An underwater acoustic positioning method based on adaptive filtering state and noise joint estimation

Abstract

The application discloses a kind of state and noise joint estimation underwater acoustic positioning method based on adaptive filtering, based on extended Kalman filter framework, the motion state of vehicle and equivalent sound velocity error are augmented to joint state vector, construct motion-sound velocity coupling state space vector, and carry out initialization operation;Time-varying observation noise variance is modeled as random variable subject to inverse gamma distribution;In state prediction process, prior prediction estimation is carried out to state space vector and state covariance matrix, and the hyperparameter of inverse gamma distribution is time updated;In the process of variation iteration update, the sound ray propagation motion compensation observation equation is constructed based on ray acoustics theory, and the Jacobian matrix is calculated;The joint posterior estimation of state and noise hyperparameter is realized by introducing variation bayes inference theory, and the two-stage hierarchical architecture of state prediction and variation iteration update is used to realize the joint posterior estimation of the position, velocity, sound velocity error and observation noise variance of vehicle.

Description

Technical Field

[0001] This invention relates to the field of underwater acoustic localization technology, and in particular to an underwater acoustic localization method based on joint estimation of state and noise using adaptive filtering. Background Technology

[0002] Long baseline (LBL) underwater acoustic positioning systems are a key technology for achieving high-precision autonomous navigation and operation of marine intelligent equipment such as automated underwater vehicles (AUVs) and remotely operated vehicles (ROVs). This system uses acoustic beacons deployed at known locations on the seabed, and the vehicle measures the two-way sound wave propagation time between itself and each beacon, combining this with sound velocity profile information to achieve three-dimensional positioning. However, achieving high-precision positioning in complex marine environments faces several technical challenges: Existing LBL positioning methods generally suffer from insufficient motion compensation. Traditional "static models" assume that the vehicle remains stationary during the interval between acoustic signal interrogation and response reception. However, acoustic signals can propagate over long distances in the deep sea for several seconds, and the vehicle's motion within this time window cannot be ignored, leading to systematic biases in positioning. Although existing motion compensation methods improve upon this by introducing constant motion correction terms or propagation time corrections, in highly maneuverable scenarios, traditional methods have limited ability to fit the continuous motion trajectory of the vehicle, making it difficult to achieve precise decoupling of the position at the time of transmission and reception.

[0003] Real-time compensation for sound velocity errors is another technical challenge. Traditional positioning methods often use constant or layered sound velocity profiles, but the marine environment is highly dynamic, and the snapshots of sound velocity profiles obtained by CTD (Conductivity, Temperature, Depth) detectors have limited timeliness and cannot represent the true sound velocity field throughout the entire operation. Although existing methods model sound velocity errors as depth-independent offsets or use multi-step estimation for compensation, sound velocity disturbances exhibit complex nonlinear changes with space and time. How to achieve adaptive dynamic estimation of sound velocity errors remains a key problem that urgently needs to be solved in this field. More importantly, existing positioning methods based on extended Kalman filtering (EKF) generally rely on the strong assumption that the observation noise covariance is known and constant. In actual underwater acoustic positioning, observation noise is affected by multiple factors such as marine environmental noise, signal multipath effects, and changes in propagation paths, exhibiting significant spatiotemporal nonstationary characteristics. Filtering methods with fixed noise parameters face the risk of convergence difficulties, accuracy loss, and even divergence under complex sea conditions, severely restricting the robustness and reliability of the positioning system. In summary, existing underwater acoustic localization technologies have significant shortcomings in the coordinated processing of motion compensation, sound velocity disturbance estimation, and noise adaptive modeling, and lack a filtering method that can systematically decouple and compensate for multi-source coupling errors. Summary of the Invention

[0004] Purpose of the invention: In order to overcome the shortcomings of the existing technology, the present invention provides an underwater acoustic localization method based on joint estimation of state and noise using adaptive filtering. Based on the extended Kalman filter framework, it adopts a two-stage hierarchical architecture of state prediction and variational iterative update to realize online joint estimation of the position, velocity, sound speed error and observation noise statistical characteristics of the vehicle.

