Underwater navigation adaptive filtering method based on krarmer lower bound constraint

Abstract

The application discloses an underwater navigation adaptive filtering method based on Cramer-Rao lower bound constraint, belongs to the technical field of underwater navigation and positioning, and is used for underwater navigation and comprising the following steps: for a discrete time system, a non-Gaussian measurement noise is modeled as a Gaussian scale mixture model; a robust innovation sequence and a weighting factor are obtained through variational iteration update, and are used for correcting a measurement information matrix and updating a posterior Cramer-Rao lower bound; and an experience estimation and the Cramer-Rao lower bound constraint are combined to adaptively adjust a process noise covariance matrix, so as to optimize state prediction. Through the closed-loop feedback and decision mechanism taking the Cramer-Rao lower bound as a theoretical performance scale, the adaptive process is broken through from the open-loop estimation depending on experience data to the intelligent optimization anchored and calibrated by the theoretical optimality criterion, so that precise decoupling and cooperation of time-varying noise tracking and abnormal interference suppression are realized, and finally the performance of underwater high-precision and robust navigation and positioning is improved.

Description

Technical Field

[0001] This invention discloses an adaptive filtering method for underwater navigation based on the Cramero lower bound constraint, belonging to the field of underwater navigation and positioning technology. Background Technology

[0002] With the increasing application of autonomous underwater vehicles (AUVs) in marine resource development and scientific research, the fusion of underwater multi-source sensors (such as LBL / INS) has become a key technology for integrated navigation. However, the complex underwater acoustic environment presents two major challenges: non-Gaussian heavy-tailed noise (such as outliers caused by multipath effects) and the time-varying nature of noise statistical characteristics (such as disturbance fluctuations caused by sea state changes). Existing technologies often address these issues through robust filtering, adaptive filtering, or a fusion of both. Adaptive filtering, such as Sage-Husa, uses the innovation sequence to back-calculate the noise covariance matrix to track noise changes, but it is essentially an empirical estimate based on historical data and lacks theoretical constraints. In non-Gaussian environments, individual large outliers are easily misjudged as an overall increase in system noise, leading to "expansion" or even divergence in the covariance estimate, and exhibiting adjustment lag. Therefore, for the current complex coupled environment of underwater time-varying noise and non-Gaussian noise, there is a lack of a closed-loop control mechanism that can both utilize data for adaptive tracking and utilize theoretical boundaries to prevent blind divergence.

[0003] To address the problem of strong coupling between non-Gaussian heavy-tailed noise and time-varying noise statistical characteristics in complex underwater dynamic environments, existing adaptive filtering methods such as Sage-Husa based on innovation feedback are essentially unconstrained open-loop empirical estimations. They lack theoretical benchmarks based on physical models and information content to monitor and limit the update range of the covariance matrix in real time. This makes it easy to misjudge abnormal deviations as increased system noise when encountering strong outlier interference, thus causing technical problems such as irrational expansion of noise covariance matrix estimation, parameter drift, and filter divergence. Summary of the Invention

[0004] The purpose of this invention is to provide an adaptive filtering method for underwater navigation based on Cramerlow lower bound constraints, in order to solve the problem that in the prior art, there is a lack of theoretical benchmarks based on physical models and information to monitor and limit the update range of the covariance matrix in real time. This leads to the easy misjudgment of abnormal deviations as increased system noise when encountering strong outlier interference, thereby causing irrational expansion of noise covariance matrix estimation, parameter drift and filter divergence.

[0005] The underwater navigation adaptive filtering method based on the Cramero lower bound constraint includes:

[0006] S1. Establish the state equation and observation equation of the discrete-time system, and represent the measurement noise as a Gaussian scale mixture model. Based on the Gaussian scale mixture model, represent the marginal probability density function of the measurement noise as an integral form of the conditional Gaussian distribution and the gamma distribution.

[0007] S2. Predict the state vector and state covariance matrix using the process noise covariance matrix. Set an iteration number threshold at each time step and perform variational iterative updates. The variational iterative updates include updating the innovation covariance matrix, calculating the expectation of the squared measurement residuals, and updating the weighting factors of the auxiliary variables. After reaching the iteration number threshold, the final robust innovation sequence and the final weighting factors are obtained.

[0008] S3. Use the Fisher information matrix to predict the information matrix, use the final weighting factor to calculate the non-Gaussian corrected measurement information matrix, and use the predicted information matrix and the non-Gaussian corrected measurement information matrix to update the posterior Cramer-Rao lower bound.

