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Description  |
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This invention relates to the detection of waveforms in electrical signals,
including those signals derived by transducer means from electromagnetic
waves and acoustic stress waves. In particular the invention relates to
signal detection of the kind in which an electrical signal is compared
with a replica or reference signal.
The invention is particularly applicable to pulse-echo techniques such as
sonar and radar. In these techniques a train of pulses of acoustic or
electromagnetic energy is transmitted into a field of view and is
reflected to a receiver from objects encountered. The functions of
transmitter and receiver may be common to a single transducer. The
transducer both generates the transmitted waveform as a pulse-modulated
output in response to electrical exitation and generates a received
electrical signal containing the waveform of the reflected pulses. In
practice, the output of the transducer contains noise in addition to the
waveforms or pulses to be detected, and this increases the difficulty of
detection. To improve detection capability, the transmitted pulse may be
frequency modulated, and the received signal may be electronically
correlated with a reference signal in the form of a replica of the
transmitted signal. Correlation techniques involve comparing the profiles
of the replica and received signals. This is commonly implemented by
storing the replica pulse profile as a series of uniformly time-sampled or
sequential values, obtaining a similar series of sequential values of the
received electrical signal, and multiplying each replica value by the
corresponding received signal value. The correlator output C.sub.out is
obtaining by summing the results of the multiplication operations to
yield:
##EQU1##
where T.sub.n and R.sub.n are the nth values of the transmitted or replica
signal and the electrical signal respectively. This output is a maximum
when the replica and electrical signal profiles match exactly, which
occurs when the electrical signal contains the waveform to be detected.
The electrical signal is sampled to provide successive sets or series of
values until the match is achieved.
The correlation technique appreciably improves the signal-to-noise
performance of this kind of detection system, but the sensitivity is
reduced if the waveform to be detected is distorted by a Doppler shift.
The effect of a Doppler shift on a pulse-modulated signal is to contract
or expand the time duration of each pulse in addition to shifting the
pulse frequency or frequency spectrum. This reduces the maximum degree of
correlation obtainable, since the time duration and profile of the
Doppler-shifted received pulse differ from those of the replica.
To overcome the problem of detecting Doppler-shifted waveforms, it is known
to employ a stored series of replicas of the waveform having varying
degrees of time duration distortion (profile contraction or expansion)
simulating varying degrees of Doppler shift. The received signal is
correlated with each replica in turn until the best degree of match is
achieved. However, for complex waveforms and frequency modulated signals
in particular, effective correlation requires a large number of replica
signals with correspondingly large storage facilities. A dedicated
main-frame computer would be required in sonar applications for example.
Furthermore, the correlation operation would be undesirably slow because
of the need to read in and compare each replica in turn.
It is an object of the invention to provide a technique for improving the
signal-to-noise performance of correlation detection systems.
According to one aspect of the invention, a method of detecting a
Doppler-shifted waveform in an electrical signal includes the steps of:
(a) storing the electrical signal and a single replica signal derived from
the waveform prior to Doppler shift,
(b) correlating one of the signals with a profile of the other signal
varying cyclically and uniformly in length distortion, and
(c) indicating degree of correlation obtained during step (b).
Where the electrical signal changes with time, such as for example a
continuous electrical signal from a sonar transducer, the electrical
signal is preferably periodically sampled and steps (a) to (c) above are
performed for each sample. A maximum degree of correlation is achieved
when the waveform to be detected is present in the stored electrical
signal, and the variation of the profile length distortion sweeps through
a position at which the replica and waveform have matching correlated
profiles.
The invention preferably includes the additional step of determining the
Doppler shift from the degree of contraction or expansion of the
correlated profile length at which the correlation output is a maximum.
Conveniently, the correlated profile length of the replica signal is
cyclically varied to simulate Doppler shift and produce a correlation
match with the waveform. Alternatively, the electrical signal itself may
be operated upon to compensate for Doppler shift in the waveform for
correlation with an undistorted replica.
