A method for estimating the relative radial motion speed of an active target based on the cepstrum principle

Abstract

The present invention discloses a method for estimating the relative radial motion speed of an active target based on the cepstrum principle, including: designing a broadband combined pulse signal as the transmitted signal of an active sonar; performing matched filtering on the sub-pulse signal in the transmitted signal and the echo signal received by the active sonar; performing cepstrum transformation on the result of the matched filtering; reading the time corresponding to the peak value in the cepstrum result, and estimating the relative radial motion speed of the target. The present invention can obtain a relatively accurate estimated value of the relative radial motion speed of the active target with less computational effort under the condition of lower signal-to-noise ratio.

Description

Technical Field

[0001] The present invention relates to the field of target parameter estimation in an active sonar system, and particularly to a method for estimating the relative radial motion speed of an active target based on the cepstrum principle. Background Art

[0002] An active sonar emits acoustic waves and receives target echo signals, extracts features from the received echoes, and thereby estimates target parameters. The commonly used transmitted signal of an active sonar is a broadband signal, and the frequency resolution of the broadband signal is poor. Using a broadband signal to estimate the relative radial motion speed of a target cannot meet the actual requirements, especially in the case of low signal-to-noise ratio.

[0003] Currently, the main method for estimating the relative radial motion speed of a target using a broadband signal is the matching pursuit method. This method traverses the matching filtering results of all target relative radial motion speed echoes and the transmitted signal, records the maximum value of the matching filtering results at different speed values, finds the maximum value among the recorded matching filtering maxima at different speeds, and takes the speed value corresponding to this maximum value as the estimated relative radial motion speed value of the target. The computational complexity of the matching pursuit method is relatively high. The higher the required measurement accuracy, the greater the amount of calculation required. The cepstrum is a non-linear signal operation method that can transform the convolution operation in a signal into an addition operation in the cepstrum domain and is often used to estimate the time delay of a target. There is currently no precedent for using the cepstrum to estimate the relative radial motion speed of an active target.

[0004] In actual situations, the motion direction of the target relative to the sonar is also a part that receives attention. In an active sonar broadband system, how to estimate the magnitude of the relative radial motion speed of the target with less computational effort and determine the relative motion direction of the target is one of the current hot issues in underwater acoustics research. Summary of the Invention

[0005] In view of this, the purpose of the present invention is to provide a method for estimating the relative radial motion speed of an active target based on the cepstrum principle to solve the technical problems mentioned in the background art. The present invention emits a combined pulse signal, based on the cepstrum principle, combines matching filtering, and can more accurately estimate the relative radial motion speed of the target with less computational effort in the case of low signal-to-noise ratio.

[0006] To achieve the above purpose, the present invention adopts the following technical solutions:

[0007] A method for estimating the relative radial motion speed of an active target based on the cepstrum principle, the method comprising:

[0008] Step S1: Construct a broadband combined pulse signal and use it as the transmission signal of the active sonar. Among them, the broadband combined pulse signal includes a sub-pulse signal and a delayed sub-pulse signal, and record the preset time delay value in the combined pulse signal;

[0009] Step S2: Set the maximum radial movement speed of the active target, and then determine the time search range in the cepstrum;

[0010] Step S3: Use the sub-pulse signal in the transmission signal to perform matched filtering with the echo signal received by the active sonar;

[0011] Step S4: Perform cepstrum transformation on the matched filtering result obtained in Step S3;

[0012] Step S5: Find the maximum value within the time search range in the cepstrum result obtained in Step S4, record the time corresponding to the maximum value, and estimate the magnitude and direction of the relative radial movement speed of the target.

[0013] Further, Step S1 includes:

[0014] The broadband combined pulse signal transmitted by the active sonar is expressed as:

[0015] u(n) = s(n) + s(n - n s ) (1)

[0016] In this formula (1), s(n) is the sub-pulse signal, s(n - n s ) is the delayed sub-pulse signal, where n s is an integer obtained by rounding τ s × f s , τ s is the preset time delay, f s is the sampling frequency of the active sonar system, and T p is the transmission period of the combined pulse signal;

[0017] The sub-pulse signal s(n) is an HFM signal, specifically expressed as:

[0018]

[0019] In this formula (2), T is the pulse width of the sub-pulse signal, A is the amplitude, f0 is the time center frequency, B is the frequency modulation width, the lowest frequency of the signal is Hertz, the highest frequency of the signal is Hertz, and n is the time point sampled at f s Hertz.

