Maximum correlation entropy underwater autonomous vehicle state estimation method based on constraint optimization
By employing the constrained optimization maximum correlation entropy Kalman filter method, the problem of insufficient estimation accuracy and robustness of traditional methods in underwater non-Gaussian noise environments is solved, achieving efficient state estimation and making it suitable for complex tasks of underwater autonomous vehicles.
Patent Information
- Application Number
- CN202510922866.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-07-04
- Publication Date
- 2025-10-31
AI Technical Summary
Traditional Kalman filtering methods suffer from insufficient estimation accuracy and robustness in non-Gaussian noise environments in autonomous underwater vehicles (AUVs). Furthermore, the optimization of kernel bandwidth and step size is not adjusted for the characteristics of the underwater environment, resulting in high computational complexity and difficulty in meeting real-time requirements.
We employ the maximum correlation entropy Kalman filter method based on constraint optimization, and reconstruct the motion model through Cholesky decomposition, transforming the bivariate optimization problem into a univariate problem. By combining gradient ascent and fixed-point iteration methods, we achieve dynamic co-optimization of kernel bandwidth and step size, thereby improving the accuracy and robustness of state estimation.
It significantly improves the accuracy and stability of AUV state estimation in non-Gaussian noise environments, reduces computational complexity, and ensures the real-time performance and adaptability of the algorithm, making it suitable for tasks such as underwater pipeline inspection, marine resource exploration, and underwater target tracking.
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Figure CN120874341A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of underwater autonomous vehicle navigation and control technology, specifically involving a maximum correlation entropy underwater autonomous vehicle state estimation method based on constraint optimization. Background Technology
[0002] In the field of navigation and state estimation for autonomous underwater vehicles (AUVs), state estimation under non-Gaussian noise interference and dynamic constraints in complex underwater environments is an extremely challenging problem. Traditional Kalman filtering (KF) and its derivative algorithms (such as Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF)) are mostly based on the minimum mean square error (MSE) criterion, assuming that the system noise follows a Gaussian distribution. However, in real-world underwater environments (such as ocean turbulence, bioacoustic interference, multipath effects, and sensor noise), noise often exhibits significant non-Gaussian characteristics (such as impulse noise and heavy-tailed noise), leading to a substantial decrease in the estimation accuracy and robustness of traditional methods. Furthermore, AUVs face unique constraints during underwater operations, such as depth limitations, obstacle avoidance constraints, and limited energy, further increasing the complexity of state estimation.
[0003] The Maximum Correlation Entropy (MCC) criterion, as an emerging nonparametric estimation method, exhibits stronger robustness to non-Gaussian noise by measuring the local similarity between two random variables. The MCC-based Maximum Correlation Entropy Kalman Filter (MCKF), by introducing a Gaussian kernel function, can effectively suppress the influence of non-Gaussian noise. However, existing Maximum Correlation Entropy Kalman Filter (MCKF) methods have the following shortcomings in underwater AUV applications: 1. The optimization of kernel bandwidth and step size was not adjusted for the characteristics of the underwater environment (such as acoustic signal attenuation, multipath interference, etc.); 2. In traditional methods, the joint optimization of kernel bandwidth and step size is a bivariate optimization problem. Direct solution is prone to getting trapped in local optima and has high computational complexity, making it difficult to meet the real-time requirements of AUV.
[0004] To address the aforementioned bottlenecks, this invention designs an efficient constrained optimization strategy that transforms the bivariate optimization problem into a univariate problem, achieving dynamic collaborative optimization of kernel bandwidth and step size. This becomes a key technological breakthrough in improving the state estimation accuracy and robustness of AUVs in non-Gaussian noise environments. Summary of the Invention
[0005] The purpose of this invention is to provide a maximum correlation entropy underwater autonomous vehicle state estimation method based on constraint optimization, which solves the problem of poor estimation performance of existing state estimation methods in underwater non-Gaussian noise environments and under specific constraints.