In a preferred embodiment of the invention the electrical signal and the
replica are sampled repetitively into respective storage means in the form
of delay lines. The replica signal is sampled at intervals which
progressively reduce to impose a progressively increasing distortion on
the replica profile, and this continues until the whole replica profile is
stored on the replica delay line. The received electrical signal is
sampled at a constant rate into its respective delay line. Both delay
lines conveniently consist of discrete series-connected elements such as
charge-coupled devices, and operate in a "bucket-brigade" mode in which an
incoming sample moves all stored samples one line element further along
the line. Delay between successive line elements is accordingly controlled
by the sampling interval, and is uniform for the electrical signal delay
line but non-uniform for the replica line. For the purposes of
correlation, uniformly-spaced elements on the received signal delay line
are connected via respective multipliers to points on the replica line
having progressively reducing spacing. The non-uniformity of connection to
the replica delay line, giving non-uniform correlation, is arranged to
compensate for the non-uniform replica sampling rate when the replica
profile is correlated. The net effect is that multiplication is performed
against a correlated replica profile which is uniformly distorted, i.e.
contracted or expanded, according to its position on the replica delay
line. Scanning the position of the replica on its delay line cyclically
varies the correlated replica profile length in a uniform manner
simulating Doppler shift, and produces a maximum correlation output when
the correlated replica profile matches the Doppler-shifted waveform
present in the electrical signal. The received signal is sampled into and
moves along its delay line until this occurs. A similar effect may be
achieved if the replica sampling intervals progressively increase and the
spacing of multiplier connection points progressively increases along the
replica delay line, and the operation of profile variation may
alternatively although less conveniently be performed on the electrical
signal rather than on the replica. Degree and sign of Doppler shift are
determinable from the relative positions of the stored profiles at a
correlation match compared with those corresponding to zero Doppler shift.
To obtain a uniformly correlated replica, it is preferred that the time
intervals between replica samples change in accordance with a geometrical
progression, and that the multiplier-connected or correlated elements of
the replica delay line are correspondingly spaced in accordance with a
like geometric progression. For a delay line composed of discrete
elements, the multipliers are connected to those elements separated by
intervals changing in a manner most nearly corresponding to a geometric
progression.
The delay lines may be of digital or analogue form, and in the former case
the samples of the electrical signal and the replica are subjected to
analogue to digital conversion before being fed to the delay lines.
To minimise the effect of phase shift between the replica and the received
signal, the electrical signal may be correlated with two replica signals
having a relative phase difference, conveniently 90.degree..
According to a further aspect of the invention, an apparatus for detecting
a Doppler-shifted waveform in an electrical signal includes:
(a) means for generating a replica signal derived from the waveform prior
to Doppler shift,
(b) means for storing the electrical and replica signals arranged to
introduce progressively increasing distortion along one stored signal,
(c) scanning means for cyclically varying the storage position of the
distorted signal, and
(d) correlating means arranged to indicate degree of correlation between
profiles of the stored signals having varying degrees of uniform relative
distortion introduced therebetween.
The apparatus preferably also includes means for performing additional
features of the method of the invention as hereinbefore broadly set out.
In particular, for continuously varying electrical signals the apparatus
preferably includes means for repetitively sampling the electrical signal,
the scanning means being arranged to operate in the interval between
samples.
The apparatus may also advantageously include means for determining the
storage position of the scanning signal at maximum correlation compared to
that corresponding to zero Doppler shift in order to determine the degree
of Doppler shift in the waveform. Conveniently the scanning means operates
on the replica, which is stored with progressively increasing distortion.
The replica may be generated by sampling means from a pulse-modulated
waveform, and stored on a delay line of series-connected elements.
Progressively increasing replica distortion may be introduced by a clock
activating both sampling and movement of the samples along the delay line
at intervals varying in accordance with a geometric progression. Further
sampling means activated at constant intervals is employed to store the
electrical signal uniformly on a second similar delay line. Each delay
line is longer than its respective signal to be stored, i.e. the replica
or the waveform to be detected.
