A UUV collaborative information reconstruction system and method based on minimum KL divergence

Abstract

The present invention proposes a UUV collaborative information reconstruction system and method based on minimum KL divergence. The system includes a receiving end and a transmitting end and a communication module for communication between the receiving end and the transmitting end. The transmitting end is provided with an INS module, an underwater acoustic ranging module, a first underwater acoustic communicator and a first underwater acoustic ranging transducer. The receiving end is provided with a second underwater acoustic communication transducer, a second underwater acoustic ranging transducer and an information fusion module. The present application uses the minimum KL divergence principle to reconstruct the missing UUV collaborative information with high precision, avoiding the shortcomings of nonlinear modeling methods such as neural networks and deep learning or improved filtering methods that cannot simultaneously take into account accuracy and real-time performance. While ensuring accuracy indicators, the calculation process is greatly simplified, which helps to reduce the engineering application difficulty of the missing information real-time reconstruction method.

Description

Technical Field

[0001] The present invention specifically relates to a UUV collaborative information reconstruction system and method based on minimum KL divergence. Background Art

[0002] With the advancement of technology and the increasing intensity of ocean exploration, single unmanned underwater vehicles (UUVs) are no longer able to cope with increasingly complex mission requirements. Therefore, scholars have turned their research direction to UUV swarm collaborative systems. Such systems can greatly expand the scope of underwater operations and improve efficiency, and play an important role in complex missions such as large-scale resource exploration, maritime rescue, and UUV collaborative operations.

[0003] Currently, typical collaborative navigation systems are categorized as master-slave and distributed. To overcome the inherent limitations of master-slave systems, distributed systems construct a free communication network, treating all UUVs as independent communication nodes for collaborative information exchange and joint correction of navigation errors. This improves collaborative information richness and UUV position observability. However, the increasing number of communication nodes in a distributed system complicates information exchange, and measurement information loss due to harsh communication environments makes collaborative navigation accuracy and robustness difficult to guarantee. This paper proposes a collaborative information reconstruction algorithm to address the challenge of high-precision UUV position reconstruction.

[0004] Currently, mainstream solutions to the problem of missing collaborative information can be divided into two categories. The first category utilizes nonlinear modeling methods such as neural networks and deep learning to establish a mapping model between collaborative information and carrier dynamic information. To address the issue of "model input / output variable optimization," Zhang proposed an improved method that first uses wavelet multiresolution analysis to suppress output noise, and then trains the mapping model based on a backpropagation neural network, effectively improving the accuracy of mapping model training. To address the issue of "model training method optimization," Wang proposed a least-squares support vector machine method. This method sets the loss function in the support vector machine optimization model as a least-squares function, thereby transforming inequality constraints into equality constraints and transforming the quadratic optimization problem of the support vector machine into a problem of solving a system of linear equations, greatly simplifying the computational complexity of the model training process. The second category involves improved filtering methods. Sun transforms a system model with uncertain random parameters into an equivalent model with certain parameters. He then uses a state dimensionality expansion method to obtain the state vector and corresponding covariance matrix of the equivalent model. Finally, based on the relationship between the expanded dimensional state and the original state and a matrix-weighted optimal fusion algorithm, he solves for the optimal state estimate of the system.

[0005] At present, the mainstream solutions to the problem of missing collaborative information can be divided into two categories. The first category is to use nonlinear modeling methods such as neural networks and deep learning to establish a mapping model between collaborative information and carrier dynamic information. When collaborative information is missing, the carrier dynamic information measured by the inertial navigation system is used as the information input of the model, and the collaborative information prediction value can be output according to the model mapping relationship, thereby restoring the normal collaborative navigation algorithm. The second category is to improve filtering methods, such as Kalman filtering and extended Kalman filtering. This type of method estimates and corrects the state of collaborative information to reduce the impact of the lack of collaborative information on system navigation. Specifically, the system model and various sensor information are used to predict and update the collaborative information, thereby improving the accuracy and robustness of the system navigation.

