A signal space transformation based line spectrum detection pre-tracking method and multi-target resolution method

Abstract

The application belongs to the technical field of underwater acoustic, and discloses a line spectrum detection front tracking method and a multi-target distinguishing method based on signal space transformation. The track energy accumulation value on the slice obtained after signal space transformation is constructed as a cost function in a particle swarm parameter optimization algorithm, so that the complexity of slice search in the transformation space is reduced, and the calculation amount is greatly reduced. Meanwhile, a hidden Markov model is established on the slice, and a Viterbi algorithm is used to track the track, compared with the method of using a Radon algorithm to integrate on the slice, the selection of the integration path is more accurate, and the processing gain is improved. The method improves the detection probability, tracking accuracy and parameter optimization speed of the uniform motion target under low signal-to-noise ratio. The searched parameters can be used as the characteristics of the target to distinguish the target, and multi-target distinguishing is realized.

Description

Technical Field

[0001] The present invention belongs to the field of underwater acoustic technology, and in particular relates to a line spectrum pre-detection tracking method and a multi-target resolution method based on signal space transformation. Background Art

[0002] Traditional detection-before-tracking (DBT) methods rely on point data processed by detector thresholding. In underwater acoustic environments with low signal-to-noise ratios (SNRs), they are prone to missed detections and false alarms, limiting the detection performance of passive sonar arrays. However, the proposed track-before-detection (TBD) method for low SNR targets offers a solution to this problem. Detection-before-detection (TBD) algorithms can be broadly categorized as detection-focused or tracking-focused, depending on their focus. Detection-focused TBD algorithms primarily utilize long-term incoherent integration to accumulate energy from signal trajectory points across multiple time frames. The difficulty with these methods lies in the nonlinearity and prediction difficulties inherent in target motion. Many methods translate this into estimation of target model motion parameters. Tracking-focused TBD methods focus on estimating and predicting the target's state at each moment. The most widely used technique is recursive Bayesian filtering. These methods establish a state transition model for the target and continuously predict and iterate based on the next moment's observations to achieve an optimal state estimate at each moment. At present, the methods focusing on target tracking have been developed to a relatively complete level. They not only track multiple targets, but also take into account the birth and death process of targets, the tracking of two targets when they intersect, and the change of target motion models over time. However, they have not yet made a major breakthrough in the requirements for the environmental signal-to-noise ratio. This is reflected in the field of passive sonar signal processing, that is, the signal-to-noise ratio requirement for accurate target trajectory tracking is that the human eye can vaguely see the target trajectory on the azimuth course map or LOFAR map.

[0003] To handle line spectrum signals in extremely low signal-to-noise ratio (SNR) environments, several space-frequency joint line spectrum detection and tracking methods have been proposed, guided by the aforementioned ideas. Since the signals acquired by the array contain three dimensions: time, frequency, and space, considering the detection and tracking of line spectra in array signals in three dimensions can achieve higher gains. For the incoherent integration of line spectra in three dimensions, a typical approach is to search for the optimal line spectrum trajectory in the time-space-frequency space and then accumulate multiple frames of FRAZ spectra along this optimal line spectrum trajectory. In the target uniform motion model established by this approach, determining a trajectory requires searching for five parameters during the target's motion. Exhaustive search methods, quadratically convergent Newton methods, simulated annealing methods, and particle swarm optimization algorithms have been proposed for iterative parameter search. Overall, these methods are still limited by the large computational overhead of searching a single curve in three dimensions. Furthermore, when the SNR is very low, the energy accumulated on the false trajectory is not necessarily lower than that on the true trajectory. A second approach is to model the time series of the frequency-azimuth angle (FRAZ) spectrum as a hidden Markov process and simultaneously estimate the frequency and azimuth angle at each moment using the Viterbi algorithm. This method leverages the stability of line spectrum signals in both azimuth and frequency dimensions to improve line spectrum detection performance under low signal-to-noise ratio (SNR) conditions. However, applying the Viterbi algorithm in three-dimensional space is computationally complex, and at extremely low SNRs, the probability of trajectory tracking is severely affected by surrounding noise at other frequencies and azimuths. Method 3 proposes a time-space frequency signal transformation method for uniform linear motion targets. By transforming the apparent azimuth, the signal trajectory points are all located on a planar slice in the three-dimensional signal space. This method uses a traversal search of the slice, which is computationally intensive. Its cost function is determined by the maximum Radon transform on the slice, assuming that the signal trajectory is a straight line on the slice. In theory, it fails to accumulate the energy values ​​of the complete signal trajectory points. To date, a simple, fast, and effective method for multi-frame accumulation of moving targets under low SNR conditions remains lacking. Summary of the Invention

[0004] The present invention provides a line spectrum pre-detection tracking method based on signal space transformation, which is used to solve the problem of the existing line spectrum pre-detection tracking based on signal space transformation having complicated and rapid calculations and large amount of calculations.

