the speed-distance curve (for a few
hundred meters), which in turn is based on raw incoming FFT data and data improved
by regression. In order to achieve the best possible results, the raw data requires some
further processing, as follows:
The FFT may contain data that doesn’t follow the real speed-track exactly. Some
data is often incorrect due to a bad antenna pattern (see later). Therefore, a histogram is
used to determine the expected value of FFT, which is considered as the middle of
tolerance, and suitable to select the right FFT values. (If the standard velocity of
projectile is available we use it as predicted value instead of the expected one by
histogram.) Only the right (selected) FFT value will be used in the following
regression/polynomial estimation.This regression is performing:
(cid:127) The replacement of the wrong/missing values in FFT’s data, thus providing
higher accuracy to the measurements.
(cid:127) The determination of the projectile’s speed at the end of gun’s barrel
(extrapolation).
The aforementioned measurement and calculation process is exposed to geometrical
distortion, coming from the fact that the radar can not be in the line with the gun’s
barrel. This geometrical problem necessitates curve correction based on calculations.
The initial phase of the curve is very sensitive to the geometric layout. Correct layout
results in effective error correction in determining tangential velocity of projectile.
Incorrect geometric layout will both render error treatment near impossible, and cause
radar coverage problems.
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After the final calculations, v (muzzle velocity) is displayed by touch screen
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or notebook. The user may choose to perform further supplementary calculations on
extrapolated data or on v according to the specific algorithm.
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2. Highlighting some of MVMR’s principles in brief summarization
When the general abbreviations are used, there is no specific explanation.
2.1. Radar coverage
Radar antenna coverage (Figure 1) is a fundamental factor in radar performance. It is
significantly affected by antenna height and elevation angle. In regards to booth error
treatment and radar coverage, layout (thus target detection) is a top priority.
The low (below the minimum) position of the radar and shot direction parallel to
ground surface forces the radar to measure under such extreme circumstances, that
measurement conflicts arise with basic physical phenomena (natural laws/lobing effect).
These ways good results are unattainable. Insufficient coverage is random with many
gaps. It results in fluctuating signal while the projectile travels along its path (Figure 1).
Figure 1.
If the gun elevation angle is near zero, the compared radar elevation angle has to be
incremented by +3…4°, which significantly improves the radar coverage. (The min
height and right angle of radar generally requires experimentation to determine the
correct values.) The gun/radar elevation angle is the same when the cannon operates in
real-world conditions.
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Figure 2.
Figure 3 shows the normal speed-trajectory (the broken parts at the end of the curve
are caused by low SNR due to long distance). Note: The curve is never displayed as
broken for the user. The trajectory is corrected based on regression.
Figure 3.
2.2. Doppler frequency measured by radar
Doppler frequency measurement according to basic equation:
f =25 /4 (commonly known form.)
d rad
The measured Doppler frequency by radar:
FFT (cid:4) f FFT
f = result s (f = result)
d d
FFT (cid:4)I FFT
range n time
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(cid:1) f :sampling frequency of ADC (the location of the ADC shown in Figure 15)
s
(cid:1) FFT :frequency according to DSP bin; in other words, the measured number
result
of Doppler periods inside of FFT
(cid:1) FFT :the number of FFT points (length) is 2048 but the number of interval
range
is only 2047, this last value is the FFT
range
(cid:1) I :integrator number/how many samples will be integrated into one sample (“n”
n
is not serial index)
(cid:1) FFT :time period of one FFT (total time period of performing one FFT;with
time
2048 samples long data)
If reference frequencies are different in FFT and in microwave stage, the Doppler
frequency measured by the radar will be:
f = FFTresult(cid:4) fs (cid:4)Cf(cid:5)100
d
FFT (cid:4)I C
range n fmicro
(cid:1) C /C Frequency error compensation (mark of f–100 comes from
f–100 fmicro
100 MHz reference frequency)
(cid:1) C :quotient of actual/nominal reference frequency of DSP (FPGA)
f–100
(cid:1) C :quotient of actual/nominal reference frequency of microwave channel.
fmicro
Notice: MVMR uses two independent reference source, because there are in
different box. The frequency sources are temperature compensated. Using the two
reference frequencies based on the same source the C /C =1.
f–100 fmicro
2.3. FFT time (time period of one FFT)
FFT is the length of time we look at the signal within one FFT.The resulted sample
time
rate is f /I .
s n
FFT (cid:4)I
range n
FFT =
time
f
s
FFT
Doppler frequency: f = result (in the radar the FFT =2047)
d range
FFT
time
The I integrator number has the former interpretation, moreover:
n
(cid:127) I : this variable is dependent on radar range (if the 500/1000/2000m/s range is
n
fixed, I is 512/256/128)
n
–or I is dependent on the automatic adjustment to optimum of the number of
n
Doppler periods within FFT .
time
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(cid:127) FFT : considered as one element of consecutive data of FFT, marked as
result
FFT or simply FFT during spectrograph (FFT is suitable for calculation
nresult n time
of distance and speed; otherwise they are determinable in other way as well.)