Correlating means may be provided by multipliers connected to uniformly
spaced elements along the electrical signal delay line and to elements
spaced along the replica delay line in accordance with a geometrical
progression. This effects correlation against a replica having a profile
which is uniformly distorted relative to that of the electrical signal.
To minimise the effect of phase shift between the waveform and the replica,
storing means may be provided for storing two replica signals which are
mutually out of phase, preferably by 90.degree.. Correlating means are
then provided for correlating the electrical signal with both stored
replicas separately.
The invention will now be described, by way of example only, with reference
to the accompanying drawings in which:
FIG. 1 is a schematic block diagram of a sonar apparatus adapted in
accordance with and for performing the method of the invention,
FIG. 2 illustrates graphically the operation of the invention,
FIGS. 3 and 4 show computer simulations of correlation outputs obtainable
by means of the invention, and
FIGS. 5 to 9 are further schematic block diagrams of apparatus in
accordance with and for carrying out the invention.
Referring to FIG. 1, the apparatus comprises separate transducers 10 and 11
acting respectively as transmitter and receiver for sonar pulses. The
transmitter 10 is fed with a sonar pulse waveform by a power amplifier 12,
and the output of the receiver 11 is fed to a second power amplifier 13.
The acoustic output of the sonar transmitter 10 is emitted into a field of
view 14 and reflected from a target 15 to the receiver 11. The output of
the receiver 11 is an electrical signal containing noise together with the
response of the receiver to the reflected acoustic waveform.
The sonar waveform is produced by a signal generator 16, and consists of a
train of pulses which may be of constant frequency or frequency modulated.
The waveform of a single sonar pulse is fed to a storage device SR1, and
the electrical signal from the receiver 11 is fed via the power amplifier
13 to a second storage device SR2. The storage devices SR1 and SR2 are in
the form of discrete series-connected elements made up of charge-coupled
devices (CCDs). SR1 contains 851 such elements and SR2 has 512, the
elements being indicated by the numbers 1 to 851 along SR1 and 1 to 512
along SR2. The electrical signal from the receiver 11 is sampled at
uniform intervals into the storage device SR1 by means of a data sampling
clock 17. The sonar pulse waveform is sampled at progressively reducing
intervals by a clock 18, the sampling intervals varying in accordance with
a geometric progression so that the ratio of successive intervals is
constant. The clock 18 is referred to as a linear period clock, since it
can be shown that a geometric progression of time intervals results in the
(n+1)th sampling time being a linear function of the nth interval between
samples.
The clock 18 operates on the storage device SR1 through a gate 20 which is
also connected to a scanning clock 21 and raster generator 22. The signal
generator 16, gate 20, raster generator 22 and clocks 18 and 21 are
connected to a control unit 23.
The storage devices SR1 and SR2 are connected to correlating means in the
form of a multiplier array 24 and summing amplifier 25. The elements 1 to
512 of SR2 are each connected to respective multipliers 24.sub.1 to
24.sub.512 of the array 24 in a uniform manner, the nth element being
connected to the nth multiplier for all n from 1 to 512. The array 24 is
however connected non-uniformly to the storage device SR1. The spacing
between array-connected elements of SR1 varies along SR1 in accordance
with a decreasing geometric progression, connected elements near element 1
being triply spaced whereas those near element 851 are singly spaced. In
view of the discrete element construction of SR1 it is not possible to
achieve exact correspondence with a geometric progression, but the
connected elements are selected to achieve this as nearly as possible as
set out in Table 1.
The summing amplifier 25 sums the outputs of the multipliers of the array
24, and provides an output signal to a display unit 26 supplied with a
raster signal by the raster generator 22. The storage devices SR1 and SR2,
the multiplier array 20 and the summing amplifier 25 may be referred to
collectively as a Doppler-scanning matched filter or unit 9 enclosed in
chain lines.