[0009] S4. Calculate the empirical estimate of the process noise covariance matrix at the previous time step using the final robust innovation sequence. Then, combine the improved Saghusa adaptive filter to calculate the empirical estimate of the process noise covariance matrix at the current time step. Construct a constraint tolerance based on the Cramero lower bound. Based on the constraint tolerance and the empirical estimate of the process noise covariance matrix at the current time step, calculate the process noise covariance matrix after tolerance constraint processing. Return the process noise covariance matrix after tolerance constraint processing to step S2 to predict the state vector at the next time step.

[0010] S1 includes S1.1, acquiring the three-axis acceleration and angular velocity of the inertial navigation system, and calculating the motion state of the autonomous underwater vehicle;

[0011] By deploying acoustic beacons at known locations on the seabed and using a long baseline positioning system, the distance between the autonomous underwater vehicle (AUV) and the acoustic beacons is measured, and the AUV's position is determined through geometric intersection.

[0012] Select velocity error, attitude error, position error, accelerometer bias, and gyroscope drift in sequence, and define the state vector in the Northeast-Eastern Sky navigation coordinate system. ;

[0013] ;

[0014] Based on inertial navigation systems and long baseline positioning systems, the state equations and observation equations of the discrete-time system are established:

[0015] ;

[0016] In the formula, The residual between the long-baseline measurements and the inertial navigation system predictions. Here is the state transition matrix. For the measurement matrix, For noise driving matrix, For process noise, Follows a pattern with a mean of 0 and a covariance of 0. The distribution, for The process noise covariance matrix at time step 1. To measure noise, For a moment.

[0017] S1 includes S1.2, constructing a hierarchical probability model for non-Gaussian noise, assuming... Following the Student-t distribution, Represented as a Gaussian scale mixture model, with a hierarchical structure defined:

[0018] ;

[0019] ;

[0020] In the formula, As an auxiliary random variable, Follows a gamma distribution. For degrees of freedom, To conform to the distribution sign, To measure the noise covariance matrix, It follows a Gaussian distribution. It is a gamma distribution;

[0021] Based on the hierarchical structure, marginal probability density function Expressed as the integral form of the conditional Gaussian distribution and the gamma distribution:

[0022] .

[0023] S2 includes, S2.1, utilizing Process noise covariance at time step Perform standard time updates:

[0024] ;

[0025] ;

[0026] In the formula, for The predicted state vector at time t. for The posterior state estimate vector at time t. for The predicted state covariance matrix at time t. for The posterior state covariance matrix at time t.

[0027] S2 includes, S2.2, in At any given time, set a threshold for the number of iterations. ,conduct The next fixed-point iteration includes updating the information covariance. :

[0028] ;

[0029] ;

[0030] In the formula, for The equivalent measurement noise covariance matrix in the i-th iteration of the time-matter variational iteration. For the number of iterations, , for Time of the first Weighting factors of auxiliary variables in the next iteration It is the transpose symbol;

[0031] Calculate the expected value of the squared measurement residuals :

[0032] ;

[0033] In the formula, The trace operator for matrices;

[0034] Update the weighting factors of the auxiliary variables:

[0035] ;

[0036] In the formula, To measure dimension, for Time of the first The weighting factor of the auxiliary variable in the next iteration.

[0037] S2 includes S2.3, and the final robust innovation sequence obtained after iterative convergence. and final weighting factor :

[0038] ;

[0039] ;

[0040] In the formula, for The state estimation vector at time t, This is the final robust state estimation vector after iterative convergence.

[0041] S3 includes, S3.1, using the recursive properties of the Fisher information matrix to calculate... Predictive information matrix at time step :

[0042] ;

[0043] In the formula, Here is the state transition matrix. for The posterior Fisher information matrix at time step;

[0044] S3 includes S3.2, calculating the measurement information matrix after non-Gaussian correction. :

[0045] .

[0046] S3 includes S3.3 and updates. A posteriori Clamello's lower bound :

[0047] ;

[0048] ;

[0049] In the formula, for The posterior Fisher information matrix at time step;

[0050] Will As The performance lower bound of the time-state estimation covariance.

[0051] S4 includes S4.1, an empirical estimate of the process noise covariance at time k using an improved Saghusa adaptive filter. :

[0052] ;

[0053] In the formula, Forgetting factor, For robust new information;

[0054] S4 includes, S4.2, constructing a constraint tolerance based on Cramer-Rao's lower bound. :

[0055] ;

[0056] In the formula, For fault tolerance coefficient, The trace operator for matrices. for The inverse of the prediction information matrix at time step.