[0005] Technical Solution: To achieve the above objectives, an underwater acoustic localization method based on joint estimation of state and noise using adaptive filtering is proposed. Based on the extended Kalman filter framework, the motion state and equivalent sound speed error of the vehicle are augmented into the joint state vector to construct a motion-sound speed coupled state space vector. The time-varying observation noise variance is modeled as a random variable following an inverse gamma distribution. Initial values ​​for the motion-sound speed coupled state space vector, the state covariance matrix, and the process noise covariance matrix are set, and the hyperparameters of the inverse gamma distribution of the observation noise variance are initialized. During state prediction, prior prediction estimation is performed on the state space vector and the state covariance matrix to obtain the state prediction vector and the state prediction covariance matrix, and the hyperparameters of the inverse gamma distribution are updated over time to obtain the predicted hyperparameters of the inverse gamma distribution.

[0006] In the variational iterative update process, based on ray acoustics theory, considering the spatiotemporal differences in the vehicle's position at the time of sound signal transmission and reception, a sound ray propagation motion compensation observation equation is constructed. Within this equation, a sound path function is constructed based on the functional relationship between the observed two-way sound ray propagation time and the state space vector. This function is then expanded using a Taylor series at the current estimated value to obtain the Jacobian matrix. Variational Bayesian inference theory is introduced, and joint posterior estimation of state and noise hyperparameters is achieved through mean-field approximation theory and variational iterative update. The state distribution and noise parameter distribution are initialized, and their posterior estimates are obtained through a fixed number of variational iterations. A two-stage hierarchical architecture of state prediction and variational iterative update is adopted to achieve online joint posterior estimation of the vehicle's position, velocity, sound speed errors, and observation noise variance.

[0007] Furthermore, the state space vector of the motion-sound speed coupling The calculation is as follows:

[0008] ,

[0009] In the formula, The three-dimensional coordinate position of the vehicle. For velocity vector, The sound speed error; the sound speed error The random walk model is used for modeling, and the calculation process is shown below:

[0010] ;

[0011] In the formula, The noise representing the sound velocity error follows a zero-mean Gaussian distribution; k is the kth filtering cycle.

[0012] Furthermore, the time-varying variance of the observation noise is modeled as a random variable following an inverse gamma distribution, where the observation noise follows a zero-mean Gaussian distribution. To observe the noise variance The inverse gamma conjugate prior distribution is assigned, and the calculation process is as follows:

[0013]

[0014] In the formula, α and β are the shape hyperparameter and scale hyperparameter, respectively. It follows an inverse gamma distribution, and exp represents the exponential operation. This is a gamma function.

[0015] Furthermore, during the state prediction process, prior prediction estimation is performed on the state space vector and the state covariance matrix to obtain the state prediction vector. and state prediction covariance matrix The calculation is as follows:

[0016] ;

[0017] ;

[0018] In the formula, Let be the state transition matrix of the motion state. The noise generated during the movement of the aircraft;

[0019] In the process of predicting the hyperparameters of the inverse gamma distribution by updating them over time, a forgetting factor λ is introduced to update the hyperparameters of the inverse gamma distribution over time, as shown in the calculation below:

[0020] ;

[0021] ;

[0022] In the formula, λ is the forgetting factor. and These represent the hyperparameter estimates of the inverse gamma distribution for the k-1 filter period, respectively. and These represent the hyperparameter predictions of the inverse gamma distribution with k filtering periods.

[0023] Furthermore, based on ray acoustics theory, and considering the spatiotemporal differences in the spacecraft's position at the time of sound signal transmission and reception, a sound ray propagation motion compensation observation equation is constructed, as shown below:

[0024]

[0025] In the formula, This represents the observed two-way sound ray propagation time during the k-th filtering cycle. This is the true value of the two-way sound ray propagation time. To observe the noise variance, in the sound ray propagation motion compensation observation equation, a sound path function is constructed based on the functional relationship between the two-way sound ray propagation time observations and the state space vector, as shown below:

[0026] ,

[0027] In the formula, The two-way sound propagation time observation value of the j-th transponder in the k-th period is given. and These represent the vehicle's position at the moment the acoustic signal was transmitted and the vehicle's position at the moment the acoustic signal was received. Let j be the position of the j-th transponder. Let f be the sound velocity profile, and f be the sound propagation time calculation function based on ray acoustics theory.

