Distance-Doppler joint estimation method based on low signal-to-noise ratio condition

Abstract

The invention discloses a distance-Doppler joint estimation method based on a low signal-to-noise ratio condition. A signal received by a sonar system is subjected to matched filtering through a plurality of HFM signals and then is output. The Doppler coefficient is estimated by combining HFM signals in different frequency sweeping directions, and matched filtering output is compensated. And fitting the matched filtering output into the hidden Markov model by using the motion model of the target. A Viterbi algorithm is used to solve a peak pair selection problem of matched filtering output, and joint distance-Doppler estimation is executed. And screening peak values in the matched filtering output again by using a constant false alarm criterion. According to the method, the output of the matched filter is fitted into the hidden Markov model by using the motion model of the target. A Viterbi algorithm is used to solve a peak pair selection problem, and joint distance-Doppler estimation is performed. The signal-to-noise ratio requirement is reduced through multi-pulse processing, and reliable extraction of the target distance-Doppler parameter can be realized under the condition of a lower signal-to-noise ratio.

Description

Technical Field

[0001] The invention belongs to the technical field of sonar target detection, and in particular relates to a distance-Doppler joint estimation method based on low signal-to-noise ratio conditions. Background Art

[0002] Sonar is a technology or equipment that uses the propagation and reflection characteristics of sound waves in water to navigate and measure distance through electroacoustic conversion and information processing. Sonar can not only be used in the military field, such as the detection, identification, tracking, positioning and navigation of submarines and surface ships, but also in torpedo guidance, mine fuses, offshore oil exploration, ship navigation, underwater operations, hydrographic surveys and seabed geological surveys. Dual-frequency sonar is a sonar with two working frequencies. These two frequencies correspond to different detection angles, thereby improving the accuracy and efficiency of detection, and can provide high-precision and high-resolution detection results, suitable for various underwater detection tasks.

[0003] The high-frequency mode of dual-frequency sonar can achieve higher resolution, but due to the higher frequency of high-frequency signals, losses occur during propagation, and these losses limit the effective range in high-frequency mode. In addition, the Doppler frequency deviation introduced by the relative motion between the target and the sonar system will also be more obvious, which greatly affects the effect of matched filtering. Usually, we use Kalman filtering to improve the accuracy of system matched filtering, but Kalman filtering cannot perform well under low signal-to-noise ratio conditions. Therefore, in order to extend the effective range in high-frequency mode and overcome the influence of relative motion between the target and the system on the detection results, a distance-Doppler joint estimation method based on low signal-to-noise ratio conditions is urgently needed. Summary of the invention

[0004] The content of this application is used to introduce concepts in a brief form, which will be described in detail in the detailed implementation section below. The content of this application is not intended to identify the key features or essential features of the technical solution claimed for protection, nor is it intended to limit the scope of the technical solution claimed for protection.

[0005] In view of the problems and shortcomings in the prior art, the present invention aims to provide a range-Doppler joint estimation method based on low signal-to-noise ratio conditions. The present invention fits all possible range-Doppler combinations of the target in multiple pulses into a hidden Markov model, and uses the Viterbi algorithm to solve the most likely range-Doppler sequence, thereby eliminating errors caused by pseudo peaks introduced by noise, reducing the signal-to-noise ratio required for range-Doppler estimation, and having better performance under low signal-to-noise ratios. This solves the problems raised in the above background technology.

[0006] To achieve the above object, the present invention provides the following technical solutions:

[0007] The present invention discloses a range-Doppler joint estimation method based on low signal-to-noise ratio conditions, comprising the following steps:

[0008] Step 1, the signal received by the sonar system is matched filtered through multiple HFM signals and then output;

[0009] Step 2, combining the HFM signal in different sweep directions to estimate the Doppler coefficient and compensate the matched filter output;

[0010] Step 3, using the target motion model to fit the matched filter output into the hidden Markov model;

[0011] Step 4, using the Viterbi algorithm to solve the peak pair selection problem of the matched filter output and perform joint range-Doppler estimation;

[0012] Step 5: Use the constant false alarm criterion to screen the peak value in the matched filter output again.