[0057] S4 includes S4.3, hour, ; hour, , For the revised version ;

[0058] S4 includes, S4.4, and will Return to step S2.1 and predict the state vector at the next time step.

[0059] Compared with the prior art, the present invention has the following beneficial effects: By introducing a closed-loop feedback and decision-making mechanism with the Cramerlow lower bound as the performance benchmark, the present invention breaks through the open-loop estimation that relies on empirical data to intelligent optimization that is subject to closed-loop anchoring and calibration based on theoretical optimality criteria. This achieves precise decoupling and coordination of time-varying noise tracking and abnormal interference suppression, and ultimately improves the performance of underwater high-precision robust navigation and positioning. Attached Figure Description

[0060] Figure 1 This is a flowchart of the technology of this invention;

[0061] Figure 2 This is a schematic diagram of the "figure-eight" maneuver trajectory of an AUV in simulation;

[0062] Figure 3 This is a graph showing the change in eastward position error over time.

[0063] Figure 4 This is a graph showing the change in northward position error over time.

[0064] Figure 5 This is a graph showing the change in celestial position error over time.

[0065] Figure 6 It is a graph showing the change in measurement confidence over time;

[0066] Figure 7 It is a graph showing how the performance lower bound changes over time;

[0067] Figure 8 It is a bar chart comparing the RMS positional errors in each direction;

[0068] Figure 9 yes Figure 2 Enlarged view of the FD region. Detailed Implementation

[0069] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention are described clearly and completely below. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0070] The underwater navigation adaptive filtering method based on the Cramero lower bound constraint includes:

[0071] S1. Establish the state equation and observation equation of the discrete-time system, and represent the measurement noise as a Gaussian scale mixture model. Based on the Gaussian scale mixture model, represent the marginal probability density function of the measurement noise as an integral form of the conditional Gaussian distribution and the gamma distribution.

[0072] S2. Predict the state vector and state covariance matrix using the process noise covariance matrix. Set an iteration number threshold at each time step and perform variational iterative updates. The variational iterative updates include updating the innovation covariance matrix, calculating the expectation of the squared measurement residuals, and updating the weighting factors of the auxiliary variables. After reaching the iteration number threshold, the final robust innovation sequence and the final weighting factors are obtained.

[0073] S3. Use the Fisher information matrix to predict the information matrix, use the final weighting factor to calculate the non-Gaussian corrected measurement information matrix, and use the predicted information matrix and the non-Gaussian corrected measurement information matrix to update the posterior Cramer-Rao lower bound.

[0074] S4. Calculate the empirical estimate of the process noise covariance matrix at the previous time step using the final robust innovation sequence. Then, combine the improved Saghusa adaptive filter to calculate the empirical estimate of the process noise covariance matrix at the current time step. Construct a constraint tolerance based on the Cramero lower bound. Based on the constraint tolerance and the empirical estimate of the process noise covariance matrix at the current time step, calculate the process noise covariance matrix after tolerance constraint processing. Return the process noise covariance matrix after tolerance constraint processing to step S2 to predict the state vector at the next time step.

[0075] S1 includes S1.1, acquiring the three-axis acceleration and angular velocity of the inertial navigation system, and calculating the motion state of the autonomous underwater vehicle;

[0076] By deploying acoustic beacons at known locations on the seabed and using a long baseline positioning system, the distance between the autonomous underwater vehicle (AUV) and the acoustic beacons is measured, and the AUV's position is determined through geometric intersection.

[0077] Select velocity error, attitude error, position error, accelerometer bias, and gyroscope drift in sequence, and define the state vector in the Northeast-Eastern Sky navigation coordinate system. ;

[0078] ;

[0079] Based on inertial navigation systems and long baseline positioning systems, the state equations and observation equations of the discrete-time system are established:

[0080] ;

[0081] In the formula, The residual between the long-baseline measurements and the inertial navigation system predictions. Here is the state transition matrix. For the measurement matrix, For noise driving matrix, For process noise, Follows a pattern with a mean of 0 and a covariance of 0. The distribution, for The process noise covariance matrix at time step 1. To measure noise, For a moment.