[0028] Furthermore, in the sound ray propagation motion compensation observation equation, the sound path function is expanded using a Taylor series at the current estimated value, retaining the first-order terms to obtain the Jacobian matrix; the calculation is shown below:

[0029]

[0030] In the formula, D represents the number of observations of all available transponders at the current moment.

[0031] Furthermore, during the variational iterative update process, the state distribution and noise parameter distribution are initialized, and then jointly updated through a fixed number of variational iterations. In the i-th variational iterative update process, the state distribution update employs an extended Kalman filter framework, which includes updating the state prediction vector and the state prediction covariance matrix. The calculation process is shown below:

[0032] ;

[0033] ;

[0034] ;

[0035] ;

[0036] In the formula, To observe the expected value of the noise variance, Let T be the identity matrix, and T be the matrix transpose operation. This is the Jacobian matrix term in the i-th variational iteration process of the k-th filtering cycle.

[0037] Furthermore, the noise parameter distribution update includes updating the hyperparameter prediction of the inverse gamma distribution, and the calculation process is as follows:

[0038]

[0039]

[0040] In the formula, is the value of the j-th row of the Jacobian matrix, and d is the number of all observations with available transponders at the current time.

[0041] Furthermore, after the variational iterative update is completed, the posterior estimate of the current time step is output, resulting in the posterior estimate of the state space vector, the posterior estimate of the state covariance matrix, and the posterior estimate of the hyperparameters of the inverse gamma distribution; the calculation is shown below:

[0042] , ;

[0043] , ;

[0044] In the formula, N is the number of iterations of the variational iteration, and j is the j-th transponder.

[0045] Beneficial effects: This invention provides an underwater acoustic localization method based on joint estimation of state and noise using adaptive filtering.

[0046] By augmenting the sound velocity error to the state vector, a motion-sound velocity coupled state space vector is constructed, enabling online compensation for systematic slant range deviations caused by spatiotemporal variations in sound velocity. Simulation and sea trial data verification show that it can effectively estimate a systematic sound velocity error of approximately 0.2-0.4 m / s, eliminating positioning errors caused by inaccurate sound velocity profiles in traditional extended Kalman filters, and reducing horizontal positioning errors from several meters to within the meter range. Variational Bayesian inference theory is introduced to model the time-varying observation noise variance as a random variable following an inverse gamma distribution. Online adaptive estimation of noise statistical characteristics is achieved through mean-field approximation and variational iteration. Experimental results show that the estimated observation noise standard deviation of this invention can accurately track the dynamic changes of real noise from 50 µs to 300 µs, effectively overcoming the limitations of traditional filters that rely on fixed noise parameters and significantly improving the robustness of the filter. Through a two-stage hierarchical architecture of state prediction and variational iterative update, joint optimal estimation of the vehicle's motion state, sound velocity error, and observation noise parameters is achieved. Simulation comparison experiments show that, under time-varying noise conditions, the root mean square error (RMSE) of the present invention is only 0.16 meters, which is significantly better than the traditional extended Kalman filter (RMSE) of 0.72 meters and the extended Kalman filter that only compensates for sound velocity error (RMSE) of 0.37 meters. Monte Carlo simulation further verifies that, under drastic noise change conditions with a rate of change as high as 0.5 µs / s, the performance degradation rate of the present invention is the smallest, demonstrating high robustness to noise dynamic characteristics. Attached Figure Description

[0047] Figure 1 This is a flowchart of an underwater acoustic localization method based on joint estimation of state and noise using adaptive filtering. Detailed Implementation

[0048] The invention will now be further described with reference to the accompanying drawings.