[0013] Furthermore, in step 3, the matched filter output is fitted into the hidden Markov model using the target motion model, which specifically includes the following steps:

[0014] Step 3.1, simplifying the state vector obtained by the sonar system into the distance and radial velocity of the target relative to the sonar system;

[0015] Step 3.2, write the output of the matched filter measured multiple times into a matrix;

[0016] Step 3.3, introduce the first-order Markov hypothesis and rewrite the matrix using the Bayesian criterion.

[0017] Furthermore, in step 4, the Viterbi algorithm is used to solve the peak pair selection problem of the matched filter output, and a joint range-Doppler estimation is performed, which specifically includes the following steps:

[0018] Step 4.1, obtaining the peak numbers of the upper and lower swept frequency matched filter outputs, and obtaining the possible states of the total number of corresponding peak numbers;

[0019] Step 4.2, define a function to represent the state of the target in the last measurement given the current state;

[0020] Step 4.3, initialize the function defined in step 4.2;

[0021] Step 4.4, obtain the most likely state sequence of the target in multiple measurements through the forward and backtracking process.

[0022] In step 5, the peak value in the matched filter output is screened again using the constant false alarm criterion, which specifically includes the following steps:

[0023] Step 5.1, calculating the cumulative distribution function according to the probability density function of the Rayleigh distribution in the output of the up-sweep matched filter measurement;

[0024] Step 5.2, calculate the false alarm probability according to the given threshold, and obtain the noise variance through the false alarm probability.

[0025] Step 5.3, calculating the peak amplitude threshold by combining the false alarm probability and the noise variance;

[0026] Step 5.4, eliminating the noise peaks that are higher than the peak amplitude threshold.

[0027] Furthermore, in step 2, the formula for estimating the Doppler coefficient is expressed as:

[0028]

[0029] Wherein, f1 and f2 represent different sweep frequencies, and T represents the time delay after obtaining distance deviation compensation.

[0030] Furthermore, in step 3.3, the matrix is ​​rewritten as follows using the Bayesian criterion:

[0031]

[0032] Among them, P(z1) represents the initial probability, z k Expressed as the target state, P(x h，k , x l，k |z k ), k = 1, ..., K represents the emission probability, and the measurement x is obtained h，k and x l，k The probability of k |z k-1 ), k = 2, ..., K: state transition probability, indicating the target changes from state z in two consecutive measurements k-1 Convert to z k probability.

[0033] Furthermore, in step 5.3, the formula of the peak amplitude threshold is:

[0034]

[0035] Among them, P f Expressed as the false alarm probability, It is expressed as the noise variance.

[0036] Compared with the prior art, the beneficial effects of the present invention are as follows: the present invention provides a distance-Doppler joint estimation method based on low signal-to-noise ratio conditions, a distance-Doppler joint estimation method based on multi-pulse processing of a combined signal of an upper and lower frequency-sweeping hyperbolic frequency modulation signal, and makes full use of the Doppler invariance of the hyperbolic frequency modulation waveform and the processing gain brought by the matched filter. While ensuring the matched filter gain under the Doppler distortion condition, the distance estimation ambiguity problem of the hyperbolic frequency modulation signal under the Doppler distortion condition is solved, and the joint estimation of the target distance-Doppler in the multi-pulse is realized. In addition, the multi-pulse matched filtering result is combined with the hidden Markov model, and the maximum likelihood target state sequence in the model is selected by the Viterbi algorithm, which reduces the signal-to-noise ratio requirement for reliable parameter estimation and improves the working distance of the system. Compared with the existing various methods based on Kalman filtering and the like, the proposed method can realize the reliable extraction of the target distance-Doppler parameters under the condition of lower signal-to-noise ratio, and does not need to accurately obtain the target distance-Doppler parameters in each return pulse. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] The drawings constituting a part of this application are used to provide a further understanding of this application, so that other features, purposes and advantages of this application become more obvious. The schematic embodiment drawings and their descriptions of this application are used to explain this application and do not constitute an improper limitation on this application. In the drawings:

[0038] Figure 1 is a flowchart of the main steps in an embodiment of the present invention;

[0039] Figure 2 This is a waveform diagram of HFM signal matched filtering in an embodiment of the present invention;

[0040] Figure 3 It is a schematic diagram of using upper and lower frequency sweep combination HFM pulses to compensate for distance estimation deviation in an embodiment of the present invention;