[0005] The present invention provides a multi-target resolution method based on signal space transformation, which is realized by analyzing the tracking results before line spectrum detection based on signal space transformation.

[0006] The present invention is achieved through the following technical solutions:

[0007] A line spectrum tracking method before detection based on signal space transformation, the line spectrum tracking method before detection is specifically as follows:

[0008] Step 1: Process the received hydrophone array signal in the time and space domain to obtain the power spectrum output expression of the target radiated sound signal in the three-dimensional space of frequency, azimuth and time;

[0009] Step 2: The power spectrum output result in the three-dimensional signal space of step 1 is transformed into an apparent azimuth according to the parameter target heading to obtain the power spectrum output result of the target radiated sound signal in the three-dimensional space of frequency-cosine value of the side angle-time;

[0010] Step 3: Based on the power spectrum output of the target radiated acoustic signal in three-dimensional space obtained in step 2, a power spectrum slice is obtained according to the parameters target speed and transmission signal frequency;

[0011] Step 4: Based on the power spectrum slices obtained in step 3, a hidden Markov model (HMM) is established.

[0012] Step 5: Based on the Hidden Markov Model (HMM) obtained in step 4, the Viterbi algorithm is used to track the target trajectory.

[0013] Step 6: Accumulate the power spectrum values ​​of the tracking target trajectory points obtained on the power spectrum slices obtained in step 3;

[0014] Step 7: Construct the power spectrum value accumulated in step 6 as the cost function in the parameter optimization algorithm;

[0015] Step 8: Using the cost function obtained in step 7 as the judgment criterion, the optimization algorithm is iterated until convergence, and then the results of target detection, parameter estimation and trajectory tracking are given.

[0016] Furthermore, step 1 is specifically to perform a short-time two-dimensional Fourier transform on the target radiated sound signal s(t) received by the horizontal linear array composed of M array elements to obtain the target radiated sound signal power spectrum output expression in the frequency-azimuth-time three-dimensional space (f-α-t):

[0017]

[0018] Among them, τ p It represents the time corresponding to the p-th segment signal obtained by sliding the time window for the p-th time, N is the number of points in each segment signal, c is the speed of sound in water, ω represents the frequency, α is the azimuth, is the wave number vector, f0 is the frequency of the single-frequency signal emitted by the target; is the distance vector between the target position at the initial moment and the geometric center position of the receiving array; suppose the time window length is T0 seconds, and it is assumed that the received signal frequency and target azimuth angle are approximately unchanged during this period of time. The corresponding signal of the pth segment is ω p ,α(τ p )express.

[0019] Furthermore, the step 2 is specifically to perform the following coordinate transformation on the target radiated sound signal power spectrum output result in the frequency-azimuth-time three-dimensional space (f-α-t):

[0020]

[0021] Where γ0 is the angle measured clockwise from the true north line to the target heading line, which is a constant. Coordinate transformation is performed based on the parameter γ0 to obtain the power spectrum output of the target radiated acoustic signal in the new three-dimensional space (f-cosθ-t).

[0022] Furthermore, the step 3 is specifically as follows: for the obtained target radiation sound signal power spectrum output in the three-dimensional space (f-cosθ-t), a straight line A in the (f-cosθ) plane is determined according to the parameters of the transmitted signal frequency f0 and the target speed v. Take a slice formed by the straight line A and the time axis t in the three-dimensional space (f-cosθ-t).

[0023] Furthermore, the step 5 is specifically to establish a hidden Markov model based on the obtained spatial slice with frequency f as the hidden state and the power spectrum value of each pixel point corresponding to frequency f and time t on the slice as the observation value;

[0024] After obtaining the target trajectory f(t) by using the Viterbi algorithm, the existence of the target is used as the hidden state, and the frequency value tracked at each moment is used as the observation value to re-establish the hidden Markov model. According to the continuity of the trajectory, the points whose distances between two consecutive moments exceed the normal range are considered to be tracking error points, that is, unreasonable points. The Viterbi algorithm is used to judge the rationality of each tracking trajectory point, and the trajectory points judged as non-existent are removed.

[0025] Furthermore, the step 7 is specifically as follows:

[0026] The power spectrum values ​​corresponding to the retained trajectory points are summed as the cost function value of the set of parameters [γ0, f0, v]. The particle swarm parameter optimization algorithm is used for iterative calculation until the parameters converge and a set of parameters [γ0, f0, v] that maximizes the cost function value is found.