The arrangement of FIG. 1 operates as follows. Referring to FIG. 2, the
control unit 23 delivers a control signal C1 activating the signal
generator 16 to produce a randomly frequency-modulated (hopping) sonar
pulse waveform S1. The signal C1 also activates the gate 20 and the linear
period clock 18 to sample the waveform S1 into the storage device SR1 at
intervals reducing in accordance with a geometric progression
corresponding to a progressively increasing sampling rate. This is
indicated by the sampling signal CK1. As each waveform sample is taken and
stored in SR1, it moves the preceding sample one element along SR1 in a
"bucket-brigade" manner. This continues until the whole of the sonar pulse
waveform is stored as a replica profile which is progressively increasing
in distortion with respect to distance along SR1 relative to the waveform.
The distortion occurs since the non-uniformity of sampling at
progressively reducing intervals produces relative to the waveform a
replica profile which progressively contracts from element 1 onwards along
SR1. The sampling intervals are chosen so that the replica fills 751
elements of SR1. SR1 acts as a non-uniform delay line in which a
progressively reducing delay is imposed by the clock 18 between stored
replica samples.
The electrical signal from the receiver 11 is processed as follows. The
data sampling clock 17 generates a signal CK2 at uniform intervals to
activate SR2 to sample instantaneous values of the electrical signal. As
each sample of the electrical signal is taken, the preceding sample is
moved one element along SR2. In this way the electrical signal profile is
arranged to fill SR2 uniformly and is periodically updated. SR2 acts as a
uniform delay line since the clock 17 imposes a uniform delay between
elements of SR2.
Between each sample of the electrical signal, the control unit activates
the gate 20 and the scanning clock 21 to shift the replica in SR1 in
accordance with the shift sense C3. At a of C3 the replica occupies SR1
elements 1 to 751, and at b it occupies elements 101 to 851, so that the
replica position is scanned through 100 elements along SR1 between samples
of the electrical signal. A scan in one direction is succeeded by a scan
in the reverse direction, the scanning clock 21 being adapted to produce
movement of the replica stepwise in either direction.
The multiplier array 24 and summing amplifier 25 produce a correlation
output consisting of the sum of the multiplied signals occupying connected
or correlated pairs of elements of SR1 and SR2. However, the replica
occupies progressively more multiplier connected or correlated elements as
it is scanned along SR1 in the direction from element 1 to element 851.
Referring to Table 1, when occupying elements 1 to 751 for example, the
replica occupies 418 correlated elements, and this increases to 477 when
elements 101 to 851 are occupied. Since the intervals between correlated
elements reduce along SR1 in a geometric progression, and the progressive
distortion or contraction of the replica with respect to the waveform is
arranged to increase in a like manner, progressively more correlations are
performed along the progressively contracting replica. The net effect is
that the correlated replica profile is compensated for progressive or
non-uniform replica distortion by the non-uniformly spaced multiplier
connections, and this profile is uniformly distorted compared to the
transmitted waveform. The correlated replica profile is however uniformly
distorted to a degree which varies with position in SR1. The apparatus is
arranged to produce a uniform contraction when the replica occupies
elements 1 to 751, the contraction decreasing with position along SR1
until the replica is centrally located. Similarly the correlated replica
is uniformly expanded when occupying elements 101 to 851, the expansion
decreasing towards the central position.
The correction display unit 26 is arranged to receive a horizontal time
base or line scan signal RL, this being produced by the raster generator
22 from the output of the scanning clock 21 controlling the replica
position in SR1. The raster generator 22 also produces a frame scan signal
RF. RF is a ramp waveform with superimposed range-Doppler crosstalk
correction, the ramp beginning with the transmission of a sonar pulse and
continuing for most of the interpulse interval. The raster generator
receives a line sync. signal C2 from the control unit 21, the signals
C2,RF and RL being shown in FIG. 2.