[0020] Further, Step S2 includes:

[0021] According to the Doppler principle, the time search range in the cepstrum is determined to be [τ s -Δτ, τ s +Δτ] seconds, where seconds, is the maximum Doppler factor, v max is the maximum radial motion speed of the active target, and c is the propagation speed of sound waves in water.

[0022] Furthermore, in step S3, using the sub-pulse signal s(n) of the transmitted signal in step S1, the received echo signal u r (n) is subjected to matched filtering through the following formula, including:

[0023]

[0024] Furthermore, the said step S4 includes:

[0025] According to the cepstrum analysis principle, the cepstrum transform is performed on the matched filtering result obtained in step S3 using the following formula, including:

[0026] c y (n) = F -1 {log|F{y(n)|} (4)

[0027] In formula (4), F{} represents the discrete Fourier transform, is the discrete Fourier transform of f(n), F -1 {} represents the inverse discrete Fourier transform, is the inverse discrete Fourier transform of F(k), N f is the number of points of the signal f(n).

[0028] Furthermore, the said step S5 includes:

[0029] Step S501: Find the time Δt corresponding to the maximum value within the range of [τ y (n) in the cepstrum result c s -Δτ, τ s +Δτ] obtained in step S4, and then perform the following judgment: c and then execute the following judgment:

[0030] According to the Doppler principle, when Δt c < τ s , the pulse width is compressed, and it is judged that the relative radial motion speed v of the target est > 0, and the target is moving closer to the sonar;

[0031] When Δt c > τ s , the pulse width is stretched, and it is judged that the relative radial motion speed v of the targetest < 0, the target moves away from the sonar;

[0032] Step S502, use the formula to calculate the relative radial motion speed of the active target and obtain its speed estimate.

[0033] The beneficial effects of the present invention are:

[0034] An estimation method for the relative radial motion speed of an active target based on the cepstrum principle provided by the present invention, by transmitting a combined pulse signal, combining the cepstrum principle and matched filtering, can accurately estimate the relative radial motion speed of the active target with a small amount of calculation under a low signal-to-noise ratio. Description of the Drawings

[0035] Figure 1 The highlight model of the active target used in Embodiment 1 and Embodiment 2;

[0036] Figure 2 For Embodiment 1, the number of echo highlights N = 2, the preset time delay value τ s = 0.5 s, the relative radial motion speed of the target v = -5 m / s, and the matched filtering result diagram at a signal-to-noise ratio of 5 dB;

[0037] Figure 3 For Embodiment 1, the number of echo highlights N = 2, the preset time delay value τ s = 0.5 s, the relative radial motion speed of the target v = -5 m / s, and the cepstrum result diagram at a signal-to-noise ratio of 5 dB;

[0038] Figure 4 For Embodiment 2, the number of echo highlights N = 4, the preset time delay value τ s = 1.5 s, and the comparison diagram of the relative radial motion speed values of the target estimated by the cepstrum method and the matching pursuit method at different signal-to-noise ratios when the relative radial motion speed of the target v = 10 m / s;

[0039] Figure 5 The flowcharts for estimating the relative radial motion speed of the active target provided in Embodiment 1 and Embodiment 2. Detailed Embodiments

[0040] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0041] Embodiment 1

[0042] See Figures 1 - 3 and Figure 5 , this embodiment provides a method for estimating the relative radial motion speed of an active target based on the cepstrum principle. The flow of this method is as shown in Figure 5 , and the method specifically includes the following steps:

[0043] Step S1: Construct a broadband combined pulse signal and use it as the transmitted signal of the active sonar. Among them, the broadband combined pulse signal includes a sub-pulse signal and a delayed sub-pulse signal, and record the preset time delay value in the combined pulse signal.