[0006] However, both of the above methods can maintain system accuracy when navigation information is missing, but they generally have the disadvantage of being difficult to balance accuracy and real-time performance, and the algorithm complexity and model training cost are relatively high, which places stringent requirements on the performance of the computing platform. Summary of the Invention

[0007] To solve the above technical problems, the present invention proposes a collaborative information reconstruction system and method based on minimum KL divergence, which improves the position prediction accuracy by establishing a kinematic model, uses Lagrange interpolation to smooth the predicted position, and uses minimum KL divergence to accurately fuse the position prediction information and measurement information, thereby improving the position accuracy by continuously reducing the KL divergence.

[0008] To achieve the above object, the technical solution adopted by the present invention is:

[0009] A UUV collaborative information reconstruction system based on minimum KL divergence is characterized by comprising a receiving end and a transmitting end and a communication module for communication between the receiving end and the transmitting end, wherein the transmitting end is provided with an INS module, an underwater acoustic ranging module, a first underwater acoustic communicator and a first underwater acoustic ranging transducer, the INS module signal is connected to the first underwater acoustic ranging transducer, a high-frequency autonomous navigation result is obtained through the dead reckoning capability of the INS module, and the position signal of the autonomous navigation result is sent to the first underwater acoustic communication transducer, the underwater acoustic ranging module signal is connected to the first underwater acoustic ranging transducer, and the time difference of the propagation path is calculated by measuring the arrival time and phase difference of the pulse signal, thereby providing the distance information between the receiving end and the transmitting end, and the distance information is transmitted to the receiving end. The receiving end is provided with a second underwater acoustic communication transducer, a second underwater acoustic ranging transducer and an information fusion module. The first underwater acoustic communication transducer and the first underwater acoustic ranging transducer are respectively connected to the second underwater acoustic communication transducer and the second underwater acoustic ranging transducer through the communication module. The first underwater acoustic communication transducer sends a communication wave to the second underwater acoustic communication transducer through the communication module. The first underwater acoustic ranging transducer sends an acoustic pulse to the second underwater acoustic ranging transducer through the communication module. The second underwater acoustic communication transducer and the second underwater acoustic ranging transducer are respectively connected to the information fusion module. The information fusion module uses the minimum KL divergence criterion to perform high-precision fusion of position prediction information and measurement information to obtain the final position.

[0010] As a preferred technical solution of the present invention: a transmitting end shell is provided outside the transmitting end, the INS module and the underwater acoustic ranging module are respectively installed in the shell, and the first underwater acoustic communicator is fixed on the transmitting end shell.

[0011] As a preferred technical solution of the present invention: a receiving end shell is provided outside the receiving end, and the second underwater acoustic communicator is fixed on the receiving end shell.

[0012] In the above structure: the UUV collaborative information reconstruction system based on minimum KL divergence proposed by the present invention includes a receiving end and a transmitting end and a communication module for communication between the receiving end and the transmitting end, wherein the transmitting end is provided with an INS module, an underwater acoustic ranging module, a first underwater acoustic communicator and a first underwater acoustic ranging transducer, and the receiving end is provided with a second underwater acoustic communication transducer, a second underwater acoustic ranging transducer and an information fusion module, wherein the receiving end is a UUV, namely a Receiving-end UUV, referred to as RUUV, and the transmitting-end UUV, namely a Transmitting-end UUV, referred to as TUUV, and the collaborative information is transmitted through two types of underwater acoustic signals, one type is used to form an acoustic pulse signal for distance measurement, and the other type is a communication wave containing UUV position information;

[0013] INS module: obtains high-frequency autonomous navigation results through the dead reckoning capability of INS;

[0014] Underwater acoustic ranging module: By measuring the arrival time and phase difference of the pulse signal, the time difference of the propagation path is calculated, thereby providing the distance information between the TUUV and the RUUV;

[0015] Information fusion module: Use the minimum KL divergence accuracy to perform high-precision fusion of position prediction information and measurement information to obtain the final position.