[0041] Figure 4 Schematic diagram of target range-Doppler estimation results using different methods in an embodiment of the present invention, (a) is the output result of the swept frequency signal matched filter on one pulse, and (b) is the time delay of the target in multiple measurements using different methods;

[0042] Figure 5 Schematic diagram of target radial velocity and time delay estimation errors under different signal-to-noise ratios in an embodiment of the present invention, (a) is radial velocity estimation, and (b) is time delay estimation. DETAILED DESCRIPTION

[0043] Embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. Although certain embodiments of the present disclosure are shown in the accompanying drawings, it should be understood that the present disclosure can be implemented in various forms and should not be construed as being limited to the embodiments set forth herein. On the contrary, these embodiments are provided to provide a more thorough and complete understanding of the present disclosure. It should be understood that the drawings and embodiments of the present disclosure are only for exemplary purposes and are not intended to limit the scope of protection of the present disclosure.

[0044] It should also be noted that, for ease of description, only the parts related to the invention are shown in the drawings. In the absence of conflict, the embodiments and features in the embodiments of the present disclosure can be combined with each other.

[0045] The present invention discloses a range-Doppler joint estimation method based on low signal-to-noise ratio conditions, and the present invention will be described in detail below with reference to the accompanying drawings and in combination with embodiments. Figure 1 As shown, the specific steps include:

[0046] Step 1, the signal received by the sonar system is matched filtered through multiple HFM signals and then output;

[0047] Step 2, combining the HFM signal in different sweep directions to estimate the Doppler coefficient and compensate the matched filter output;

[0048] Step 3, using the target motion model to fit the matched filter output into the hidden Markov model;

[0049] Step 4, using the Viterbi algorithm to solve the peak pair selection problem of the matched filter output and perform joint range-Doppler estimation;

[0050] Step 5: Use the constant false alarm criterion to screen the peak value in the matched filter output again.

[0051] Since the Doppler distortion caused by target motion will affect the processing gain of matched filtering, the HFM signal has an advantage in detecting moving targets due to its Doppler invariance. Figure 2 As shown. However, the Doppler invariance of this waveform comes at the expense of the deviation in the target distance estimation. Therefore, it is necessary to consider the compensation of the distance deviation when using the HFM signal. We assume that an HFM signal with a frequency range from f1 to f2 can be expressed as,

[0052]

[0053] Where k = (f1-f2) / f1f2T, T is the duration of the waveform. According to formula 1, the instantaneous frequency of the HFM signal can be written as,

[0054]

[0055] Similarly, if the signal after Doppler distortion is written as s(αt), then the corresponding instantaneous frequency f α (t) can be expressed as,

[0056]

[0057] By comparing Formula 2 and Formula 3, we can find that Doppler distortion causes the instantaneous frequency of the signal to shift by (1-α) / αkf1, which means that under the condition of Doppler distortion, the shape of the matched filter output will not change, making the HFM signal invariant to Doppler distortion. However, correspondingly, the shift of the instantaneous frequency will cause the peak after matched filtering to move accordingly, resulting in a deviation in the estimation of the target distance.

[0058] The distance deviation in the matched filter output can be solved by transmitting multiple HFM signals with different parameters. Observing formula 3, it can be found that the peak offset of the matched filter output is different under the same Doppler distortion condition for HFM waveforms with different parameters. In particular, when the frequency change direction of the HFM waveform is different, under the same Doppler coefficient condition, the peak movement direction in the matched filter is opposite. Then, the combined HFM signal with different sweep directions is used to estimate the Doppler coefficient and compensate for the distance estimation deviation, such as Figure 3 As shown. We assume that the two pulses with different sweep directions have the same bandwidth B, but the frequency modulation directions are opposite. Referring to Formula 1, the transmitted signal c(t) composed of these two signals can be expressed as,

[0059]

