TBD method for weak target under range ambiguity combining sparse representation

Abstract

This invention discloses a TBD (Target Breakdown Dictation) method for weak targets under range ambiguity combined with sparse representation, belonging to the field of data processing technology. It acquires ambiguity-inducing sensor range measurement data and performs sparse decomposition and reconstruction using sparse representation to initially estimate the ambiguity of the target's position. The ambiguity track is initiated using the Hough Transform TBD algorithm, and range deambiguity is achieved by combining the Chinese Remainder Theorem. The pulse interval increment is modeled as a Markov chain, predicted using a Long Short-Term Memory (LSTM) network, and the state prediction value is deambigued based on the predicted value. This prediction is then correlated with the current unambiguous measurement and filtered to complete the track update. Track management is performed, including canceling failed tracks and initiating new tracks, and this process is repeated until tracking ends. This invention achieves effective target detection, stable tracking, and continuous management in scenarios with sensor range ambiguity and low signal-to-noise ratio, improving deambiguity accuracy and tracking robustness, and is suitable for complex detection scenarios such as weak targets.

Description

Technical Field

[0001] This invention belongs to the field of sensor data processing technology, specifically relating to a weak target TBD method combining sparse representation under distance ambiguity. Background Technology

[0002] In existing technologies, the detection and tracking of weak targets often employs the pre-detection tracking (TBD) method. TBD accumulates measurement data over a long period, trading time for a higher signal-to-noise ratio, to simultaneously detect and extract the trajectory of weak targets, thus achieving effective detection and tracking. However, existing TBD methods primarily address situations where distance measurements are unambiguous. When the sensor operates in a high pulse repetition frequency mode, the distance measurement becomes ambiguous. In such cases, the target distance measurement cannot reflect the target's true distance, resulting in inaccurate and ineffective data accumulation, ultimately rendering existing pre-detection tracking methods ineffective.

[0003] In practical applications, when sensors use high repetition rate (PRR) mode to detect and track weak targets, they face a highly coupled problem of range measurement ambiguity and low target echo signal-to-noise ratio (SNR). Existing TBD methods cannot accumulate measurement data under range measurement ambiguity conditions and lack dedicated management mechanisms for track initiation, failure cancellation, and new track initiation. Affected by factors such as range measurement ambiguity and low target echo SNR, existing methods are prone to problems such as low target detection probability, accumulation of measurement errors when the target moves across range ambiguity intervals, low track initiation success rate, and poor tracking continuity.

[0004] It is evident that existing technologies are ill-suited to scenarios with ambiguous distance measurements, exhibiting problems such as low target detection probability, accumulation of measurement errors when the target moves across ambiguous distance ranges, poor tracking continuity, and a lack of a trajectory management system; these are the shortcomings of existing technologies.

[0005] In view of this, it is very necessary to provide a weak target TBD method combined with sparse representation under distance ambiguity in order to solve the above-mentioned defects in the prior art. Summary of the Invention

[0006] The purpose of this invention is to address the shortcomings of existing technologies, such as low target detection probability, accumulation of measurement errors when the target moves across the ambiguity range, poor tracking continuity, and lack of a track management system, by providing a weak target TBD method that combines sparse representation under ambiguity range conditions.

[0007] To achieve the above objectives, the present invention provides the following technical solution: This invention provides a weak target TBD method combined with sparse representation under distance ambiguity, specifically including the following steps: Step S1: Obtain the distance ambiguity measurement from the sensor; Step S2: Based on the principle of sparse representation, perform sparse decomposition and reconstruction on the fuzzy distance measurement to obtain the fuzzy position measurement; Step S3: Determine whether the number of accumulated consecutive blurred position measurements has reached the preset track start frame number threshold K; if it has not reached the track start frame number threshold K, return to step S1 and continue to accumulate blurred position measurements; if it has reached the track start frame number threshold K, proceed to step S4. Step S4: Based on the accumulated continuous K-frame fuzzy position measurements, the fuzzy target track is obtained by starting the track using the TBD method based on Hough transform; the fuzzy target track is then defuzzified by distance based on the Chinese Remainder Theorem to obtain the initial target track. Step S5: After obtaining the initial target track, repeat steps S1 and S2 to obtain the fuzzy position measurement at the current time. A pulse interval increment tracking model and prediction network were constructed, and the pulse interval increment prediction value was obtained based on the initial target trajectory. Step S6: Based on the initial target trajectory and pulse interval increment prediction value, perform distance defuzzification processing on the fuzzy position measurement at the current moment to obtain the true target distance and unfuzzy measurement; The unambiguous measurement is associated with the track, and the track is updated using Kalman filtering to obtain the target track updated at the current time. Step S7: Perform full lifecycle management on the established tracks, including canceling consecutive tracks that have not been successfully associated; and performing trajectory verification on consecutive multi-frame measurements that are not associated with any existing tracks, and after confirmation, starting as a new target track.

[0008] Furthermore, step S1 specifically includes: In the high pulse repetition frequency working mode, the distance measurement of the sensor is subject to periodic ambiguity: the target distance value directly observed by the sensor is the remainder of the target's true distance divided by the sensor's maximum unambiguous distance, which cannot directly reflect the target's true position. Step S1 is used to obtain the original sensor observation data under this ambiguity state. Multiple frequency alternation working ambiguity is used to obtain weak target echo signals; An analog-to-digital (A / D) conversion operation is performed on the sensor echo signal to obtain the raw digital observation data for the k-th signal processing cycle. Due to distance measurement ambiguity, the raw digital observation data is defined as distance ambiguity measurement and represented as a two-dimensional matrix. The number of rows in the two-dimensional matrix corresponds to the number of distance cells. The number of columns corresponds to the number of azimuth units. The numerical values ​​of each element in the matrix represent the quantization intensity of the echo signal within a specific range-azimuth resolution unit.

[0009] The distance measurement obtained at the current moment is ambiguous. The data is transmitted to a data processing computer and serves as the input data source for all subsequent processing steps.