[0044] In this embodiment, step S1 specifically includes:

[0045] The active sonar transmits a broadband combined pulse signal, which is expressed as:

[0046] u(n) = s(n) + s(n - n s ) (1)

[0047] In the formula (1), s(n) is the sub-pulse signal, and s(n - n s ) is the delayed sub-pulse signal, where n s is an integer obtained by rounding τ s × f s . The preset time delay value τ s is 0.5 seconds, the sampling frequency f s of the active sonar system is 5000 Hz, and the transmission period T p of the combined pulse signal is 10 seconds;

[0048] The above sub-pulse signal s(n) is an HFM signal, which is specifically expressed as:

[0049]

[0050] In the formula (2), the pulse width T of the sub-pulse signal is 1 second, the amplitude A is 1, the time center frequency f0 is 1000 Hz, the frequency modulation width B is 500 Hz, the lowest frequency of the signal is Hz, the highest frequency of the signal is Hz, and n is the time point sampled at f s Hz.

[0051] Step S2: Set the maximum possible radial motion speed of the active target, and then determine the time search range in the cepstrum.

[0052] Specifically, in this embodiment, step S2 includes:

[0053] According to the Doppler principle, the time search range in the cepstrum is determined to be [τ s -Δτ, τ s +Δτ] seconds, where seconds, is the maximum Doppler factor, the maximum radial velocity v at which the active target may appear max is 15 m / s, and the propagation speed c of sound waves in water is 1500 m / s.

[0054] Step S3: Use the sub-pulse signal in the transmitted signal to perform matched filtering with the echo signal.

[0055] Specifically, in this embodiment, a simulated echo signal is used, such as Figure 1 the bright spot model shown. In this figure, N represents the number of bright spots of the target, and u' i (n) is the echo generated by the i-th bright spot, and L i is the distance between the i-th bright spot and the sonar.

[0056] In this embodiment, the target has N = 2 bright spots, and the echo signal is obtained using the following formula:

[0057]

[0058] In this formula (3), u' i (n) = s' i (n) + s' i (n - n s ), where

[0059]

[0060]

[0061] In formulas (4) and (5), b i is the reflection coefficient of the i-th bright spot. According to the Doppler principle, when the radial velocity v of the active target is -5 m / s, the resampled signal frequency is Hertz, n i is the integer after rounding, and n rs is τ s × f rs the integer after rounding.

[0062] More specifically, in this embodiment, the reflection coefficients of the two bright spots are b1 = 0.6 and b2 = 0.9 respectively, and the distances of the two bright spots from the sonar are L1 = 200 m and L2 = 230 m respectively.

[0063] Among them, s'(n) in formulas (4) and (5) is specifically expressed as:

[0064]

[0065] In formula (6), n' is the time point sampled at f p Hz within the range of [0, T rs , is the random phase added to the i-th bright spot, which is a random number within the range of [0, 2π], n(n) is the system noise, and the signal-to-noise ratio is 5 dB;

[0066] Using the sub-pulse signal s(n) of the transmitted signal in step S1, the received echo signal u r (n) is subjected to matched filtering through the following formula, including:

[0067]

[0068] In this formula (7), u r () and s() represent the two signals for matched filtering, n is the abscissa of the final result of the matched filtering, and i is the intermediate quantity in the calculation and accumulation process; the obtained matched filtering result is as Figure 2 . More specifically, the result obtained is only for the condition of the signal-to-noise ratio of -5 dB set in this embodiment.

[0069] Step S4: Perform cepstrum transformation on the matched filtering result obtained in step S3.

[0070] Specifically, in this embodiment, this step S4 includes:

[0071] According to the cepstrum analysis principle, the following formula is used to perform cepstrum transformation on the matched filtering result obtained in step S3, including:

[0072] c y (n) = F -1 {log|F{y(n)|} (8)

[0073] In formula (8), F{} represents the discrete Fourier transform, is the discrete Fourier transform of f(n), F -1 {} represents the inverse discrete Fourier transform, is the inverse discrete Fourier transform of F(k), N f is the number of points of the signal f(n), and the obtained cepstrum result is as Figure 3 .

[0074] Step S5: Find the maximum value within the time search range in the cepstrum result obtained in step S4, record the time corresponding to this maximum value, and estimate the magnitude and direction of the relative radial motion speed of the target.

