Signal processing method for eliminating velocity ambiguity in pulse phase dry method velocity measurement
Technical Field
The invention belongs to the technical field of signal processing methods, and particularly relates to a signal processing method for eliminating velocity ambiguity in pulse dry method velocity measurement.
Background
The method realizes the measurement of the velocity of a target object or a medium by using a Pulse-to-Pulse Coherent Doppler (Pulse-to-Pulse Coherent Doppler) method, and is widely applied to the fields of sonar and radar. For example, the meteorological radar realizes the measurement of atmospheric wind speed by using the method, the airborne radar realizes the speed measurement to the ground, and the ground radar realizes the speed measurement to an air target; an Acoustic Doppler Current Profiler (ADCP) realizes fluid flow velocity profile measurement by using the method, and medical ultrasound realizes blood flow measurement by using the method.
The basic principle of pulse coherent Doppler method speed measurement is that two identical radio frequency (radar or sonar) pulses s (T) are transmitted successively at a fixed interval T, and the pulse width is TbThe radio frequency pulse is scattered or reflected by a target (radar target or particle in water, etc.) in the medium, forming an echo. As shown in fig. 1.
Since the propagation speed of the radio frequency signal is much greater than the moving speed of the target, when the time interval between two times of transmitting the ultrasonic wave is short, the characteristics of the target do not change substantially, and the echoes corresponding to the two transmitted pulses can be considered to be coherent. However, the Doppler frequency shift f of the radio frequency echo is caused by the moving speed of the targetdThereby causing the width and the emission time interval of the echo signal of the radio frequency pulse to stretch.
If the moving speed of the target relative to the radio frequency transmitting and receiving device (leaving) is v and the propagation speed of the radio frequency signal is c, the delay of the second radio frequency pulse echo relative to the first pulse echo is:
by detecting the amount of change Δ T of the time interval according to the formula (1), the target velocity v can be obtained.
In consideration of signal expansion and contraction, the echo signals corresponding to two transmit pulses can be expressed as:
wherein x is1(t) and x2(T) two received echo signals (corresponding to a transmission interval of T), n1(t) and n2And (T) is zero-mean stationary complex Gaussian noise independent of the signal, and delta T is the time difference between two echo signals arriving at the radio frequency transceiver caused by target motion. Assuming that the noise is uncorrelated with the noise, and the signal is uncorrelated with the noise, x1(t) and x2(t) a cross-correlation function of
R12(τ)=R11(τ-ΔT) (4)
It can be seen that the cross-correlation function contains the time delays of the two signals.
The basic principle of the pulse coherent Doppler velocity measurement method is as follows: by aligning the target position (corresponding to echo time T in FIG. 1)r) And performing corresponding windowing interception on the two echo signals to obtain two sections of echo signal segments, and performing correlation processing to directly obtain the time delay of the two sections of signals, thereby obtaining the time interval variation.
However, since the accuracy of the correlation measurement delay is affected by the sampling rate, and when the sampling rate is not high enough, the error is large, in the case of high-accuracy measurement, the phase of the cross-correlation function is generally measured by using a cross-spectrum method or a cross-covariance method, so as to obtain the delay. According to the wiener-xinkeng theorem, the relationship between the signal cross-power spectral density function and the source signal self-power spectral density function can be known:
wherein f is the signal frequency, G
12(f) As a function of the cross-correlation R
12(τ) spectrum, i.e. cross-power spectral density function of the echo signal segments; g
11(f) As an autocorrelation function R
11The frequency spectrum of (tau) is a function of the self-power spectral density of the source signal,
the phase difference between the cross power spectrum and the self power spectrum density function can be obtained according to the phase difference between the cross power spectrum and the self power spectrum density function:
in the formula (6), E [, ]]Meaning that Δ T is averaged over all available frequencies, or may be centered at a frequency f0At instead. Then, the velocity can be obtained from the equation (2).