[0010] Furthermore, step S2 specifically includes: To achieve a preliminary estimate of the target state in fuzzy measurement under low signal-to-noise ratio conditions, a sparse matrix is ​​constructed based on the characteristics of the sensor's transmitted signal and sparse representation theory. The echo signal is then sparsely decomposed and reconstructed using a complete set of basis functions. A sparse matrix is ​​defined as an M-row N-column matrix, denoted as Ψ; From the low signal-to-noise ratio range ambiguity measurement, sparse representation and sparse reconstruction techniques are used to initially determine the existence of the target and estimate its ambiguity state measurement; this process is the basis for subsequent track initiation and fine tracking; specifically, the following operations are performed: The distance ambiguity measurement received by the computer from the sensor data at time k. Rearrange all its elements in column order to construct an N-dimensional one-dimensional measurement column vector, denoted as . ; The obtained one-dimensional measurement column vector Project onto the constructed sparse matrix Ψ; To determine whether the measurement at the current moment contains a potential target signal, an adaptive detection threshold is set. The adaptive detection threshold is determined by both the noise level and the estimated target signal level, and is calculated as follows: Calculate the noise level reference value , where σ is the noise standard deviation; Calculate the target signal level reference value Where SNR is the target signal-to-noise ratio; Pick With 0.75 ( The larger of the two values ​​will be used as the final detection threshold. The formula is as follows:

[0011] in, This is a noise level reference value. This is the reference value for the target signal level. Project the vector The absolute value or energy value of each element is compared with the threshold γ; if the value of all elements is lower than the threshold γ, it is determined that there is no target at the current moment, and the processing flow returns to step S1 to obtain the measurement at the next moment; if there is at least one element whose value is higher than or equal to the threshold γ, it is determined that there may be a target, and the subsequent state estimation steps are continued.

[0012] Construct a random observation matrix This satisfies the constraints on the observation matrix in sparse representation theory; the perception matrix is ​​then calculated. It is a random observation matrix. The product with the sparse matrix Ψ, i.e. This sensing matrix is ​​used for dimensionality reduction observation of high-dimensional signals. A one-dimensional measurement column vector is obtained using the minimum absolute shrinkage and selection operator algorithm. The sparse representation under the atomic library minimizes the objective function as follows:

[0013] in, Describes the l2 norm of a vector. Let λ represent the l1 norm of the vector, and λ be the regularization penalty factor used to control the sparsity of the solution. Solving the above optimization problem yields a sparse coefficient vector. ; sparse coefficient vector The position of the non-zero value corresponds to the atom that best matches the current measurement; In the sparse coefficient vector In the process, find the element with the largest absolute value and record its index number, then calculate the fuzzy distance measurement of the target. And fuzzy orientation measurement ; Fuzzy measurement in polar coordinates ( , The coordinate transformation formula is used to convert the measurement to fuzzy position in a rectangular coordinate system. , The specific expression is as follows:

[0014] Where cos and sin are the cosine and sine functions, respectively.

[0015] Furthermore, step S3 specifically includes: The algorithm path is determined by comparing the currently processed cumulative data frame number k with the preset track start frame number K: If the cumulative number of frames k is less than the preset starting number of track frames K, then return to step S1 and continue to collect and process the measurement data of the next frame. If the accumulated frame number k is equal to the preset track start frame number K, then proceed to step S4 and use the accumulated K frames of fuzzy measurement to start the fuzzy track. If the cumulative number of frames k is greater than the preset starting number of track frames K, then proceed to step S5 to predict the target pulse interval based on the started track.

[0016] Furthermore, step S4 specifically includes the following steps: Step S4 initiates the track initiation process based on the accumulated K consecutive frames of ambiguous position measurements. Since the current measurement is a distance-ambiguous measurement, a track needs to be formed based on the ambiguous data before deambiguation processing is performed. This step includes the following two consecutive operations: Step S41: Collect the blurred position measurements of the target in the Cartesian coordinate system for K consecutive frames to form a blurred measurement set; this set is represented as:

[0017] Where k is the current time, and K is the minimum number of frames required to start the preset trajectory.

[0018] The aforementioned K-frame fuzzy measurement set is used for track initiation using the TBD method based on Hough transform. Accumulation and detection are performed in the parameter space consisting of range-azimuth-time, detecting potential linear motion trajectories from time-series points with low signal-to-noise ratio. Through this process, one or more initial target tracks are formed. Since the range dimension of the input measurements is fuzzy, the track obtained from this initiation is a fuzzy target track, denoted as […]. ; Specifically, the mathematical process is described as follows: Assuming the target moves at a constant velocity in a straight line within the detection plane, its trajectory is parameterized as its initial position. ) and speed ( The TBD method based on Hough transform constructs a four-dimensional discrete parameter space as an accumulator, with the specific expression as follows:

[0019] For the accumulated set of K-frame blurred position measurements, traverse each discrete unit θ=( in the four-dimensional discrete parameter space) , , , The accumulated value obtained by this unit. Calculated by the following formula:

[0020] in,( , () represents the measured coordinates of the i-th frame; The time difference between the i-th frame and the starting frame is given by [the time difference]. The accumulated K frames are renumbered chronologically from the earliest frame i=1 to the current frame i=K. Assuming the sensor sampling interval is T, the time difference between the i-th frame and the first frame is [the time difference]. =(i 1)T; It is a preset distance tolerance threshold used to determine whether the measurement point matches the position predicted by the parameter θ; ( ) is an indicator function; its value is 1 when the condition is true, and 0 otherwise. This represents the L2 norm of a vector.

[0021] The essence of this accumulation process is that it is a sequence derived from real motion parameters. The determined trajectory, whose multiple frames of true echoes will continuously fall near the predicted state, thus in Significant peaks are generated; while random noise is difficult to accumulate effectively on specific parameter units; After the accumulation is complete, in the accumulator array { In}, detect all that satisfy Local peak value; The detection threshold is set according to the system's false alarm probability requirements; For each detected peak unit =( , , , This corresponds to an initial track; the predicted state of this track in frame i is:

[0022] All peak parameters that meet the conditions and its corresponding position sequence Recorded as the initial fuzzy target track .

[0023] Step S42: Process the fuzzy target track obtained in step S41. Distance defuzzification is performed based on the Chinese Remainder Theorem to recover the true distance information of the target; The Chinese Remainder Theorem provides a theoretical solution for dealing with a class of congruence equations. In this method, the fuzzy distance values ​​of the same target observed by the sensor at different repetition periods or at different times are regarded as a set of congruence equations, and the maximum unfuzzy distance of the sensor is the modulus. By solving this set of congruence equations, the true distance of the target in the extended unfuzzy distance space is uniquely determined. Applying the Chinese Remainder Theorem to fuzzy tracks For each location point in the equation, the fuzzy distance is calculated. The unambiguous true distance is analyzed and combined with the orientation information to obtain the unambiguous initial target track, denoted as . After completing this step, the process returns to step S1 to continue the measurement processing and subsequent steps at the next moment. Furthermore, the fuzzy processing of distance solutions based on the Chinese Remainder Theorem specifically includes: For the fuzzy target track obtained in step S41 Extract the fuzzy distance measurement sequence of L consecutive time points contained therein:

[0024] Where L≤K; The blurred distance of the l-th frame is relative to the observation modulus of that frame. , satisfying 0≤ < ; The azimuth angle of the l-th frame; The sensor system, through switching operating parameters or possessing multi-channel observation capabilities, ensures that the maximum unambiguous distance parameter actually in effect when acquiring the sequence is within [the specified range]. , ,…, The moduli vary between each other, and these moduli are pairwise coprime, i.e., satisfying... ; Calculate the modulus of the product using the Chinese Remainder Theorem; for each ,calculate And solve its modular inverse. , making ; Find the smallest positive integer solution to obtain the true distance estimate of the target at the reference time; use the true distance estimate obtained from the solution... Inversely derive a baseline fuzzy integer:

[0025] in, The selected reference module; Based on the constraint of the continuity of target motion, the fuzzy integer corresponding to each time k on the track is obtained recursively. ;for the flight path Each fuzzy location point in ( , ), calculate its unambiguous true distance:

[0026] in, The maximum unambiguous distance is the nominal value of the system. Will Convert to rectangular coordinates ( , This constitutes an unambiguous initial target track. .