[0006] The technical solution adopted in this invention is: a maximum correlation entropy underwater autonomous vehicle state estimation method based on constraint optimization, and the specific operation steps are as follows: Step 1, AUV Model Construction and Initialization: Construct an underwater motion model for the AUV and a measurement model with non-Gaussian noise; and... The estimated values of the AUV's state vectors, covariance matrix, parameter kernel bandwidth, and step size are initialized at each time step, and the iteration threshold is set. ; Step 2, AUV prior state estimation: Calculate the prior state based on the AUV underwater motion model and measurement model. The prior state estimate and covariance matrix at time t; Step 3, Reconstruct the AUV motion model: (This step involves reconstructing the motion model from step 2.) The prior state estimates and covariance matrix at time t are used to reconstruct the motion model through Cholesky decomposition; Step 4, Construct the AUV cost function: Based on the motion model decomposed and reconstructed in Step 3, design a dedicated AUV cost function based on the maximum correlation entropy criterion, and use the gradient ascent method to iteratively update the weight vector; Step 5, Constrained Bandwidth and Step Size Update: The bivariate problem is transformed into a univariate problem through constraint optimization, realizing the coordinated optimization of kernel bandwidth and step size; Step 6, AUV posterior state estimation: Based on the AUV motion equations and measurement equations obtained in Step 1, the prior predictions of the AUV obtained in Step 2, and the optimal bandwidth obtained in Step 5, the AUV posterior state is updated using a fixed-point iterative method. The posterior state estimate at time t; Step 7, Iteration Termination Judgment: Compare the estimated value of the current step with the estimated value of the previous step to determine the iteration termination. Step 8, Covariance Update: Update the posterior covariance matrix based on the posterior update value and covariance of the AUV model; Step 9: Repeat steps 2-8 until the AUV state estimation process is complete.
[0007] The invention is further characterized by: Step 1 is as follows: Step 1.1, assuming the AUV's motion state is constant, use and The motion state of an AUV is described by its position and velocity in the direction of motion, and the state vector of the AUV underwater motion model is defined. , express Position and velocity in direction, express Position and velocity in the direction; The equation of motion of the AUV is as shown in equation (1): (1) And a measurement model with non-Gaussian noise and underwater environmental interference, as shown in equation (2): (2) in, express The 4-dimensional state vector of the AUV at time t. express The 2D measurement vector at time t. and These represent the state transition matrix and observation matrix, which are unique to AUVs. and These are the AUV observation noise and measurement noise, which are both zero-mean and uncorrelated. ; It is observation noise The covariance matrix, It measures noise. The covariance matrix; It is an expectation; Step 1.2, let Given a small positive number The initial estimate is set as the threshold for stopping the iteration. and the initial covariance matrix Given an initial value for the kernel bandwidth and initial step size ; Step 2 is implemented as follows: Based on the prediction steps of Kalman filtering, the prior state estimate of the AUV can be obtained, as shown in equation (3), and the prior covariance matrix can be obtained, as shown in equation (4): (3) (4) Step 3 is as follows: Step 3.1, based on the AUV motion model given above, we can obtain... (5) in yes The identity matrix,
[0008] at the same time,
[0009] in, Through the The matrix obtained by performing Cholesky decomposition; Step 3.2, multiply equation (5) on the left. get: (6) make , , The reconstructed AUV motion model is obtained: (7) Step 4 shall be implemented in the following manner: Step 4.1: Based on the reconstructed AUV motion model, the error can be obtained. ,in, yes The One element, yes The One element; Step 4.2, Correlation entropy measures the local similarity between two random variables. Given two random variables X and Y, their correlation entropy is: (8) in It is a translation-invariant Mercer kernel. yes The joint distribution function. Generally, the Gaussian kernel function is... An ideal choice, its expression is: (9) in, Represents the core bandwidth; Step 4.3, compared to the minimum mean square error criterion (MSE), this method proposes a method based on the maximum correlation entropy criterion (MCC) to calculate the AUV-specific cost function based on the maximum correlation entropy criterion: (10) Step 4.4: Apply the gradient ascent method to the weight vector of the AUV. Update: (11) Step 4.5, since the step size and kernel bandwidth change synchronously from large to small values, the selection of optimization parameters also follows this synchronous change, so (11) is updated to: (12) Step 4.6, using Subtract both sides of equation (12) and square them, then let We can obtain: (13) in,