As can be seen from equation (6), the difference in phase between the cross-power spectrum and the self-power spectrum density function is due to
The range of variation is limited to [ - π, π]Phase values beyond this range are folded to [ - π, π]Interval, so there is an upper limit of the measurement speed using the pulse coherent Doppler velocimetry method, i.e.
Vm=c/(4f0T) (7)
The maximum measurable speed. Velocity aliasing occurs when velocity measurements are taken above this upper limit, so that the maximum measurable velocity range is [ -V ]m,+Vm]. The cross-correlation calculation can also be performed by quadrature demodulating the received signal to obtain the baseband signal, and thenAnd solving the time delay of the cross-correlation function peak value of the baseband signal.
Since the maximum measurable distance is limited by the transmission interval, is
Rm=cT/2 (8)
The simultaneous equations (7) and (8) show that:
namely, the range-distance dilemma, the maximum measurable speed is limited by the equation (9) when the distance is measured for a certain distance. When the real target speed exceeds the maximum measurable speed of the system, the real speed value can be mapped into a measurable speed interval in a certain corresponding relation, and a one-to-many mapping relation between the measured value and the real value of the speed is caused, namely the speed is fuzzy. For example, the true flow rate value in a flow rate measurement scenario is 4VmThe measured value is 0, while the real flow velocity value in the scene is 6VmWhen, the measured value is also 0. The correspondence between the actual and measured values of the flow rate can be expressed as
vt=va-2nVm (10)
Wherein v isaRepresenting true flow velocity, vtRepresenting the measured flow rate, and n is an integer representing the number of folds. The speed blur limits the application of this method to a large extent.
Various solutions have been proposed by many researchers to address the problem of speed ambiguity. The idea of resolving the ambiguity is to introduce redundant speed information and resolve the speed ambiguity by using the relationship between the measured values; the method mainly comprises the following steps:
(1) double pulse-repetition time (Dual PRT): using two different sets of transmit pulse repetition time intervals (T)1,T2) Two different maximum measurable speeds (V) are obtainedm1And Vm2) According to the speed mapping relation, obtaining a combination of 'maximum speed-folding times' under different time interval conditions, thereby solving a real speed v; for example, the above two timesAt intervals, the measured values of the true velocity v are respectively (v)1And v2) Can be expressed as
When the real speed value exceeds Vm1And Vm2At minimum value of both, v1And v2And are different within certain ranges. Due to v1And v2Is a measured value of the same real speed, both corresponding to the real speeds V, Vm1And Vm2Result in n1And n2The possibility of inter-difference exists, which provides the possibility of resolving the velocity ambiguity. Let Vm1And Vm2Has a ratio of
Vm1/Vm2=C1/C2 (12)
Wherein C is1And C2Is a positive integer greater than 1 and relatively prime, and 2C2>C1>C2. The maximum measurable speed of system expansion is C1And C2Least common multiple and normalization factor V ofm1/C1(or V)m2/C2) The product of (a). For example, Vm1=2m/s,Vm23m/s, the maximum measurable speed of the system expansion is 6m/s, and the maximum measurable speed after the deblurring process can be expressed as
Vm=C1Vm2=C2Vm1 (13)
When the true speed is-Vm~VmIn between, even if-V is exceededm1~Vm1or-Vm2~Vm2Can also be accurately estimated; FIG. 2 shows the folding of velocity when measuring velocity in a streaming scenario using two sets of pulse intervals, where v1The maximum measurable speed of the corresponding system is 3m/s, v2The corresponding maximum measurable speed of the system is 2 m/s. When the true velocity value exceeds 2m/s, the measured value v2Will be folded and realAt a velocity value exceeding 3m/s, the measured value v1Can also be folded; however, the two sets of speeds are different in the number of folds, and the folding pattern of the two sets of measurements is repeated at a period of 12 m/s. As can be seen from the above description, the double pulse repetition time method has a limited measurement range in which to extend.