[0060] Where s + (t) is the forward sweep signal, the frequency changes from f1 to f2, and s - (t) is a negative sweep signal, and the frequency changes from f2 to f1. Under the simplification of point targets, the echo signal can be expressed as Ac(αt-τ), where A is the amplitude coefficient introduced by sound propagation and reflection, α is the Doppler coefficient introduced by target motion, and τ is the time delay introduced by target distance. According to formula 3, using the upper sweep signal s + (t) After matched filtering, the corresponding peak value t + Located in + =τ / α+(α-1) / αkf1. Similarly, using the down-sweep signal s - (t) After matched filtering, the corresponding peak value t - Located at - =τ / α+T / α-(α-1) / αkf2. Let T α =t --t + , the Doppler coefficient α can be estimated using the following formula:

[0061]

[0062] Substituting the Doppler coefficient α into the peak value t + or peak value t - The delay τ after distance deviation compensation can be obtained. Although the combined HFM waveform can compensate for the distance deviation while maintaining the matched filter processing gain, the accuracy of the result is based on the correct selection of peak pairs. When the signal-to-noise ratio is high, the peak pair used to compensate for the distance estimation deviation can be directly found from the matched filter output. As the signal-to-noise ratio gradually decreases, Figure 3 There will be many peaks from noise in the output of the matched filter. Therefore, in order to obtain accurate Doppler and distance estimates of the target, it is necessary to design an algorithm to select the correct peak pair.

[0063] However, when the signal-to-noise ratio is low, the output of the matched filter contains a large number of peaks generated by noise. In order to ensure the accuracy of the Doppler and distance estimation results, it is necessary to select the correct peak pairs from a large number of peaks. Compared with the traditional tracking algorithm that relies on a single measurement result, the pre-detection tracking algorithm directly processes several ambiguous measurement results, and then directly gives the trajectory information of the target in these measurement results based on the target motion and system measurement model. Therefore, starting from the target motion model, the present invention proposes a pre-detection tracking algorithm suitable for dual-frequency HFM signals, realizing distance-Doppler joint estimation under low signal-to-noise ratio, which is used to improve the performance of target recognition. Specifically, it includes the following steps:

[0064] Step 3.1, simplifying the state vector obtained by the sonar system into the distance and radial velocity of the target relative to the sonar system;

[0065] Step 3.2, write the output of the matched filter measured multiple times into a matrix;

[0066] In step 3.3, the first-order Markov hypothesis is introduced and the matrix is ​​rewritten using the Bayesian criterion.

[0067] Specifically, for the state vector z of the underwater target, this paper simplifies it to include two variables, namely the distance d relative to the sonar system and the radial velocity v relative to the system. Then the state vector z of the target in the kth pulse echo is k It can be expressed as,

[0068] z k =[d k , v k ] T ;Formula 6

[0069] Based on the definition of the state vector, the target state motion model can be expressed as:

[0070]

[0071] Where T s is the time interval between two consecutive measurements, w k，d and w k，v is the noise component, which is used to adapt to the change of the target motion mode. On this basis, the state sequence Z of the target in the total number of K pulse echoes can be expressed as Z = [z1, ..., z k ]. If the filter output corresponding to the forward sweep signal in the kth pulse echo is defined as x h，k ∈N×1, the negative sweep signal filter output is defined as x l，k ∈N×1, where N is the length of the matched filter output. On this basis, the output of the matched filter with a total of K measurements can be written in matrix form, defined as X h =[x h，1 , …, x h，K ] and X l =[x l，1 , …, x l，K ]. Based on the above definition, the problem that the algorithm needs to solve can be expressed as, In order to introduce the first-order Markov hypothesis, that is, the state of the target in the current measurement is only related to the state in the previous measurement, it is rewritten through the Bayesian criterion as follows:

[0072]

[0073] Among them, P(z1) represents the initial probability, z k Expressed as the target state, P(x h，k , x l，k |z k ), k = 1, ..., K represents the emission probability, and the measurement x is obtained h，k and x l，k The probability of k |z k-1 ), k = 2, ..., K: state transition probability, indicating the target changes from state z in two consecutive measurements k-1 Convert to z k probability.

[0074] After determining the expression of each probability in Formula 8, the Viterbi algorithm can be used to solve the maximum likelihood estimation problem shown in Formula 8. Specifically, the following steps are included:

[0075] Step 4.1, obtaining the peak numbers of the upper and lower swept frequency matched filter outputs, and obtaining the possible states of the total number of corresponding peak numbers;

[0076] Step 4.2, define a function to represent the state of the target in the last measurement given the current state;

[0077] Step 4.3, initialize the function defined in step 4.2;

[0078] Step 4.4, obtain the most likely state sequence of the target in multiple measurements through the forward and backtracking process.