[0027] Furthermore, the step 8 is specifically as follows:

[0028] The maximum value of the cost function obtained by the search is compared with the detection threshold set according to the actual ocean environment to obtain the target detection result;

[0029] When it is higher than the detection threshold, it is determined that the target exists, otherwise the target does not exist;

[0030] When the target is determined to exist, the set of parameters corresponding to the maximum cost function value is the target parameter estimation result;

[0031] The trajectory tracking result on the power spectrum slice in the transformation space corresponding to this set of parameters is the target line spectrum trajectory.

[0032] Furthermore, the multi-target resolution method uses the target detection, parameter estimation and trajectory tracking results generated by the above-mentioned line spectrum detection-before-tracking method based on signal space transformation.

[0033] A line spectrum pre-detection tracking system based on signal space transformation, wherein the line spectrum pre-detection tracking system uses the line spectrum pre-detection tracking method based on signal space transformation, and the line spectrum pre-detection tracking system is specifically:

[0034] The data processing module performs time-space processing on the received hydrophone array signal and provides the power spectrum output expression of the target radiated sound signal in the three-dimensional space of frequency-azimuth-time.

[0035] The three-dimensional space construction module transforms the power spectrum output in the three-dimensional signal space into an apparent azimuth according to the target heading parameter, and obtains the power spectrum output of the target radiated sound signal in the three-dimensional space of frequency-cosine value of the side angle-time;

[0036] Power spectrum slice acquisition module: Based on the power spectrum output of the target radiation sound signal in the three-dimensional space, the power spectrum slice is obtained according to the parameters of target speed and transmission signal frequency;

[0037] The Hidden Markov Model (HMM) calculation module establishes a Hidden Markov Model (HMM) based on the obtained power spectrum slices; tracks the target trajectory using the Viterbi algorithm; and accumulates the power spectrum values ​​of the tracked target trajectory points obtained from the obtained power spectrum slices.

[0038] The cost function module constructs the accumulated power spectrum value as the cost function in the parameter optimization algorithm; using the obtained cost function as the judgment criterion, the optimization algorithm is iterated until convergence;

[0039] The display module gives the results of target detection, parameter estimation and trajectory tracking based on the calculation of the cost function module.

[0040] A multi-target resolution system based on signal space transformation is implemented using the multi-target resolution method based on signal space transformation.

[0041] The beneficial effects of the present invention are:

[0042] By constructing the cumulative energy value of the trajectory on the slice obtained after signal space transformation into the cost function in the particle swarm parameter optimization algorithm, the present invention reduces the complexity of slice search in the transformed space and significantly reduces the amount of computation. Simultaneously, a hidden Markov model is established on the slice, and the trajectory is tracked using the Viterbi algorithm. Compared with the method of using the Radon algorithm for integration on the slice, the selection of the integral path is more accurate, thereby improving the processing gain. This method improves the detection probability, tracking accuracy, and parameter optimization speed of uniformly moving targets under low signal-to-noise ratio conditions. Targets can also be distinguished using the searched parameters as target features, achieving multi-target resolution. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 It is a flow chart of the method of the present invention.

[0044] Figure 2 It is a schematic diagram of a model of a linear array receiving target radiation signal according to the present invention.

[0045] Figure 3 Schematic diagram of the target motion model of the present invention.

[0046] Figure 4 It is a schematic diagram of the position of the signal of the present invention in three-dimensional space.

[0047] Figure 5 It is the simulation target motion trajectory diagram of the present invention.

[0048] Figure 6 This is the first time that the Viterbi algorithm is used to track the target trajectory in the present invention.

[0049] Figure 7 This is the result graph after the non-target points are eliminated using the Viterbi algorithm for the second time in the present invention. DETAILED DESCRIPTION

[0050] In the following description, specific details such as specific system structures and technologies are provided for illustration rather than limitation to facilitate a thorough understanding of the embodiments of the present application. However, it should be clear to those skilled in the art that the present application may be implemented in other embodiments without these specific details. In other cases, detailed descriptions of well-known systems, devices, circuits, and methods are omitted to avoid obstructing the description of the present application with unnecessary details.

[0051] It will be understood that when used in this specification and the appended claims, the term "comprising" indicates the presence of described features, integers, steps, operations, elements and / or components, but does not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components and / or groups thereof.

[0052] It should also be understood that the terms used in the specification of the present application are only for the purpose of describing particular embodiments and are not intended to be limiting of the present application. As used in the specification and the appended claims of the present application, the singular forms "a," "an" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise.

[0053] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate one implementation of the present application and Figure 1-7 In order to clearly and completely describe the technical solutions in the embodiments of the present application, it should be apparent that the described embodiments are only a part of the embodiments of the present application, but not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work fall within the scope of protection of the present application.