[0049] like Figure 1 As shown, an underwater acoustic localization method based on joint estimation of state and noise using adaptive filtering is proposed. Based on the extended Kalman filter framework, the motion state and equivalent sound speed error of the vehicle are augmented into the joint state vector to construct a motion-sound speed coupled state space vector. The time-varying observation noise variance is modeled as a random variable following an inverse gamma distribution. Initial values ​​for the motion-sound speed coupled state space vector, the state covariance matrix, and the process noise covariance matrix are set, and the hyperparameters of the inverse gamma distribution of the observation noise variance are initialized. During state prediction, prior prediction estimation is performed on the state space vector and the state covariance matrix to obtain the state prediction vector and the state prediction covariance matrix, and the hyperparameters of the inverse gamma distribution are updated over time to obtain the predicted hyperparameters of the inverse gamma distribution.

[0050] In the variational iterative update process, based on ray acoustics theory, considering the spatiotemporal difference of the spacecraft's position at the time of sound signal transmission and reception, a sound ray propagation motion compensation observation equation is constructed. Within this equation, a sound path function is constructed based on the functional relationship between the two-way sound ray propagation time observation value and the state space vector. This function is then expanded using a Taylor series at the current estimated value to obtain the Jacobian matrix. Variational Bayesian inference theory is introduced, and joint posterior estimation of the state and noise hyperparameters is achieved through mean-field approximation theory and variational iterative update. The state distribution and noise parameter distribution are initialized, and then jointly updated through a fixed number of variational iterations. The system obtains posterior estimates of the state distribution and noise parameter distribution. The posterior estimate of the state distribution includes the posterior estimate of the state space vector and the posterior estimate of the state covariance matrix. The posterior estimate of the state space vector serves as the current real-time positioning result of the vehicle, which includes the vehicle's position, velocity, and sound speed errors. The posterior estimate of the noise parameter distribution includes the posterior estimate of the hyperparameters of the inverse gamma distribution. Based on the posterior estimate of the hyperparameters of the inverse gamma distribution, the posterior estimate of the observation noise variance can be obtained. A two-stage hierarchical architecture of state prediction and variational iterative update is adopted to achieve online joint posterior estimation of the vehicle's position, velocity, sound speed errors, and observation noise variance. The posterior estimates of the state distribution and the noise parameter distribution are used for filtering recursion in the next time step, entering the next filtering cycle. Returning to the state prediction process, the state prediction process and variational iterative update process are repeated until the solution for all positioning cycles is completed.

[0051] The state space vector of motion-sound speed coupling The calculation is as follows:

[0052] ,

[0053] In the formula, The three-dimensional coordinate position of the vehicle. For velocity vector, The sound speed error; the sound speed error The random walk model is used for modeling, and the calculation process is shown below:

[0054] ;

[0055] In the formula, The process noise of the sound velocity error in the k-th filtering cycle follows a zero-mean Gaussian distribution; k is the k-th filtering cycle.

[0056] Set the initial value of the state space vector of motion-sound speed coupling The covariance matrix of the initial values ​​of the state vector process noise covariance matrix Initialize the hyperparameters of the inverse gamma distribution of the observation noise. and The aircraft's operating state is described using either a constant velocity (CV) model or a constant acceleration (COA) model. When using the CV model, a state estimation vector is constructed based on the (k-1)th filtering cycle. Obtain the state prediction vector for the k-th filtering period. The state transition equations are shown below:

[0057] ;

[0058] In the formula, Let be the state transition matrix of the motion state. The process noise covariance matrix follows a zero-mean Gaussian distribution; the state transition matrix of the motion state is obtained through the state transition equation. .

[0059] The time-varying variance of observation noise is modeled as a random variable following an inverse gamma distribution, where the observation noise follows a zero-mean Gaussian distribution. To observe the noise variance The inverse gamma conjugate prior distribution is assigned, and the calculation process is as follows:

[0060]

[0061] In the formula, α and β are the shape hyperparameter and scale hyperparameter, respectively. It follows an inverse gamma distribution, and exp represents the exponential operation. The gamma function is used. In normal Kalman filtering, the observed noise variance is... The model is based on Gaussian white noise, which cannot be jointly estimated with the state space vector for posterior estimation; therefore, the variance of the observation noise is not included. Assign an inverse gamma conjugate prior distribution; such that the observation noise variance and state space vector Being in the same distribution is beneficial for achieving joint posterior estimation in subsequent variational iteration updates.