[0010] in, Noise-free prior error ; Step 5 is as follows: Step 5.1, by minimizing It can make After experiencing the steepest decay, But minimize This is an unconstrained multi-parameter optimization problem, which is extremely difficult to solve directly. Therefore, this method constructs a step size and kernel bandwidth constraint: (14) Step 5.2: By constructing the constraints, the original bivariate optimization problem is transformed into a univariate optimization problem. The expression after the transformation to univariate is: (15) Step 5.3, find the answer to (15) regarding... Partial derivative: (16) Step 5.4, let After calculation, we get: (17) In order to eliminate (17) ,make ; Step 5.5: To ensure a smooth update of the core bandwidth, this method ultimately adopts the following update strategy: (18) in,
[0011] Step 5.6: Further calculate the step size based on the constructed constraint condition (14). ; Step 6 shall be implemented in the following manner: Step 6.1: Obtain the updated values of each state vector based on steps 3 and 5. (19) (20) (twenty one) (twenty two) (twenty three) (twenty four) in, , It is a diagonal matrix, and the elements on the diagonal are determined by the Gaussian kernel function. Calculated; m、n These are measurement vectors. and state vector The dimension; This is the Kalman gain matrix, used to update the state estimate; Step 6.2: Obtain the posterior state estimate based on the updated values of each state vector and the prior state estimate; (25) Step 7 is as follows: If condition (26) is met, then stop the iteration and let ;otherwise, Continue iterating through step 4; (26) Step 8 shall be implemented in the following manner: Update the posterior covariance matrix, let Then return to step 2; (27) The beneficial effects of this invention are: 1. By introducing the maximum correlation entropy criterion (MCC) to replace the traditional minimum mean square error criterion (MSE), the correlation entropy is used to measure the local similarity of random variables, which significantly enhances the ability to suppress impulse noise and heavy-tailed distributed noise (such as sonar interference and multipath effects) in the underwater environment, and solves the problem of decreased estimation accuracy and robustness of traditional Kalman filtering in underwater non-Gaussian noise environment.
[0012] 2. By combining constrained optimization strategies, the bivariate optimization problem of kernel bandwidth and step size is transformed into a univariate problem. The gradient ascent method and fixed-point iteration method are used to achieve dynamic synergistic adjustment of both. The kernel bandwidth adaptively adjusts the local measurement range of the relevant entropy to adapt to changes in the underwater environment, while the step size optimizes the iterative convergence speed. The synergistic effect of these two methods significantly improves the accuracy and stability of AUV state estimation.
[0013] 3. By reconstructing the AUV motion model through Cholesky decomposition, the complex underwater nonlinear problem is transformed into an optimization problem in linear space, significantly reducing the computational complexity of high-dimensional optimization. Simultaneously, it avoids the tendency of traditional bivariate optimization to get trapped in local optima, ensuring the algorithm's computational efficiency and reliability in real-time underwater operations.
[0014] 4. The algorithm is specifically optimized for the characteristics of AUV underwater operations. By iteratively updating the posterior state estimate and covariance matrix, it can effectively handle the dynamic changes in the state of the AUV system, providing a high-precision state estimation solution for complex tasks such as underwater pipeline inspection, marine resource exploration, and underwater target tracking.