[0054] In the following description, a large number of specific details are set forth in order to facilitate a thorough understanding of the present application, but the present application can also be implemented in other ways different from those described herein, and those skilled in the art can make similar generalizations without departing from the connotation of the present application, therefore the present application is not limited by the specific embodiments disclosed below.

[0055] Embodiment one

[0056] A line spectrum detection pre-tracking method based on signal space transformation, the line spectrum detection pre-tracking method is specifically,

[0057] Step 1: performing space-time domain processing on the received hydrophone array signal to give a target radiated acoustic signal power spectrum output expression in a frequency-azimuth angle-time three-dimensional space;

[0058] Step 2: performing apparent azimuth transformation on the power spectrum output result in the three-dimensional signal space of step 1 according to the parameter target heading to obtain a target radiated acoustic signal power spectrum output result in a frequency-ship angle cosine value-time three-dimensional space;

[0059] Step 3: based on the target radiated acoustic signal power spectrum output result in the three-dimensional space obtained in step 2, obtaining a power spectrum slice according to the parameter target speed and the transmitted signal frequency;

[0060] Step 4: based on the power spectrum slice obtained in step 3, establishing a hidden Markov HMM model;

[0061] Step 5: based on the hidden Markov HMM model obtained in step 4, tracking the target trajectory by using the Viterbi algorithm;

[0062] Step 6: accumulating the power spectrum values on the tracking target trajectory points obtained on the power spectrum slice obtained in step 3;

[0063] Step 7: Construct the power spectrum value accumulated in step 6 as the cost function in the parameter optimization algorithm (such as particle swarm optimization algorithm);

[0064] Step 8: Using the cost function obtained in step 7 as the judgment criterion, the optimization algorithm is iterated until convergence, and then the results of target detection, parameter estimation and trajectory tracking are given.

[0065] Furthermore, the step 1 performs spatiotemporal processing on the received hydrophone array signal to provide a power spectrum output expression of the target radiated acoustic signal in the three-dimensional space of frequency, azimuth, and time. Specifically, the target radiated acoustic signal s(t) received by the M-element horizontal line array is processed in segments:

[0066] s m (τ p ,n)=s((τ p -1)T b +n)

[0067] τ p =1,2,...,P, n=1,2,...,T0f s ,m=1,2,...,M

[0068] The data is divided into P segments, τ p Represents the pth segment signal, each segment signal length is T0 seconds, and the segment step is T b Seconds, f s is the sampling rate of the signal, τ p represents slow time, n represents fast time, and m is the array element number.

[0069] Perform N-point DFT on the received signal on each array element, N = T0·f s .

[0070]

[0071] In the T0 second time, the frequency and azimuth of the received signal can be approximately unchanged, here we use ω p ,α(τ p )express, The Doppler effect caused by the target motion is τ p The frequency value received by the array at time , where is the target velocity vector, is the wave number vector is the distance vector between the target and the center receiving array element at the initial moment, d is the array element spacing, ω0 and f0 are the frequencies of the single-frequency signal transmitted by the target.

[0072] Perform frequency domain beamforming on each segment of the array signal after DFT, compensate for the phase difference between the base arrays caused by the azimuth angle α, and then superimpose them to obtain the target radiation sound signal power spectrum output expression in the frequency-azimuth-time three-dimensional space (f-α-t):

[0073]

[0074] The above formula can be simplified as:

[0075]

[0076] Among them, τ p It represents the time corresponding to the p-th segment signal obtained by sliding the time window for the p-th time, N is the number of points in each segment signal, c is the speed of sound in water, ω represents the frequency, α is the azimuth, is the wave number vector, f0 is the frequency of the single-frequency signal emitted by the target; is the distance vector between the target position at the initial moment and the geometric center position of the receiving array; suppose the time window length is T0 seconds, and it is assumed that the received signal frequency and target azimuth angle are approximately unchanged during this period of time. The corresponding signal of the pth segment is ω p ,α(τ p )express.

[0077] Furthermore, in step 2, the power spectrum output result in the three-dimensional signal space is transformed into an apparent azimuth according to the parameter target heading, and the power spectrum output result of the target radiated sound signal in the three-dimensional space of frequency-cosine value of the side angle-time is obtained. Specifically, from the Doppler effect, it can be known that the frequency of the received signal at any time is:

[0078]

[0079] Where θ, θ∈[0,180°] is the side angle, which is the angle between the target's motion direction and the distance vector at the target's position. For a target moving at a constant speed, f0, v, and c are all constants, that is, the relationship between f(t) and cosθ(t) is linear.