[0062] In the state prediction process, prior prediction estimation is performed on the state space vector and the state covariance matrix to obtain the state prediction vector. and state prediction covariance matrix The calculation is as follows:

[0063] ;

[0064] ;

[0065] In the formula, Let be the state transition matrix of the motion state. The noise generated during the movement of the aircraft; This is the state estimation vector for the (k-1)th filtering cycle. Let be the state prediction vector for the k-th filtering period; The state estimation covariance matrix for the (k-1)th filtering cycle. Let be the state prediction covariance matrix for the k-th filtering period.

[0066] In the process of predicting the hyperparameters of the inverse gamma distribution by updating them over time, a forgetting factor λ is introduced to update the hyperparameters of the inverse gamma distribution over time. This allows for time-varying noise statistics and prevents the prior distribution from becoming overly sharp. The calculation is shown below:

[0067] ;

[0068] ;

[0069] In the formula, λ is the forgetting factor. and These represent the hyperparameter estimates of the inverse gamma distribution for the k-1 filter period, respectively. and These represent the hyperparameter predictions of the inverse gamma distribution with k filtering periods.

[0070] Based on ray acoustics theory, and considering the spatiotemporal differences in the spacecraft's position at the time of sound signal transmission and reception, a sound ray propagation motion compensation observation equation is constructed, as shown below:

[0071]

[0072] In the formula, This represents the observed two-way sound ray propagation time during the k-th filtering cycle. This is the true value of the two-way sound ray propagation time. To observe the noise variance.

[0073] In the sound ray propagation motion compensation observation equation, the sound path function is constructed based on the functional relationship between the two-way sound ray propagation time observation value and the state space vector, and is calculated as follows:

[0074] ,

[0075] In the formula, The two-way sound propagation time observation value of the j-th transponder in the k-th period is given. and These represent the vehicle's position at the moment the acoustic signal was transmitted and the vehicle's position at the moment the acoustic signal was received. Let j be the position of the j-th transponder. Let f be the sound velocity profile, and f be the sound propagation time calculation function based on ray acoustics theory.

[0076] Based on ray acoustics theory, the observed two-way sound propagation time is solved using Snell's law and differential calculation methods. The calculation process is shown below:

[0077]

[0078] In the formula, and These represent the depth of the vehicle in the water at the time of sound signal transmission and the depth of the vehicle in the water at the time of sound signal reception, respectively. and The acoustic ray parameters during the sound signal transmission process and the acoustic ray parameters during the sound signal reception process are respectively solved using Newton's method from the horizontal propagation distance of the sound ray.

[0079] In the extended Kalman filter framework, the acoustic path function is expanded using a Taylor series at the current estimated value in the acoustic ray propagation motion compensation observation equation. This is equivalent to expanding the acoustic path function of the (k-1)th filtering cycle using a Taylor series at the current initial value x0; the calculation is shown below:

[0080] ;

[0081] By retaining the first-order terms in the acoustic path function of the Taylor series expansion, we obtain the Jacobian matrix; the calculation is shown below:

[0082]

[0083] In the formula, D represents the number of observations from all available transponders at the current time, and the Jacobian matrix is ​​used for measurement updates in the extended Kalman filter.

[0084] In the variational iterative update process, variational Bayesian inference theory is introduced. The joint posterior estimation of state and noise hyperparameters is achieved through mean-field approximation theory and variational iterative update, i.e., joint posterior estimation of the state distribution and noise parameter distribution. First, the mean-field approximation theory is applied to the state distribution and noise parameter distribution to factorize the joint posterior distribution of the state distribution and noise parameter distribution, as calculated below:

[0085] ;

[0086] In the formula, It follows a Gaussian distribution. The distribution is an inverse gamma distribution, solved by minimizing the Kullback-Leibler divergence between the approximate posterior and the true posterior. The optimal distribution satisfies:

[0087] ;

[0088] ;

[0089] In the formula, Represented as state The posterior mean estimate, The state covariance matrix; For shape parameters, The scaling parameter is used to factorize the joint posterior distribution of the state distribution and the noise parameter distribution, so that the joint distribution of the state distribution and the noise parameter distribution is approximately the product of two distributions. This optimizes the joint posterior estimation in the variational iterative update, transforming the complex joint posterior estimation into a posterior estimation of two distributions, thus providing conditions for subsequent variational iterative updates.