[0015] 5. The algorithm of this invention fully considers the special characteristics of the underwater environment and significantly improves the adaptability and engineering practical value of AUV in different underwater operation scenarios through adaptive parameter adjustment. Attached Figure Description
[0016] Figure 1 This is a global flowchart of the maximum correlation entropy underwater autonomous vehicle state estimation method based on constraint optimization of the present invention; Figure 2 This invention relates to the maximum correlation entropy (MCKF) state estimation method for autonomous underwater vehicles (AUVs) based on constrained optimization, and its application in state estimation within a simulation scenario of uniform motion of an AUV. State estimation result diagram; Figure 3 This is a comparison chart of the mean square error (MSE) of the total direction in state estimation of the maximum correlation entropy underwater autonomous vehicle (AUV) based on the constraint optimization-based maximum correlation entropy Kalman filtering method (MCKF) in a simulation scenario of uniform motion of an AUV. Detailed Implementation
[0017] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments, so that the advantages and features of the present invention can be more readily understood by those skilled in the art.
[0018] Example 1 To verify the effectiveness of this invention, a typical motion simulation scenario of an autonomous underwater vehicle (AUV) was constructed, with a sampling period of 1 second, 1000 Monte Carlo simulations, and a smoothing factor of 0.99. The specific motion process of the AUV target is as follows: starting from the origin, it moves in uniform linear motion on a two-dimensional plane. During the motion, due to the uncertainty of the marine environment, the target trajectory fluctuates due to process noise interference. Simultaneously, when the sonar sensor collects target position observation data, impulse noise is superimposed to simulate signal interference in the actual scene. This is implemented according to the following steps: Step 1, AUV Model Construction and Initialization: Construct an underwater motion model for the AUV and a measurement model with non-Gaussian noise; and... The estimated values, covariance matrix, parameter kernel bandwidth, and step size of the AUV state model at each time step are initialized, and the iteration threshold is set. ; The specific steps are as follows: Step 1.1, assuming the AUV's motion state is constant, use and The motion state of an AUV is described by its position and velocity in a certain direction; the state value of an AUV is... The equation of motion for an AUV is as follows:
[0019] in, It is a state transition matrix unique to AUVs. It is the sampling interval and the observation noise. The covariance is:
[0020] in, It is to observe the noise intensity; The measurement model with non-Gaussian noise and underwater environmental interference is as follows:
[0021] in, Indicates time Two-dimensional measurement vector, This represents the observation matrix unique to AUVs, measuring noise. The covariance is:
[0022] in, It measures noise intensity. and These are AUV observation noise and measurement noise, which are both zero-mean and uncorrelated. Step 1.2: Initialize the relevant parameters: , , , ,
[0023] Step 2, AUV prior state estimation: Calculate the prior state based on the AUV motion model and measurement model. The prior state estimate and covariance matrix at time t; Based on the prediction steps of Kalman filtering, the prior state estimate of the AUV can be obtained.
[0024] The prior covariance matrix is as follows:
[0025] Step 3, Reconstruct the AUV motion model: (This step involves reconstructing the motion model from step 2.) The prior state estimates and covariance matrix at time t are used to reconstruct the motion model through Cholesky decomposition; The specific steps are as follows: Step 3.1, based on the AUV motion model given above, we can obtain...