[0016] A UUV collaborative information reconstruction method based on minimum KL divergence is characterized by comprising the following steps:

[0017] S1: The transmitter's position information calculated by the INS module is obtained through communication waves, and the distance measurement information is obtained through acoustic pulse signals. The cooperative information propagation time includes the underwater acoustic signal propagation time and signal processing time. Due to the large amount of information in the communication data packet, the receiver needs time to splice and reconstruct it. Therefore, the position information received by the receiver has a delay error. The communication delay is the time from the transmitter sending the pulse to the receiver receiving the communication wave information. The cooperative information propagation follows the "sequential arrival" principle, but once the expiration time exceeds the measurement period, the cooperative information will be out of order and lost.

[0018] S2: Establish a constant acceleration model. Use the UUV position before information loss to establish a constant acceleration model, and substitute the historical position into this model to make a preliminary prediction of the missing position.

[0019] The discrete state equation is as follows:

[0020] X(k+1)=Φ CA ·X(k)+T CA ·W(k)

[0021] in x(k) is the position at time k, is the speed at time k, is the acceleration at time k, the initial velocity is obtained by the first-order difference of the position, and the initial acceleration is obtained by the second-order difference of the position. W(k) is white noise, Φ CA is the state transition matrix, Γ CA is the noise allocation matrix,

[0022]

[0023] Where: T is the sampling period;

[0024] S3: Use Lagrange interpolation to fit the UUV position before and after the information loss, establish a high-order position polynomial, and use it to smooth the preliminary predicted position obtained in step S2.

[0025] The basic form of the Lagrange interpolation polynomial is as follows:

[0026] L n (x j )=y k l k (± j )=y j (j=0,1,…,n)

[0027] Where, l k (x j ) represents the k-th interpolation basis function when the independent variable x takes the j-th value. The specific form is shown in the following formula:

[0028]

[0029] Among them, x0, x1, ..., x n is the horizontal coordinate value of the known data point, and l k (x j ) is brought in to get:

[0030]

[0031] Apply the Lagrange interpolation polynomial to the coordinate values ​​between the data points to obtain smoothed data;

[0032] S4: Perform kernel density estimation on historical data to obtain the location prior distribution, perform kernel density estimation on observed data to obtain the likelihood function, calculate the marginal likelihood function using the total probability formula, and finally calculate the location posterior distribution according to Bayes' theorem;

[0033] S5: Use distance observations to correct the position prediction error. Since distance information is transmitted through underwater acoustic pulses, it can be used as a reliable measurement information constraint error boundary. Therefore, the minimum KL divergence criterion is used to perform high-precision fusion of predicted position information and measurement information. The difference between the solution position distribution and the target posterior distribution can be effectively measured based on the KL divergence value. By adjusting the position distribution of the measurement constraint and continuously reducing the KL divergence value, the solution position accuracy can be improved. When the KL divergence is reduced to the preset threshold, the solution position can be output as the final result, completing the TUUV position information reconstruction.

[0034] The KL divergence calculation formula is as follows:

[0035]

[0036] Among them, P is the posterior distribution of position, Q is the prior probability distribution of position,

[0037] KL divergence is a quantitative indicator that measures the similarity between any two probability distributions. Since it is not required to obey a Gaussian distribution, it maintains information integrity to the greatest extent possible. The overlap between the predicted prior distribution of the transmitter position and the position distribution of the measurement constraint is the target posterior distribution of the transmitter position.

[0038] As a preferred technical solution of the present invention: the specific steps of step S4 are as follows:

[0039] S41. Determine the prior distribution and use kernel estimation to obtain the prior distribution f(x) about the parameter x based on the historical position data.

[0040] S42. Treat each data point at the position predicted by the constant acceleration model as a sample in the distribution. For each predicted position, select the corresponding kernel function K(u), bring each position point into the kernel function K(u), and calculate the kernel function value of the position point.