The scanning clock 21 moves the replica stepwise from one end of SR1 to the
other, correlation being performed at each step. The replica is then
scanned by the clock 21 in the opposite direction along SR1 after the next
electrical signal sample. Scanning the position of the replica along SR1
towards element 851 simulates a sonar waveform varying in Doppler shift
from positive (approaching target) through zero when the replica is
central to negative (receding target). The output of the summing amplifier
25 is maximum when the waveform of a received sonar pulse is present in
the electrical signal stored in SR2, and the replica has reached a point
in its scan where the simulated Doppler shift of the replica matches that
of the waveform. The intensity of the display unit 26 is arranged to
brighten in proportion to the correlation output signal, and reaches a
maximum at maximum correlation between the scanning replica and the
electrical signal in SR2. The horizontal time base scale is calibrated to
give relative target velocity, derived from Doppler shift and replica
position. The vertical time base is calibrated in terms of target range,
since received pulses or waveforms from more distant targets appear later
in SR2. The position of maximum intensity on the display may accordingly
be read directly to yield both relative velocity and range of a
sonar-detected target.
A minor degree of range-to-Doppler crosstalk is experienced in the
apparatus of FIG. 1, since Doppler-contracted signals are correlated
earlier as they move along SR2 than occurs for Doppler-expanded signals.
This is corrected by slightly modifying the ramp frame scan signal RF as
shown in FIG. 2, so that the ramp slope changes when each sample is taken
into SR2.
FIGS. 3 and 4 show computer simulations of Doppler scanning correlator
outputs, and illustrate correlation for sonar pulses having frequency
modulation which is respectively linear "V-chirp" and random or hopping.
The latter corresponds to S1 in FIG. 2. Since it is difficult to
illustrate intensity variation graphically, in FIGS. 3 and 4 the
correlator output has been added to the vertical time base. The peak in
either case indicates maximum correlation and hence Doppler shift and the
position of the base of either peak indicates target range. The peaks are
sharp, greatly facilitating target location and determination of Doppler
shift.
Parameters of the apparatus shown in FIG. 1 are as follows. For a sonar
system, a probable maximum relative velocity between transmitter and
target would be 50 m/sec or 100 knots. This would be positive or negative,
ie towards or away from the sonar transmitter. A total Doppler scan in SR1
of 100 elements corresponds to .+-.50 elements either side of zero Doppler
shift. This provides 2% resolution, 1 m/sec or 2 knots. The Doppler shift
at a relative velocity of 100 knots is .+-.6.6%, so the length of the
Doppler-shifted waveform in SR2 varies from 93.4% to 106.6% of its
unshifted length. The maximum change in correlated profile length over a
scan of 100 elements in SR1 is arranged to correspond to this. The
correlated profile length as has been mentioned varies from 418 to 477
multiplier-connected elements of SR1, the ratio of 418 to 477 being equal
to 93.4/106.6, or about 0.875. The data sampling clock 17 is arranged to
sample the electrical signal at a rate which is appropriate to achieve
storage of the waveform on between 418 and 477 elements of SR2, according
to Doppler shift.
The numbers of elements, the replica scan, and the geometrical progression
employed in SR1 and SR2 are chosen as follows. A convenient size for SR2
is chosen as 512 elements, and a suitable geometric progression and
corresponding replica scan length are calculated to yield the desired
degree of Doppler shift variation. The 512th term of the geometric
progression then determines the size of SR1, in this case 851 elements.
The maximum and minimum correlated replica sizes, equal to the maximum and
minimum Doppler-shifted waveforms which can be correlated, are then
determined from the number of correlated elements in SR1 occupied by the
replica at either end its scan.
The maximum scanning and sampling rates are dictated by the shortest time a
signal may be shifted from one element to the next along SR1 or SR2, and
this gives the minimum clock period. For an array of charge-coupled
devices, the minimum clock period is 0.1 microseconds. The minimum scan
time is the product of the minimum clock period and the number of elements
scanned in SR1 together with some allowance for multipliers to settle.
For the linear period clock 18, the ratio of the longest to the shortest
replica sampling interval is about 3.51. A small quantisation error occurs
since the multiplier-connected or correlated elements of SR1 are spaced in
a manner which does not correspond exactly to a geometric progression, but
only as nearly as possible for a linear array of discrete elements. The
error may be reduced by increasing the number of replica samples taken at
the expense of increased scanning time and additional storage
requirements--the number of elements in SR1 and SR2.