[0075] Specifically, in this embodiment, step S5 includes:

[0076] Step S501: Locate the cepstrum result c y (n) obtained in step S4 within the range of [τ s -Δτ, τ s +Δτ], and find the corresponding time Δt of the maximum value. c More specifically, in this implementation, Δt c is 0.5034 seconds. According to the Doppler principle, at this time, Δt c > τ s , the pulse width is stretched, and it is determined that the relative radial motion speed v est < 0, indicating that the target is moving away from the sonar.

[0077] Step S502: Use the formula to calculate that the relative radial motion speed of the active target is -5.1 m / s, with an estimation error of 2%. The running time of this embodiment is 0.10488 seconds.

[0078] Embodiment 2

[0079] Refer to Figure 1 , Figure 4 and Figure 5 . Similarly, this embodiment also provides an estimation method for the relative radial motion speed of an active target based on the cepstrum principle. The process of this method is also as shown in Figure 5 , and specifically includes:

[0080] Step S1: Construct a broadband combined pulse signal and use it as the transmission signal of the active sonar. Among them, the broadband combined pulse signal includes a sub-pulse signal and a delayed sub-pulse signal, and record the preset time delay value in the combined pulse signal.

[0081] In this embodiment, step S1 specifically includes:

[0082] The broadband combined pulse signal transmitted by the active sonar is expressed as:

[0083] u(n) = s(n) + s(n - n s ) (1)

[0084] In formula (1), s(n) is the sub-pulse signal, and s(n - n s ) is the delayed sub-pulse signal, where n s is the integer obtained by rounding τ s × f s . The preset time delay value τ s is 1.5 seconds, the sampling frequency f s of the active sonar system is 10,000 Hz, and the transmission period T of the combined pulse signalp is 10 seconds;

[0085] The above sub-pulse signal s(n) is an HFM signal, specifically expressed as:

[0086]

[0087] In this formula (2), the pulse width T of the sub-pulse signal is 1 second, the amplitude A is 1, the time center frequency f0 is 1000 Hz, the frequency modulation width B is 500 Hz, the lowest frequency of the signal is Hz, and the highest frequency of the signal is Hz, and n is the time point sampled at f s Hz.

[0088] Step S2: Set the maximum radial movement speed at which the active target may appear, and then determine the time search range in the cepstrum.

[0089] Specifically, in this embodiment, this step S2 includes:

[0090] According to the Doppler principle, determine the time search range in the cepstrum as [τ s -Δτ, τ s +Δτ] seconds, where seconds, is the maximum Doppler factor, the maximum radial speed v at which the active target may appear max is 15 m / s, and the propagation speed c of sound waves in water is 1500 m / s.

[0091] Step S3: Use the sub-pulse signal in the transmitted signal to perform matched filtering with the echo signal.

[0092] Specifically, in this embodiment, use the simulated echo signal, such as Figure 1 the bright spot model shown. In this figure, N represents the number of bright spots of the target, and u' i (n) is the echo generated by the i-th bright spot, and L i is the distance between the i-th bright spot and the sonar.

[0093] In this embodiment, the target has 4 bright spots, and the echo signal is obtained using the following formula:

[0094]

[0095] In this formula (3), u' i (n) = s' i (n) + s' i (n - n s ), where

[0096]

[0097]

[0098] In formulas (4) and (5), b i is the reflection coefficient of the i-th bright spot. According to the Doppler principle, when the radial velocity v of the active target is 10 m / s, the resampled signal frequency is Hertz, n i is an integer after rounding, and n rs is s × f rs an integer after rounding.

[0099] More specifically, in this embodiment, the reflection coefficients of the four bright spots are b1 = 0.5, b2 = 0.9, b3 = 0.7, and b4 = 0.4 respectively, and the distances of the four bright spots from the sonar are L1 = 500 m, L2 = 530 m, L3 = 575 m, and L4 = 596 m respectively.

[0100] Among them, s'(n) in formulas (4) and (5) is specifically expressed as:

[0101]

[0102] In formula (6), n' is the time point sampled at f p Hertz within the range of [0, T rs , is the random phase added to the i-th bright spot, which is a random number within the range of [0, 2π], and n(n) is the system noise. To illustrate the anti-noise performance of the present invention, in this embodiment, simulated echo signals with different signal-to-noise ratios are generated, and the change range of the signal-to-noise ratio is [-20, 20] dB, and the change accuracy is 1 dB.

