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CN111273296B - Iterative deconvolution-time reversal target detection and distance estimation method - Google Patents

Iterative deconvolution-time reversal target detection and distance estimation method Download PDF

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CN111273296B
CN111273296B CN202010123948.1A CN202010123948A CN111273296B CN 111273296 B CN111273296 B CN 111273296B CN 202010123948 A CN202010123948 A CN 202010123948A CN 111273296 B CN111273296 B CN 111273296B
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scattering coefficient
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CN111273296A (en
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李春晓
郭明飞
丁浩
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Zhejiang University of Technology ZJUT
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S15/00—Systems using the reflection or reradiation of acoustic waves, e.g. sonar systems
    • G01S15/02—Systems using the reflection or reradiation of acoustic waves, e.g. sonar systems using reflection of acoustic waves
    • G01S15/06—Systems determining the position data of a target
    • G01S15/08—Systems for measuring distance only
    • G01S15/10—Systems for measuring distance only using transmission of interrupted, pulse-modulated waves
    • G01S15/101—Particularities of the measurement of distance
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
    • G01S13/06—Systems determining position data of a target
    • G01S13/08—Systems for measuring distance only
    • G01S13/10—Systems for measuring distance only using transmission of interrupted, pulse modulated waves
    • G01S13/103—Systems for measuring distance only using transmission of interrupted, pulse modulated waves particularities of the measurement of the distance
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/023—Interference mitigation, e.g. reducing or avoiding non-intentional interference with other HF-transmitters, base station transmitters for mobile communication or other radar systems, e.g. using electro-magnetic interference [EMI] reduction techniques
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/52—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S15/00
    • G01S7/52001—Auxiliary means for detecting or identifying sonar signals or the like, e.g. sonar jamming signals

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  • Engineering & Computer Science (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Acoustics & Sound (AREA)
  • Radar Systems Or Details Thereof (AREA)
  • Measurement Of Velocity Or Position Using Acoustic Or Ultrasonic Waves (AREA)

Abstract

The invention provides an iterative deconvolution-time inverse target detection and distance estimation method, which is characterized in that correlation is obtained according to a received signal and a transmitted signal to obtain a mutual ambiguity function; meanwhile, the correlation between the transmitted signal and the self-correlation is obtained from the ambiguity function; the ambiguity problem caused by the transmitted signal is eliminated by an iterative deconvolution mode, and the time expansion problem caused by multipath propagation is eliminated by a time reversal method. Simulation results prove that the method can obtain the distance resolution and the anti-noise capability which are far higher than those of matched filtering, and is suitable for the application of an active sonar/radar system.