[0026] in yes The identity matrix,
[0027] at the same time,
[0028] in Through the The matrix obtained by performing Cholesky decomposition; Multiply the formulas in steps 3.2 and 3.1 on the left. get:
[0029] make , , The reconstructed AUV motion model is obtained:
[0030] Step 4, Construct the AUV cost function: Based on the motion model decomposed and reconstructed in Step 3, design a dedicated AUV cost function based on the maximum correlation entropy criterion, and iteratively update the weight vector using the gradient ascent method; specifically, implement it according to the following steps: Step 4.1: Based on the reconstructed AUV motion model, the error can be obtained. ,in, yes The One element, yes The One element; Step 4.2, Correlation entropy measures the local similarity between two random variables. Given two random variables X and Y, their correlation entropy is:
[0031] in It is a translation-invariant Mercer kernel. yes The joint distribution function. Generally, the Gaussian kernel function is... An ideal choice, its expression is
[0032] in, Represents the core bandwidth; Step 4.3: Compared with the minimum mean square error criterion (MSE), this method proposes a method based on the maximum correlation entropy criterion (MCC) to calculate the AUV-specific cost function based on the maximum correlation entropy criterion; Step 4.4: Apply the gradient ascent method to the weight vector of the AUV. Update:
[0033] Step 4.5: Since the step size and kernel bandwidth change synchronously from large to small values, the selection of optimization parameters also follows this synchronous change. Therefore, the above formula is updated as follows:
[0034] Step 4.6, using Subtract both sides of the above equation and square them, then let... We can obtain:
[0035] in,
[0036] in, Noise-free prior error ; Step 5, Constrained Bandwidth and Step Size Update: The bivariate problem is transformed into a univariate problem through constraint optimization, realizing the coordinated optimization of kernel bandwidth and step size; Step 6, AUV posterior state estimation: Based on the AUV motion equations and measurement equations obtained in Step 1, the prior predictions of the AUV obtained in Step 2, and the optimal bandwidth obtained in Step 5, the AUV posterior state is updated using a fixed-point iterative method. The posterior state estimate at time t; Step 6.1: Based on the updated values of each state vector of the AUV obtained in Steps 3 and 5,
[0037]
[0038]
[0039] Step 6.2: Obtain the posterior state estimate based on the updated values of each AUV model and the prior state estimate;
[0040] Step 7, Iteration Termination Judgment: Compare the estimated value of the current step with the estimated value of the previous step to determine the iteration termination. If the following condition is met, then stop the iteration and let ;otherwise, Continue iterating through step 4;
[0041] Step 8, Covariance Update: Update the posterior covariance matrix based on the posterior update value and covariance of the AUV model; Update the posterior covariance matrix, let Then return to step 2;
[0042] Step 9: Repeat steps 2-8 until the AUV state estimation process is complete. The final state estimation result is shown in the figure below. Figure 2 As shown in the figure, the final mean square error plot is as follows. Figure 3 As shown.
[0043] In Example 1, the maximum correlation entropy underwater autonomous vehicle state estimation method based on constraint optimization demonstrated superior performance. For example... Figure 2 As shown, under non-Gaussian noise interference, the estimated trajectory of the proposed method is closer to the true value than the traditional maximum correlation entropy Kalman filter (MCKF) method, especially in the mid- and late-stages. Figure 3 As can be seen, the proposed method consistently yields a lower error curve than the traditional Maximum Correlation Entropy Kalman Filter (MCKF) method, with the error range remaining stable between 50 and 150, while the MCKF method's error exceeds 200. Within the 600-1000 time step range, although the error difference fluctuates slightly, the constraint-optimized maximum correlation entropy autonomous underwater vehicle (AUV) state estimation method maintains its accuracy advantage. With increasing time steps, the constraint-optimized maximum correlation entropy AUV state estimation method does not exhibit performance degradation; its mean square error (MSE) curve remains consistently stable and significantly lower than that of the traditional method.
[0044] Example 2 This invention presents a maximum correlation entropy underwater autonomous vehicle (AUV) state estimation method based on constraint optimization. The method involves constructing an AUV underwater motion model; initializing model parameters; reconstructing the motion model through Cholesky decomposition; designing a dedicated AUV cost function based on maximum correlation entropy; iteratively updating the weight vector using the gradient ascent method; transforming the bivariate problem into a univariate problem through constraint optimization, achieving coordinated optimization of kernel bandwidth and step size; and finally outputting the posterior state estimate and covariance matrix.