[0027] Furthermore, step S5 specifically includes: Step S5, assuming the initial target trajectory has been initiated (i.e., k>K), predicts the number of distance ambiguity intervals that the target may traverse between adjacent detection periods, specifically by performing the following continuous operations: Step S51: Define the pulse interval increment as the number of fuzzy intervals that the target traverses within adjacent sampling intervals T; Based on the target's maximum possible radial velocity with the maximum unambiguous distance Calculate the maximum number of fuzzy intervals that the target's radial motion can traverse within the sampling interval T. The calculation formula is as follows:

[0028] The function round() represents the rounding operation on the calculation result; The range of fuzzy intervals within which the true distance of a target may change within a single sampling period is defined; Step S52: Model the temporal evolution of the change in the number of fuzzy intervals to which the target's true distance belongs between adjacent time moments, i.e., the increment of the pulse interval, as a Markov chain moving through a finite state space, whose state transition probabilities reflect the randomness of the target's motion; specifically including the following steps: Based on the maximum number of fuzzy intervals Define the state space of a Markov chain as a space containing (2×) A finite set S of +1) discrete states:

[0029] Each state Corresponding to a specific pulse interval increment d, ; The specific physical meaning of a state is defined as follows: state Indicates the true distance of the target from k The ambiguity interval at time 1 has crossed away from the sensor. A fuzzy interval; state This indicates that the true distance to the target remains at k at time k. Within the same fuzzy interval at time 1, no interval crossing occurred; state Indicates the true distance of the target from k The ambiguity interval at time 1 has crossed towards the sensor. A fuzzy interval; Other intermediate states This indicates the positive or negative range being crossed within the corresponding span.

[0030] make ∈S represents the state corresponding to the pulse interval increment of the target at time k.

[0031] Step S53: To predict the next state of the Markov chain in real time and accurately, this method uses a Long Short-Term Memory (LSTM) network as the predictor. The specific implementation is as follows: A Long Short-Term Memory (LSTM) network is constructed as the prediction network for the target pulse interval increment. The input to the LSM network is the target state information from multiple consecutive historical time points, including position, velocity, and the historical pulse interval increment sequence. By learning the temporal pattern of the target motion, the target pulse interval increment at time k-1 is predicted in one step, and the predicted value of the target pulse interval increment at time k is output. This process specifically includes: Construct the input sequence for the Long Short-Term Memory (LSTM) network, making the input of the LSM network at time k a sequence of target state information from M consecutive historical time steps:

[0032] Wherein, the state vector at each time step Includes the target state information at that moment, defined as:

[0033] in,( ) is the estimated position of the target in the rectangular coordinate system at time t. ) represents the corresponding velocity estimate. The increment of the pulse interval at time t; Input sequence Input Long Short-Term Memory (LSTM) network; the LSM network consists of input gates Forgotten Gate Output gate Cell state and hidden state Composition; for each time step t in the sequence; Set the last time step t=k 1's hidden state Through a fully connected output layer, it is mapped to the prediction of the target pulse interval increment; Through a Softmax function Transformed into a probability distribution on the discrete state space S:

[0034] probability vector Each element corresponds to a state The predicted probability of ∈S is used, and the pulse interval increment d corresponding to the state with the highest probability is taken as the predicted pulse interval increment value at time k. :

[0035] in, ; Predicted pulse interval increment As prior information, it is passed to step S6 to perform distance defuzzification processing on the state prediction value obtained based on the target motion model; By establishing a Markov chain, a structured probabilistic model for the evolution of the pulse interval increment is provided. A Long Short-Term Memory (LSTM) network is used as a data-driven predictor, enabling accurate and adaptive prediction of the increment at the next time step within this model framework. This combination allows the algorithm to effectively handle the problem of random variations in the number of distance ambiguities caused by target motion.

[0036] Furthermore, step S6 specifically includes: After obtaining the initial target track After obtaining the predicted value of the pulse interval increment at time k, perform the following steps: For the initial target track confirmed in the previous moment Perform state prediction; based on the state transition equation corresponding to the preset uniform or uniformly accelerated motion model of the target, extrapolate the position and velocity state of the target at time k-1 in one step to obtain the predicted state of the target at time k. , ) and its covariance .

[0037] Obtain the fuzzy distance measurement at time k. , Predicting values ​​using pulse interval increments And the fuzzy integer from the target track at the previous moment. Calculate the fuzzy integer of the prediction at the current time:

[0038] Based on this, the fuzzy distance measurement is defuzzified to obtain the true target distance:

[0039] The candidate distance and orientation Unambiguous measurement converted to Cartesian coordinate system And calculate the corresponding measurement noise covariance. .

[0040] To predict the state ( , Centered on a specific point, a correlated gate is defined. The threshold of the correlated gate is calculated using unambiguous measurements. With the predicted state ( , The normalized distance between them is used to determine the method, specifically including: Calculate the innovation vector , representing the difference vector between the unambiguous measurement and the predicted state, reflects the deviation between observation and prediction, and is expressed as:

[0041] Calculate the new information covariance matrix :

[0042] in, This is the observation matrix.

[0043] Calculate the normalized distance between the unambiguous measurement and the predicted state. :

[0044] Set an association threshold, if If the value is less than the association threshold, it is determined to be an unambiguous measurement. If the signal falls into the associated gate, the association is successful; otherwise, the association is considered to have failed.

[0045] Unambiguous measurements that are successfully associated As an effective observation, it is input into the Kalman filter and compared with the predicted state ( , ) Perform measurement updates to obtain a precise estimate of the target state at time k. , ) and its updated error covariance ; If the association fails, the predicted state is used as a precise estimate of the target state at the current moment, that is, let ,and = In standard Kalman filtering, the covariance before updating is actually... Its value is greater than the value updated by measurement. .

