 |
Description  |
|
|
BACKGROUND OF THE INVENTION
Radars have generally used analog signal processing for a tracking loop to
maintain output data of range, velocity and/or acceleration data for
subsequent use. However, accuracy of such systems is limited due to, among
other things, shifting of the frequency spectrum of the returned echo due
to motion of the antenna or motion of the echo producing target with
respect to the antenna. Attempts to improve the accuracy by digitizing the
signals and utilizing digital processing accentuate these errors
particularly if the processing converts signals from the time domain to
the frequency domain, for example, in a fast fourier transformer since the
errors now show up as shifts in the frequency components.
SUMMARY OF THE INVENTION
The aforementioned problem is overcome and other advantages are provided by
an FMCW system for radar and sonar which provides an estimate of target
range as well as a measurement of the radial components of target velocity
and acceleration. In accordance with the invention, the system
incorporates a spectrum analysis of the difference between the actual
range of the target and the estimated range of the target to accomplish a
measurement of the target range which is substantially free of the
aforementioned error resulting from the radial components of target
velocity and acceleration. The system includes analog-to-digital
converters for converting the analog radar signals to a digital format.
The difference between the actual and the estimated ranges is accomplished
by a mixing of the received target echo signal with a replica of the
transmitted signal, the replica being suitably modified, in a manner to be
described, to provide an estimate of range which is free of the radial
velocity and radial acceleration of the target. The mixing may be
accomplished by analog or digital multiplication employing both real and
imaginary components to provide complex digital signals suitable for use
by a fast Fourier transformer. The difference signal appearing at the
output of the mixer is then applied to a fast Fourier transformer (FFT)
which provides a spectrum analysis of the difference signal, the spectrum
analysis comprising a set of complex digital frequency terms which are
obtained from a set of samples of the difference signal.
In a preferred embodiment of the invention, the transmitted continuous wave
signal is modulated in frequency with a sinusoidal pattern, the sinusoidal
pattern providing Fourier frequency components which are described by
Bessel functions. The period of the sinusoidal pattern is much longer, an
exemplary ten times longer, than the round-trip propagation time of a
radar signal, or sonar signal, propagating between the system and the
target. Thereby, the measurement of range is accomplished by using the
quasi-linear region of the sinusoidal pattern. The spacing between the
spectral lines is dependent on the repetition frequency of the sinusoidal
modulation pattern as well as on the relative movement between the target
and the radar system. For stationary targets, the spacing of the spectral
lines is constant. For targets having a constant radial component of
velocity, the spectrum is scaled but, for adequate measurement accuracy,
the spacing between the lines may still be regarded as being constant.
However, for the case of a radial component of acceleration of the target,
the spacing and magnitudes of the spectral lines are so altered that a
linear sweep of frequency modulation must be applied to the replica signal
to compensate for the acceleration term. Accordingly, the system is
provided with a second order tracking loop, responsive to the relative
magnitudes of the spectral terms, and an estimator of target radial
acceleration, responsive to successive values of the spectral terms, which
individually modify the replica signal so as to cancel the effects of the
Doppler induced modulation on the echo signal. Thereby, a precise
measurement of the range can be made by comparing the echo with the
modified replica. The preferred embodiment of the invention will be
described with reference to a radar, it being understood that the
teachings apply also to sonar for underwater target location and medical
ultrasound for noninvasive imaging or moving organs in a living organism.
BRIEF DESCRIPTION OF THE DRAWINGS
The aforementioned aspects and other features of the invention are
explained in the following description taken in connection with the
accompanying drawings wherein:
FIG. 1 is a block diagram of a radar system incorporating the invention;
FIG. 2 shows waveforms of signals on lines A and B of FIG. 1;
FIG. 3 shows a frequency difference as a function of time for various
round-trip propagation times of the radar signal between an antenna and a
target aircraft of FIG. 1, FIG. 3 representing the difference in frequency
between the two graphs of FIG. 2;
FIG. 4 is a block diagram of a range deviation estimator of FIG. 1;
FIG. 5 is a block diagram of a range tracking filter of FIG. 1;
FIG. 6 is a block diagram of a range rate tracking filter of FIG. 1; and
FIG. 7 is a block diagram of an acceleration estimator of FIG. 1.