[0090] Then, variational iterative updates are performed on the state distribution and noise hyperparameter distribution to achieve joint posterior estimation. The state distribution and noise parameter distribution are initialized. , ; , The state distribution and noise parameter distribution are jointly updated through a fixed number of variational iterations. During the i-th variational iteration, the state distribution update employs an extended Kalman filter framework, which includes updating the state prediction vector and the state prediction covariance matrix. The calculation process is shown below:

[0091] ;

[0092] ;

[0093] ;

[0094] ;

[0095] In the formula, To observe the expected value of the noise variance, Let T be the identity matrix, and T be the matrix transpose operation. This is the Jacobian matrix term in the i-th variational iteration process of the k-th filtering cycle.

[0096] The expected value of the observation noise variance The expected value of the observation noise variance is obtained by calculating the expected value of the observation noise variance modeled as following an inverse gamma distribution. The calculation process is as follows:

[0097]

[0098] In the formula, E represents the desired computational operation. Represented as The calculation formula for time; the observed noise variance is replaced by the expected noise value of the previous iteration, and the innovation vector is calculated first. The innovation vector is the difference between the observed two-way sound propagation time of the actual transponder and the observed quantity calculated through the observation function, wherein... The two-way sound propagation time observation value of the visible transponder at the current moment. The observation function is defined as follows: each transponder's observation has an innovation vector, and the expected value of all innovation vectors is used to calculate the observation noise variance.

[0099] The noise parameter distribution update includes updating the hyperparameter prediction of the inverse gamma distribution, and the calculation process is as follows:

[0100]

[0101]

[0102] In the formula, is the value of the j-th row of the Jacobian matrix, and the second term is used to compensate for the impact of state estimation uncertainty on noise estimation; d is the number of all available transponders at the current time. The two-way sound propagation time observation value of the j-th transponder in the k-th filtering cycle.

[0103] After the variational iterative update is completed, the posterior estimate of the current time step is output, resulting in the posterior estimates of the state space vector, the state covariance matrix, and the hyperparameters of the inverse gamma distribution; the calculations are shown below:

[0104] , ;

[0105] , ;

[0106] In the formula, N is the iteration number of the variational iteration, and j is the j-th transponder; the posterior estimation of the hyperparameters based on the inverse gamma distribution can obtain the posterior estimate of the observation noise variance, which reflects the statistical characteristics of the observation noise.

[0107] In the two-stage hierarchical architecture of state prediction and variational iterative update, the state prediction stage completes further prediction of the state and covariance, as well as the time update of the inverse gamma hyperparameter. The variational iterative update stage alternately performs state updates and noise parameter updates through a preset number of variational iterative updates, typically 2-3 times. Finally, the output and recursion stages produce posterior estimates of the state space vector, the state covariance matrix, and the inverse gamma distribution hyperparameters, which are used for filtering and recursion at the next time step. The posterior estimate of the state space vector serves as the real-time positioning result of the vehicle. These estimates are then used as inputs for the state prediction at the next time step. The process then returns to the state prediction stage, repeating the state prediction and variational iterative update processes until the entire positioning cycle is solved.

[0108] Example: The specific key parameter configurations are as follows: the standard deviation of process noise is set according to the dynamic characteristics of the aircraft, wherein the standard deviation of acceleration process noise is taken as 0.05 (m / s). 2 The forgetting factor λ = 0.98 is used to balance the weights of historical information and new observation information; the number of variational iterations is N = 3, and it has been verified that 2-3 iterations are sufficient to converge to a stable solution; in the initial state covariance, the location variance is set to (10m). 2 The velocity variance is set to 1 (m / s). 2 The variance of the sound velocity error is set to (2 m / s). 2 Initial inverse gamma hyperparameters: and This corresponds to a relatively wide prior distribution.