[0045] Example 3 This invention presents a maximum correlation entropy underwater autonomous vehicle state estimation method based on constraint optimization, the specific operation steps of which are as follows: Step 1: Construct an underwater motion model for the AUV and a measurement model with non-Gaussian noise; and... The estimated values of the AUV's state vectors, covariance matrix, parameter kernel bandwidth, and step size are initialized at each time step, and the iteration threshold is set. ; Step 2: Calculate based on the AUV underwater motion model and measurement model. The prior state estimate and covariance matrix at time t; Step 3, in step 2 The prior state estimates and covariance matrix at time t are used to reconstruct the motion model through Cholesky decomposition; Step 4: Based on the motion model decomposed and reconstructed in Step 3, design a dedicated cost function for AUV based on the maximum correlation entropy criterion, and iteratively update the weight vector using the gradient ascent method. Step 5: Transform the bivariate problem into a univariate problem through constraint optimization, and achieve synergistic optimization of kernel bandwidth and step size; Step 6: Based on the AUV underwater motion model and measurement model obtained in Step 1, the prior prediction value of the AUV obtained in Step 2, and the optimal kernel bandwidth obtained in Step 5, update the kernel bandwidth using the fixed-point iteration method. The posterior state estimate at time t; Step 7: Compare the estimated value of the current step with the estimated value of the previous step to determine the termination of the iteration; Step 8: Update the posterior covariance matrix based on the posterior update values and covariance of the AUV model; Step 9: Repeat steps 2-8 until the AUV state estimation process is complete.
[0046] Example 4 Based on Example 3, step 1 is as follows: Step 1.1, set the state vector of the AUV underwater motion model as follows: , express Position and velocity in direction, express Position and velocity in the direction; the equation of motion of the AUV is as shown in equation (1): (1) And a measurement model with non-Gaussian noise and underwater environmental interference, as shown in equation (2): (2) in, express The 4-dimensional state vector of the AUV at time t. express The 2D measurement vector at time t. and These represent the state transition matrix and observation matrix, which are unique to AUVs. and These are the AUV observation noise and measurement noise, which are both zero-mean and uncorrelated. , It is observation noise The covariance matrix, It measures noise. The covariance matrix; It is an expectation; Step 1.2, let Given a positive number The initial estimate is set as the threshold for stopping the iteration. and the initial covariance matrix Given an initial value for the kernel bandwidth and initial step size .
[0047] Example 5 Based on Example 4, step 2 is as follows: Based on the prediction steps of Kalman filtering, the prior state estimate of the AUV is obtained as shown in equation (3); the prior covariance matrix is shown in equation (4): (3) (4).
[0048] Step 3 is as follows: Step 3.1, based on the AUV underwater motion model, obtain (5) in, yes The identity matrix,
[0049] at the same time,
[0050] in, Through the The matrix obtained by performing Cholesky decomposition; Step 3.2, multiply equation (5) on the left. get: (6) make , , The reconstructed AUV motion model is obtained: (7).
[0051] Example 6 Based on Example 5, step 4 is as follows: Step 4.1: Based on the reconstructed AUV motion model, obtain the error. ,in, yes The One element, yes The One element; Step 4.2, Correlation entropy measures the local similarity between two random variables. Given two random variables X and Y, their correlation entropy is: (8) in, It is a translation-invariant Mercer kernel. yes The joint distribution function; the Gaussian kernel function is An ideal choice, its expression is: (9) in, Represents the core bandwidth; Step 4.3: Calculate the AUV-specific cost function based on the maximum correlation entropy criterion (MCC) using the MCC method: (10) Step 4.4: Apply the gradient ascent method to the weight vector of the AUV. Update: (11) Step 4.5: Since the step size and kernel bandwidth change synchronously from large to small values, the selection of optimization parameters also follows this synchronous change. Therefore, (11) is updated as follows: (12) Step 4.6, using Subtract both sides of equation (12) and square them, then let ,get: (13) in,
[0052] in, Noise-free prior error .