[0041] S43. Construct the likelihood function, which is determined by the probability distribution of the observed variables. It refers to the probability or density of the observed data under the condition of given x, expressed as P(D|x), where D = {d1, d2, ..., d n}, perform kernel density estimation on it, and obtain the estimation function f(d). Through the estimation function, we can get P(D|x), as shown in the following formula:

[0042] P(D|θ)=f(d1)*f(d2)*…*f(d n )

[0043] S44. Calculate the marginal likelihood function. The marginal likelihood function is denoted as P(D), which is the probability of observing the data. It can be calculated by applying the total probability formula, that is, marginalizing the integral of the parameter x:

[0044] P(D)=∫P(D|x)f(x)dx

[0045] S45. Calculate the posterior distribution. According to Bayes' theorem, the posterior distribution can be obtained by multiplying the prior distribution, the likelihood function, and the marginal likelihood function:

[0046]

[0047] As a preferred technical solution of the present invention: in step S41: the specific steps of solving the position prior distribution are as follows:

[0048] S411. Treat each data point at the position predicted by the constant acceleration model as a sample in the distribution. For each predicted position, select the corresponding kernel function K(u), bring each position point into the kernel function, and calculate the kernel function value of the position point.

[0049] S412. Sum the kernel function values ​​of all position points and divide by the number of samples to obtain the kernel density estimate of the position, where u = xx i , x is the position of the point to be estimated, x i The sample set X = x1, x2…, x n A data point in , n is the number of samples, h is the bandwidth, determined by cross-validation method,

[0050]

[0051] S413. Normalize the estimated kernel density function to obtain the probability density distribution.

[0052]

[0053] In the above structure: the present invention uses the minimum KL divergence principle to reconstruct the missing UUV collaborative information with high precision, avoiding the shortcomings of nonlinear modeling methods such as neural networks and deep learning or improved filtering methods that cannot take into account both accuracy and real-time performance at the same time. While ensuring the accuracy index, the calculation process is greatly simplified, which helps to reduce the difficulty of engineering application of the missing information real-time reconstruction method.

[0054] Compared with the prior art, the present invention has the following beneficial effects:

[0055] The present invention improves the position prediction accuracy by establishing a kinematic model, uses the Lagrange interpolation method to smooth the predicted position, adopts the minimum KL divergence accuracy to perform high-precision fusion of position prediction information and measurement information, and improves the position accuracy by continuously reducing the KL divergence. The present invention uses the minimum KL divergence principle to reconstruct the missing UUV collaborative information with high precision, avoiding the shortcomings of nonlinear modeling methods such as neural networks and deep learning or improved filtering methods that cannot take into account both accuracy and real-time performance at the same time. While ensuring the accuracy index, the calculation process is greatly simplified, which helps to reduce the difficulty of engineering application of the real-time reconstruction method of missing information. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 It is a block diagram of collaborative information reconstruction system;

[0057] Figure 2 It is a working diagram of the collaborative information reconstruction system;

[0058] Figure 3 It is a flow chart of the collaborative information reconstruction method;

[0059] Figure 4 It is a schematic diagram of the collaborative information dissemination scenario;

[0060] Figure 5 This is a diagram of the data fusion principle based on minimum KL divergence. DETAILED DESCRIPTION

[0061] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments:

[0062] Existing technologies struggle to simultaneously ensure real-time performance and reconstruction accuracy, resulting in a long-standing lack of an ideal solution to the problem of collaborative information loss. In light of this, this paper proposes a breakthrough in real-time reconstruction of missing location information, focusing on real-time performance while also taking into account reconstruction accuracy. This approach provides a solid theoretical foundation for addressing the serious problem of information loss caused by communication delays.

[0063] like Figure 1-2 As shown, the present invention proposes a UUV collaborative information reconstruction system based on minimum KL divergence, including a receiving end and a transmitting end and a communication module for communication between the receiving end and the transmitting end, the transmitting end is provided with an INS module, an underwater acoustic ranging module, a first underwater acoustic communicator and a first underwater acoustic ranging transducer, the INS module signal is connected to the first underwater acoustic ranging transducer, and a high-frequency autonomous navigation result is obtained through the dead reckoning capability of the INS module, and the position signal of the autonomous navigation result is sent to the first underwater acoustic communication transducer, the underwater acoustic ranging module signal is connected to the first underwater acoustic ranging transducer, and the time difference of the propagation path is calculated by measuring the arrival time and phase difference of the pulse signal, thereby giving the distance information between the receiving end and the transmitting end, and the distance The information is sent to the first underwater acoustic ranging transducer. The receiving end is provided with a second underwater acoustic communication transducer, a second underwater acoustic ranging transducer and an information fusion module. The first underwater acoustic communication transducer and the first underwater acoustic ranging transducer are respectively connected to the second underwater acoustic communication transducer and the second underwater acoustic ranging transducer through the communication module. The first underwater acoustic communication transducer sends a communication wave to the second underwater acoustic communication transducer through the communication module. The first underwater acoustic ranging transducer sends an acoustic pulse to the second underwater acoustic ranging transducer through the communication module. The second underwater acoustic communication transducer and the second underwater acoustic ranging transducer are respectively connected to the information fusion module. The information fusion module uses the minimum KL divergence criterion to perform high-precision fusion of position prediction information and measurement information to obtain the final position.