[0103] More specifically, the signal-to-noise ratio of this embodiment is not a fixed value, but 40 echoes with signal-to-noise ratios ranging from -20 to 20 dB are generated, and a velocity estimation is performed for each echo, for a total of 40 velocity estimations.

[0104] Using the sub-pulse signal s(n) of the transmitted signal in step S1, the following formula is used to perform matched filtering with the echo signal u r (n) respectively, including:

[0105]

[0106] Performing the same operation on the echo signals with different signal-to-noise ratios can obtain the matched filtering results with different signal-to-noise ratios;

[0107] Step S4: performing cepstrum transform on the matched filtering result obtained in step S3.

[0108] Specifically, in this embodiment, step S4 includes:

[0109] According to the cepstrum analysis principle, the matched filtering result obtained in step S3 is subjected to cepstrum transformation using the following formula, including:

[0110] c y (n) = F -1 {log|F{y(n)|} (8)

[0111] In formula (8), F{} represents discrete Fourier transform, is the discrete Fourier transform of f(n), F -1 {} represents the inverse discrete Fourier transform, is the inverse discrete Fourier transform of F(k), N f is the number of points of the signal f(n). The same operation is performed on the matched filtering results obtained in step S3 at different signal-to-noise ratios to obtain cepstrum results at different signal-to-noise ratios.

[0112] Step S5: Find the maximum value within the time search range in the cepstrum result obtained in step S4, record the time corresponding to the maximum value, and estimate the magnitude and direction of the target's relative radial motion speed.

[0113] Specifically, in this embodiment, step S5 includes:

[0114] Find the cepstrum result c obtained in step S4 y (n)[τ s -Δτ,τ s +Δτ] the time Δt corresponding to the maximum value in the range c , according to the Doppler principle, using the formula The relative radial velocity of the active target is calculated. The same operation is performed on the cepstrum results at different signal-to-noise ratios to obtain the relative radial velocity values at different signal-to-noise ratios. The total running time of the cepstrum method in this embodiment is 2.0493 seconds, which is the total time for 40 velocity estimations. More specifically, in this embodiment, the method of this embodiment is executed once for each echo with different signal-to-noise ratio. In this embodiment 2, steps S1-S5 are executed a total of 40 times.

[0115] Step S6: Compare with the results of the motion speed estimated by the traditional matching pursuit method. The matching pursuit method uses the simulated echo signal in this embodiment. The speed range corresponding to the atom library constructed by the matching pursuit method is [-15, 15] m / s, and the accuracy is 0.05 m / s. Use the signals in the atom library to perform matching filtering with the echo signal one by one, find the case with the largest amplitude among all the matching filtering results, and use the speed value of the signal corresponding to this case as the estimated value of the speed. Perform the same operation on the echo signals with different signal-to-noise ratios to obtain the speed estimated values using the matching pursuit method at different signal-to-noise ratios. The total running time of the matching pursuit method in this embodiment is 785.6234 seconds.

[0116] Figure 4 This is a comparison chart of the target relative radial motion speed values estimated by the method of the present invention and the matching pursuit method under different signal-to-noise ratio conditions. The signal-to-noise ratio of the echo signal is used as the abscissa, and the speed estimated value is used as the ordinate. When the signal-to-noise ratio of the echo signal is lower than -5 dB, the error of the target relative radial motion speed estimated by the matching pursuit method gradually increases; the method of this embodiment estimates that the target relative radial motion speed value is close to the set value of 10 m / s within the range of [-20, 20] dB of the echo signal-to-noise ratio. Compared with the traditional matching pursuit method, the method of the present invention has a smaller amount of calculation, a faster running speed, and can still accurately estimate the target relative radial motion speed value under lower signal-to-noise ratio conditions.

[0117] In summary, as can be seen from the results of Embodiment 1 and Embodiment 2, the present invention can obtain good estimation accuracy, and has simple calculation steps and a small amount of calculation. At the same time, it has good anti-noise ability and is suitable for estimating the target relative radial motion speed of active sonar.