DESCRIPTION OF THE PREFERRED EMBODIMENT
Referring now to FIGS. 1 and 2, there is seen a radar system 20 comprising
a transmitter 22 and a receiver 24 which are coupled via a
transmit-receive circuit 26 to an antenna 28 for transmitting signals to a
target, shown as an exemplary aircraft 30, and for receiving echoes
therefrom. The system 20 further comprises a signal processor 32 and a
display 34, the processor 32 being coupled to both the transmitter 22 and
the receiver 24 for extracting range and range rate data therefrom and
presenting the data on the display 34.
The transmitter 22 comprises a voltage controlled oscillator 36, a mixer
38, an oscillator 40 which provides the carrier frequency, an amplifier
42, and a modulator 44 which modulates the frequency of the oscillator 36.
The modulator 44 comprises a clock 46, a square wave generator 48 and a
low pass filter 50. The modulator 44 provides a sinusoidal waveform at a
frequency designated by clock pulses of the clock 46. The generator 48, in
response to the clock pulses of the clock 46, provides a square waveform
signal which is applied to the filter 50. The filter 50 extracts the
fundamental component of the square wave, the fundamental component being
a sine wave signal which has the desired frequency and is applied to the
oscillator 36 for modulating the frequency thereof. For example, the
oscillator 36 may produce a nominal frequency of 10 megahertz (MHz) which
is modulated at an exemplary modulation frequency of 100 hertz (Hz) with a
frequency deviation of 100 kilohertz (kHz). The carrier frequency of the
oscillator 40 may have an exemplary value of 10 gigahertz (GHz), the mixer
38 being coupled to both the oscillators 36 and 40 for translating the
signal of the oscillator 36 to the x-band carrier of the oscillator 40.
The signal of the mixer 38 is amplified by the amplifier 42 to a power
level suitable for transmission to the target aircraft 40.
The receiver 24 is seen to comprise an amplifier 52, mixers 54 and 56, and
a 90.degree. phase shifter 58. The amplifier 52 amplifies the echo
received from the aircraft 30 to a suitable amplitude for operating the
mixers 54 and 56, the amplifier 52 being understood to include a bandpass
filter which is tuned to the frequency of the echo as is well known in
radar systems. A reference signal from the oscillator 40 is applied
directly to the mixer 54 and, via the phase shifter 58, to the mixer 56
for providing in-phase and quadrature translation of the echo signal to
in-phase and quadrature intermediate frequencies (IF). The IF signals of
the mixers 54 and 56 are seen to fan into line B whereby they are coupled
to the processor 32. Also, a reference signal from the oscillator 36 is
coupled via line A to the processor 32 to permit a comparison between the
transmitted signal and the echo signal.
As seen in FIG. 2, the signals on the lines A and B have the same frequency
modulation pattern, the pattern on line B being delayed from that on line
A. The clock 46 of FIG. 1 serves as the source of timing signals,
identified by the legend C, for the elements of the processor 32 as well
as for generating the modulation waveform to provide a common time base
for the measurement of the target range. As seen in FIG. 2, the period of
the modulation waveform is much longer than the propagation time of the
signal from the antenna 28 to the target and back to the antenna 28.
Thereby, a measurement utilizing the leading edges of the modulation
waveform is performed within a substantially linear region of the
sinusoidal waveform.
Referring also to FIG. 3, there is seen a graph of the frequency difference
between the frequencies of the modulation waveforms of the two graphs in
FIG. 2. For durations of propagation time to the target which are small
compared to the period of the modulation waveform, FIG. 3 shows a
substantially linear relationship of frequency difference versus
propagation delay. The range of the target is proportional to the
propagation delay and, accordingly, the delay serves as a measure of the
target range.