[0046] Precise estimation of the target state at time k ( , Update track Get the target trajectory updated at time k. ; Furthermore, step S7 specifically includes: Step S7 maintains and manages established tracks and initiates tracks for new targets to ensure continuous tracking capability for multiple targets or when targets reappear. This step includes two parallel logical operations: canceling failed tracks and initiating new tracks. The cancellation of failed tracks applies to every established and maintained target track. Perform a confirmation status judgment; if a certain track fails to be successfully associated with any measurement obtained and defuzzified through steps S3 and S4 at the current time in two consecutive processing moments, that is, no measurement falls into the associated gate of the track, then the track is determined to be invalid; the system will cancel this invalid track, declare the target has disappeared, and release the computing and storage resources occupied by the track. The initiation of a new trajectory involves determining whether all unambiguous measurements not successfully associated with any existing trajectory within the current timeframe and a preceding period could originate from a new target. Based on a modified logical trajectory initiation method, a set of free measurements that are not associated with any existing trajectory for K consecutive frames and possess continuity and rationality in spatial motion logic is processed. By examining the constraints of multi-frame measurements in terms of position, velocity, and acceleration, a valid potential trajectory is identified. When the free measurements of K consecutive frames satisfy the initiation logic, a new target trajectory is established and denoted as the new trajectory. This information will be incorporated into the system's track database for subsequent maintenance and updates.

[0047] After completing the track management in this step, the process returns to step S4 and repeats steps S4 to S7 until the system is shut down, thereby achieving continuous detection and stable tracking of weak targets in the detection airspace.

[0048] The beneficial effects of this invention are as follows: by denoising the sensor echo signal through sparse representation, the probability of target detection is effectively improved; a pulse interval increment tracking model and a prediction model are constructed, which adaptively learn the target motion law and predict the pulse interval increment, adapting to the situation where the target motion crosses the distance ambiguity interval, providing reliable prior information for distance deambiguity and effective accumulation of measurement data; by combining the Hough transform TBD algorithm and Kalman filtering, the success rate of starting weak target tracks is improved; and a full life cycle track management mechanism including failed track cancellation and new track start is established, adapting to complex scenarios with multiple targets and target temporary disappearance / reappearance, reducing the probability of tracking jumps and target loss, and enhancing the fault tolerance and stability of track updates. Therefore, it is evident that the present invention has substantial features and progress compared with the prior art, and the beneficial effects of its implementation are also obvious. Attached Figure Description

[0049] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0050] Figure 1 This embodiment provides a flowchart of a weak target TBD method that combines sparse representation under distance ambiguity. Detailed Implementation

[0051] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. The following embodiments are explanations of the present invention, but the present invention is not limited to the following implementation methods.

[0052] Example 1: This embodiment provides a weak target TBD method combined with sparse representation under distance ambiguity, such as... Figure 1 As shown, the specific steps include: Step S1: Obtain the distance ambiguity measurement from the sensor; Step S2: Based on the principle of sparse representation, perform sparse decomposition and reconstruction on the fuzzy distance measurement to obtain the fuzzy position measurement; Step S3: Determine whether the number of accumulated consecutive blurred position measurements has reached the preset track start frame number threshold K; if it has not reached the track start frame number threshold K, return to step S1 and continue to accumulate blurred position measurements; if it has reached the track start frame number threshold K, proceed to step S4. Step S4: Based on the accumulated continuous K-frame fuzzy position measurements, the fuzzy target track is obtained by starting the track using the TBD method based on Hough transform; the fuzzy target track is then defuzzified by distance based on the Chinese Remainder Theorem to obtain the initial target track. Step S5: After obtaining the initial target track, repeat steps S1 and S2 to obtain the fuzzy position measurement at the current time. A pulse interval increment tracking model and prediction network were constructed, and the pulse interval increment prediction value was obtained based on the initial target trajectory. Step S6: Based on the initial target trajectory and pulse interval increment prediction value, perform distance defuzzification processing on the fuzzy position measurement at the current moment to obtain the true target distance and unfuzzy measurement; The unambiguous measurement is associated with the track, and the track is updated using Kalman filtering to obtain the target track updated at the current time. Step S7: Perform full lifecycle management on the established tracks, including canceling consecutive tracks that have not been successfully associated; and performing trajectory verification on consecutive multi-frame measurements that are not associated with any existing tracks, and after confirmation, starting as a new target track.

[0053] Furthermore, step S1 specifically includes: In the high pulse repetition frequency working mode, the distance measurement of the sensor has periodic ambiguity: the directly observed target distance value is the remainder of the target's true distance divided by the maximum unambiguous distance, which cannot directly reflect the target's true position. Step S1 is used to obtain the original observation data under this ambiguity state. Multiple frequency alternation working ambiguity is used to obtain weak target echo signals; An analog-to-digital (A / D) conversion operation is performed on the sensor echo signal to obtain the raw digital observation data for the k-th signal processing cycle. Due to distance measurement ambiguity, the raw digital observation data is defined as distance ambiguity measurement and represented as a two-dimensional matrix. The number of rows in the two-dimensional matrix corresponds to the number of distance cells. The number of columns corresponds to the number of azimuth units. The numerical values ​​of each element in the matrix represent the quantization intensity of the echo signal within a specific range-azimuth resolution unit.

[0054] The distance measurement obtained at the current moment is ambiguous. The data is transmitted to a data processing computer and serves as the input data source for all subsequent processing steps.

[0055] Furthermore, step S2 specifically includes: To achieve a preliminary estimate of the target state in fuzzy measurement under low signal-to-noise ratio conditions, a sparse matrix is ​​constructed based on the characteristics of the sensor's transmitted signal and sparse representation theory. The echo signal is then sparsely decomposed and reconstructed using a complete set of basis functions. A sparse matrix is ​​defined as an M-row N-column matrix, denoted as Ψ; From the low signal-to-noise ratio range ambiguity measurement, sparse representation and sparse reconstruction techniques are used to initially determine the existence of the target and estimate its ambiguity state measurement; this process is the basis for subsequent track initiation and fine tracking; specifically, the following operations are performed: The distance ambiguity measurement received by the computer at time k is processed. Rearrange all its elements in column order to construct an N-dimensional one-dimensional measurement column vector, denoted as . ; The obtained one-dimensional measurement column vector Project onto the constructed sparse matrix Ψ; To determine whether the measurement at the current moment contains a potential target signal, an adaptive detection threshold is set. The adaptive detection threshold is determined by both the noise level and the estimated target signal level, and is calculated as follows: Calculate the noise level reference value , where σ is the noise standard deviation; Calculate the target signal level reference value Where SNR is the target signal-to-noise ratio; Pick With 0.75 ( The larger of the two values ​​will be used as the final detection threshold. The formula is as follows:

[0056] in, This is a noise level reference value. This is the reference value for the target signal level. Project the vector The absolute value or energy value of each element is compared with the threshold γ; if the value of all elements is lower than the threshold γ, it is determined that there is no target at the current moment, and the processing flow returns to step S1 to obtain the measurement at the next moment; if there is at least one element whose value is higher than or equal to the threshold γ, it is determined that there may be a target, and the subsequent state estimation steps are continued.