(2) Multi-pulse repetition time method: including triple PRT, and multiple PRT (M-PRT), such as 9-PRT, which actually uses more pulse repetition time to extend the range of measurable velocities; the more pulse repetition time intervals are used, the larger the extendable velocimetry range is, but the more complex the algorithm is, the lower the reliability is.
(3) Double-pulse repetition frequency method (Dual-pulse repetition frequency, Dual-PRF): the transmitting terminal alternately transmits two beams of PRF with different pulse repetition frequencies1And PRF2The pulse train signal of (2) measures the target speed at two pulse repetition frequencies, and according to the formula (11), the two speed measurement values are equal or have a certain correlation, and the speed ambiguity can be solved by using the two correlated speed measurement values. This method is practically equivalent to the double pulse repetition period method.
(4) Multi-pulse carrier frequency method: each group of pulses adopts different carrier frequency combinations, and different phase differences can be obtained by the same Doppler frequency shift, so that different maximum measurable speeds can be obtained; the more the number of available frequency bands, the larger the expandable speed measurement range, but due to the limited frequency band resources, the expandable speed measurement range of the method is also limited.
(5) Multiple time-carrier frequency combination method: the multi-pulse repetition time is combined with a multi-carrier method to obtain a larger measurable speed range.
However, no matter the multi-pulse repetition time, the multi-carrier frequency or the combination of the two, the final expandable speed measurement range is limited, when the real speed exceeds the range capable of being effectively solved, the problem of speed folding (blurring) still exists, and the more the number of used repetition cycles is, the more the number of carrier frequency bands is, the more the algorithm is complex, and the worse the anti-interference capability is.
Disclosure of Invention
Aiming at the problem of velocity ambiguity (folding) widely existing in pulse coherent Doppler velocity measurement in the field of radar or sonar, the invention aims to provide a signal processing method for eliminating velocity ambiguity in pulse coherent Doppler velocity measurement.
In order to achieve the purpose, the invention adopts the following technical scheme:
a method for eliminating velocity ambiguity in pulse phase dry method velocity measurement comprises the following steps: the method comprises the following steps of speed pre-measurement, artificial delay speed measurement and speed weighting.
1. The speed prediction amount is realized by a method of adding a basic speed 11 and a speed offset amount 12 in an interval. As shown in fig. 3.
Firstly, determining a maximum measurable speed range 14 according to the maximum measurable speed 13 of a pulse coherent Doppler method, dividing the whole speed space into a plurality of speed intervals 15 by taking the maximum measurable speed range 14 as a unit, and marking each speed interval 15 by an integer number 16; the lower boundary speed of each speed interval 15 is the value of the lower boundary speed of the interval, the upper boundary speed is the value of the upper boundary speed of the interval, and the median of each speed interval 15 is taken as the basic speed 11 of the interval.
Secondly, obtaining the time difference between two echoes of the concerned target by using a time difference estimation method, such as a cross-correlation method; and (3) according to the speed value obtained by calculating the time difference, namely the rough-measured speed, searching the speed interval 15 where the rough-measured speed is located according to the rough-measured speed, and determining the basic speed 11 corresponding to the rough-measured speed.
Thirdly, a phase difference method, such as a cross power spectrum method, a cross covariance method and the like, is utilized to obtain an accurate phase difference between two echoes of the concerned target; and then estimating the accurate time delay by the phase difference, and calculating the speed offset 12 in the interval by the accurate time delay, wherein the speed offset 12 in the interval is a positive (or negative) speed offset value relative to the central value of the interval.
Finally, an original pre-measuring speed is obtained by adding the speed offset 12 in the interval to the basic speed 11, and the original pre-measuring speed is used as a speed pre-measuring result.
2. The artificial delay speed measurement is mainly characterized in that a time delay is artificially added to one echo signal, a speed offset corresponding to the time delay is generated on the basis of the original pre-measured speed, and the problem that the speed near the 15 boundary of each speed interval possibly generates interval jump (misjudgment) is solved. As shown in fig. 4.