[0053] Step 5 is as follows: Step 5.1, by minimizing Make After experiencing the steepest decay, But minimize This is an unconstrained multi-parameter optimization problem, which is extremely difficult to solve directly. Therefore, a constraint condition of step size and kernel bandwidth is constructed: (14) Step 5.2: By constructing the constraints, the original bivariate optimization problem is transformed into a univariate optimization problem. The expression after the transformation to univariate is: (15) Step 5.3, calculate the equation (15) with respect to... Partial derivative: (16) Step 5.4, let After calculation, we get: (17) In order to eliminate formula (17) ,make ; Step 5.5: To ensure a smooth update of the core bandwidth, the following update strategy is ultimately adopted: (18) in, ; Step 5.6: Further calculate the step size based on the established constraints. .
[0054] Step 6 is as follows: Step 6.1: Based on the updated values of each state variable obtained in Steps 3 and 5, (19) (20) (twenty one) (twenty two) (twenty three) (twenty four) Step 6.2: Obtain the posterior state estimate based on the updated values of each state variable and the prior state estimate; (25).
[0055] 9. The maximum correlation entropy underwater autonomous vehicle state estimation method based on constraint optimization according to claim 1, characterized in that step 7 is as follows: If the condition of formula (26) is met, then stop the iteration and let ;otherwise, Continue iterating through step 4; (26).
[0056] Step 8 is as follows: Update the posterior covariance matrix, let Then return to step 2; (27).
Claims
1. A state estimation method for underwater autonomous vehicles based on maximum correlation entropy using constrained optimization, characterized in that, Construct an underwater motion model for an AUV; initialize model parameters; reconstruct the motion model through Cholesky decomposition; design a dedicated cost function for AUVs based on maximum correlation entropy; iteratively update the weight vector using the gradient ascent method; transform the bivariate problem into a univariate problem through constraint optimization, achieving coordinated optimization of kernel bandwidth and step size; finally, output the posterior state estimate and covariance matrix.
2. The maximum correlation entropy underwater autonomous vehicle state estimation method based on constrained optimization according to claim 1, characterized in that, The specific operating steps are as follows: Step 1: Construct an underwater motion model for the AUV and a measurement model with non-Gaussian noise; and... The estimated values of the AUV's state vectors, covariance matrix, parameter kernel bandwidth, and step size are initialized at each time step, and the iteration threshold is set. ; Step 2: Calculate based on the AUV underwater motion model and measurement model. The prior state estimate and covariance matrix at time t; Step 3, in step 2 The prior state estimates and covariance matrix at time t are used to reconstruct the motion model through Cholesky decomposition; Step 4: Based on the motion model decomposed and reconstructed in Step 3, design a dedicated cost function for AUV based on the maximum correlation entropy criterion, and iteratively update the weight vector using the gradient ascent method. Step 5: Transform the bivariate problem into a univariate problem through constraint optimization, and achieve synergistic optimization of kernel bandwidth and step size; Step 6: Based on the AUV underwater motion model and measurement model obtained in Step 1, the prior prediction value of the AUV obtained in Step 2, and the optimal kernel bandwidth obtained in Step 5, update the kernel bandwidth using the fixed-point iteration method. The posterior state estimate at time t; Step 7: Compare the estimated value of the current step with the estimated value of the previous step to determine the termination of the iteration; Step 8: Update the posterior covariance matrix based on the posterior update values and covariance of the AUV model; Step 9: Repeat steps 2-8 until the AUV state estimation process is complete.
3. The maximum correlation entropy underwater autonomous vehicle state estimation method based on constrained optimization according to claim 2, characterized in that, Step 1 is as follows: Step 1.1, set the state vector of the AUV underwater motion model as follows: , express Position and velocity in direction, express Position and velocity in the direction; the equation of motion of the AUV is as shown in equation (1): （1） And a measurement model with non-Gaussian noise and underwater environmental interference, as shown in equation (2): （2） in, express The 4-dimensional state vector of the AUV at time t. express The 2D measurement vector at time t. and These represent the state transition matrix and observation matrix, which are unique to AUVs. and These are the AUV observation noise and measurement noise, which are both zero-mean and uncorrelated. , It is observation noise The covariance matrix, It measures noise. The covariance matrix; It is an expectation; Step 1.2, let Given a positive number The initial estimate is set as the threshold for stopping the iteration. and the initial covariance matrix Given an initial value for the kernel bandwidth and initial step size .