The quantisation errors could be eliminated by employing as storage devices
continuous or stepless delay line, the correlated or multiplier-connected
points being spaced alon SR1 exactly in accordance with a geometric
progression. In practice however it is found to be convenient to employ
linear arrays of discrete elements, and quantisation errors are not
serious in the embodiment described.
FIG. 5 illustrates a modification to the circuit of FIG. 1 to compensate
for charge transfer inefficiency and leakage experienced in charge-coupled
devices, which would tend to degrade stored signals. Parts of FIG. 5
corresponding to FIG. 1 are like-numbered but with a prefix of 100. The
waveform from the signal generator 16 is sampled at non-uniform intervals
into a digital store 127 by the linear period clock 118. If the
transmitted signal were computer-generated the store 127 might form an
integral part of the signal generator 116. The waveform in the digital
store 127 is available both for supplying the sonar output from the
transmitter 110 and for periodically refreshing the replica stored in
SR101. It is not necessary to employ a digital store in combination with
SR102, since the electrical signal in SR102 is periodically refreshed with
fresh signal samples by the data sampling clock 117.
The replica stored in SR101 may be refreshed after every Doppler scan from
the digital store 127 at the expense of increasing the scan period
appreciably.
Since the store 127 is digital, whereas SR101 and the transmitter 110 are
analogue, the waveform and replica output signals from the store 127
undergo digital to analogue conversion before being fed respectively to
the transmitter 110 and SR101.
FIG. 6 shows a modification to the arrangement of FIG. 5 in which
equivalent parts have like references with a prefix 200. In FIG. 6, a
multiplexing device 228 is arranged to allow random access to each element
of SR201 to refresh the replica from the waveform stored in the digital
store 227. By means of the multiplexer 228, a small number of replica
samples in SR201 may be refreshed during each Doppler scan on a rota
basis. After a given number of scans the replica may then be wholly
refreshed. This allows the total scan time to be reduced as compared to
that for the FIG. 5 arrangement.
A further embodiment of the invention is illustrated in FIG. 7, in which
previously described parts are indicated by like references with the
prefix 300. In this embodiment, the storage device SR301 is of digital
form, this being particularly economical if the replica is a simple binary
or two-state waveform. A multiplier array 329 is provided by a network of
analogue switches, since each replica sample stored on a respective
element of SR301 corresponds only to an "ON" or "OFF" state. The effect of
this is to correlate with the phase information in the waveform, rather
than with amplitude and phase information as in the FIGS. 1, 5 and 6
arrangements.
FIG. 8 illustrates a further embodiment of the invention in which
previously described parts have like references with the prefix 400. In
FIG. 8, the Doppler scanning matched filter 409 comprises digital stores
SR401 and SR402 with a microprocessor array 430 for multiplication or
correlation purposes. The digital stores SR401 and SR402 are provided by
digital shift registers. Further rationalisation may be carried out by
integrating SR401, SR402, the multiplexer array 430 and the signal
generator 416 to produce an integrated array processor. SR401 may also be
used to store a master replica of the sonar waveform. The transmitted
acoustic sonar signal may then be generated directly from the stored
replica, a separate signal generator being unnecessary. New transmitted
signals may be generated by a computer and stored digitally in SR401 prior
to transmission. This arrangement also avoids any requirement to refresh
the replica, since digital stores do not degrade with time significantly.
FIG. 9 shows a further embodiment of the invention arranged to compensate
for phase shift between the replica and the waveform. Parts corresponding
to those previously described have like references with the prefix 500.
The circuit of FIG. 9 corresponds to any of the arrangements of FIGS. 1,
5, 6, 7 or 8 but including twin Doppler matched scanning filters 509 and
509Q. In filter 509 the electrical signal from the receiver 511 is
correlated with an in-phase replica signal S1, and in filter 509Q
correlation is against a quadrature replica signal S1Q. The correlation
outputs of the filters 509 and 509Q are squared, and then summed by the
amplifier 525 for subsequent display on the unit 526. If the sonar pulse
waveform experiences a phase shift .theta. before being received by the
receiver 511, the correlation outputs of the filters 509 and 509Q will be
proportional to cos.sup.2 .theta. and sin.sup.2 .theta. respectively.