[0064] A transmitting end shell is provided outside the transmitting end, the INS module and the underwater acoustic ranging module are respectively installed in the shell, and the first underwater acoustic communicator is fixed on the transmitting end shell.

[0065] A receiving end shell is provided outside the receiving end, and the second underwater acoustic communicator is fixed on the receiving end shell.

[0066] The present invention proposes a UUV collaborative information reconstruction system based on minimum KL divergence, including a receiving end and a transmitting end and a communication module for communication between the receiving end and the transmitting end, wherein the transmitting end is provided with an INS module, an underwater acoustic ranging module, a first underwater acoustic communicator and a first underwater acoustic ranging transducer, and the receiving end is provided with a second underwater acoustic communication transducer, a second underwater acoustic ranging transducer and an information fusion module, wherein the receiving end is a UUV, namely a receiving-end UUV, referred to as RUUV, and the transmitting-end UUV, namely a transmitting-end UUV, referred to as TUUV, and the collaborative information is transmitted through two types of underwater acoustic signals: one type is used to form an acoustic pulse signal for distance measurement, and the other type is a communication wave containing UUV position information;

[0067] INS module: obtains high-frequency autonomous navigation results through the dead reckoning capability of INS;

[0068] Underwater acoustic ranging module: By measuring the arrival time and phase difference of the pulse signal, the time difference of the propagation path is calculated, thereby providing the distance information between the TUUV and the RUUV;

[0069] Information fusion module: Use the minimum KL divergence accuracy to perform high-precision fusion of position prediction information and measurement information to obtain the final position.

[0070] like Figure 3 As shown, the present invention also proposes a UUV collaborative information reconstruction method based on minimum KL divergence, which includes the following steps:

[0071] S1: The transmitter position information calculated by the INS module is obtained through the communication wave, and the distance measurement information is obtained through the acoustic pulse signal. The cooperative information propagation time includes the underwater acoustic signal propagation time and the signal processing time. Due to the large amount of information in the communication data packet, the receiving end needs time to splice and reconstruct it. Therefore, the position information received by the receiving end has a delay error. The communication delay is the time from the transmitter sending the pulse to the receiver receiving the communication wave information. The cooperative information propagation follows the "sequential arrival" principle, but once the expiration time exceeds the measurement period, the cooperative information will be out of order and lost; Figure 4 As shown,

[0072] Because pulse train signal processing is simple, the delay is very short and can be ignored; however, the communication data packet has a large amount of information and is seriously affected by multipath propagation. The receiving end needs a long time to splice and reconstruct it, so the position information received by the receiving end often has a large delay error.

[0073] S2: Establish a constant acceleration model. Use the UUV position before information loss to establish a constant acceleration model, and substitute the historical position into this model to make a preliminary prediction of the missing position.

[0074] The discrete state equation is as follows:

[0075] X(k+1)=Φ CA ·X(k)+Γ CA ·W(k)

[0076] in x(k) is the position at time k, is the speed at time k, is the acceleration at time k, the initial velocity is obtained by the first-order difference of the position, and the initial acceleration is obtained by the second-order difference of the position. W(k) is white noise, Φ CA is the state transition matrix, Γ CA is the noise allocation matrix,

[0077]

[0078] Where: T is the sampling period;

[0079] S3: Use Lagrange interpolation to fit the UUV position before and after the information loss, establish a high-order position polynomial, and use it to smooth the preliminary predicted position obtained in step S2.