In accordance with the invention, it is noted that the use of the
sinusoidal frequency modulation provides a spectrum to both the
transmitted signal and the echo which has the form of a line spectrum
wherein the spectral lines are spaced apart by multiples of the modulation
frequency. The processor 32 provides a range estimate in the form of a
signal having the same modulation as the echo and which coincides
temporally therewith. By matching the delay of the estimate with the
propagation delay of the echo, the processor 32 obtains the range of the
target. As will be described hereinafter, in accordance with the
invention, the processor 32 utilizes the spectral components for adjusting
the range estimate to provide coincidence between the signal representing
the range estimate and the echo signal. In view of the frequency
modulation, the range data is obtained from a frequency measurement.
Furthermore, since the processor 32 employs a feedback loop wherein the
frequency of the range estimate is compared to the frequency of the echo,
as will be described hereinafter, the measurements are obtained in the
manner of a sliding window in the frequency spectrum wherein the sliding
is due to a Doppler shift associated with movement of the target. Thus, a
feature of the inventive processing of the echo signal is the capability
to perform the range measurement independently of the Doppler frequency, a
single term of the spectrum, the J.sub.O Bessel term as will be described
hereinafter, being found in the loop error signal when a proper match is
obtained between the range estimate and the echo. Thus, the target radial
velocity may be regarded as being normalized during the signal processing
of the processor 32 since the measurement is accomplished independently of
the magnitude of the radial velocity.
The processor 32 is seen to comprise three mixers 61-63, an
analog-to-digital converter 64, a fast Fourier transformer 66, a range
deviation estimator 68 which will be described with reference to FIG. 4, a
range tracking filter 70 which will be described in FIG. 5, a range rate
tracking filter 72 which will be described with reference to FIG. 6, an
acceleration estimator 74 which will be described with reference to FIG.
7, a digital inverter 76, a swept frequency generator 78 and a voltage
controlled oscillator 80. The mixer 61 is seen to comprise two sections,
one for the in-phase signal and one for the quadrature signal on line B.
The mixer 61 is seen to comprise two sections, one for the in-phase signal
and one for the quadrature signal on line B. The mixer 61 provides a pair
of output signals, one from each section of the mixer 61, each section of
the mixer 61 being understood to include well-known bandpass filters for
extracting output signals having frequencies equal to the difference in
frequency between the signals on line B and the signal, identified in the
Figure as the range estimate, from the mixer 62. The converter 64 is
similarly understood to include two sections for converting each signal of
the pair of signals from the mixer 61 to a pair of digital signals which
form the real and imaginary parts of a complex digital signal provided by
the converter 64 and applied to the transformer 66. The converter 64 is
strobed by clock pulses from the clock 46 for sampling the signals of the
mixer 61 at a rate equal to, and preferably somewhat greater than, the
Nyquist sampling rate.
The transformer 66, as is well known, in response to clock signals of the
clock 46, accepts a sequence of the complex digital samples from the
inverter 64 to provide a sequence of complex digital numbers representing
the magnitude and phase of a set of Fourier spectral components of the
output signal of the mixer 61. The spacing between the spectral lines, in
the frequency domain, is dependent on the number of samples in the
foregoing sequence, a larger number of samples in the sequence providing a
finer resolution of the spectrum. For example, in the situation wherein
the modulating frequency of the modulator 44 has been selected at 100 Hz,
in which case the spectral lines of the output signal of the mixer 61 are
spaced apart at intervals of 100 Hz, the transformer 66 is advantageously
provided with a spectral resolution of a smaller frequency increment, an
exemplary 50 Hz, for making an accurate measurement of Doppler frequency.
With respect to the sampling rate of the transformer 66, the foregoing
sequence, or batch, of input samples to the transformer 66 occupies an
interval of time which may be referred to as the batch interval. Thus, one
set of spectral lines is obtained per batch interval. And, similarly, with
respect to a single line of the spectrum such as the line for the J.sub.0
term of the spectrum, samples of the J.sub.0 term appear at the output
terminal of the transformer 66 at a rate wherein the intersample interval
is equal to the batch interval. As a further example, if the converter 64
is strobed at a rate of 100 kHz, and a sequence of 1024 samples is
employed for each batch, then Doppler data of a moving target is obtained
from the J.sub.0 term at a rate of approximately 100 samples per second.