[0082] S1 includes S1.2, constructing a hierarchical probability model for non-Gaussian noise, assuming... Following the Student-t distribution, Represented as a Gaussian scale mixture model, with a hierarchical structure defined:

[0083] ;

[0084] ;

[0085] In the formula, As an auxiliary random variable, Follows a gamma distribution. For degrees of freedom, To conform to the distribution sign, To measure the noise covariance matrix, It follows a Gaussian distribution. It is a gamma distribution;

[0086] Based on the hierarchical structure, marginal probability density function Expressed as the integral form of the conditional Gaussian distribution and the gamma distribution:

[0087] .

[0088] S2 includes, S2.1, utilizing Process noise covariance at time step Perform standard time updates:

[0089] ;

[0090] ;

[0091] In the formula, for The predicted state vector at time t. for The posterior state estimate vector at time t. for The predicted state covariance matrix at time t. for The posterior state covariance matrix at time t.

[0092] S2 includes, S2.2, in At any given time, set a threshold for the number of iterations. ,conduct The next fixed-point iteration includes updating the information covariance. :

[0093] ;

[0094] ;

[0095] In the formula, for The equivalent measurement noise covariance matrix in the i-th iteration of the time-matter variational iteration. For the number of iterations, , for Time of the first Weighting factors of auxiliary variables in the next iteration It is the transpose symbol;

[0096] Calculate the expected value of the squared measurement residuals :

[0097] ;

[0098] In the formula, The trace operator for matrices;

[0099] Update the weighting factors of the auxiliary variables:

[0100] ;

[0101] In the formula, To measure dimension, for Time of the first The weighting factor of the auxiliary variable in the next iteration.

[0102] S2 includes S2.3, and the final robust innovation sequence obtained after iterative convergence. and final weighting factor :

[0103] ;

[0104] ;

[0105] In the formula, for The state estimation vector at time t, This is the final robust state estimation vector after iterative convergence.

[0106] S3 includes, S3.1, using the recursive properties of the Fisher information matrix to calculate... Predictive information matrix at time step :

[0107] ;

[0108] In the formula, Here is the state transition matrix. for The posterior Fisher information matrix at time step;

[0109] S3 includes S3.2, calculating the measurement information matrix after non-Gaussian correction. :

[0110] .

[0111] S3 includes S3.3 and updates. A posteriori Clamello's lower bound :

[0112] ;

[0113] ;

[0114] In the formula, for The posterior Fisher information matrix at time step;

[0115] Will As The performance lower bound of the time-state estimation covariance.

[0116] S4 includes S4.1, an empirical estimate of the process noise covariance at time k using an improved Saghusa adaptive filter. :

[0117] ;

[0118] In the formula, Forgetting factor, For robust new information;

[0119] S4 includes, S4.2, constructing a constraint tolerance based on Cramer-Rao's lower bound. :

[0120] ;

[0121] In the formula, For fault tolerance coefficient, The trace operator for matrices. for The inverse of the prediction information matrix at time step.

[0122] S4 includes S4.3, hour, ; hour, , For the revised version ;

[0123] S4 includes, S4.4, and will Return to step S2.1 and predict the state vector at the next time step.

[0124] The following description, in conjunction with the accompanying drawings and embodiments, further illustrates the process of this invention. Figure 1 As shown, the system inputs LBL / INS (Long Baseline / Inertial Navigation System) observations, performs non-Gaussian noise modeling, and then performs variational Bayesian robust state estimation based on the modeling results. The estimation is then split into two branches. The first branch utilizes the estimation results... An improved Sage-Husa adaptive estimation is performed, outputting a target state estimate; the second branch performs online CRB calculation, and the CRB calculation result is combined with the target state estimate from the first branch to determine whether it exceeds the theoretical tolerance of the CRB. If it does not exceed the tolerance (i.e., If the condition is normal, then a correction within the theoretical tolerance limit will be performed. If the theoretical tolerance is exceeded (i.e.) If it is, it is judged as abnormal and a correction beyond the theoretical tolerance is performed. Then output the corrected process noise covariance matrix. ,Will Feedback is fed into the variational Bayesian robust state estimation step to predict the target state at the next time step.

[0125] A highly dynamic "figure-eight" maneuver trajectory is generated using simulation, including acceleration, constant speed, deceleration, and turning states, to simulate the maneuvering state of an AUV in underwater missions. Four fixed beacons are set up in the simulation area to simulate an LBL (Low-Low-Low) positioning environment. Considering the influence of the beacon array geometry, the four beacons are symmetrically positioned. Continuous anomalous noise interference is introduced at two specific time intervals during the total motion duration to test the algorithm's effectiveness. The KF (Knowledge, Functions, and Fire) algorithm, a representative of the traditional adaptive algorithm AKF (Active Adaptive Functions), and the method of this invention are compared.