[0080] The basic form of the Lagrange interpolation polynomial is as follows:

[0081] L n (x j )=y k l j (x j )=y j (j=0,1,…,n)

[0082] Where, l k (x j ) represents the k-th interpolation basis function when the independent variable x takes the j-th value. The specific form is shown in the following formula:

[0083]

[0084] Among them, x0, x1, ..., x n is the horizontal coordinate value of the known data point, and l k (x j ) is brought in to get:

[0085]

[0086] Apply the Lagrange interpolation polynomial to the coordinate values ​​between the data points to obtain smoothed data;

[0087] S4: Perform kernel density estimation on historical data to obtain the location prior distribution, perform kernel density estimation on observed data to obtain the likelihood function, calculate the marginal likelihood function using the total probability formula, and finally calculate the location posterior distribution according to Bayes' theorem;

[0088] S5: Use distance observations to correct the position prediction error. Since the distance information is transmitted through underwater acoustic pulses, the probability of delay and loss is small, so it can be used as a reliable measurement information constraint error boundary. Therefore, the minimum KL divergence criterion is used to perform high-precision fusion of the predicted position information and the measurement information. The difference between the solution position distribution and the target posterior distribution can be effectively measured based on the KL divergence value. By adjusting the position distribution of the measurement constraint and continuously reducing the KL divergence value, the solution position accuracy can be improved. When the KL divergence is reduced to the preset threshold, the solution position can be output as the final result to complete the TUUV position information reconstruction.

[0089] The KL divergence calculation formula is as follows:

[0090]

[0091] Among them, P is the posterior distribution of position, Q is the prior probability distribution of position,

[0092] KL divergence is a quantitative indicator that measures the similarity between any two probability distributions. Since it is not required to obey the Gaussian distribution, it maintains the information integrity to the greatest extent. The overlap between the predicted prior distribution of the transmitter position and the position distribution of the measurement constraint is the target posterior distribution of the transmitter position, such as Figure 5 shown.

[0093] As a preferred technical solution of the present invention: the specific steps of step S4 are as follows:

[0094] S41. Determine the prior distribution and use kernel estimation to obtain the prior distribution f(x) about the parameter x based on the historical position data.

[0095] S42. Treat each data point at the position predicted by the constant acceleration model as a sample in the distribution. For each predicted position, select the corresponding kernel function K(u), bring each position point into the kernel function K(u), and calculate the kernel function value of the position point.

[0096] S43. Construct the likelihood function, which is determined by the probability distribution of the observed variables. It refers to the probability or density of the observed data under the condition of given x, expressed as P(D|x), where D = {d1, d2, ..., d n}, perform kernel density estimation on it, and obtain the estimation function f(d). Through the estimation function, we can get P(D|x), as shown in the following formula:

[0097] P(D|θ)=f(d1)*f(d2)*…*f(dn )

[0098] S44. Calculate the marginal likelihood function. The marginal likelihood function is denoted as P(D), which is the probability of observing the data. It can be calculated by applying the total probability formula, that is, marginalizing the integral of the parameter x:

[0099] P(D)=∫P(D|x)f(x)dx

[0100] S45. Calculate the posterior distribution. According to Bayes' theorem, the posterior distribution can be obtained by multiplying the prior distribution, the likelihood function, and the marginal likelihood function:

[0101]

[0102] As a preferred technical solution of the present invention: in step S41: the specific steps of solving the position prior distribution are as follows:

[0103] S411. Treat each data point at the position predicted by the constant acceleration model as a sample in the distribution. For each predicted position, select the corresponding kernel function K(u), bring each position point into the kernel function, and calculate the kernel function value of the position point.

[0104] S412. Sum the kernel function values ​​of all position points and divide by the number of samples to obtain the kernel density estimate of the position, where u = xx i , x is the position of the point to be estimated, x i The sample set X = x1, x2…, x n A data point in , n is the number of samples, h is the bandwidth, determined by cross-validation method,

[0105]

[0106] S413. Normalize the estimated kernel density function to obtain the probability density distribution.