[0079] Each pair of peaks corresponds to a possible target state. For the measurement result of the kth pulse, the number of peaks obtained by the matched filtering of the up-sweep signal is M k , and the number of peaks from the down-sweep matched filter output is N k , then the total number can be M k N k The possible states of Where m and n are t + and t - The subscript of the peak position τ in the matched filter output, that is, the state of the target in a certain measurement can be represented by the coordinates composed of the peak numbers. On this basis, the function γ is defined k () is used to indicate the state of the target in the last measurement under a given current state. For example, γ k (m, n) = (p, q) means that in the kth measurement, for the state with coordinates (m, n), the state coordinates in the k-1th measurement are (p, q). In addition, we define the function δ k (), expressed as,

[0080]

[0081] Based on the above definition, the method of using the Viterbi algorithm to solve the maximum likelihood problem shown in Formula 8 can be divided into three steps: initialization, forward and backtracking: Initialization is expressed as,

[0082] γ1(m,n)=0

[0083] δ1(m,n)=P[x1|z1=s(m,n)]P[z1=s(m,n)]; Formula 10

[0084] Where m = 1, ..., M1, n = 1, ..., N1. The forward process is expressed as,

[0085]

[0086] P[z k =s(m,n)|z k-1 =s(p,q)]δ k-1([p, q])

[0087]

[0088] P[z k =s(m,n)|z k-1 =s(p,q)]δ k-1 ([p, q]); Formula 11

[0089] Where k = 2, ..., K, K is the total number of measurements, m = 1, ...M k , n=1,…N k , p=1,…M k-1 And q = 1, ... N k-1 After the forward process, the most likely state coordinate sequence is stored in the function γ k (), k = 1, ..., K, and the joint probability is stored in the function δ k (), k = 1, ..., K. Through the backtracking process, we can obtain the state sequence when formula 8 reaches the maximum value. First, start from the measurement result of the last K pulse, expressed as,

[0090]

[0091] Where m = 1, ..., M K And n = 1, ..., N K After determining the state in the last measurement, backtrack using the previous results to obtain the state sequence of the target in all measurements as follows:

[0092]

[0093] Where k = 1, ..., K-1. The Viterbi algorithm can quickly solve the maximum value problem shown in Formula 8 and obtain the most likely state sequence of the target in multiple measurements. By observing the solution process, it can be found that the complexity of the algorithm depends on the number of possible states of the target. In order to reduce the number of possible states of the target, it is necessary to further screen the peaks in the matched filter output.

[0094] Under the influence of noise, the matched filter output will contain a large number of pseudo peaks, and each pseudo peak pair will correspond to a possible target state. Therefore, these peaks introduced by noise will increase the computational burden of the tracking algorithm. In order to speed up the operation speed of the algorithm when applied, it is necessary to screen the peaks in the matched filter output. In order to make the threshold used for screening adaptive according to the actual signal, the present invention adopts the constant false alarm criterion to screen the peaks in the matched filter output.

[0095] Step 5.1, calculating the cumulative distribution function based on the probability density function of the Rayleigh distribution in the output of the up-sweep matched filter measurement;

[0096] Step 5.2, calculate the false alarm probability according to the given threshold, and obtain the noise variance through the false alarm probability;

[0097] Step 5.3, calculate the peak amplitude threshold by combining the false alarm probability and the noise variance;

[0098] Step 5.4, the noise peaks that are higher than the peak amplitude threshold are eliminated.