Firstly, on the basis of original time delay 21 of original two echo signals, artificially delaying one echo signal for a period of time, namely adding an artificial time delay 22; the artificial delay 22 is typically added to the second echo and may be implemented by means of zero insertion in the digital domain.
Secondly, the speed value is recalculated through the speed prediction quantity to obtain a delay prediction quantity speed, and an artificial speed offset is added to the delay prediction quantity speed relative to the original prediction quantity speed.
The artificial time delay 22 generally adopts an additional phase difference approximately pi (within a range of pi ± pi/2) generated corresponding to two echoes, or an artificial speed offset approximately pi (within a range of the maximum measurable speed 13 plus or minus 1/2) of the maximum measurable speed 13, so that the speed at the boundary of the speed interval 15 is artificially moved to the vicinity of the center (the basic speed 11) of the speed interval 15, and the probability of generating interval jump is reduced.
The artificial time delay speed measurement can also use different time delay values to carry out multiple times of measurement, and by utilizing the time difference estimation method and the phase difference method, the basic speed after artificial time delay and the speed offset of the speed interval in which the basic speed is positioned are re-determined and added to obtain a plurality of time delay pre-measurement speeds.
And finally, subtracting the artificial speed offset corresponding to the artificial delay from the delay pre-measuring speed to obtain the corrected delay pre-measuring speed. In practical operation, the manual delay speed measurement may be performed by performing one or more manual delay operations only when the original predicted speed is near the boundary of the speed interval 15 (i.e., the lower boundary speed of the speed interval 15 plus 1/2 the maximum measurable speed 13 and the upper boundary speed of the speed interval 15 minus 1/2 the maximum measurable speed 13, where 1/2 the maximum measurable speed 13 may also be represented as the width of the 1/4 speed interval 15), so as to obtain one or more corrected delay predicted speeds.
3. The speed weighting is to give different weights to the original pre-measuring speed and the corrected delay pre-measuring speed, and is used for eliminating the measuring result with the maximum hop probability of the occurrence interval and keeping the result with the smaller hop probability of the interval. As shown in fig. 5.
Firstly, a weight function 30 in each speed interval 15 is determined, in each speed interval 15, the value of the weight function is determined by the original pre-measuring speed and the delay pre-measuring speed, and when the original pre-measuring speed and the delay pre-measuring speed are in different bit values of the speed interval 15, different weight coefficients are given to the original pre-measuring speed and the corrected delay pre-measuring speed. When the original pre-measuring speed and the delay pre-measuring speed are near the upper and lower boundaries of the speed interval 15 (within 1/2 ranges of the maximum measurable speed 13 increased or decreased by the speed values of the upper and lower boundaries), a weight (weight is less than or equal to 0.5) close to or equal to 0 is taken, and when the original pre-measuring speed and the delay pre-measuring speed are near the center (basic speed 11) of the speed interval, a weight (weight is more than or equal to 0.5) close to or equal to 1 is taken; when the difference is between the upper and lower boundaries and the central value (basic speed 11), the value is taken according to a certain weight function 30.
The weighting function 30 may be any function between the positive slope linear function 31 and the "inverse zigzag" polygonal function 32, and between the negative slope linear function 33 and the "zigzag" polygonal function 34, as shown by the dashed lines in fig. 5; the "break point" velocities of the polyline functions 32, 34 are at 1/2 between the boundary value and the center value of the velocity interval 15, and the specific functional form may be determined by optimizing the global velocity measurement result traversing the entire velocity range from low to high, or may be determined empirically.
Secondly, according to the positions of the original pre-measuring speed and the delay pre-measuring speed in the speed interval, determining respective weights according to a weight function 30.
And finally, correcting the delay pre-measuring speed, namely removing the artificial delay 22 processing to obtain the corrected delay pre-measuring speed, and then carrying out weighting processing together with the original pre-measuring speed to obtain a final speed measuring result.