[0080] The power spectrum output of the target radiated sound signal in the frequency-azimuth-time three-dimensional space (f-α-t) is transformed into the following coordinates:

[0081]

[0082] Where γ0 is the angle measured clockwise from the true north line to the target heading line, which is a constant. Coordinate transformation is performed based on the set parameter γ0 to obtain the power spectrum output result of the target radiated sound signal in the new three-dimensional space (f-cosθ-t).

[0083] Further, the step 3 is based on the obtained target radiation acoustic signal power spectrum output result in three-dimensional space, and the power spectrum slice is obtained according to the parameter target speed and the transmission signal frequency, specifically, for the obtained target radiation acoustic signal power spectrum output result in the (f-cosθ-t) three-dimensional space, a straight line A in the (f-cosθ) plane is determined according to the parameter transmission signal frequency f0 and the target speed v, A slice is taken in the (f-cosθ-t) three-dimensional space by the straight line A and the time axis t.

[0084] Further, after the target trajectory f(t) is tracked by using the Viterbi algorithm, a hidden Markov model (HMM) is established again by taking the target existence or nonexistence as a hidden state and taking the frequency value tracked at each moment as an observation value, according to the continuity of the trajectory, it is considered that the points with a distance between two continuous moments exceeding a normal range are the tracking error points, that is, unreasonable points, the Viterbi algorithm is used to judge the rationality of each tracking trajectory point, and the trajectory points with the target nonexistence are removed.

[0085] Further, the step 7 constructs the power spectrum value accumulated in the step 6 as a cost function in a parameter optimization algorithm (for example, a particle swarm optimization algorithm), and specifically,

[0086] The power spectrum values corresponding to the remaining trajectory points are added, and the added value is taken as a cost function value of the parameter group [γ0, f0, v], the particle swarm parameter optimization algorithm is used for iterative calculation until the parameters converge, and a parameter group [γ0, f0, v] that makes the cost function value maximum is found.

[0087] Further, the step 8 takes the cost function obtained in the step 7 as a judgment criterion, iteratively calculates the optimization algorithm until convergence, and then gives the target detection, parameter estimation and trajectory tracking result, and specifically,

[0088] The maximum value of the searched cost function is compared with a detection threshold value set according to the actual marine environment to obtain a target detection result;

[0089] When the detection threshold value is higher, it is determined that the target exists, otherwise the target does not exist;

[0090] When the target is determined to exist, a parameter group corresponding to the maximum cost function value is the target parameter estimation result;

[0091] The trajectory tracking result in the transformation space corresponding to the parameter group is the target line spectrum trajectory.

[0092] Embodiment two

[0093] As Figure 1As shown, for the received array signal, firstly, the base array data is subjected to short-time Fourier transform in time and space two-dimensions to obtain multi-frame FRAZ spectrum, i.e. (f-a-t) three-dimensional space. The search range of the motion target parameters γ0, f0 and v is set, for each set of parameters γ0, f0 and v in the particle swarm iteration process, a slice is obtained through signal space transformation, twice Viterbi algorithm is applied to the slice to track the trajectory in the slice and to judge whether each trajectory point target exists or not, finally the real trajectory points obtained in the slice are subjected to energy accumulation, the accumulation value is taken as the cost function, i.e. the energy value of the set of parameters, according to the size of the value, the iteration is continuously carried out until the algorithm converges, the optimal parameter estimation value of the target is obtained. According to the obtained optimal parameter value of the target, the slice can be obtained, and the tracking and detection of the target on the slice are realized. The following is the construction process of the cost function.

[0094] As shown in Figure 2 , a target model of uniform linear motion, the origin of the coordinate system is placed with an M-element linear array for receiving target signals. It is assumed that the time when the base array receives the signal is t, the target is located at point A when t=0, and moves at a speed of a uniform linear motion along a certain heading, and radiates a single-frequency signal of ω0 during the motion process. is the distance vector from point A to the coordinate origin, and the distance vector from point B where the target is located at any time t to the coordinate origin is It is assumed that the target is located in the far field of the base array during the motion process, so the received signal can be approximately considered as a plane wave, and the coordinate of any element on the X-axis is (x, 0), α s (t) is the incident azimuth angle of the signal at time t.

[0095] The received base array signal can be expressed as:

[0096]

[0097] In the expression, A is the signal amplitude, is the wave number vector, c is the sound speed in water, and n(t, x) is the background noise.