[0109] The convergence of the variational Bayesian extended Kalman filter is guaranteed by the mean-field approximation and fixed-point iteration. Theoretical analysis shows that, under the conditions that the observation model is differentiable and the noise distribution satisfies the conjugate prior assumption, the variational iteration monotonically decreases the Kullback-Leibler divergence, and the iteration sequence converges to a local optimum. In practical applications, 2-3 iterations are sufficient to obtain a sufficiently accurate approximate posterior distribution. The output is the posterior estimate of the state-space vector at the current time step. As the real-time positioning result of the vehicle, the posterior estimate of the hyperparameters of the inverse gamma distribution is output. and As input to the next time step state prediction step, and based on the posterior estimation of hyperparameters of the inverse gamma distribution. and It can calculate the variance of observation noise, thereby enabling online estimation of the statistical characteristics of observation noise; repeat the state prediction process and variational iterative update process until the solution of all positioning cycles is completed.

[0110] This invention has been verified using publicly available data from marine AUV measurements at the Nankai Trough in Japan. The root mean square error (RMSE) for horizontal positioning is 0.89 meters. The error distribution histogram shows that the vast majority of positioning results are concentrated in the 0-1 meter range, with very few samples having an error greater than 2 meters. Comparative analysis shows that the RMSE of the traditional extended Kalman filter is 4.68 meters, while the RMSE of the extended Kalman filter that only compensates for sound velocity error is 1.83 meters. Compared with the traditional extended Kalman filter and the extended Kalman filter that only compensates for sound velocity error, this invention significantly improves positioning accuracy, and the error curve is smoother with a smaller peak error. This demonstrates the systematic decoupling and compensation capability of this invention for motion-sound velocity-noise coupling errors in real and complex marine environments.

[0111] The above description is merely a preferred embodiment of the present invention. Those skilled in the art can make several modifications and optimizations based on the above disclosure without departing from the basic principles described above. These modifications and optimizations should be considered within the scope of protection as understood by the present invention.

Claims

1. A method for underwater acoustic localization based on joint estimation of state and noise using adaptive filtering, characterized in that: Based on the extended Kalman filter framework, the motion state and equivalent sound speed error of the vehicle are augmented into the joint state vector to construct a motion-sound speed coupled state space vector. The time-varying observation noise variance is modeled as a random variable following an inverse gamma distribution. Initial values ​​of the motion-sound speed coupled state space vector, the initial value of the state covariance matrix, and the process noise covariance matrix are set, and the hyperparameters of the inverse gamma distribution of the observation noise variance are initialized. During the state prediction process, the state space vector and the state covariance matrix are estimated a priori to obtain the state prediction vector and the state prediction covariance matrix, and the hyperparameters of the inverse gamma distribution are updated over time to obtain the hyperparameter predictions of the inverse gamma distribution. During the variational iterative update process, based on ray acoustics theory, considering the spatiotemporal difference of the vehicle's position at the time of sound signal transmission and reception, a sound ray propagation motion compensation observation equation is constructed. In the acoustic propagation motion compensation observation equation, an acoustic path function is constructed based on the functional relationship between the two-way acoustic propagation time observation value and the state space vector. The acoustic path function is then expanded using a Taylor series at the current estimated value to obtain the Jacobian matrix. Variational Bayesian inference theory is introduced, and joint posterior estimation of state and noise hyperparameters is achieved through mean-field approximation theory and variational iterative update. The state distribution and noise parameter distribution are initialized, and the state distribution and noise parameter distribution are jointly updated through a fixed number of variational iterations to obtain posterior estimates of the state distribution and noise parameter distribution. A two-stage hierarchical architecture of state prediction and variational iterative update is adopted to achieve online joint posterior estimation of the vehicle's position, velocity, sound speed error, and observation noise variance.

2. The underwater acoustic localization method based on joint estimation of state and noise using adaptive filtering as described in claim 1, characterized in that: The state space vector of motion-sound speed coupling The calculation is as follows: ， In the formula, The three-dimensional coordinate position of the vehicle. For velocity vector, The sound speed error; the sound speed error The random walk model is used for modeling, and the calculation process is shown below: ； In the formula, The noise representing the sound velocity error follows a zero-mean Gaussian distribution; k is the kth filtering cycle.