4. The maximum correlation entropy underwater autonomous vehicle state estimation method based on constrained optimization according to claim 3, characterized in that, Step 2 is as follows: Based on the prediction steps of Kalman filtering, the prior state estimate of the AUV is obtained as shown in equation (3); the prior covariance matrix is shown in equation (4): (3) (4)。 5. The maximum correlation entropy underwater autonomous vehicle state estimation method based on constrained optimization according to claim 4, characterized in that, Step 3 is as follows: Step 3.1, based on the AUV underwater motion model, obtain (5) in, yes The identity matrix, at the same time, in, Through the The matrix obtained by performing Cholesky decomposition; Step 3.2, multiply equation (5) on the left. get: (6) make , , The reconstructed AUV motion model is obtained: (7)。 6. The maximum correlation entropy underwater autonomous vehicle state estimation method based on constrained optimization according to claim 5, characterized in that, Step 4 is as follows: Step 4.1: Based on the reconstructed AUV motion model, obtain the error. ,in, yes The One element, yes The One element; Step 4.2, Correlation entropy measures the local similarity between two random variables. Given two random variables X and Y, their correlation entropy is: (8) in, It is a translation-invariant Mercer kernel. yes The joint distribution function; the Gaussian kernel function is An ideal choice, its expression is: (9) in, Represents the core bandwidth; Step 4.3: Calculate the AUV-specific cost function based on the maximum correlation entropy criterion (MCC) using the MCC method: (10) Step 4.4: Apply the gradient ascent method to the weight vector of the AUV. Update: (11) Step 4.5: Since the step size and kernel bandwidth change synchronously from large to small values, the selection of optimization parameters also follows this synchronous change. Therefore, (11) is updated as follows: (12) Step 4.6, using Subtract both sides of equation (12) and square them, then let ,get: (13) in, in, No noise prior error .
7. The maximum correlation entropy underwater autonomous vehicle state estimation method based on constrained optimization according to claim 6, characterized in that, Step 5 is as follows: Step 5.1, by minimizing Make After experiencing the steepest decay, But minimize This is an unconstrained multi-parameter optimization problem, which is extremely difficult to solve directly. Therefore, a constraint condition of step size and kernel bandwidth is constructed: (14) Step 5.2: By constructing the constraints, the original bivariate optimization problem is transformed into a univariate optimization problem. The expression after the transformation to univariate is: (15) Step 5.3, calculate the equation (15) with respect to... Partial derivative: (16) Step 5.4, let After calculation, we get: (17) In order to eliminate formula (17) ,make ; Step 5.5: To ensure a smooth update of the core bandwidth, the following update strategy is ultimately adopted: (18) in, ; Step 5.6: Further calculate the step size based on the established constraints. .
8. The maximum correlation entropy underwater autonomous vehicle state estimation method based on constrained optimization according to claim 7, characterized in that, Step 6 is as follows: Step 6.1: Based on the updated values of each state variable obtained in Steps 3 and 5, (19) (20) (21) (22) (23) (24) in, , It is a diagonal matrix, and the elements on the diagonal are determined by the Gaussian kernel function. Calculated; m、n These are measurement vectors. and state vector The dimension; This is the Kalman gain matrix, used to update the state estimate; Step 6.2: Obtain the posterior state estimate based on the updated values of each state variable and the prior state estimate; (25)。 9. The maximum correlation entropy underwater autonomous vehicle state estimation method based on constrained optimization according to claim 1, characterized in that, Step 7 is as follows: If the condition of formula (26) is met, then stop the iteration and let ; otherwise, Continue iterating through step 4; (26)。 10. The maximum correlation entropy underwater autonomous vehicle state estimation method based on constrained optimization according to claim 9, characterized in that, Step 8 is as follows: Update the posterior covariance matrix, let Then return to step 2; (27)。