[0126] Figure 2 The image shows the true trajectory, the positions of four fixed beacons (B1–B4), and the estimated trajectories using three filtering methods. The FD region is extracted and magnified; the magnified result is shown below. Figure 9 As shown, the method of the present invention (red) is closer to the real path in trajectory tracking, especially in turning and high-maneuver sections, where it outperforms traditional Kalman filtering and adaptive Kalman filtering, demonstrating its strong robustness and high precision. Figure 3 The error performance of the three methods in eastward position estimation was compared. The method of this invention maintains the lowest error level, and the error increase during periods of interference is significantly smaller than that of the traditional method, indicating that it can effectively suppress the influence of abnormal measurements. Figure 4 The error performance of the three methods in northward position estimation was compared. The method of this invention maintains the lowest error level, and the error increase during periods of interference is significantly smaller than that of the traditional method, indicating that it can effectively suppress the influence of abnormal measurements. Figure 5 The error performance of the three methods in celestial position estimation was compared. The method of this invention maintains the lowest error level, and the error increase during periods of interference is significantly smaller than that of the traditional method, indicating that it can effectively suppress the influence of abnormal measurements. Figure 6 Showing A value closer to 1 indicates a higher confidence level in the measurement data, while a value closer to 0 indicates severe interference. The graph shows the situation during periods of strong interference. The system automatically reduces the weight of abnormal measurements to avoid degradation of filtering performance. Figure 7 This reflects the change in the lower bound of the optimal estimation accuracy. The CRB is moderately relaxed during periods of interference, consistent with the actual error trend, indicating that this lower bound can reasonably reflect the achievable estimation limit of the system and provide a reliable constraint benchmark for the adaptive process. Figure 8 The root mean square error (RMS) of the three methods in the east, north, and celestial directions was compared. The method of this invention achieves the lowest RMS value in all directions, demonstrating its overall superiority in positioning.

[0127] according to analyze, The closer the value is to 1, the higher the confidence level of the measurement data; the closer it is to 0, the lower the confidence level. The confidence level significantly decreased at the two locations where strong interference was added in the experiment. The performance lower bound is the lower bound for evaluating the root mean square error of the position, obtained by taking the square root of the trace of the position state of the PCRB matrix. The curve of the performance lower bound generally shows a downward trend, indicating that as filtering progresses, the position uncertainty decreases and gradually converges. For the two locations with strong interference, due to... The amount of information measured is close to 0. As the value approaches zero, the amount of effective information decreases, the accuracy drops, and the performance lower bound widens.

[0128] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. An adaptive filtering method for underwater navigation based on Cramero lower bound constraints, characterized in that, include: S1. Establish the state equation and observation equation of the discrete-time system, and represent the measurement noise as a Gaussian scale mixture model. Based on the Gaussian scale mixture model, represent the marginal probability density function of the measurement noise as an integral form of the conditional Gaussian distribution and the gamma distribution. S2. Predict the state vector and state covariance matrix using the process noise covariance matrix. Set an iteration number threshold at each time step and perform variational iterative updates. The variational iterative updates include updating the innovation covariance matrix, calculating the expectation of the squared measurement residuals, and updating the weighting factors of the auxiliary variables. After reaching the iteration number threshold, the final robust innovation sequence and the final weighting factors are obtained. S3. Use the Fisher information matrix to predict the information matrix, use the final weighting factor to calculate the non-Gaussian corrected measurement information matrix, and use the predicted information matrix and the non-Gaussian corrected measurement information matrix to update the posterior Cramer-Rao lower bound. S4. Calculate the empirical estimate of the process noise covariance matrix at the previous time step using the final robust innovation sequence. Then, combine the improved Saghusa adaptive filter to calculate the empirical estimate of the process noise covariance matrix at the current time step. Construct a constraint tolerance based on the Cramero lower bound. Based on the constraint tolerance and the empirical estimate of the process noise covariance matrix at the current time step, calculate the process noise covariance matrix after tolerance constraint processing. Return the process noise covariance matrix after tolerance constraint processing to step S2 to predict the state vector at the next time step.