[0098] As shown in the motion target model of Figure 2 , it can be seen that the azimuth angle α s of the target during the motion process changes with time, and the frequency of the received signal changes with time, according to the above analysis, the frequency of the received signal can be considered as f(t) = is basically not affected by cosα s (t). The non-stationary signal received by the above base array is subjected to short-time Fourier transform in time and space two-dimensions as follows:

[0099]

[0100] Substitute the received array signal into the non-stationary signal to perform short-time Fourier transform in two dimensions of space and time and simplify it to get the following formula:

[0101]

[0102] Wherein, is the received signal frequency at time t. At any time t in the frequency-azimuth-time three-dimensional signal space, when the azimuth angle α and the frequency f coincide with the actual target signal incident azimuth angle and the received signal frequency, the value of S(f,α,t) is the maximum value of the frequency-azimuth plane (FRAZ plane) corresponding to time t.

[0103] By sliding the window function and performing a two-dimensional Fourier transform, the function expression of the received signal in the three-dimensional space represented by the three axes of frequency-azimuth-time (f-α-t) is obtained, as shown in the figure: Figure 4 (a) shows a curve on a surface in three-dimensional space.

[0104] like Figure 3 As shown, the azimuth angle α defined in the array coordinate system xOy s ,α s ∈[0,180] and the beam angle θ defined in the target coordinate system x'By' can be linked to the target heading γ0. During the uniform motion of the target, γ0 does not change with time and is a constant. According to the definition of the beam angle, the frequency at any time t in S(f,α,t) is:

[0105]

[0106] According to Figure 3 The geometric relationship shown in the figure is used to transform the coordinates of the signal space (f-α-t) as follows to obtain the new signal space (f-cosθ-t):

[0107]

[0108] The position of the signal in the new space is Figure 4 As shown in (b), since the relationship between f(t) and cosθ(t) is linear, it can be seen that the trajectory points of the signal are all on a two-dimensional plane, and the signal can be expressed in the new three-dimensional space as A curve on the , according to the parameters frequency f0 and speed v, the slice can be obtained, that is Figure 4 The blue plane in (b).

[0109] like Figure 5 The target motion trajectory simulated by Matlab is shown below. Figure 6To select the simulation data spectrum level signal-to-noise ratio is -25dB, and the results of the slice to establish a hidden Markov model, and use the Viterbi algorithm to track each time the target frequency. The step 5 is based on the obtained hidden Markov HMM model, the Viterbi algorithm is used to track the target trajectory, specifically, based on the obtained spatial slice with frequency f as the hidden state, the power spectrum value of each frequency f and time t on the pixel point on the slice is taken as the observation value, the hidden Markov HMM model is established;

[0110] The establishment of hidden Markov model needs to determine the hidden state, observation value and three elements, that is, {X, Z, λ}, wherein λ=[π, A, B]; the hidden state X=[f1,...f i ,...,f N ] in the slice is the signal frequency, the power spectrum value p(k,i) of each frequency corresponding to each time on the slice is the observation value Z=[z1,...z k ,...,z K ], wherein i represents the state number, k represents the time number. The state transition matrix A satisfies the Gaussian distribution with mean 0 and variance , then the probability of frequency transition from the i-th unit to the j-th unit can be expressed as:

[0111]

[0112] , wherein f i is the center frequency of the i-th frequency interval [f i+1 , f shift ], and f ij is the maximum deviation range of state i. The h k matrix is normalized to obtain the elements in the state transition matrix A:

[0113]

[0114] B in the three elements is the measurement probability matrix, which can be given by the power spectrum nonparametric integral method in the case that the signal-to-noise ratio is unknown:

[0115]

[0116] Due to the lack of prior value, we let the initial probability vector π obey the uniform distribution, and for the frequency containing N intervals, π is expressed as:

[0117]

[0118] Further, the hidden Markov HMM model is established again, specifically, in the second hidden Markov model, the hidden state X of the target includes two kinds of target existence and target nonexistence, which are represented by H1: φ k =1 and H0: φk =0 means that the observation value Z = [f1,...,f k ,...f K ] is the frequency value at each moment;

[0119] The new state transfer matrix A is set to:

[0120]

[0121] Since the target trajectory has continuity in frequency, that is, the frequency value of the next moment appears near the previous moment with a high probability, the false trajectory generated by noise does not have this characteristic; the trajectory frequencies under the two assumptions are modeled as:

[0122]

[0123] Among them, cst is a constant and is greater than 1. is the average value of the trajectory azimuth at the previous moment, and the instantaneous value at the previous moment can be taken; one advantage of this modeling is that under the H0 condition, there is no correlation between the front and back azimuth distributions, while under the H1 condition, there is a correlation between the front and back trajectories.