2.4. Distance measured by radar
The FFT gives the measured number of periods within of FFT , which means
result time
the distance traveled during the completion of one FFT.
The Doppler Periods (DP) is physically expressed such:
t s
2(cid:4)s 2
DP = f (cid:4)t= (cid:7)DP=(cid:6) f (t)dt= (cid:6)s(t)dt
d d
(cid:8) (cid:8)
0 0
The integral form is perfect, but muzzle velocity versus time is nearly linear and thus
considered as constant in short range, however the radar processing is a sampled
system which operates with sum as integral.
(cid:1) (cid:8):wavelength of the transmitted signal (microwave)
(cid:1) s:distance (path)
(cid:1) t:time
(cid:1) DP:Doppler periods
Doppler periods mean the distance traveled during a given time:
n
DopplerPeriods(n)=DP(n)=(cid:11)FFT DP =FFT
nresult n n
0
f FFT (cid:4)c (cid:8)
DP(s)=2(cid:4)s(cid:4) mw (cid:12)(cid:12)s (FFT )= result = FFT
1FFT result result
c 2(cid:4)f 2
mw
discreteKas=(cid:11)sn =(cid:11)FF2Tn(cid:4)rfesult(cid:4)c =(cid:8)2(cid:11)FFTnresult
n n mw n
(Path under one FFT time)
(cid:1) f :frequency of microwave channel
mw
(cid:1) (cid:8):is the wavelength of microwave channel
(cid:1) c:speed of electromagnetic propagation
(cid:1) s (FFT): path inside FFT
1FFT time
(cid:1) s(n): function of path versus n(serial) number of FFT
(cid:1) s :path/distance traveled within one FFT priod
1FFT
(cid:1) s :path length during the FFT
n n
(cid:1) s:path length
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(cid:1) FFT :FFT for a specific period, as result
result
(cid:1) FFT =FFT : considered as nth FFT which has one dominant frequency
n nresult
bin, otherwise: element of consecutive FFT data of spectrograph.
2.5. Velocity measurement by radar
From measured Doppler frequency the radial speed:
c(cid:4) f
v(FFT , f , f ,I ,FFT )=FFT s
result mw s n range result
2(cid:4) f (cid:4)FFT (cid:4)I
mw range n
Elements of spectrograph:
The spectrograph contains consecutive FFT results representing the current
speed value (but before that the extractor selects the appropriate FFT components so
that the trajectory would be a single-valued curve)
(cid:8)(cid:4)FFT I (cid:4)FFT
v = nresult (cid:7) FFT = n range (cid:7)
n time
2(cid:4)FFT f
time s
c(cid:4) f
(cid:7)v =FFT s
n nresult 2(cid:4) f (cid:4)FFT (cid:4)I
mw range n
Note: muzzle velocity (v ) based on spectrograph’s curve, but its determination is after
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calculation of regression, extrapolation and user specific calculation/interpretation…
2.6. FFT well suited to optimum Doppler period
The following equation determines the optimal sample-ratio (for FFT)through I value
n
(in the interest of high precision):
c(cid:4) f
I (v )=FFT s (cid:12)
n st expected
2(cid:4) f (cid:4)FFT (cid:4)v
mw range st
2.228(cid:4)105
(cid:12){FFT =1900} (cid:12)I (v )=
expected n st
v
st
with given radar parameters
(cid:127) v :is the standard muzzle velocity coming from spec table.
st
However I will be rounded to the nearest integer because the integrator number
n
indicates how many samples will be integrated into one sample.
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(cid:13)(cid:19) c(cid:4) f (cid:13)(cid:16)
In(vst)=round(cid:18)FFTexpected s (cid:15)
(cid:13)(cid:17) 2(cid:4) fmw(cid:4)FFTrange(cid:4)vst(cid:13)(cid:14)
Generally 5% tolerance is enough around standard velocity, therefore
FFT =0.95FFT ,so the equation is:
expected range
(cid:19)0.475(cid:4)c(cid:4)f (cid:16)
In(vst)=round(cid:18) s(cid:15)
(cid:17) fmw(cid:4)vst (cid:14)
This value will be automatically adjusted to the integrator (Figure 4).