In the embodiment of FIG. 1, it is noted that the mixers 61-63 provide an
analog mixing function. By way of alternative embodiments, it is noted
that the mixers 61-63 may be composed of digital multipliers for
accomplishing the mixing functions digitally. To accomplish the
alternative digital implementation of the mixers 61-63, as may be
desirable in the situation wherein the entire processor 32 is to be
accomplished by digital microcircuits, the converter 64 would be placed in
line B to provide digital signals for the mixer 61, the output terminal of
the mixer 61 being coupled directly to the transformer 66. Similarly, an
additional converter (not shown) would be provided in line A for
converting the reference signal therein to a digital format for the mixer
63.
The processor 32 is constructed in a feedback configuration having both an
outer loop and an inner loop. The outer loop is seen to comprise the
converter 64, the transformer 66, the estimator 68, the range tracking
filter 70, the oscillator 80, and the mixers 61-63. The inner loop shares
the converter 64, the transformer 66, and the range deviation estimator 68
with the outer loop. The inner loop further comprises the range rate
tracking filter 72, the acceleration estimator 74, the inverter 76, and
the swept frequency generator 78, the inner loop being closed by the
mixers 61 and 62. The inner loop compensates for movement of the target
relative to the antenna, the compensation permitting the outer loop to
function as though the target were stationary. Accordingly, in analyzing
the operation of the outer loop, it may be presumed that the target is
stationary.
The error signal for the feedback configuration is found at the output
terminal of the transformer 66. As can be seen with reference to FIGS. 2
and 3, the data provided by the system 20 is in the form of a frequency
and its time of occurrence. The frequency resulting from the mixing of the
range estimate with the target echo on line B, as shown in FIG. 1 adjacent
the transformer 66, is seen to be composed of the sum of a fixed term
F.sub.o plus the modulation f.sub.m (t) provided by the modulator 44 as a
function of time, plus the modulation f.sub.m (t-.tau.) as delayed by the
round-trip propagation time .tau. to the aircraft 30, plus a term f.sub.R
(.tau.), which is provided by the oscillator 80 and is proportional to the
propagation time .tau. and the range R. The frequency components resulting
from the mixing of the range estimate with the target echo on line B are
extracted by the transformer 66. Accordingly, the signal provided by the
transformer 66 is identified as the range error in FIG. 1.
The feedback configuration provides a waveform, namely, the waveform of the
aforementioned range estimate, which has the same form as the echo signal
received on line B, this being accomplished with the aid of the
transmitted reference signal on line A. Thus, the reference signal on line
A provides the processor 32 with the requisite waveform, while the
processor 32 provides the compensation for the round-trip propagation
delay between the antenna 28 and the target to provide the range estimate
in temporal coincidence with the echo on line B. In the case of a
stationary target, there is a direct relationship between the frequency of
the echo and the target range as may be seen with reference to FIGS. 2 and
3. The frequency difference increases with target range or, equivalently,
the round-trip propagation time. As was noted hereinabove, the modulation
waveform has a period much longer than that of the propagation time, the
frequency difference between the two graphs of FIG. 2 rising linearly as a
function of range for propagation times which are relatively short
compared to the period of the modulation. The linearity drops off for
larger values of propagation time as is shown by a dashed portion of the
trace of FIG. 3. Accordingly, the delay compensation to be provided by the
processor 32 is accomplished by offsetting the frequency of the reference
signal of line A. In the case of a stationary target, the offsetting is
fully accomplished by the oscillator 80 providing the signal on line D to
the mixer 63, the frequency of that signal being portrayed in FIG. 3. In
the event of a moving target, the compensation of the inner loop provides
an additional frequency offset of the generator 78 which is combined with
that of the oscillator 80 by means of the frequency addition of the mixers
63 and 62. Accordingly, the voltage applied to the oscillator 80 for
controlling its frequency is proportional to the propagation time and to
the target range (or loop range in the case of a bi-static radar system,
not shown) in both the cases of a stationary target and a moving target.