[0057] Construct a random observation matrix This satisfies the constraints on the observation matrix in sparse representation theory; the perception matrix is ​​then calculated. It is a random observation matrix. The product with the sparse matrix Ψ, i.e. This sensing matrix is ​​used for dimensionality reduction observation of high-dimensional signals. A one-dimensional measurement column vector is obtained using the minimum absolute shrinkage and selection operator algorithm. The sparse representation under the atomic library minimizes the objective function as follows:

[0058] in, Describes the l2 norm of a vector. Let λ represent the l1 norm of the vector, and λ be the regularization penalty factor used to control the sparsity of the solution. Solving the above optimization problem yields a sparse coefficient vector. ; sparse coefficient vector The position of the non-zero value corresponds to the atom that best matches the current measurement; In the sparse coefficient vector In the process, find the element with the largest absolute value and record its index number to calculate the fuzzy distance measurement of the target. And fuzzy orientation measurement ; Fuzzy measurement in polar coordinates ( , The coordinate transformation formula is used to convert the measurement to fuzzy position in a rectangular coordinate system. , The specific expression is as follows:

[0059] Where cos and sin are the cosine and sine functions, respectively.

[0060] Furthermore, step S3 specifically includes: The algorithm path is determined by comparing the currently processed cumulative data frame number k with the preset track start frame number K: If the cumulative number of frames k is less than the preset starting number of track frames K, then return to step S1 and continue to collect and process the measurement data of the next frame. If the accumulated frame number k is equal to the preset track start frame number K, then proceed to step S4 and use the accumulated K frames of fuzzy measurement to start the fuzzy track. If the cumulative number of frames k is greater than the preset starting number of track frames K, then proceed to step S5 to predict the target pulse interval based on the started track.

[0061] Furthermore, step S4 specifically includes the following steps: Step S4 initiates the track initiation process based on the accumulated K consecutive frames of ambiguous position measurements. Since the current measurement is a distance-ambiguous measurement, a track needs to be formed based on the ambiguous data before deambiguation processing is performed. This step includes the following two consecutive operations: Step S41: Collect the blurred position measurements of the target in the Cartesian coordinate system for K consecutive frames to form a blurred measurement set; this set is represented as:

[0062] Where k is the current time, and K is the minimum number of frames required to start the preset trajectory.

[0063] The aforementioned K-frame fuzzy measurement set is used for track initiation using the TBD method based on Hough transform. Accumulation and detection are performed in the parameter space consisting of range-azimuth-time, detecting potential linear motion trajectories from time-series points with low signal-to-noise ratio. Through this process, one or more initial target tracks are formed. Since the range dimension of the input measurements is fuzzy, the track obtained from this initiation is a fuzzy target track, denoted as […]. ; Specifically, the mathematical process is described as follows: Assuming the target moves at a constant velocity in a straight line within the detection plane, its trajectory is parameterized as its initial position. ) and speed ( The TBD method based on Hough transform constructs a four-dimensional discrete parameter space as an accumulator, with the specific expression as follows:

[0064] For the accumulated set of K-frame blurred position measurements, traverse each discrete unit θ=( in the four-dimensional discrete parameter space) , , , The accumulated value obtained by this unit. Calculated by the following formula:

[0065] in,( , () represents the measured coordinates of the i-th frame; The time difference between the i-th frame and the starting frame is given by [the time difference]. The accumulated K frames are renumbered chronologically from the earliest frame i=1 to the current frame i=K. Assuming the sensor sampling interval is T, the time difference between the i-th frame and the first frame is [the time difference]. =(i 1)T; It is a preset distance tolerance threshold used to determine whether the measurement point matches the position predicted by the parameter θ; ( ) is an indicator function; its value is 1 when the condition is true, and 0 otherwise. This represents the L2 norm of a vector.

[0066] The essence of this accumulation process is that it is a sequence derived from real motion parameters. The determined trajectory, whose multiple frames of true echoes will continuously fall near the predicted state, thus in Significant peaks are generated; while random noise is difficult to accumulate effectively on specific parameter units; After the accumulation is complete, in the accumulator array { In}, detect all that satisfy Local peak value; The detection threshold is set according to the system's false alarm probability requirements; For each detected peak unit =( , , , This corresponds to an initial track; the predicted state of this track in frame i is:

[0067] All peak parameters that meet the conditions and its corresponding position sequence Recorded as the initial fuzzy target track .

[0068] Step S42: Process the fuzzy target track obtained in step S41. Distance defuzzification is performed based on the Chinese Remainder Theorem to recover the true distance information of the target; The Chinese Remainder Theorem provides a theoretical solution for dealing with a class of congruence equations. In this method, the fuzzy distance values ​​of the same target observed at different repetition periods or at different times are regarded as a set of congruence equations, and the maximum unfuzzy distance of the sensor is the modulus. By solving this set of congruence equations, the true distance of the target in the extended unfuzzy distance space is uniquely determined. Applying the Chinese Remainder Theorem to fuzzy tracks For each location point in the equation, the fuzzy distance is calculated. The unambiguous true distance is analyzed and combined with the orientation information to obtain the unambiguous initial target track, denoted as . After completing this step, the process returns to step S1 to continue the measurement processing and subsequent steps at the next moment. Furthermore, the fuzzy processing of distance solutions based on the Chinese Remainder Theorem specifically includes: For the fuzzy target track obtained in step S41 Extract the fuzzy distance measurement sequence of L consecutive time points contained therein:

[0069] Where L≤K; The blurred distance of the l-th frame is relative to the observation modulus of that frame. , satisfying 0≤ < ; The azimuth angle of the l-th frame; The system, through switching operating parameters or possessing multi-channel observation capabilities, ensures that the maximum unambiguous distance parameter actually in effect when acquiring the sequence is within [the specified range]. , ,…, The moduli vary between each other, and these moduli are pairwise coprime, i.e., satisfying... Then the true distance of the target The following system of congruence equations is satisfied:

[0070] Calculate the modulus of the product using the Chinese Remainder Theorem:

[0071] For each ,calculate And solve its modular inverse. , making The unique solution to the system of congruence equations modulo M is:

[0072] Taking the smallest positive integer solution, we obtain the true distance estimate of the target at the reference time:

[0073] Using the true distance estimate obtained from the solution Inversely derive a baseline fuzzy integer:

[0074] in, The selected reference module; Based on the constraint of the continuity of target motion, the fuzzy integer corresponding to each time k on the track is obtained recursively. ;for the flight path Each fuzzy location point in ( , ), calculate its unambiguous true distance:

[0075] in, The maximum unambiguous distance is the nominal value of the system. Will Convert to rectangular coordinates ( , This constitutes an unambiguous initial target track. .