Figure 4.
The majority of velocity measurement results (components) fall within the
margin of tolerance. If velocity measurement is out-of-tolerance (5%), serious
malfunction of the gun, projectile or radar will occur.
The radial velocity component (with I (v )) can be obtained:
n st
(cid:8)(cid:4)FFT f (cid:4)(cid:8)(cid:4)FFT
v = nresult = s nresult
n
2(cid:4)FFT (cid:19)0.475(cid:4)c(cid:4) f (cid:16)
time 2(cid:4)round(cid:18) s(cid:15)
(cid:17) fmw(cid:4)vst (cid:14)
(one speed component based on one FFT period)
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2.7. Section of path between the FFT’s results
On the projectile’s path the FFT results give samples (points on path), covering the
speed and the distance traveled. The path (distance traveled) during FFT period:
(cid:8) (cid:8)
s = (cid:4)FFT = (cid:4)DP
1 result
2 2
The path section if radar automatically adjusts the optimum DP:
(cid:8)
s = (cid:4)DP(cid:20)950(cid:8)
1
2
s =11.4 m (at 25 GHz)
1
s =28.5 m (at 10 GHz)
1
2.8. Improving the probability of detection by FFT method in multipath area
The improvement of the probability of detection by FFT-SNR is standard, but the
method is different in multipath areas. Referring back to Section 2.1 where the incorrect
geometric layout gives the wrong radar coverage, the way of improving the probability
of detection at multipath area, is:
– the decrement of s ,which means at the same time
1
– the reduction of DP,and
– the deterioration of accuracy, and
– a shorter FFT (with keeping the improvement factor of FFT by the same
time
number of bins).
When the circumstances of radar-gun-ground layout are incorrect and antenna
pattern is fragmented, the reduced DP makes sense. The echo signal is strongly
fluctuated on the projectile’s path (due to the gaps in radar coverage), but the short s
1
ensures higher probability for FFT to be successful. Some short and gap-free sections
can exists on the projectile-path where the “good-bad” data ratio is higher, which is
enough for uploading the FFT with correct input data – so some FFT gives a good
result which can build up a successful regression. (The FFT with reduced right data not
only decreases the magnitude but also widens the spectra.)
The reduced DP can be adjusted automatically at the expense of accuracy. E.g. the
first goal was 1900 DP. If automatic adjustment is set to 1900/950/475 DP value, the s
1
is 11.4/5.7/2.85 m at 25 GHz (s =(cid:8)(cid:21)DP/2).
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The forced s reduction can ensure (as partly mentioned) that: between gaps of radar
1
coverage, the SNR and data continuity can satisfy the FFT’s requirement giving correct
results for more sections with a length of 2.85 m or 5.7 m under FFT . Naturally the
time
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mentioned DP value is practical, but not tied to this fixed one. In practice this method
has demonstrated its relevance. The short s value also alleviates the effect of
1
(disadvantageous) Doppler frequency sweep/slip, as detailed later on. The 25 GHz
frequency gives shorter s value as than the generally used 10 GHz.
1
3. Some of MVMR’s more complex principles
Figure 5 shows the factors determining measurement accuracy.
Figure 5.
The MVMR’s complexity comes from geometric layout. The accuracy of
measurement is generally under 0,1% (0.025…0.05% is characteristic), therefore the
analysis of the error source is important.
3.1. Measurement accuracy coming from radar components
The two instances of frequency reference are less important (as a result of excellent
ppm values) than the DSP component.
Frequency References: Using two different frequencies based on the same source
results in cancellation of both errors. Thus the reference frequencies are present error-
components, but may prove irrelevant depending on whether their sources are the same.
DSP: The number of FFT’s points basically determines the radar’s measurement
accuracy. Generally 2048 points of FFT is used. The accuracy is ±1/4096.
3.2. Errors originated by layout (GUN-RADAR GEOMETRY)
(cid:127) Radial velocity is measured by radar, however we need a calculation for
tangential velocity (vector). This velocity is exposed to the effect of geometric
layout (Figure 6).
(cid:127) Deriving from the same geometric layout problem, the precise radial velocity
measurement is adversely influenced by frequency sweep/slip. As a result, radar
164 AARMS 11(2) (2012)