Referring now to FIG. 4, the range deviation estimator 68 receives the
range error on line 82 from the transformer 66 in the form of spectral
lines, and provides on line 84 a voltage having an amplitude proportional
to the range error. The estimator 68 provides on line 86 a voltage having
a magnitude proportional to the range rate. In the upper left corner of
FIG. 4 is presented an exemplary graph 88 of the signal on line 82 for the
situation wherein the range estimate of FIG. 1 does not fully coincide
with the target echo on line B of FIG. 1. Such a spectrum is
characteristic of a sinusoid wherein the frequency thereof is modulated
with a sinusoidal modulation pattern, the spectrum being described in the
book "Reference Data for Radio Engineers", fifth edition, published by
Howard W. Sams & Co. in 1968, at pages 21-7 and 21-8. The spectrum of the
graph 88 has lines at the specific frequencies, or output slots, of the
transformer 66 of FIG. 1. The spectrum of the graph 88 is seen to be a
line spectrum with the magnitudes of the frequency components being given
by Bessel terms, the lines being spaced apart in increments of the
modulation frequency.
When the range estimate is in temporal coincidence with the received echo,
only the J.sub.0 term appears in the spectrum. The magnitude of the
J.sub.0 term is proportional to the strength, or amplitude, of the
received echo signal. Its location, or address, along the frequency axis
is proportional to the range rate, or Doppler frequency, of the target. In
view of the aforementioned exemplary spacing of 50 Hz between the output
frequency slots of the transformer 66, the possible locations of the
J.sub.0 term are quantized to increments of 50 Hz along the frequency
axis. In the event that the range estimate does not fully coincide
temporally with the received echo, then the higher Bessel terms, such as
the J.sub.1 and the J.sub.2 terms, appear. The ratio of the magnitude of
the sum of the J.sub.1 term to the magnitude of the J.sub.0 term is a
measure of the lack of temporal coincidence and, hence, a measure of the
error signal for the outer loop of the processor 32. In the event of
target acceleration in the radial direction between the antenna 28 and the
target aircraft 30 of FIG. 1, the spectral lines of the graph 88 are seen
to broaden, the broadening being manifested by the appearance of digital
terms at neighboring output frequency slots of the transformer 66 with a
diminution of the amplitude of the various spectral lines of the graph 88.
The higher-order spectral lines constitute a residual frequency modulation
which is utilized by the estimator 68 to provide the error signals on the
lines 84 and 86 which drive the outer and inner loops of the processor 32
to bring the range estimate into coincidence with the received echo. A
shifting of the position of the J.sub.0 term to the right indicates that
the target is drawing near to the antenna 28, while a shifting to the left
of the graph 88 indicates that the target is receding from the antenna 28.
The estimator 68 is seen to comprise a threshold unit 90, a computation
unit 92, a selector 94, a multiplier 96, and a source 98 of a scale factor
for use in the multiplication operation of the multiplier 96. The
threshold unit 90 comprises a gate 100, a comparator 102, and a source 104
of a reference signal for use by the comparator 102. The selector 94
comprises a memory 106, an address generator 108 for addressing the memory
106, gates 110 and 112, a comparator 114, registers 117, 118 and 119,
adders 121 and 122, and encoder 124.
The spectral terms on line 82 are coupled sequentially through the
threshold unit 90 to the selector 94. The comparator 102 in the threshold
unit 90 compares the amplitudes of each of the spectral terms with a
reference signal from the source 104 to insure that only such terms as are
above the noise level are coupled to the selector 94. In the case of
spectral terms having an amplitude greater than that of the reference, the
comparator 102 activates the gate 100 to pass the spectral term to the
selector 94. Spectral terms having an amplitude lower than the threshold
are inhibited by the gate 100 from entering the selector 94.