[0076] Furthermore, step S5 specifically includes: Step S5, assuming the initial target trajectory has been initiated (i.e., k>K), predicts the number of distance ambiguity intervals that the target may traverse between adjacent detection periods, specifically by performing the following continuous operations: Step S51: Define the pulse interval increment as the number of fuzzy intervals that the target traverses within adjacent sampling intervals T; Based on the target's maximum possible radial velocity with the maximum unambiguous distance Calculate the maximum number of fuzzy intervals that the target's radial motion can traverse within the sampling interval T. The calculation formula is as follows:

[0077] The function round() represents the rounding operation on the calculation result; The range of fuzzy intervals within which the true distance of a target may change within a single sampling period is defined; Step S52: Model the temporal evolution of the change in the number of fuzzy intervals to which the target's true distance belongs between adjacent time moments, i.e., the increment of the pulse interval, as a Markov chain moving through a finite state space, whose state transition probabilities reflect the randomness of the target's motion; specifically including the following steps: Based on the maximum number of fuzzy intervals Define the state space of a Markov chain as a space containing (2×) A finite set S of +1) discrete states:

[0078] Each state Corresponding to a specific pulse interval increment d, ; The specific physical meaning of a state is defined as follows: state Indicates the true distance of the target from k The ambiguity interval at time 1 has crossed away from the sensor. A fuzzy interval; state This indicates that the true distance to the target remains at k at time k. Within the same fuzzy interval at time 1, no interval crossing occurred; state Indicates the true distance of the target from k The ambiguity interval at time 1 has crossed towards the sensor. A fuzzy interval; Other intermediate states This indicates the positive or negative range being crossed within the corresponding span.

[0079] make Let S represent the state corresponding to the pulse interval increment at time k. The one-step state transition probability matrix P of this Markov chain is defined as follows:

[0080] Among them, matrix elements Indicates from state Transition to state The probability satisfies The model can freely transition between states within adjacent detection periods; that is, for any i, j, the following holds true. ≥0, used to describe the random dynamic change characteristics of the increment of the target distance in the fuzzy interval; state transition probability. It can be set based on prior knowledge of the target's motion characteristics.

[0081] Step S53: To predict the next state of the Markov chain in real time and accurately, this method uses a Long Short-Term Memory (LSTM) network as the predictor. The specific implementation is as follows: A Long Short-Term Memory (LSTM) network is constructed as the prediction network for the target pulse interval increment. The input to the LSM network is the target state information from multiple consecutive historical time points, including position, velocity, and the historical pulse interval increment sequence. By learning the temporal pattern of the target motion, the target pulse interval increment at time k-1 is predicted in one step, and the predicted value of the target pulse interval increment at time k is output. This process specifically includes: Construct the input sequence for the Long Short-Term Memory (LSTM) network, making the input of the LSM network at time k a sequence of target state information from M consecutive historical time steps:

[0082] Wherein, the state vector at each time step Includes the target state information at that moment, defined as:

[0083] in,( ) is the estimated position of the target in the rectangular coordinate system at time t. ) represents the corresponding velocity estimate. The increment of the pulse interval at time t; Input sequence Input Long Short-Term Memory (LSTM) network; the LSM network consists of input gates Forgotten Gate Output gate Cell state and hidden state Composition; For each time step t in the sequence, the core computation process of the network unit is as follows:

[0084] in, ( ) represents the Sigmoid activation function, tanh() represents the hyperbolic tangent activation function, and ⊙ represents element-wise multiplication. and These are the parameter weight matrix and bias vector to be trained in the network, respectively. The network learns and memorizes the long-term temporal dependencies of the target motion through the above gating mechanism. Set the last time step t=k 1's hidden state Through a fully connected output layer, the prediction is mapped to the target pulse interval increment. The output layer is calculated as follows:

[0085] in, and The weights and biases of the output layer; Through a Softmax function Transformed into a probability distribution on the discrete state space S:

[0086] probability vector Each element corresponds to a state The predicted probability of ∈S is used, and the pulse interval increment d corresponding to the state with the highest probability is taken as the predicted pulse interval increment value at time k. :

[0087] in, ; Predicted pulse interval increment As prior information, it is passed to step S6 to perform distance defuzzification processing on the state prediction value obtained based on the target motion model; By establishing a Markov chain, a structured probabilistic model for the evolution of the pulse interval increment is provided. A Long Short-Term Memory (LSTM) network is used as a data-driven predictor, enabling accurate and adaptive prediction of the increment at the next time step within this model framework. This combination allows the algorithm to effectively handle the problem of random variations in the number of distance ambiguities caused by target motion.

[0088] Furthermore, step S6 specifically includes: After obtaining the initial target track After obtaining the predicted value of the pulse interval increment at time k, perform the following steps: For the initial target track confirmed in the previous moment Perform state prediction; based on the state transition equation corresponding to the preset uniform or uniformly accelerated motion model of the target, extrapolate the position and velocity state of the target at time k-1 in one step to obtain the predicted state of the target at time k. , ) and its covariance .

[0089] Obtain the fuzzy distance measurement at time k. , Predicting values ​​using pulse interval increments And the fuzzy integer from the target track at the previous moment. Calculate the fuzzy integer of the prediction at the current time:

[0090] Based on this, the fuzzy distance measurement is defuzzified to obtain the true target distance:

[0091] The target's true distance and location Unambiguous measurement converted to Cartesian coordinate system And calculate the corresponding measurement noise covariance. .

[0092] To predict the state ( , Centered on a specific point, a correlated gate is defined. The threshold of the correlated gate is calculated using unambiguous measurements. With the predicted state ( , The normalized distance between them is used to determine the method, specifically including: Calculate the innovation vector , representing the difference vector between the unambiguous measurement and the predicted state, reflects the deviation between observation and prediction, and is expressed as:

[0093] Calculate the new information covariance matrix :

[0094] in, This is the observation matrix.

[0095] Calculate the normalized distance between the unambiguous measurement and the predicted state. :

[0096] Set an association threshold, if If the value is less than the association threshold, it is determined to be an unambiguous measurement. If the signal falls into the associated gate, the association is successful; otherwise, the association is considered to have failed.