[0107]

[0108] The present invention uses the minimum KL divergence principle to reconstruct the missing UUV collaborative information with high precision, avoiding the shortcomings of nonlinear modeling methods such as neural networks and deep learning or improved filtering methods that cannot take into account both accuracy and real-time performance at the same time. While ensuring accuracy indicators, the calculation process is greatly simplified, which helps to reduce the difficulty of engineering application of the missing information real-time reconstruction method.

[0109] The present invention improves the position prediction accuracy by establishing a kinematic model, uses the Lagrange interpolation method to smooth the predicted position, adopts the minimum KL divergence accuracy to perform high-precision fusion of position prediction information and measurement information, and improves the position accuracy by continuously reducing the KL divergence. The present invention uses the minimum KL divergence principle to reconstruct the missing UUV collaborative information with high precision, avoiding the shortcomings of nonlinear modeling methods such as neural networks and deep learning or improved filtering methods that cannot take into account both accuracy and real-time performance at the same time. While ensuring the accuracy index, the calculation process is greatly simplified, which helps to reduce the difficulty of engineering application of the real-time reconstruction method of missing information.

[0110] The above description is merely a preferred embodiment of the present invention and does not constitute any other form of limitation to the present invention. Any modification or equivalent variation based on the technical essence of the present invention shall still fall within the scope of protection claimed by the present invention.

Claims

1. A UUV collaborative information reconstruction method based on minimum KL divergence, characterized by: The steps include: S1: The transmitter's position information, calculated by the INS module, is obtained through communication waves, and distance measurement information is obtained through acoustic pulse signals. The cooperative information propagation time includes the underwater acoustic signal propagation time and signal processing time. Due to the large amount of information in the communication data packet, the receiver needs time to splice and reconstruct it. Therefore, the position information received by the receiver has a delay error. The communication delay is the time from the transmitter sending the pulse to the receiver receiving the communication wave information. The cooperative information propagation follows the "order of arrival" principle. However, if the expiration time exceeds the measurement period, the cooperative information will be out of sequence and lost. S2: Establish a constant acceleration model. Use the UUV position before information loss to establish a constant acceleration model, and substitute the historical position into this model to make a preliminary prediction of the missing position. The discrete state equation is as follows: ； in for The location at the moment, for The speed of time, for The acceleration at the moment, the initial velocity is obtained by the first-order difference of the position, and the acceleration at the initial moment is obtained by the second-order difference of the position. is white noise, is the state transition matrix, is the noise allocation matrix, ， ; Where: T is the sampling period; S3: Use Lagrange interpolation to fit the UUV position before and after the information loss, establish a high-order position polynomial, and use it to smooth the preliminary predicted position obtained in step S2. The basic form of the Lagrange interpolation polynomial is as follows: ； Where, Indicates independent variables Take the first The first The interpolation basis function is shown in the following formula: , ; in, is the horizontal coordinate value of the known data point, Bring in: ; Apply the Lagrange interpolation polynomial to the coordinate values ​​between the data points to obtain smoothed data; S4: Perform kernel density estimation on historical data to obtain the location prior distribution, perform kernel density estimation on observed data to obtain the likelihood function, calculate the marginal likelihood function using the total probability formula, and finally calculate the location posterior distribution according to Bayes' theorem; S5: Use distance observations to correct the position prediction error. Since the distance information is transmitted through underwater acoustic pulses, it serves as a reliable measurement information to constrain the error boundary. Therefore, the minimum KL divergence criterion is used to perform high-precision fusion of the predicted position information and the measurement information. The difference between the solution position distribution and the target posterior distribution can be effectively measured based on the KL divergence value. By adjusting the position distribution of the measurement constraint and continuously reducing the KL divergence value, the solution position accuracy can be improved. When the KL divergence is reduced to the preset threshold, the solution position is output as the final result, completing the TUUV position information reconstruction. The KL divergence calculation formula is as follows: ; Among them, P is the posterior distribution of position, Q is the prior probability distribution of position, KL divergence is a quantitative indicator that measures the similarity between any two probability distributions. Since it is not required to obey a Gaussian distribution, it maintains information integrity to the greatest extent possible. The overlap between the predicted prior distribution of the transmitter position and the position distribution of the measurement constraint is the target posterior distribution of the transmitter position.