The selector 94, as will be described hereinafter, stores the values of the
spectral lines in the memory 106. The values of the J.sub.0 term and the
J.sub.1 terms are read out of the memory 106 into the computation unit 92
which, as seen by the formula in FIG. 4, computes the sum of the positive
and negative J.sub.1 terms, and then divides the sum by the magnitude of
the J.sub.0 term to provide the range error signal on line 84. As noted
hereinabove, the presence of the higher-order terms shown an error in the
estimate of the target range and of the round-trip propagation time such
that the range estimate does not coincide with the received echo.
Essentially, only the J.sub.1 term appears for a slight error in the range
estimate. Further Bessel terms such as the J.sub.2 and the J.sub.3 terms
appear in the presence of successively poorer estimates of the target
range. However, even though the higher-order terms are representative of
an error in the range estimate, the J.sub.1 and the J.sub.0 terms, provide
a sufficiently accurate measure of the range error for frequency
modulation indices of the modulator 44 which are less than or equal to
unity. Also, even in the situation of a varying radial velocity of the
target, the compensation provided by the inner loop of FIG. 1 results in
the presence of primarily the J.sub.0 and J.sub.1 terms in the spectrum
after the inner loop has provided its compensation. Accordingly, a
sufficiently accurate representation of the error signal is obtained by
the computation involving only the J.sub.1 and J.sub.0 terms.
The selector 94 selects the J.sub.0 term and the two J.sub.1 terms from the
error spectrum provided by the transformer 66. The selection is
accomplished by detecting the spectral line with the largest amplitude,
this line being the J.sub.0 term. The two J.sub.1 terms are then
understood to be equally spaced about the J.sub.0 term at a spacing equal
to multiples of the FFT spectral resolution or spacing of the output slots
of the transformer 66. For example, in the event that the spectral
resolution is half of the modulation frequency, as in the aforementioned
exemplary modulation frequency of 100 Hz with a spacing of 50 Hz between
output slots of the transformer 66, then the J.sub.1 terms are spaced
apart from the J.sub.0 term by two of the frequency slots. In the event
that the transformer 66 provides a finer frequency resolution with a slot
spacing of only 25 Hz, then the 100 Hz line spacing of the spectral lines
in the graph 88 is equal to a spacing of four frequency slots of the
transformer 66. In the addressing of the memory 106 by the address
generator 108, it is noted that the generator 108 is strobed by clock
pulses from the clock 46 of FIG. 1 as is the transformer 66 so that the
generator 108 can address a separate slot in the memory 106 corresponding
to each output frequency slot of the transformer 66. Accordingly, as the
spectral lines are sequentially presented by the transformer 66 to the
estimator 68, each of the spectral lines which are passed by the threshold
unit 90 are sequentially stored in the memory 106 at locations
corresponding to the locations of the frequency slots of the transformer
66. Upon determining the address of the largest spectral line, the J.sub.0
term, the addresses of the two J.sub.1 terms are then obtained by simply
adding an integer to the address and subtracting the integer from the
address of the J.sub.0 term wherein the integer is equal to the foregoing
number of frequency slots between the spectral lines and the graph 88. The
integer is identified by the legend k in FIG. 4.
The spectral lines coupled from the threshold unit 90 to the memory 106 are
also coupled to the gate 110 and to the comparator 114 which compares the
magnitude of each spectral line to the magnitude of the largest previously
occurring spectral line. The magnitude of the largest previously occurring
spectral line is stored in the register 117. When the magnitude of the
most recent spectral line exceeds that which is stored in the register
117, the comparator 114 activates the gate 110 for entering the larger
spectral line into the register 117, the register 117 then discarding the
previously stored spectral line. In addition, the gate 110 also applies to
the register 118 the address of the most recent spectral line, the address
being the same address as is applied by the generator 108 to the memory
106. Thus, the two registers 117-118 store both the magnitude and the
address of the largest spectral line. It is recalled that the amplitude of
the largest spectral line, the J.sub.0 term represents the strength of the
echo signal, while the position of the J.sub.0 term along the frequency
axis, the position being designated by the address of the frequency slot
of the transformer 66, is a measure of the Doppler frequency and range
rate of the target. Accordingly, at the conclusion of the transmission of
the sequence of spectral lines from the threshold unit 90 to the memory
106, a clock signal from the clock 46 of FIG. 1 strobes the gate 112 to
pass the address of the J.sub.0 term from the register 118 to the
multiplier 96. The multiplier 96 then multiplies the address by a scale
factor from the source 98 to convert the address to the range rate which
appears on line 86 and, as noted above, is proportional to both the
address and to the Doppler frequency.