[0097] Unambiguous measurements that are successfully associated As an effective observation, it is input into the Kalman filter and compared with the predicted state ( , ) Perform measurement updates to obtain a precise estimate of the target state at time k. , ) and its updated error covariance The specific expression is:

[0098]

[0099]

[0100] in, Kalman gain; If the association fails, the predicted state is used as a precise estimate of the target state at the current moment, that is, let ,and = In standard Kalman filtering, the covariance before updating is actually... Its value is greater than the value updated by measurement. .

[0101] Precise estimation of the target state at time k ( , Update track Get the target trajectory updated at time k. ; Furthermore, step S7 specifically includes: Step S7 maintains and manages established tracks and initiates tracks for new targets to ensure continuous tracking capability for multiple targets or when targets reappear. This step includes two parallel logical operations: canceling failed tracks and initiating new tracks. The cancellation of failed tracks applies to every established and maintained target track. Perform a confirmation status judgment; if a certain track fails to be successfully associated with any measurement obtained and defuzzified through steps S3 and S4 at the current time in two consecutive processing moments, that is, no measurement falls into the associated gate of the track, then the track is determined to be invalid; the system will cancel this invalid track, declare the target has disappeared, and release the computing and storage resources occupied by the track. The initiation of a new trajectory involves determining whether all unambiguous measurements not successfully associated with any existing trajectory within the current timeframe and a preceding period could originate from a new target. Based on a modified logical trajectory initiation method, a set of free measurements that are not associated with any existing trajectory for K consecutive frames and possess continuity and rationality in spatial motion logic is processed. By examining the constraints of multi-frame measurements in terms of position, velocity, and acceleration, a valid potential trajectory is identified. When the free measurements of K consecutive frames satisfy the initiation logic, a new target trajectory is established and denoted as the new trajectory. This information will be incorporated into the system's track database for subsequent maintenance and updates.

[0102] Furthermore, the modified logical track initiation method specifically includes: At each processing time k, fuzzy position measurements are generated; after the above steps for association decision, they are divided into associated measurements and free measurements. The associated measurement has been successfully matched with an existing track and is used for status updates.

[0103] The free measurements are those that have failed to be successfully associated with any existing track; let the set of free measurements at the current time k be:

[0104] Each of them The position in a rectangular coordinate system; For each batch of free measurements from the same potential target, a temporary track file, or hypothetical track, is maintained; the file records the historical measurement sequence, current state, and a track confidence score for the potential track. For each free measure at the current time k ∈ Attempt to associate with all existing temporary track files; the association criteria are the same as in step S6: Based on the historical state in the temporary track file, predict its position at time k; Calculate free measurement The normalized distance (Mahaviron distance) between the predicted state and the actual state. ; like If the value is less than the preset initial association threshold, the free measurement is considered to be temporarily attributed to this temporary track, and the association is successful. If the association is successful, the free measure Add the corresponding temporary track to the historical sequence. Using this measurement, update the state of this temporary track through a simplified filter. Simultaneously, increase the confidence score of this temporary track. The score increment can be correlated with the quality of the measurement or the magnitude of the associated residuals.

[0105] If the association fails, then it is the free measurement. Create a new temporary track file, use it as the first frame observation, initialize the state and velocity, and assign an initial confidence score.

[0106] Furthermore, for each temporary track, at each time k, the following judgment is made: Determine whether the temporary track has been successfully associated with free measurements for at least K frames in the most recent consecutive N frames; Verify the motion rationality of the temporary track's historical state sequence, including whether the calculated velocity and acceleration are within the physical possibilities of the target; whether the heading changes are smooth without abrupt jumps; whether the trajectory formed by the measurement points in space conforms to common motion models; and whether the cumulative confidence score of the temporary track exceeds a preset initial score threshold.

[0107] A temporary track is determined to represent a real, newly formed target only if it simultaneously meets the above conditions. In this case, the temporary track is upgraded to a formal target track that can proceed to step S6 for stable tracking. And incorporate it into the system's track database; If a temporary track fails to be successfully associated with any measurement within L consecutive frames, or if its confidence score is below a deletion threshold, the system determines that the hypothesis has failed, deletes the temporary track file, and releases the resources it occupies.

[0108] After completing the track management in this step, the process returns to step S4 and repeats steps S4 to S7 until the system is shut down, thereby achieving continuous detection and stable tracking of weak targets in the detection airspace.

[0109] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. The methods disclosed in the embodiments are described simply because they correspond to the systems disclosed in the embodiments; relevant details can be found in the method section.

[0110] Those skilled in the art will further recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of the various examples have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.

[0111] In the embodiments provided by this invention, it should be understood that the disclosed systems, methods, and approaches can be implemented in other ways. For example, the system embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between systems or units may be electrical, mechanical, or other forms.

[0112] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0113] In addition, the functional modules in the various embodiments of the present invention can be integrated into one processing unit, or each module can exist physically separately, or two or more modules can be integrated into one unit.

[0114] Similarly, in the various embodiments of the present invention, each processing unit can be integrated into a functional module, or each processing unit can exist physically, or two or more processing units can be integrated into a functional module.

[0115] The steps of the methods or algorithms described in conjunction with the embodiments disclosed herein can be implemented directly by hardware, a software module executed by a processor, or a combination of both. The software module can be located in random access memory (RAM), main memory, read-only memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, removable disk, CD-ROM, or any other form of storage medium known in the art.

[0116] Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0117] The above-disclosed embodiments are merely preferred embodiments of the present invention, but the present invention is not limited thereto. Any non-creative variations that can be conceived by those skilled in the art, as well as any improvements and modifications made without departing from the principles of the present invention, should fall within the protection scope of the present invention.

Claims

1. A weak target TBD method combining sparse representation under distance ambiguity, characterized in that, Includes the following steps: Step S1: Obtain the distance ambiguity measurement from the sensor; Step S2: Based on the principle of sparse representation, perform sparse decomposition and reconstruction on the fuzzy distance measurement to obtain the fuzzy position measurement; Step S3: Determine whether the number of accumulated consecutive blurred position measurements has reached the preset track start frame number threshold K; if it has not reached the track start frame number threshold K, return to step S1 and continue to accumulate blurred position measurements; if it has reached the track start frame number threshold K, proceed to step S4. Step S4: Based on the accumulated continuous K-frame fuzzy position measurements, the fuzzy target track is obtained by starting the track using the TBD method based on Hough transform; the fuzzy target track is then defuzzified by distance based on the Chinese Remainder Theorem to obtain the initial target track. Step S5: After obtaining the initial target track, repeat steps S1 and S2 to obtain the fuzzy position measurement at the current time. A pulse interval increment tracking model and prediction network were constructed, and the pulse interval increment prediction value was obtained based on the initial target trajectory. Step S6: Based on the initial target trajectory and pulse interval increment prediction value, perform distance defuzzification processing on the fuzzy position measurement at the current moment to obtain the true target distance and unfuzzy measurement; The unambiguous measurement is associated with the track, and the track is updated using Kalman filtering to obtain the target track updated at the current time. Step S7: Perform full lifecycle management on the established tracks, including canceling consecutive tracks that have not been successfully associated; and performing trajectory verification on consecutive multi-frame measurements that are not associated with any existing tracks, and after confirmation, starting as a new target track.