[0118] Details not described in the present invention are all well-known technologies to those skilled in the art.

[0119] The preferred specific embodiments of the present invention have been described in detail above. It should be understood that those of ordinary skill in the art can make many modifications and variations according to the concept of the present invention without creative work. Therefore, all technical solutions that can be obtained by those skilled in the art in the technical field of the present invention based on the concept of the present invention through logical analysis, reasoning or limited experiments on the basis of the prior art should be within the protection scope determined by the claims.

Claims

1. An estimation method for the relative radial motion speed of an active target based on the cepstrum principle, characterized in that, The method includes: Step S1: Construct a broadband combined pulse signal and use it as the transmission signal of the active sonar. Among them, the broadband combined pulse signal includes a sub-pulse signal and a delayed sub-pulse signal, and record the preset time delay value in the combined pulse signal; Step S2: Set the maximum radial movement speed of the active target, and then determine the time search range in the cepstrum; Step S3: Perform matched filtering on the sub-pulse signal in the transmission signal and the echo signal received by the active sonar; Step S4: Perform cepstrum transformation on the matched filtering result obtained in Step S3; Step S5: Find the maximum value within the time search range in the cepstrum result obtained in Step S4, record the time corresponding to the maximum value, and estimate the magnitude and direction of the relative radial movement speed of the target.

2. The estimation method of the relative radial motion speed of an active target based on the cepstrum principle according to claim 1, characterized in that The said Step S1 includes: The active sonar transmits a broadband combined pulse signal, which is expressed as: u(n) = s(n) + s(n - n s ) (1) In the formula (1), s(n) is the sub-pulse signal, and s(n - n s ) is the sub-pulse signal after delay, where n s is an integer obtained by rounding τ s × f s , τ s is the preset time delay, and f s is the sampling frequency of the active sonar system; The sub-pulse signal s(n) is an HFM signal, and is specifically expressed as: In the formula (2), T is the pulse width of the sub-pulse signal, A is the amplitude, f0 is the time center frequency, B is the frequency modulation width, the lowest frequency of the signal is Hertz, the highest frequency of the signal is Hertz, n is the time point sampled at f s Hertz.

3. The estimation method of the relative radial motion speed of an active target based on the cepstrum principle according to claim 2, wherein The said Step S2 includes: According to the Doppler principle, the time search range in the cepstrum is determined to be [τ s -Δτ, τ s +Δτ] seconds, where seconds, is the maximum Doppler factor, v max is the maximum radial motion speed of the active target, and c is the propagation speed of sound waves in water.

4. The estimation method of the relative radial motion speed of an active target based on the cepstrum principle according to claim 3, characterized in that, In step S3, using the sub-pulse signal s(n) of the transmitted signal in step S1, the following formula is used to perform matched filtering with the received echo signal u r (n), including:

5. The estimation method of the relative radial motion speed of an active target based on the cepstrum principle according to claim 4, characterized in that The said Step S4 includes: According to the cepstrum analysis principle, perform cepstrum transformation on the matched filtering result obtained in Step S3 by using the following formula, including: c y (n) = F -1 {log|F{y(n)|} (4) In formula (4), F{} represents the discrete Fourier transform, which is the discrete Fourier transform of f(n), and F -1 {} represents the inverse discrete Fourier transform, which is the inverse discrete Fourier transform of F(k), and N f is the number of points of the signal f(n).

6. The estimation method of the relative radial motion speed of an active target based on the cepstrum principle according to claim 5, characterized in that The said Step S5 includes: Step S501: Locate the cepstrum result c obtained in step S4 y (n) within [τ s -Δτ, τ s +Δτ], and the corresponding time Δt of the maximum value c , and then perform the following judgment: According to the Doppler principle, when Δt c <τ s , the pulse width is compressed, and the relative radial motion speed v of the target is judged est >0, and the target moves closer to the sonar; When Δt c > τ s , the pulse width is stretched, and the relative radial motion speed v of the target is judged est < 0, the target moves away from the sonar; Step S502: Use the formula to calculate the relative radial motion speed of the active target and obtain its speed estimate value.

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