[0124] Therefore, the likelihood function matrix B can be written as:

[0125]

[0126] Where ρ is the likelihood ratio detection threshold, which is calculated as:

[0127]

[0128] Where Δf max is the maximum value of the frequency change within the sliding time window step Δt, and Δf is the frequency change during the motion process, that is, the Doppler shift, which can be obtained based on the parameters f0, v and geometric relationship of the selected slice:

[0129]

[0130] Among them, R CPA is the distance between the CPA point and the target, h is the distance between the target position and the CPA point position, and the above formula reaches its maximum value when h = 0, that is:

[0131]

[0132] Define the two states of target existence and non-existence to appear with equal probability, that is,

[0133]

[0134] The Viterbi algorithm is applied again to obtain a sequence of trajectory points close to the true trajectory, the number of trajectory points on different slices is different, and a power spectrum value on a slice corresponding to a trajectory point is accumulated, and the value is used as a cost function of a particle swarm optimization algorithm.

[0135] Embodiment three

[0136] A multi-target resolution method based on signal space transformation, which uses the results of target detection, parameter estimation and trajectory tracking generated by the above-mentioned signal space transformation-based line spectrum pre-tracking method to realize multi-target resolution.

[0137] Embodiment four

[0138] A line spectrum pre-tracking system based on signal space transformation, which uses the above-mentioned signal space transformation-based line spectrum pre-tracking method, and specifically,

[0139] A data processing module, which performs space-time domain processing on the received hydrophone array signal and gives a target radiated acoustic signal power spectrum output expression in a frequency-azimuth-time three-dimensional space;

[0140] A three-dimensional space construction module, which performs an apparent bearing transformation on the power spectrum output result in the three-dimensional signal space according to a parameter target heading to obtain a target radiated acoustic signal power spectrum output result in a frequency-ship angle cosine value-time three-dimensional space;

[0141] A power spectrum slice acquisition module, which acquires a power spectrum slice according to a parameter target speed and a transmitted signal frequency based on the obtained target radiated acoustic signal power spectrum output result in the three-dimensional space;

[0142] A hidden Markov model (HMM) calculation module, which establishes a hidden Markov model (HMM) based on the obtained power spectrum slice, tracks a target trajectory by using a Viterbi algorithm, and accumulates power spectrum values on trajectory points on the acquired power spectrum slice;

[0143] A cost function module, which constructs the accumulated power spectrum values as a cost function in a parameter optimization algorithm, and performs iterative calculation on the optimization algorithm until convergence is achieved by taking the obtained cost function as a judgment criterion;

[0144] A display module, which gives the results of target detection, parameter estimation and trajectory tracking according to the calculation of the cost function module.

[0145] Embodiment five

[0146] A multi-target resolution system based on signal space transformation, which uses the above-mentioned signal space transformation-based multi-target resolution method to realize multi-target resolution.

[0147] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or make equivalent replacements for some of the technical features therein. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be included in the scope of protection of the present invention.

Claims

1. A line spectrum tracking method based on signal space transformation before detection, characterized in that: The line spectrum pre-detection tracking method is specifically as follows: Step 1: Perform time-space processing on the received hydrophone array signal to give the power spectrum output expression of the target radiated sound signal in the three-dimensional space of frequency-azimuth-time; Step 2: The power spectrum output result in the three-dimensional signal space of step 1 is transformed into an apparent azimuth according to the parameter target heading to obtain the power spectrum output result of the target radiated sound signal in the three-dimensional space of frequency-cosine value of the side angle-time; Step 3: Based on the power spectrum output of the target radiated acoustic signal in three-dimensional space obtained in step 2, a power spectrum slice is obtained according to the parameters target speed and transmission signal frequency; Step 4: Based on the power spectrum slices obtained in step 3, a hidden Markov model (HMM) is established. Step 5: Based on the Hidden Markov Model (HMM) obtained in step 4, the Viterbi algorithm is used to track the target trajectory. Step 6: Accumulate the power spectrum values ​​of the tracking target trajectory points obtained on the power spectrum slices obtained in step 3; Step 7: Construct the power spectrum value accumulated in step 6 as the cost function in the parameter optimization algorithm; Step 8: Using the cost function obtained in step 7 as the judgment criterion, the optimization algorithm is iterated until convergence, and then the results of target detection, parameter estimation and trajectory tracking are given.

2. The line spectrum tracking method based on signal space transformation according to claim 1, characterized in that: Specifically, step 1 is to perform a short-time two-dimensional Fourier transform on the target radiated sound signal s(t) received by the horizontal linear array composed of M array elements to obtain the target radiated sound signal power spectrum output expression in the frequency-azimuth-time three-dimensional space (f-α-t): Among them, τ p It represents the time corresponding to the p-th segment signal obtained by sliding the time window for the p-th time, N is the number of points in each segment signal, c is the speed of sound in water, ω represents the frequency, α is the azimuth, is the wave number vector, f0 is the frequency of the single-frequency signal emitted by the target; is the distance vector between the target position at the initial moment and the geometric center position of the receiving array; suppose the time window length is T0 seconds, and it is assumed that the received signal frequency and target azimuth angle are approximately unchanged during this period of time. The corresponding signal of the pth segment is ω p ,α(τ p )express.