These outputs accordingly sum to the square of the waveform correlation
signal without phase shift.
The FIG. 9 arrangement embodies four storage devices, two for the
electrical signal and two for the replica. If necessary both phases of the
replica may be correlated against a single stored electrical signal to
avoid employing a fourth storage device. It is envisaged however that the
storage devices would be laid down in pairs each on a single substrate, in
which case it will be convenient to employ two pairs.
TABLE 1
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DOPPLER SCAN SIMULATION
DEVICE PARAMETERS
______________________________________
SOUND VELOCITY 1500.00 MPS
MAX DOPPLER SHIFT 0.0660
NO OF DOPPLER LEVELS 100
NO OF CORRELATION POINTS
512
NO OF EFFECTIVE POINTS 418 to 477
NO OF STAGE IN NUTDL(SR1)
851
MIN CLOCK PERIOD 0.00000010
SEC
DATA SAMPLING PERIOD 0.00001796
SEC
SAMPLING FACTOR 1
MIN SCAN TIME 0.00001010
SEC
WAVEFORM PULSE LENGTH 0.00800000
SEC
RATIO OF
LONGEST TO SHORTEST PERIOD
3.51
NORMLZD QUANT TIME ERROR
SDEV 0.1955
NUTAP POSITIONS 1 TO 851
(Correlator-connected points in SR1)
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1 178 322 442 546 638 719 793
4 180 324 444 548 639 720 794
7 183 326 446 549 640 722 795
10 185 328 447 551 642 723 796
13 188 330 449 552 643 724 797
16 190 332 451 554 644 725 798
19 192 334 452 555 646 726 799
22 195 336 454 557 647 728 800
25 197 338 456 558 648 729 801
28 200 340 458 560 650 730 803
31 202 341 459 561 651 731 804
34 204 343 461 563 652 732 805
37 207 345 463 564 653 733 806
40 209 347 464 565 655 735 807
43 211 349 466 567 656 736 808
45 214 351 468 568 657 737 809
48 216 353 469 570 659 738 810
51 218 355 471 571 660 739 811
54 221 357 473 573 661 740 812
57 223 359 474 574 662 742 813
60 225 361 476 576 664 743 814
63 227 363 477 577 665 744 815
65 230 365 479 578 666 745 816
68 232 367 481 580 668 746 817
71 234 368 482 581 669 747 818
74 237 370 484 583 670 748 819
77 239 372 486 584 671 750 820
79 241 374 487 586 673 751 821
82 243 378 489 587 674 752 822
85 245 378 490 588 675 753 824
88 248 380 492 590 676 754 825
90 250 382 494 591 678 755 826
93 252 383 495 593 679 756 827
96 254 385 497 594 680 758 828
99 257 387 498 595 681 759 829
101 259 389 500 597 683 760 830
104 261 391 502 598 684 761 831
107 263 393 503 600 685 762 832
109 265 394 505 601 686 763 833
112 267 396 506 602 688 764 834
115 270 398 508 604 689 765 835
117 272 400 509 605 690 767 836
120 274 402 511 607 691 768 837
123 276 404 513 608 693 769 838
125 278 405 514 609 694 770 839
128 280 407 516 611 695 771 840
130 282 409 517 612 696 772 841
133 285 411 519 613 698 773 842
135 287 413 520 615 699 774 843
138 289 414 522 616 700 775 844
141 291 416 523 618 701 776 845
143 293 418 525 619 702 778 846
146 295 420 527 620 704 779 847
148 297 421 528 622 705 780 848
151 299 423 530 623 706 781 849
153 301 425 531 624 707 782 850
156 303 427 533 626 708 783 851
158 305 428 534 627 710 784
161 307 430 536 628 711 785
163 309 432 537 630 712 786
166 311 434 539 631 713 787
168 314 435 540 632 714 789
171 316 437 542 634 716 790
173 318 439 543 635 717 791
176 320 441 545 636 718 792
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