2. The method according to claim 1, characterized in that, In step S2, the sparse decomposition and reconstruction of the fuzzy distance measurement based on the sparse representation principle to obtain the fuzzy position measurement includes: The sparse coefficient vector is obtained by using the minimum absolute shrinkage and selection operator algorithm. The mathematical expression is: in, Describes the l2 norm of a vector. Let λ denote the l1 norm of the vector, and λ be the regularization penalty factor. The one-dimensional measurement column vector is obtained by vectorizing the row vector of the distance fuzzy measurement. For the perception matrix, , Let Ψ be the random observation matrix, and Ψ be the constructed sparse matrix; It is a sparse coefficient vector; In the sparse coefficient vector In the process, find the element with the largest absolute value and record its index number. The fuzzy position measurement is then obtained through calculation.

3. The method according to claim 2, characterized in that, In step S4, the process of initiating the track using the TBD method based on Hough transform to obtain the fuzzy target track specifically involves: A four-dimensional discrete parameter space is constructed as an accumulator, and a detection threshold is set; the four dimensions of the four-dimensional discrete parameter space include initial distance, initial orientation, distance change rate, and orientation change rate. For the accumulated K-frame blurred position measurements, traverse each discrete unit in the four-dimensional discrete parameter space and accumulate them; After the accumulation is completed, detect all local peak values ​​that satisfy the detection threshold in the accumulator array; The peak parameters that meet the conditions and their corresponding position sequences are recorded as the initial fuzzy target track.

4. The method according to claim 3, characterized in that, In step S4, the distance defuzzification processing of the fuzzy target track based on the Chinese remainder theorem to obtain the initial target track is specifically as follows: For a fuzzy target track, extract a fuzzy distance measurement sequence for L consecutive time moments; According to the Chinese Remainder Theorem, the product modulus is calculated; the smallest positive integer solution is taken to obtain the true distance estimate of the target at the reference time; and a reference fuzzy integer is derived from the true distance estimate obtained by solving the problem. Based on the continuity constraint of the target motion, the fuzzy integer corresponding to each time k in the fuzzy target trajectory is obtained by recursion from the fuzzy integer of the reference. Based on the fuzzy integers and fuzzy distance measurements at each time point, calculate the unfuzzy true distance at each time point; The unambiguous true distances and corresponding azimuth measurements at all times are converted into Cartesian coordinates to form an unambiguous initial target track.

5. The method according to claim 1, characterized in that, Step S5 specifically includes: Define the pulse interval increment and model the time evolution of the pulse interval increment as a Markov chain; Construct a long short-term memory network to predict the pulse interval increment in the state space defined by the Markov chain based on the initial target trajectory, and obtain the predicted pulse interval increment value at the current time k.

6. The method according to claim 5, characterized in that, The Markov chain is based on the maximum number of fuzzy intervals. Build, including (2× +1) discrete states, whose state space S is represented as: Each state Corresponding to a specific pulse interval increment d, ;state Indicates the true distance of the target from k The ambiguity interval at time 1 crosses away from the sensor. A fuzzy interval; state This indicates that the true distance to the target remains at time k. Within the same fuzzy interval at time 1, no interval crossing occurred; state Indicates the true distance of the target from k The ambiguity interval at time 1 is crossed towards the sensor. A fuzzy interval.

7. The method according to claim 6, characterized in that, The prediction process of the Long Short-Term Memory network specifically includes: The sequence of target state information over M consecutive historical time points is used as input; The hidden state of the last time step of the Long Short-Term Memory network is mapped to a prediction of the pulse interval increment through a fully connected output layer; The output of the fully connected output layer is transformed into a probability distribution in the discrete state space S by using a Softmax function; Take the state corresponding to the maximum probability value in the probability distribution, and use the pulse interval increment corresponding to that state as the predicted pulse interval increment value at time k.

8. The method according to claim 7, characterized in that, In step S6, the process of performing distance deblurring on the current ambiguous position measurement to obtain the true target distance and the unambiguous measurement specifically includes: Predict the state of the target trajectory confirmed in the previous moment; Based on the state transition equation corresponding to the pre-set uniform or uniformly accelerated motion model of the target, the position and velocity state of the target at time k-1 are extrapolated in one step to obtain the predicted state of the target at time k. Obtain the fuzzy distance measurement at time k; use the pulse interval increment prediction value and the fuzzy integer at time k-1 obtained from the target track to calculate the predicted fuzzy integer at the current time; The true target distance at time k is obtained by defuzzifying the fuzzy distance measurement based on the predicted fuzzy integer; Convert the target's true distance and orientation into unambiguous measurements in a Cartesian coordinate system.

9. The method according to claim 8, characterized in that, In step S6, associating the unambiguous measurement with the track and updating the track using Kalman filtering specifically includes: A correlation gate is set centered on the predicted state of the target; Calculate the normalized distance between the unambiguous measurement and the predicted state, and compare it with a preset association threshold; If the normalized distance is less than the association threshold, the association is considered successful. The unambiguous measurement is used as an effective observation and input into the Kalman filter for measurement update to obtain a precise estimate of the target state at time k. If the normalized distance is not less than the association threshold, the association is determined to be unsuccessful, and the predicted state is directly used as the precise estimate of the target state at time k. The target trajectory is updated using the precise estimate of the target state at time k, resulting in the updated target trajectory at time k.

10. The method according to claim 9, characterized in that, In step S7, the trajectory verification adopts a correction-based logical trajectory initiation method, which specifically includes the following steps: At each time k, measurements that have not been successfully associated with any existing track are recorded as free measurements; and a temporary track file is created, which includes historical measurement sequences, status and confidence scores. For each free measurement at the current time k, attempt to make a correlation decision with each temporary track; If the association is successful, the free measurement is added to the historical measurement sequence of the corresponding temporary track, and the status and confidence score of the temporary track are updated; if the association fails, a new temporary track is established based on the free measurement. For each temporary track, at each moment it is determined whether it meets the initial confirmation conditions. If a temporary track meets all the initial confirmation conditions at the same time, it is confirmed as a new target track. If a temporary track fails to associate successfully or its score is lower than the deletion threshold within L consecutive frames, it is deleted.

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