[0099] Specifically, in order to achieve constant false alarm peak screening, it is necessary to use the noise variance σ 2 And the preset false alarm probability P F Determine the corresponding detection threshold l D For each peak, there are two possibilities, H0 and H1. H0 represents the peak being generated by interference or noise, and H1 represents the peak being generated by the target. Then, when H0 is assumed to be true, x h，k (m) obeys Rayleigh distribution under Gaussian white noise conditions and is expressed as:

[0100]

[0101] According to the probability density function of Rayleigh distribution in formula 14, the cumulative distribution function of Rayleigh distribution can be expressed as,

[0102] F(x)=1-exp(-x 2 / 2σ 2 ); Formula 15

[0103] Then, for a given threshold l d =x, false alarm probability P f Can be written as

[0104] P f =1-F(x)=exp(-x 2 / 2σ 2 ); Formula 16

[0105] At this time, according to the specified false alarm probability P f and the noise variance estimate calculated by Equation 14 The peak amplitude threshold l can be derived D for

[0106]

[0107] In practical applications, a larger false alarm probability can be selected to retain the peak value from the target as much as possible. At the same time, due to the introduction of the peak screening mechanism, the noise peak can also be eliminated, reducing the computational complexity of estimating the target state sequence.

[0108] Experimental data

[0109] In order to generate signals with different signal-to-noise ratios, the present invention uses the awgn function in Matlab software to add noise to the signal to achieve the required signal-to-noise ratio. Since the methods involved in the comparison are all based on single measurement results, the Kalman filter is used to process the results of multiple measurements in the numerical experiment. The observation and state transition noise in the Kalman filter are set to the same diagonal matrix diag (0.01, 1), and accordingly, the initial value directly adopts the result obtained by the first pulse. Based on the above settings, the following two groups of experiments are carried out:

[0110] Experiment 1: Under a -20dB signal-to-noise ratio, process 20 consecutive pulses and show the processing results of different methods. Under this signal-to-noise ratio, there are many false peaks in the matched filter, such as Figure 4 (a) shows that the calculation result of a single pulse is less accurate. The processing results of 20 consecutive pulses using different methods are shown in Figure 4 As shown in (b), the result obtained by a single pulse is unreliable, resulting in a large error between the final estimated result and the true value. In contrast, the proposed method does not directly estimate the target state through the single pulse result, but uses all possible target states in all pulses for estimation, avoiding the problem of unreliable single pulse results and achieving reliable estimation of parameters.

[0111] Experiment 2: Monte Carlo simulation was used to evaluate the performance of different algorithms at different SNR levels. The performance comparison was based on the root mean square error (RMSE) of radial velocity and time delay estimation. All parameters except the SNR were the same as the previous numerical experiments. In order to obtain a relatively smooth curve, 5000 Monte Carlo simulations were performed for each SNR. The results are shown in Figure 2. Figure 5 Observation Figure 5 It can be found from the results in that under the experimental scenario setting in this section, the proposed method reduces the signal-to-noise ratio requirement for parameter estimation by about 10dB.

[0112] By comparison Figure 5From the results in , we can see that the noises output by the two matched filters are correlated. Therefore, at low signal-to-noise ratios, the performance of the CPM method is even worse than that of the traditional matched filter-based method. Although the SSS method is capable of high-resolution velocity estimation, it has a high requirement for the signal-to-noise ratio because it cannot fully utilize the signal-to-noise ratio gain brought by the matched filter. In addition, as the noise power increases, it becomes increasingly difficult to obtain valid data segments, which further reduces the accuracy of the method. Figure 5 In (a), the SNR required for CPM to accurately estimate the radial velocity of the target is about -7dB, after which the error rises and eventually stabilizes. This is because as the SNR decreases, the peak generated by the correlated noise gradually becomes dominant, while the position of the noise correlation peak does not change. Therefore, the velocity estimate is constant. Figure 5 In (b), there are two flat areas in the error of delay estimation using CPM. This is because the delay estimation in CPM still relies on the result of matched filtering. The first flat area is a constant speed estimation error and ends at about -15dB. At this time, the processing gain of the matched filter is not enough to combat the low signal-to-noise ratio, and the pseudo-peak amplitude generated by the noise is greater than the target peak amplitude. Due to the limited analysis window length, the delay estimation error gradually flattens after -22dB. Figure 5 In (a), the signal-to-noise ratio required for SSS to accurately estimate the target radial velocity is about -10 dB. As the signal-to-noise ratio decreases, the velocity estimation error gradually stabilizes due to the limitation of the velocity spectrum analysis interval in the algorithm. However, since this error is smaller than that of the CPM method and the pulse repetition interval is not large, about 200 ms, Figure 5 In (b), the delay error has not yet increased significantly. Since the SSS estimation of the target distance also depends on the matched filtering result, the signal-to-noise ratio when the delay error increases significantly is consistent with the signal-to-noise ratio when the matched filtering gain is insufficient, which is about -15dB.