Description

Iterative deconvolution-time reversal target detection and distance estimation method
Technical Field
The invention is mainly applied to an active sonar/radar system, relates to an iterative deconvolution-time inverse target detection and distance estimation method, and particularly relates to a filtering method for detecting and positioning a target by an echo of a transmitted signal. The invention mainly considers the target with low motion speed or static, and does not consider the Doppler problem caused by the moving target.
Background
Active sonar/radar is a system that detects a target by transmitting a signal and receiving a target echo signal. The task of an active sonar/radar system is not only to detect echo signals buried in noise or reverberation, to estimate the distance to a target, but also to distinguish the target from the reverberation to reduce the false alarm probability.
Matched filtering, i.e. solving a cross-ambiguity function between a received signal and a transmitted signal, is a signal processing method commonly adopted by active sonar/radar. In order to ensure that the active sonar/radar has sufficient gain to improve detection performance, it is generally necessary to transmit a signal with a large bandwidth B and a sufficiently long pulse width T. In order to accurately estimate the range of the target, the active sonar/radar system needs to have a high range resolution, which today depends mainly on the waveform of the transmitted signal. Different waveforms have different resolution characteristics, for example, a PCW signal has good doppler resolution, which is inversely proportional to pulse width; but range resolution is poor, while chirp has a higher range resolution, inversely proportional to bandwidth, but insensitive to doppler. Meanwhile, since the shallow sea is a multipath propagation environment, delay spread caused by a channel may affect performance of matched filtering.
Disclosure of Invention
In order to overcome the problem that the output gain and resolution of matched filtering are limited by waveforms, the invention provides an iterative deconvolution-time inverse target detection and distance estimation method. In theory, the resolution of this method can reach the pulse level, and in practical applications, depends only on the choice of the window function and the window length.
In order to achieve the technical purpose, the invention adopts the following technical scheme:
an iterative deconvolution-time reversal target detection and distance estimation method comprises the following steps:
s1, defining the front and back propagation of the channel and the weighting of the target scattering coefficient to the received signal as a generalized target scattering coefficient; modeling a received signal;
s2, normalizing the self-ambiguity function energy of the transmitted signal, and normalizing the mutual ambiguity function energy of the received signal and the transmitted signal; expressing a cross-ambiguity function as a convolution of a self-ambiguity function and a generalized target scattering coefficient; iteratively solving a generalized target scattering coefficient according to the self-ambiguity and the mutual ambiguity;
s3, Fourier transform is carried out on the generalized target scattering coefficient, when the generalized target scattering coefficient is combined, the generalized target scattering coefficient is inversely equal to phase conjugation, and when the generalized target scattering coefficient is multiplied by the generalized target scattering coefficient, the ambiguity caused by a channel can be eliminated, so that a frequency domain where the target scattering energy coefficient is located is obtained; performing inverse Fourier transform on the target scattering energy coefficient;
s4, solving a function curve of the scattering energy coefficient and the time delay of the target along with the regular movement of the window function;
s5, searching the scattering energy coefficient and time delay of the targetSetting a threshold value, wherein the peak value point larger than the threshold value is the time delay corresponding to the target according to ro＝c×voAnd/2, calculating the distance corresponding to the target, wherein c represents the speed of sound or the speed of light.
As one of the preferable embodiments of the present invention, step S1 specifically includes:
by h (t) is meant the forward direction h under shallow sea conditionsf(t) and backward multipath propagation hb(t) the induced channel delay spread function, h (t) can be expressed as if there are N propagation paths in total
Figure BDA0002393847070000021
Let the scattering coefficient of the target be denoted as c (t) = coδ(t-τo) Then the generalized target scattering coefficient, which includes forward and backward propagation and the target scattering coefficient, is expressed as follows:
Figure BDA0002393847070000022
the received signal can be expressed as:
Figure BDA0002393847070000023
wherein
Figure BDA0002393847070000024
Representing a convolution.
As one of the preferable embodiments of the present invention, step S2 specifically includes:
the self-ambiguity function of the transmitted signal s (t) being
Figure BDA0002393847070000025
Where t represents time, τ represents time delay, and x represents conjugation; normalizing self-ambiguity function energy
Figure BDA0002393847070000026
The cross-ambiguity function of the received signal r (t) and the transmitted signal is