3. The underwater acoustic localization method based on joint estimation of state and noise using adaptive filtering as described in claim 1, characterized in that: The time-varying variance of observation noise is modeled as a random variable following an inverse gamma distribution, where the observation noise follows a zero-mean Gaussian distribution. To observe the noise variance The inverse gamma conjugate prior distribution is assigned, and the calculation process is as follows: In the formula, α and β are the shape hyperparameter and scale hyperparameter, respectively. It follows an inverse gamma distribution, and exp represents the exponential operation. This is a gamma function.

4. The underwater acoustic localization method based on joint estimation of state and noise using adaptive filtering as described in claim 1, characterized in that: In the state prediction process, prior prediction estimation is performed on the state space vector and the state covariance matrix to obtain the state prediction vector. and state prediction covariance matrix The calculation is as follows: ； ； In the formula, Let be the state transition matrix of the motion state. The noise generated during the movement of the aircraft; In the process of predicting the hyperparameters of the inverse gamma distribution by updating them over time, a forgetting factor λ is introduced to update the hyperparameters of the inverse gamma distribution over time, as shown in the calculation below: ； ； In the formula, λ is the forgetting factor. and These represent the hyperparameter estimates of the inverse gamma distribution for the k-1 filter period, respectively. and These represent the hyperparameter predictions of the inverse gamma distribution with k filtering periods.

5. The underwater acoustic localization method based on joint estimation of state and noise using adaptive filtering according to claim 1, characterized in that: Based on ray acoustics theory, and considering the spatiotemporal differences in the spacecraft's position at the time of sound signal transmission and reception, a sound ray propagation motion compensation observation equation is constructed, as shown below: In the formula, This represents the observed two-way sound ray propagation time during the k-th filtering cycle. This is the true value of the two-way sound ray propagation time. To observe the noise variance, in the sound ray propagation motion compensation observation equation, a sound path function is constructed based on the functional relationship between the two-way sound ray propagation time observations and the state space vector, as shown below: ， In the formula, The two-way sound propagation time observation value of the j-th transponder in the k-th period is given. and These represent the vehicle's position at the moment the acoustic signal was transmitted and the vehicle's position at the moment the acoustic signal was received. Let j be the position of the j-th transponder. Let f be the sound velocity profile, and f be the sound propagation time calculation function based on ray acoustics theory.

6. The underwater acoustic localization method based on joint estimation of state and noise using adaptive filtering according to claim 5, characterized in that: In the sound ray propagation motion compensation observation equation, the sound path function is expanded using a Taylor series at the current estimated value, retaining the first-order terms to obtain the Jacobian matrix; the calculation is shown below: In the formula, D represents the number of observations of all available transponders at the current moment.

7. The underwater acoustic localization method based on joint estimation of state and noise using adaptive filtering as described in claim 1, characterized in that: During the variational iterative update process, the state distribution and noise parameter distribution are initialized, and then jointly updated through a fixed number of variational iterations. In the i-th variational iterative update process, the state distribution update adopts an extended Kalman filter framework, which includes updating the state prediction vector and the state prediction covariance matrix. The calculation process is shown below: ； ； ； ； In the formula, To observe the expected value of the noise variance, Let T be the identity matrix, and T be the matrix transpose operation. This is the Jacobian matrix term in the i-th variational iteration process of the k-th filtering cycle.

8. The underwater acoustic localization method based on joint estimation of state and noise using adaptive filtering as described in claim 7, characterized in that: The noise parameter distribution update includes updating the hyperparameter prediction of the inverse gamma distribution, and the calculation process is as follows: In the formula, is the value of the j-th row of the Jacobian matrix, and d is the number of all observations with available transponders at the current time.

9. The underwater acoustic localization method based on joint estimation of state and noise using adaptive filtering as described in claim 8, characterized in that: After the variational iterative update is completed, the posterior estimate of the current time step is output, resulting in the posterior estimates of the state space vector, the state covariance matrix, and the hyperparameters of the inverse gamma distribution; the calculations are shown below: ， ； ， ； In the formula, N is the number of iterations of the variational iteration, and j is the j-th transponder.

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