3. The line spectrum tracking method based on signal space transformation according to claim 1, characterized in that: Specifically, step 2 is to perform the following coordinate transformation on the target radiated sound signal power spectrum output result in the frequency-azimuth-time three-dimensional space (f-α-t): Where γ0 is the angle measured clockwise from the true north line to the target heading line, which is a constant. Coordinate transformation is performed based on the parameter γ0 to obtain the power spectrum output of the target radiated acoustic signal in the new three-dimensional space (f-cosθ-t).

4. The line spectrum tracking method based on signal space transformation according to claim 3, characterized in that: Specifically, step 3 includes: outputting the power spectrum of the target radiated sound signal in the three-dimensional space (f-cosθ-t), and determining a straight line A in the (f-cosθ) plane according to the parameters of the transmitted signal frequency f0 and the target speed v. Take a slice formed by the straight line A and the time axis t in the three-dimensional space (f-cosθ-t).

5. The line spectrum tracking method based on signal space transformation according to claim 4, characterized in that: Specifically, step 5 is to establish a hidden Markov model based on the obtained spatial slice with frequency f as the hidden state and the power spectrum value of each pixel point corresponding to frequency f and time t on the slice as the observation value; After obtaining the target trajectory f(t) by using the Viterbi algorithm, the existence of the target is used as the hidden state, and the frequency value tracked at each moment is used as the observation value to re-establish the hidden Markov model. According to the continuity of the trajectory, the points whose distances between two consecutive moments exceed the normal range are considered to be tracking error points, that is, unreasonable points. The Viterbi algorithm is used to judge the rationality of each tracking trajectory point, and the trajectory points judged as non-existent are removed.

6. The line spectrum tracking method based on signal space transformation before detection according to claim 5, characterized in that: The step 7 is specifically as follows: The power spectrum values ​​corresponding to the retained trajectory points are summed as the cost function value of the set of parameters [γ0, f0, v]. The particle swarm parameter optimization algorithm is used for iterative calculation until the parameters converge and a set of parameters [γ0, f0, v] that maximizes the cost function value is found.

7. The line spectrum tracking method based on signal space transformation before detection according to claim 6, characterized in that: The step 8 is specifically as follows: The target detection result is obtained by comparing the maximum value of the cost function obtained by the search with the detection threshold set according to the actual ocean environment; When it is higher than the detection threshold, it is determined that the target exists, otherwise the target does not exist; When the target is determined to exist, the set of parameters corresponding to the maximum cost function value is the target parameter estimation result; The trajectory tracking result on the power spectrum slice in the transformation space corresponding to this set of parameters is the target line spectrum trajectory.

8. A multi-target resolution method based on signal space transformation, characterized in that: The multi-target resolution method uses the target detection, parameter estimation and trajectory tracking results generated by the line spectrum detection and tracking method based on signal space transformation as described in claim 1 or 7.

9. A line spectrum detection tracking system based on signal space transformation, characterized in that: The line spectrum pre-detection tracking system uses the line spectrum pre-detection tracking method based on signal space transformation as described in any one of claims 1 to 7. Specifically, the line spectrum pre-detection tracking system comprises: The data processing module performs time-space processing on the received hydrophone array signal and provides the power spectrum output expression of the target radiated sound signal in the three-dimensional space of frequency-azimuth-time. The three-dimensional space construction module transforms the power spectrum output in the three-dimensional signal space into an apparent azimuth according to the target heading parameter, and obtains the power spectrum output of the target radiated sound signal in the three-dimensional space of frequency-cosine value of the side angle-time; Power spectrum slice acquisition module: Based on the power spectrum output of the target radiation sound signal in the three-dimensional space, the power spectrum slice is obtained according to the parameters of target speed and transmission signal frequency; The Hidden Markov Model (HMM) calculation module builds a Hidden Markov Model (HMM) based on the obtained power spectrum slices and uses the Viterbi algorithm to track the target trajectory. Accumulate the power spectrum values ​​of the tracking target trajectory points obtained on the acquired power spectrum slices; The cost function module constructs the accumulated power spectrum value as the cost function in the parameter optimization algorithm; Using the obtained cost function as the judgment criterion, the optimization algorithm is iterated until convergence; The display module gives the results of target detection, parameter estimation and trajectory tracking based on the calculation of the cost function module.

10. A multi-target resolution system based on signal space transformation, characterized in that: The multi-target resolution system is implemented using the multi-target resolution method based on signal space transformation as described in claim 8.

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