In order to obtain the addresses of the two J.sub.1 terms, the foregoing
integer k is to be added to the address of the J.sub.0 term to obtain the
address of the J.sub.1 term to the right of the J.sub.0 term in the graph
88, the integer k being subtracted from the address of the J.sub.0 term to
provide the address of the J.sub.1 term to the left of the J.sub.0 term in
the graph 88. The integer k is provided by a source 124 of a digital
signal, such as an encoder, for setting the spacing of the spectral lines
on the graph 88 in accordance with the number of resolution elements, or
frequency slots, of the transformer 66 between adjacent ones of the
spectral lines of the graph 88. The adder 121 sums together the value of k
with the address of the J.sub.0 term while the adder 122 subtracts the
value of k from the address of the J.sub.0 term. The output signals of the
adder 121 and 122 are the addresses of the J.sub.1 terms, these addresses
being stored in the register 119. The strobe signal from the clock 46 of
FIG. 1 strobes the register 119 to address the memory 106 to read out the
stored J.sub.0 and J.sub.1 terms from the memory 106 to the computation
unit 92. The computation unit 92 then performs the aforementioned
computation with the spectral terms to provide the range error signal on
line 84.
Referring now to FIG. 5, there is seen a block diagram of the range
tracking filter 70 of FIG. 1 which receives the range error signal on line
84 and provides the range on line 126. The filter 70 comprises summers
129-130, multipliers 133-134, sources 137-138 of signals serving as scale
factors, and integrators 141-142. The components of the filter 70 may
function in either an analog fashion or in a digital fashion. In the
analog case, the signals on lines 84 and 126 are understood to be analog
voltages having amplitudes which represent, respectively, the range error
and the range. The summers 129-130 are in the form of operational
amplifiers having summing input terminals. The multipliers 133-134 are in
the form of gain control amplifiers wherein the scale factors from the
sources 137-138 are analog voltages which are applied to the gain control
terminal. The integrators 141-142 take the form of operational amplifiers
having a capacitor in the feedback circuit to provide the function of an
integrator. In the event that the components of the filter 70 are to
function in a digital fashion, the signals on the lines 84 and 126 have a
digital format, it being understood that the computation unit 92 of FIG. 4
would provide a digitally formatted signal on line 84. The summers 129-130
take the form of digital adders, the multipliers 133-134 are digital
multipliers, the scale factor signals are digital signals, and the
integrators 141-142 may be any one of a number of well-known digital
integrating circuits as are commonly employed in computers and other
digital equipment.
The filter 70 is in the form of a second order filter in view of the double
integration provided by the integrators 141-142. The integrator 141
includes a feed forward path comprising the multiplier 134 and the summer
130. The output signal at line 126 is fed back to the input summer 129
wherein the output signal is subtracted from the signal on line 84. The
time constant and response time of the filter 70 is selected by the
magnitude of the scale factor from the source 138, that factor being
multiplied in the multiplier 134 by the signal on line 144. The overall
loop gain is selected by the magnitude of the scale factor from the source
137, that factor being multiplied in the multiplier 133 by the signal on
line 146. The output signal of the filter 70 on line 126 is proportional
to the range of the target from the antenna 28 in FIG. 1, the signal on
line 126 being applied to the display 34 of FIG. 1 for displaying the
range, and to the oscillator 80 for providing the sinusoid on the line D
having the frequency proportional to the range as has been described
hereinabove.