Figure BDA0002393847070000031
Normalizing mutual ambiguity function energy
Figure BDA0002393847070000032
The expression of the received signal in step 1 is substituted into the cross-ambiguity function, which can be seen as the convolution of the generalized scattering coefficient and the self-ambiguity function
Figure BDA0002393847070000033
The generalized target scattering coefficient with time delay v is expressed as p (v), then
Figure BDA0002393847070000034
Where m represents the number of iterations.
As one of the preferable embodiments of the present invention, step S3 specifically includes:
if the iteration number is M, the finally obtained generalized target scattering coefficient is rhoM(v) Is shown as
ρM(v)=h(v)*c(v)；
The problem of delay spread caused by multipath propagation still exists;
ρv(Ω) represents a time window (v, v + w)o) Fourier transform of the generalized target scattering coefficient in (1) expressed as
Figure BDA0002393847070000035
Wherein Ω represents frequency; w (t) denotes a window function, which is expressed as if a rectangular window is selected
Figure BDA0002393847070000036
woRepresents the length of the window;
by adopting a time reversal processing method, the generalized target scattering coefficient is multiplied by the generalized target scattering coefficient according to time reversal equal to phase conjugation, and the obtained target scattering energy coefficient is expressed as a frequency domain
Figure BDA0002393847070000037
If the channel is normalized, | h (Ω) |2=1；
And carrying out inverse Fourier transform on the scattering energy coefficient of the target to obtain:
Figure BDA0002393847070000041
compared with the prior art, the invention has the beneficial effects that:
the invention adopts an iterative deconvolution method to eliminate the self-blurring problem of the transmitting signal, solves the problem that the distance resolution is limited by the waveform of the transmitting signal, and obtains very good reverberation resistance. In addition, the time reversal processing method solves the problem of time delay expansion of the channel and ensures the application of the method in the shallow sea environment.
The method of the invention is very convenient to execute, has higher distance resolution and higher gain, has strong anti-noise capability, and gradually enhances the anti-noise capability along with the increase of the iteration times until reaching a stable level.
Drawings
FIG. 1 is a schematic flow diagram of the process of the present invention.
Fig. 2 shows the distance resolution for matched filtering.
Fig. 3 shows the distance resolution of the present invention.
Figure 4 shows the anti-noise capability of the matched filtering.
Fig. 5 illustrates the noise immunity of the present invention.
FIG. 6 illustrates multipath resistance for matched filtering
Fig. 7 illustrates the multipath resistance of the present invention.
Detailed Description
The technical solution of the present invention will be further explained with reference to the attached drawings and tables.
As shown in fig. 1, the iterative deconvolution-time inverse target detection and distance estimation method according to the present invention includes the following steps:
s1, defining the front and back propagation of the channel and the weighting of the target scattering coefficient to the received signal as a generalized target scattering coefficient; modeling a received signal;
s2, normalizing the self-ambiguity function energy of the transmitted signal, and normalizing the mutual ambiguity function energy of the received signal and the transmitted signal; expressing the cross-ambiguity function as the convolution of the self-ambiguity function and the generalized scattering coefficient; iteratively solving a generalized target scattering coefficient according to the self-ambiguity and the mutual ambiguity;
s3, Fourier transform is carried out on the generalized target scattering coefficient, when the generalized target scattering coefficient is combined, the generalized target scattering coefficient is inversely equal to phase conjugation, and when the generalized target scattering coefficient is multiplied by the generalized target scattering coefficient, the ambiguity caused by a channel can be eliminated, so that a frequency domain where the target scattering energy coefficient is located is obtained; performing inverse Fourier transform on the target scattering energy coefficient;
s4, solving a function curve of the scattering energy coefficient and the time delay of the target along with the regular movement of the window function;
s5, searching the peak point of the function curve of the scattering energy coefficient and the time delay of the target, setting a threshold value, wherein the peak point larger than the threshold value is the time delay corresponding to the target, and calculating the time delay according to ro＝c×voAnd/2, calculating the distance corresponding to the target, wherein c represents the speed of sound or the speed of light.
The method comprises the following concrete steps:
if h (τ) is used to represent the channel delay spread due to forward and backward multipath propagation in shallow sea conditions, then h (t) can be expressed as h (τ) if there are N propagation paths in total
Figure BDA0002393847070000051
Let the scattering coefficient of the target be denoted as c (t) ═ coδ(t-τo) Then the generalized target scattering coefficient is expressed as follows:
Figure BDA0002393847070000052