[0113] The above descriptions are only some preferred embodiments of the present disclosure and an explanation of the technical principles used. Those skilled in the art should understand that the scope of the invention involved in the embodiments of the present disclosure is not limited to the technical solutions formed by a specific combination of the above-mentioned technical features, but should also cover other technical solutions formed by any combination of the above-mentioned technical features or their equivalent features without departing from the above-mentioned inventive concept. For example, the above-mentioned features are replaced with the technical features with similar functions disclosed in the embodiments of the present disclosure (but not limited to) and the technical solutions formed.

Claims

1. A range-Doppler joint estimation method based on low signal-to-noise ratio conditions, characterized in that: The steps include: Step 1, the signal received by the sonar system is matched filtered through multiple HFM signals and then output; Step 2, combining the HFM signal in different sweep directions to estimate the Doppler coefficient and compensate the matched filter output; Step 3, using the target motion model to fit the matched filter output into the hidden Markov model; Step 4, using the Viterbi algorithm to solve the peak pair selection problem of the matched filter output and perform joint range-Doppler estimation; Step 5: Use the constant false alarm criterion to screen the peak value in the matched filter output again.

2. The range-Doppler joint estimation method based on low signal-to-noise ratio conditions according to claim 1, characterized in that: In step 3, the matched filter output is fitted into the hidden Markov model using the target motion model, which specifically includes the following steps: Step 3.1, simplifying the state vector obtained by the sonar system into the distance and radial velocity of the target relative to the sonar system; Step 3.2, write the output of the matched filter measured multiple times into a matrix; Step 3.3, introduce the first-order Markov hypothesis and rewrite the matrix using the Bayesian criterion.

3. The range-Doppler joint estimation method based on low signal-to-noise ratio conditions according to claim 2, characterized in that: In step 4, the Viterbi algorithm is used to solve the peak pair selection problem of the matched filter output, and a joint range-Doppler estimation is performed, which specifically includes the following steps: Step 4.1, obtaining the peak numbers of the upper and lower swept frequency matched filter outputs, and obtaining the possible states of the total number of corresponding peak numbers; Step 4.2, define a function to represent the state of the target in the last measurement given the current state; Step 4.3, initialize the function defined in step 4.2; Step 4.4, obtain the most likely state sequence of the target in multiple measurements through the forward and backtracking process.

4. The range-Doppler joint estimation method based on low signal-to-noise ratio conditions according to claim 3, characterized in that: In step 5, the peak value in the matched filter output is screened again using the constant false alarm criterion, which specifically includes the following steps: Step 5.1, calculating the cumulative distribution function according to the probability density function of the Rayleigh distribution in the output of the up-sweep matched filter measurement; Step 5.2, calculate the false alarm probability according to the given threshold, and obtain the noise variance through the false alarm probability. Step 5.3, calculating the peak amplitude threshold by combining the false alarm probability and the noise variance; Step 5.4, eliminating the noise peaks that are higher than the peak amplitude threshold.

5. The range-Doppler joint estimation method under low signal-to-noise ratio conditions according to claim 4, characterized in that: In step 2, the formula for estimating the Doppler coefficient is expressed as: Wherein, f1 and f2 represent different sweep frequencies, and T represents the time delay after obtaining distance deviation compensation.

6. The range-Doppler joint estimation method under low signal-to-noise ratio conditions according to claim 4, characterized in that: In step 3.3, the matrix is ​​rewritten as follows using the Bayesian criterion: Among them, P(z1) represents the initial probability, z k Expressed as the target state, P(x h，k , x l，k |z k ), k = 1, ..., K represents the emission probability, and the measurement x is obtained h，k and x l，k The probability of k |z k-1 ), k = 2, ..., K: state transition probability, indicating the target changes from state z in two consecutive measurements k-1 Convert to z k probability.

7. The range-Doppler joint estimation method under low signal-to-noise ratio conditions according to claim 4, characterized in that: In step 5.3, the formula of the peak amplitude threshold is: Among them, P f Expressed as the false alarm probability, It is expressed as the noise variance.

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