Referring now to FIG. 6, the range rate tracking filter 72 filters the
range rate signal on line 86 to provide a filtered range rate signal on
line 148 for the acceleration estimator 74 on FIG. 1. The filter 72
comprises a multiplier 150, a source 152 of a scale factor, a summer 154
and a delay unit 156. The components of the filter 72 may operate in
either an analog or digital fashion, as was described with reference to
the filter 70 of FIG. 5. Assuming a digital implementation of the filter
72 of FIG. 6, the delay unit 156 provides a delay equal to the batch
interval as was described previously with reference to the sampling rate
of the transformer 66 of FIG. 1. Thus, it is seen that the signal on line
86 is summed, via the summer 154, with the previously occurring signal,
the previously occurring signal having been delayed by the delay unit 156.
In addition, the previously occurring signal, before being applied to the
summer 154, is scaled at the multiplier 150 by the scale factor of the
source 152. The scale factor is less than unity so that the previously
occurring sample is reduced in amplitude before being summed with the
present sample on line 86 at the summer 154. The procedure repeats with
the foregoing sum being scaled and summed together with the next sample on
line 86. The configuration of the filter 72 is sometimes referred to as a
one-pole integrator.
Referring now to FIG. 7, the acceleration estimator 74 provides the
derivative of the input range rate signal on line 148, the derivative
appearing at the output terminal on line 158. The estimator 74 comprises
two delay units 161-162, two summers 165-166, two multipliers 169-170 and
two sources 173-174 of scale factors for use by the multipliers 169 and
170. The summer 165 forms the difference between a sample of the range
rate and the previous sample of the range rate. The delay of the delay
unit 161, as well as the delay of the delay unit 162, are the same as the
delay of the delay unit 156 of FIG. 6. The scale factor of the source 173
is proportional to the reciprocal of the batch interval so that, upon
multiplying the output sum of the summer 165, at the multiplier 169 by the
scale factor of the source 173, the sum of the summer 165 is effectively
divided by the length of time of the batch interval. Thus, the output
signal of the multiplier 169 is in the form of the derivative of the range
rate, the derivative being recognized as the ratio of the difference of
two samples of the range rate divided by the time interval between the two
samples. The summer 166, the delay unit 162, the multiplier 170 and the
source 174 are seen to correspond with, and to function as, the components
of the filter of the FIG. 6. Thus, the output signal of the estimator 74
on line 158 is the filtered derivative of the range rate of the input
signal on line 148.
With reference also to FIG. 1, the range rate signal on line 86 and the
derivative thereof on line 158 are coupled to the display 34 for the
displaying of the range rate, or target velocity, and the derivative
thereof, namely, the target acceleration. The sense of the target
acceleration on line 158 is inverted by the inverter 76 to provide the
compensation for the acceleration at the mixer 62. The generator 78
provides a sinusoidal signal having a frequency which is swept linearly in
time, the rate of sweep being proportional to the amplitude of the signal
applied to a control terminal of the generator 78 by the inverter 76.
Thus, in the absence of target acceleration, the rate of frequency
sweeping is zero with the result that the output frequency of the
generator 78 is constant. As the target recedes from the antenna 28, or
draws near to the antenna 28, the effect of the radial acceleration on the
range estimate at the output terminal of the mixer 62 is compensated by
the swept frequency of the generator 78. Due to the compensation, the
energies of the spectral terms on line 82 (portrayed in the graph 88 of
FIG. 4) do not spill over into adjacent frequency slots of the transformer
66 with the result that the J.sub.0 and J.sub.1 terms predominate to
provide a well defined error signal on line 84 for operating the outer
loop to provide the desired range on line 126 and the corresponding
frequency offset on line D. Thus, the spectrum of the difference between
the range estimate and the echo has been utilized to provide the range,
the radial velocity and the radial acceleration of the target.
It is understood that the above-described embodiment of the invention is
illustrative only and that modifications thereof may occur to those
skilled in the art. Accordingly, it is desired that this invention is not
to be limited to the embodiment disclosed herein but is to be limited only
as defined by the appended claims.
* * * * *
|
|
 |
|
</ |