wherein
Figure BDA0002393847070000053
Represents a convolution in which pno＝ρnco，τno＝τn+τo。
The received signal may be represented as follows:
Figure BDA0002393847070000054
the received signal is correlated with the transmitted signal, and the cross-ambiguity function can be expressed as:
Figure BDA0002393847070000055
as can be seen from equation (3), the cross-ambiguity function χ is knowncUnder the conditions of (tau) and self-ambiguity chi (tau), the generalized scattering coefficient rho (tau) of the target is obtained, which is the problem of unwinding.
The process of unrolling is to find an estimate of the cross-ambiguity function
Figure BDA0002393847070000056
The minimum distance to the mutual ambiguity function, Cssiz-r minimum, is expressed as
Figure BDA0002393847070000061
The above formula has a minimum value when a (x) is b (x).
This task is as follows: giving a non-negative function χc(τ) and χ (τ), and
Figure BDA0002393847070000062
and
Figure BDA0002393847070000063
we want to find a non-negative function p (τ) that is required to minimize the following equation
Figure BDA0002393847070000064
All ρ (v) satisfying the above formula can be expressed as
Figure BDA0002393847070000065
(6) The solution of formula satisfies the Kuhn-Tucker condition:
Figure BDA0002393847070000066
the condition that the equal sign is satisfied is that rho (v) is more than or equal to 0, and the method meets the condition;
(7) the two ends of formula are multiplied by rho (v) and equal sign is taken, the solution can be realized by iteration mode:
Figure BDA0002393847070000067
wherein m is iteration times, and the finally obtained generalized target scattering coefficient is set as rhoM(v) Then, the following equation is satisfied:
Figure BDA0002393847070000068
as can be seen from the expression (9), the problem of delay spread caused by multipath still exists, and the Fourier transform of the expression (9) is obtained
ρM(Ω)=c(Ω)×h(Ω) (10)
According to the time reversal equal to the phase conjugation, the product is obtained by multiplying the time reversal equal to the phase conjugation with the phase conjugation
ρM(Ω)=c(Ω)×h(Ω)×c*(Ω)×h*(Ω)＝|c(Ω)|2＝P(Ω) (11)
If the channel function is normalized, i.e. | h (Ω) |2=1；
Inverse Fourier to time domain, obtained
Figure BDA0002393847070000071
And (3) calculating a function curve P (v) of the scattering energy coefficient and the time delay of the target along with the regular movement of the window function. The shift of the window function here can be understood as:
the time point defined by the transmitted signal is 0 time, woRepresenting the length of the time window, P (0) corresponds to the first time window (0, w)o) The corresponding scattering energy coefficient of the target; the window function being regularly shifted, e.g. the start of the second time window being (w)o，wo+wo) The scattering energy coefficient of the corresponding target is P (w)0) The windowing method is a windowing method without overlap, or the starting time of the second time window is (0.5 w)o，0.5wo+wo) The scattering energy coefficient of the corresponding target is P (w)0) The windowing method is a windowing method with overlap; the window function continues to move according to the rule until the received signals at all the moments are processed; a curve p (v) of the scattering energy coefficient of the target as a function of the time delay is obtained.
Outputting a function curve graph of the scattering energy coefficient and the time delay of the target, seeing a peak point in the graph, setting a threshold value, setting the peak point which is larger than the threshold value, namely the time delay corresponding to the target according to ro＝c×voAnd/2, calculating the distance corresponding to the target, wherein c represents the speed of sound or the speed of light. As shown in fig. 5, the distance of the peak point at the target is known, i.e. 10 meters.
Assuming a target is located at 10 meters, when the resolution of the matched filter and the present invention is studied, the echo of the target is assumed to be pure without noise and without considering the influence caused by multipath, and the transmitted signal is a chirp signal with a center frequency of 12kHz and a bandwidth of 4 kHz. From fig. 2 it can be seen that the 3dB range resolution of matched filtering is 0.3 meters, while from fig. 3 it can be seen that the range resolution after 12 iterations of the invention is an impulse.
Assuming a target is located at 10 meters, now considering the noise in the target echo, assuming a signal-to-noise ratio of 6dB, it can be seen from fig. 4 that the noise can be pushed to-30 dB by matched filtering, and it can be seen from fig. 5 that the method can be pushed to-1200 dB.
Considering the influence of multipath, considering three paths, namely direct waves, primary sea bottom reflected waves and primary sea surface reflected waves, it can be seen from fig. 6 that a plurality of peak points appear in the matched filtering, but after the method passes through the time delay spread of the multipath cancellation, it can be seen from fig. 7 that only one peak point exists.
It should be noted that the above embodiments can be freely combined as necessary. The foregoing has outlined rather broadly the preferred embodiments and principles of the present invention and it will be appreciated that those skilled in the art may devise variations of the present invention that are within the spirit and scope of the appended claims.