2. The underwater navigation adaptive filtering method based on Cramero lower bound constraints according to claim 1, characterized in that, S1 includes S1.1, acquiring the three-axis acceleration and angular velocity of the inertial navigation system, and calculating the motion state of the autonomous underwater vehicle; By deploying acoustic beacons at known locations on the seabed and using a long baseline positioning system, the distance between the autonomous underwater vehicle (AUV) and the acoustic beacons is measured, and the AUV's position is determined through geometric intersection. Select velocity error, attitude error, position error, accelerometer bias, and gyroscope drift in sequence, and define the state vector in the Northeast-Eastern Sky navigation coordinate system. ; ； Based on inertial navigation systems and long baseline positioning systems, the state equations and observation equations of the discrete-time system are established: ； In the formula, The residual between the long-baseline measurements and the inertial navigation system predictions. Here is the state transition matrix. For the measurement matrix, For noise driving matrix, For process noise, Follows a pattern with a mean of 0 and a covariance of 0. The distribution, for The process noise covariance matrix at time step 1. To measure noise, For a moment.

3. The underwater navigation adaptive filtering method based on Cramero lower bound constraints according to claim 2, characterized in that, S1 includes S1.2, constructing a hierarchical probability model for non-Gaussian noise, assuming... Following the Student-t distribution, Represented as a Gaussian scale mixture model, with a hierarchical structure defined: ； ； In the formula, As an auxiliary random variable, Follows a gamma distribution. For degrees of freedom, To conform to the distribution sign, To measure the noise covariance matrix, It follows a Gaussian distribution. It is a gamma distribution; Based on the hierarchical structure, marginal probability density function Expressed as the integral form of the conditional Gaussian distribution and the gamma distribution: 。 4. The underwater navigation adaptive filtering method based on Cramero lower bound constraints according to claim 3, characterized in that, S2 includes, S2.1, utilizing Process noise covariance at time step Perform standard time updates: ； ； In the formula, for The predicted state vector at time t. for The posterior state estimate vector at time t. for The predicted state covariance matrix at time t. for The posterior state covariance matrix at time t.

5. The underwater navigation adaptive filtering method based on Cramero lower bound constraints according to claim 4, characterized in that, S2 includes, S2.2, in At any given time, set a threshold for the number of iterations. ,conduct The next fixed-point iteration includes updating the information covariance. : ； ； In the formula, for The equivalent measurement noise covariance matrix in the i-th iteration of the time-matter variational iteration. For the number of iterations, , for Time of the first Weighting factors of auxiliary variables in the next iteration It is the transpose symbol; Calculate the expected value of the squared measurement residuals : ； In the formula, The trace operator for matrices; Update the weighting factors of the auxiliary variables: ； In the formula, To measure dimension, for Time of the first The weighting factor of the auxiliary variable in the next iteration.

6. The underwater navigation adaptive filtering method based on Cramero lower bound constraints according to claim 5, characterized in that, S2 includes S2.3, and the final robust innovation sequence obtained after iterative convergence. and final weighting factor : ； ； In the formula, for The state estimation vector at time t, This is the final robust state estimation vector after iterative convergence.

7. The underwater navigation adaptive filtering method based on Cramero lower bound constraints according to claim 6, characterized in that, S3 includes, S3.1, using the recursive properties of the Fisher information matrix to calculate... Predictive information matrix at time step : ； In the formula, Here is the state transition matrix. for The posterior Fisher information matrix at time step; S3 includes S3.2, calculating the measurement information matrix after non-Gaussian correction. : 。 8. The underwater navigation adaptive filtering method based on Cramero lower bound constraints according to claim 7, characterized in that, S3 includes S3.3 and updates. A posteriori Clamello's lower bound : ； ； In the formula, for The posterior Fisher information matrix at time step; Will As The performance lower bound of the time-state estimation covariance.

9. The underwater navigation adaptive filtering method based on Cramero lower bound constraints according to claim 8, characterized in that, S4 includes S4.1, an empirical estimate of the process noise covariance at time k using an improved Saghusa adaptive filter. : ； In the formula, Forgetting factor, For robust new information; S4 includes, S4.2, constructing a constraint tolerance based on Cramer-Rao's lower bound. : ； In the formula, For fault tolerance coefficient, The trace operator for matrices. for The inverse of the prediction information matrix at time step.

10. The underwater navigation adaptive filtering method based on Cramero lower bound constraints according to claim 4, characterized in that, S4 includes S4.3, hour, ; hour, , For the revised version ; S4 includes, S4.4, and will Return to step S2.1 and predict the state vector at the next time step.

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