The invention brings the technical effects that:
when the pulse coherent Doppler technology is adopted to measure the speed, the value range of the detected phase difference is limited to [ -pi, pi ], so that the upper limit of the measuring speed exists, and the maximum measurable speed range is limited; velocity values exceeding this range are folded into the maximum measurable velocity range, i.e. so-called "velocity blur" occurs. The method of the invention adopts a method of dividing speed intervals and adopting interval basic speed and interval speed offset to realize speed measurement, the basic speed is determined by a time difference measurement result and is not influenced by phase folding, and the phase difference method only measures the speed offset in the interval, thereby avoiding the problem of speed folding (blurring). Because the speed value is the position where the probability of section jump is the maximum when the speed value is at the boundary value of the section, and the probability of section jump is the minimum when the speed value is at the center of the section, the method of the invention adopts a method of adding artificial time delay to artificially move the speed at the boundary of the section to the vicinity of the center of the speed section, so that the probability of section jump is reduced; and finally, different weights are given to the original pre-measurement speed and the delay pre-measurement speed, the result with the maximum hopping probability is removed, the result with the smaller hopping probability is reserved, and the overall measurement result is stable and accurate through the optimal weight function setting. The method eliminates the speed ambiguity in the pulse coherent Doppler technology speed measurement, and is not limited by the real speed range.
Drawings
Fig. 1 is a schematic diagram of velocity measurement principle by impulse coherent doppler method.
Fig. 2 is a velocity ambiguity diagram for pulse repetition time.
FIG. 3 is a schematic of velocity prediction.
In the figure: 11-base speed; 12-speed offset; 13-maximum measurable speed; 14-maximum measurable speed range; 15-speed interval; 16-speed interval number.
Fig. 4 is a schematic diagram of the original delay and the added artificial delay of the secondary echo signal.
In the figure: 21-original time delay; 22-artificial delay.
Fig. 5 is a weight value taking method of different pre-measured speed values in a speed space.
In the figure: 30-weight function; 31-positive slope linear function; 32- "inverse Z-shaped" polyline function; 33-negative slope linear function; 34- "Z-shaped" polyline function.
FIG. 6 is a cross-correlation function R12And a time delay value delta T determined by the peak positionRSchematic representation.
Detailed Description
In order to make the aforementioned and other features and advantages of the invention more comprehensible, embodiments accompanied with figures are described in detail below.
The embodiment provides a signal processing method for eliminating velocity ambiguity in pulse dry method velocity measurement, which comprises the following steps:
1) and dividing speed intervals and determining the basic speed of each interval.
Selecting proper working frequency f according to actual working scene
0And frequency bandwidth B, designing proper emission pulse waveform s (t); according to the maximum measurement distance R required in the actual working scene
mDetermining the pulse repetition time T of the pulse coherent Doppler method; calculating the maximum measurable velocity V from the pulse repetition time T using equation (7)
m(ii) a At maximum measurable speed range [ -V ]
m,+V
m]The interval is a unit, the whole speed space is divided into a plurality of speed intervals 15, and starting from a central interval corresponding to the speed 0, the integer serial number of each positive and negative speed interval is marked as n ═ 0, ± 1, ± 2, ± 3,. until the speed covers all possible real speed ranges, the nth interval speed is: [ (2n-1) V
m,(2n+1)V
m](ii) a Median value of interval 2nV
mThe basic speed of the interval is obtained; the number n is also used to represent the measured speed for 2V when the true speed falls in the interval
mThe number of folds of (c); the division is such that the phase difference calculated according to equation (6)
The value corresponding to the boundary of each section is
The value corresponding to the center of each speed interval is
2) And obtaining a rough time delay measurement result, namely a rough measurement speed, by a time difference estimation method, such as a cross-correlation method, and determining a speed interval in which the rough measurement speed is positioned and obtaining a basic speed of the rough measurement speed. The concrete implementation method comprises the following steps:
firstly, the rough measurement speed is obtained by performing cross-correlation processing on the two echo signals. Other time difference detection or estimation methods may be used in practice. Transmitting two identical radio frequency pulses s (T) at a pulse repetition time interval T, and receiving a target echo signal in a medium; performing quadrature demodulation on the two echo signals to obtain baseband signals of the two echo signals, (in actual operation, the signals may not be converted to the baseband, but the received echo signals are directly subjected to subsequent processing), and then according to the time correspondence, two signal segments (as shown in fig. 1) corresponding to the target position of interest are intercepted, and are marked as x1(t) and x2(t); for two intercepted signal segments x1(t) and x2(T) calculating a cross-correlation function, and determining the original time delay delta T of the cross-correlation function according to the peak position of the cross-correlation functionRAs shown in fig. 6.