2. The UUV collaborative information reconstruction method based on minimum KL divergence according to claim 1 is characterized by: The specific steps of step S4 are as follows: S41. Determine the prior distribution and use kernel estimation to obtain the parameters based on historical position data. Prior distribution of , S42. Treat each data point at the position predicted by the constant acceleration model as a sample in the distribution. For each predicted position, select the corresponding kernel function , bring each position point into the kernel function , calculate the kernel function value of the position point, S43. Construct the likelihood function, which is determined by the probability distribution of the observed variables. The probability or density of the observed data under the condition of ,in , perform kernel density estimation on it and get the estimation function , obtained by estimating the function , as shown in the following formula: ; S44. Calculate the marginal likelihood function, which is expressed as , is the probability of observing the data, calculated by applying the total probability formula, that is, for the parameter Integral marginalization: ; S45. Calculate the posterior distribution. According to Bayes' theorem, the posterior distribution is obtained by multiplying the prior distribution, the likelihood function, and the marginal likelihood function: 。 3. The UUV collaborative information reconstruction method based on minimum KL divergence according to claim 2 is characterized by: In step S41: the specific steps of solving the position prior distribution are as follows: S411. Treat each data point at the position predicted by the constant acceleration model as a sample in the distribution. For each predicted position, select the corresponding kernel function , bring each position point into the kernel function and calculate the kernel function value of the position point, S412. Sum the kernel function values ​​of all position points and divide them by the number of samples to obtain the kernel density estimate of the position, where , is the position of the point to be estimated, Is a sample set A data point in , n is the number of samples, h is the bandwidth, determined by cross-validation method, ; S413. Normalize the estimated kernel density function to obtain the probability density distribution. 。 4. The system of the UUV collaborative information reconstruction method based on minimum KL divergence according to claim 1 is characterized by: The invention comprises a receiving end and a transmitting end and a communication module for communicating between the receiving end and the transmitting end. The transmitting end is provided with an INS module, an underwater acoustic ranging module, a first underwater acoustic communicator and a first underwater acoustic ranging transducer. The INS module signal is connected to the first underwater acoustic ranging transducer, and a high-frequency autonomous navigation result is obtained through the dead reckoning capability of the INS module, and the position signal of the autonomous navigation result is sent to the first underwater acoustic communication transducer. The underwater acoustic ranging module signal is connected to the first underwater acoustic ranging transducer, and the time difference of the propagation path is calculated by measuring the arrival time and phase difference of the pulse signal, thereby giving the distance information between the receiving end and the transmitting end, and sending the distance information to the first underwater acoustic ranging transducer. The receiving end is provided with a second underwater acoustic communication transducer, a second underwater acoustic ranging transducer and an information fusion module. The first underwater acoustic communication transducer and the first underwater acoustic ranging transducer are respectively connected to the second underwater acoustic communication transducer and the second underwater acoustic ranging transducer through the communication module. The first underwater acoustic communication transducer sends a communication wave to the second underwater acoustic communication transducer through the communication module. The first underwater acoustic ranging transducer sends an acoustic pulse to the second underwater acoustic ranging transducer through the communication module. The second underwater acoustic communication transducer and the second underwater acoustic ranging transducer are respectively signal-connected to the information fusion module. The information fusion module uses the minimum KL divergence criterion to perform high-precision fusion of position prediction information and measurement information to obtain the final position.

5. The system of the UUV collaborative information reconstruction method based on minimum KL divergence according to claim 4 is characterized by: A transmitting end shell is provided outside the transmitting end, the INS module and the underwater acoustic ranging module are respectively installed in the shell, and the first underwater acoustic communicator is fixed on the transmitting end shell.

6. The system of the UUV collaborative information reconstruction method based on minimum KL divergence according to claim 5 is characterized by: A receiving end shell is provided outside the receiving end, and the second underwater acoustic ranging transducer is fixed on the receiving end shell.

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