Claims (2)

1. An iterative deconvolution-time reversal target detection and distance estimation method is characterized by comprising the following steps:
s1, defining the front and back propagation of the channel and the weighting of the target scattering coefficient to the received signal as a generalized target scattering coefficient; modeling a received signal;
s2, normalizing the self-ambiguity function energy of the transmitted signal, and normalizing the mutual ambiguity function energy of the received signal and the transmitted signal; expressing a cross-ambiguity function as a convolution of a self-ambiguity function and a generalized target scattering coefficient; iteratively solving a generalized target scattering coefficient according to the self-ambiguity and the mutual ambiguity;
s3, Fourier transform is carried out on the generalized target scattering coefficient, when the generalized target scattering coefficient is combined, the generalized target scattering coefficient is inversely equal to phase conjugation, and when the generalized target scattering coefficient is multiplied by the generalized target scattering coefficient, the ambiguity caused by a channel is eliminated, so that the frequency domain of the target scattering energy coefficient is obtained; performing inverse Fourier transform on the target scattering energy coefficient;
s4, solving a function curve of the scattering energy coefficient and the time delay of the target along with the regular movement of the window function;
s5, searching the peak point of the function curve of the scattering energy coefficient and the time delay of the target, setting a threshold value, wherein the peak point larger than the threshold value is the time delay corresponding to the target, and calculating the time delay according to ro＝c×voCalculating the distance corresponding to the target, wherein c represents the speed of sound or the speed of light;
step S2 specifically includes:
the self-ambiguity function of the transmitted signal s (t) being
Figure FDA0003272332040000011
Where t represents time, τ represents time delay, and x represents conjugation; normalizing self-ambiguity function energy
Figure FDA0003272332040000012
The cross-ambiguity function of the received signal r (t) and the transmitted signal is
Figure FDA0003272332040000013
Normalizing mutual ambiguity function energy
Figure FDA0003272332040000014
Substituting the expression of the received signal in the step 1 into a mutual ambiguity function, and expressing the expression as the convolution of the scattering coefficient of the generalized target and a self-ambiguity function
Figure FDA0003272332040000021
The generalized target scattering coefficient with time delay v is expressed as p (v), then
Figure FDA0003272332040000022
Wherein m represents the number of iterations;
step S3 specifically includes:
if the iteration number is M, the finally obtained generalized target scattering coefficient is rhoM(v) Is shown as
ρM(v)＝h(v)*c(v)；
The problem of delay spread caused by multipath propagation still exists;
ρv(Ω) represents a time window (v, v + w)o) Fourier transform of the generalized target scattering coefficient in (1) expressed as
Figure FDA0003272332040000023
Wherein Ω represents frequency; w (t) denotes a window function, woRepresents the length of the window;
by adopting a time reversal processing method, according to the time reversal equal to phase conjugation, the scattering energy coefficient of the target is obtained and expressed as
Figure FDA0003272332040000024
If the channel is normalized, i.e., | h (Ω) |2 ═ 1;
and carrying out inverse Fourier transform on the scattering energy coefficient of the target to obtain:
Figure FDA0003272332040000025
2. the method of claim 1, wherein: step S1 specifically includes:
by h (t) is meant the forward direction h under shallow sea conditionsf(t) and backward multipath propagation hb(t) the resulting channel delay spread function, h (t) is expressed as if there are a total of N propagation paths
Figure FDA0003272332040000031
Let the scattering coefficient of the target be denoted as c (t) ═ coδ(t-τo) Then the generalized target scattering coefficient, which includes forward and backward propagation and the target scattering coefficient, is expressed as follows:
Figure FDA0003272332040000032
the received signal is then expressed as:
Figure FDA0003272332040000033
wherein
Figure FDA0003272332040000034
Representing a convolution.
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