Secondly, the rough measurement velocity v is calculated according to the formula (2)R:
And based on the rough measured velocity vRCalculating the value of the folding times n:
if v isR≥0,
If v isR<0,
Int [ ] in the formulas (14a) (14b) represents a rounding operation.
Finally, the central speed 2nV of the interval n is takenmIs the base speed of the raw speed.
3) And carrying out accurate delay estimation by adopting a phase difference method to obtain the speed offset in the interval. The method of the invention uses a cross-power spectrum method to solve the phase difference, and estimates the accurate time delay according to a formula (6)
And then calculating the speed offset in the interval by using the formula (2):
4) finding the original pre-measured velocity v0:
v0=2nVm+vP (15)
5) Artificially adding time delay and recalculating time delay pre-measuring speed v1The method comprises the following specific operation steps:
for one of the echo signals x2(T) artificially delaying the time, wherein the added artificial time is delta TDAnd in actual operation, the following steps are taken:
or
Or other value such that the speed obtains approximately V
mOr V
m/2,3V
mA/2 or other speed offset. The delayed signal becomes x
2(t-ΔT
D)。
Repeating the steps 2), 3), 4) and 5). Obtaining the time delay Delta T of the cross-correlation function peak value after time delay by repeating the step 2)
RDRepeating the step 3) to obtain a new group of folding times n
DRepeating the step 4) to obtain the cross-power spectrum time delay after time delay
And velocity offset v
PDRepeating the step 5) to obtain the delay pre-measuring speed v
D:
vD=2nDVm+vPD;
Subtracting the speed offset generated by artificial time delay, and calculating the corrected time delay pre-measuring speed v obtained by one-time artificial time delay1:
(6) And carrying out speed weighting processing to obtain a final speed measurement result.
According to a predetermined weight function, according to the original pre-measured speed v0And a delay pre-measured velocity vDDetermining the original predicted speed v at the position in the speed interval0Weight value w of0And corrected delay-predicted measurement speed v1Weight w of velocity1And weighting the speed pre-measurement result. The main criterion is to eliminate the result of the predicted speed near the boundary of the speed interval and to retain the result near the center of the speed interval. For example, if the velocity v is originally pre-measured0When the interval boundary is close, the delay pre-measuring speed v after artificial delayDWill be close to the center of the interval, i.e. with w0=0,w1=1。
The invention weights the measurement speed by adopting a weight function curve designed by a global speed error minimum criterion:
v=w0v0+w1v1 (18)
obviously, it is also possible to use multiple sets of delays to obtain different delay pre-measurement speeds: v. of1,v2,v3,., obtaining the weight of each delay pre-measurement speed according to the weight function: w is a1,w2,w3,...
Finally, the total measurement speed is obtained:
wherein, Σ wi=w0+w1+w2+w3+...
The above embodiments are only intended to illustrate the technical solution of the present invention and not to limit the same, and a person skilled in the art can modify the technical solution of the present invention or substitute the same without departing from the spirit and scope of the present invention, and the scope of the present invention should be determined by the claims.