A method for underwater acoustic localization sound velocity compensation based on vertical total time delay random walk

Abstract

This invention discloses an underwater acoustic positioning sound velocity compensation method based on vertical total time delay random walk, belonging to the field of underwater acoustic navigation and positioning. The method includes: collecting two-way time delay observation data in underwater acoustic positioning; establishing an ocean sound velocity compensation formula; defining the vertical total time delay and establishing a conversion function between ocean sound velocity variation and vertical total time delay; calculating a coarse prior value of the vertical total time delay based on the conversion function, and using a first-order Markov process to calculate the random walk noise of the vertical total time delay; using the two-way time delay observation data, the coarse prior value, and the random walk noise, accurately estimating the vertical total time delay using an extended Kalman filter, and then substituting it into the conversion function to obtain the ocean sound velocity variation, thus achieving sound velocity compensation. This invention eliminates the need for additional sound velocity measurement equipment, enables real-time online compensation of ocean sound velocity variation errors, improves underwater acoustic positioning efficiency, and enhances the temporal resolution of ocean sound velocity variation detection.

Description

Technical Field

[0001] This invention relates to the field of underwater acoustic navigation and positioning technology, and in particular to an underwater acoustic positioning sound velocity compensation method based on vertical total time delay random walk. Background Technology

[0002] Underwater acoustic navigation and positioning technology is a core technology supporting key areas such as monitoring seafloor crustal movement, marine resource exploration, and underwater engineering operations. This technology calculates target location by measuring the propagation time of acoustic signals underwater and combining this with sound speed information. However, the complexity of the marine environment, especially the spatiotemporal variations in ocean sound speed, is the primary source of error limiting its positioning accuracy, efficiency, and reliability.

[0003] Ocean sound speed is primarily influenced by temperature, salinity, and pressure, exhibiting significant and continuous temporal and spatial variations. Traditionally, sound speed has been measured directly or indirectly using instruments such as sound velocity profilers and temperature-salinity-depth (TDT) meters to construct sound velocity profile models for sound ray correction. However, these measurement methods have inherent limitations: firstly, their observations are discrete in time and sparse in space, making it difficult to capture rapidly changing ocean hydrological processes (such as internal waves and eddies) in real time and continuously; secondly, frequent profiling measurements in the operational area significantly increase operational costs and time consumption, failing to meet the needs of rapid, real-time positioning applications.

[0004] To improve the timeliness of positioning, sequential processing algorithms such as extended Kalman filtering have been introduced into the field of underwater acoustic positioning, aiming to achieve real-time data processing. However, sequential algorithms are extremely sensitive to state model errors. Due to the lack of an effective and refined mathematical model for the time-varying characteristics of ocean sound speed, sound speed variation errors are often simply treated as white noise or as secondary interference to position state parameters during the filtering process. This leads to biased or even divergent filtering estimates, making it difficult to maintain high-precision positioning in long-term continuous observation. Specifically, the propagation delay error caused by sound speed variations is not modeled and estimated as an independent state with clear physical meaning and time-varying laws, making it impossible for the positioning system to adaptively "learn" and "compensate" for this dynamic environmental error.

[0005] Therefore, existing technologies face a prominent contradiction in real-time underwater acoustic positioning: on the one hand, the time-varying characteristics of ocean sound speed are a major source of error that must be carefully processed; on the other hand, there is a lack of an efficient method to effectively parameterize, dynamically model, and compensate online for time delay errors caused by sound speed variations without relying on intensive field measurements. This results in positioning accuracy, stability, and time resolution failing to meet the increasingly demanding application requirements. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention provides an underwater acoustic positioning sound velocity compensation method based on vertical total time delay random walk, aiming to achieve real-time online compensation for ocean sound velocity variation errors, improve underwater acoustic positioning efficiency, and enhance the temporal resolution of ocean sound velocity variation detection without the need for additional sound velocity measurement equipment.

[0007] To achieve the above objectives, the technical solution of the present invention is as follows:

[0008] A method for underwater acoustic positioning sound velocity compensation based on vertical total time delay random walk includes the following steps:

[0009] Step 1: Collect two-way time delay observation data for underwater acoustic positioning;

[0010] Step 2: Establish the ocean sound speed compensation formula, and quantify the sound speed compensation as the two-way time delay of the sound propagation path caused by the change of ocean sound speed.

[0011] Step 3: Define the total vertical time delay, convert the two-way time delay of the sound propagation path into an equivalent quantity of the two-way time delay of the vertical propagation path, and establish a conversion function between the change of ocean sound speed and the total vertical time delay.

[0012] Step 4: Calculate a rough prior value of the total vertical delay based on the transformation function, and use a first-order Markov process to calculate the random walk noise of the total vertical delay;

[0013] Step 5: Using the two-way time delay observation data, the coarse prior value of the total vertical time delay, and the noise of the random walk process, the total vertical time delay of the random walk is accurately estimated using an extended Kalman filter. Then, the accurately estimated total vertical time delay is substituted into the transformation function to obtain the ocean sound speed change, thereby achieving sound speed compensation.

[0014] In the above scheme, the specific method of step two is as follows:

[0015] In the calendar Time, relative to the reference speed of sound Using slow speed Sound propagation path The integral parameterizes the sound speed compensation into the ocean sound speed variation. Caused two-way time delay in sound propagation path The formula is as follows:

[0016] ;

[0017] ;

[0018] In the formula, and They are located in the horizontal position and depth Changes in ocean sound speed and slowness, This refers to the sound propagation path.

[0019] In the above scheme, the total vertical delay defined in step three is as follows:

[0020] ;

[0021] In the formula, It is the total vertical delay. Sound propagation path The grazing angle, using trigonometric functions to determine the sound propagation path Switch to vertical path .

[0022] In the above scheme, step three establishes the following conversion function between ocean sound speed variation and total vertical time delay:

[0023] ;

[0024] In the formula, It is the two-way sound path length. It is the average speed of sound. It is related to the sound propagation path glancing angle Related mapping functions, It refers to changes in the speed of sound in the ocean.

[0025] In the above scheme, in step four, based on the transformation function, the reference sound speed... A rough prior value for calculating the total vertical time delay. ;

[0026] Then, based on the coarse prior value of the total vertical delay... The random walk noise with vertical total time delay is constructed using a first-order Markov process. The formula is as follows:

[0027] ;

[0028] In the formula, yes The time interval between Represents the mathematical expectation. , They represent , The approximate prior value of the total vertical delay at each moment.

[0029] In the above scheme, the specific method of step five is as follows:

[0030] Step 5.1: Using the rough prior value of the total vertical delay obtained in Step 4 and the noise of the random walk process, predict the state prediction value of the current epoch based on the state estimate value of the previous epoch.

[0031] Step 5.2: Calculate the innovation vector at the current epoch based on underwater acoustic positioning two-way time delay observation data and state vector prediction values;

[0032] Step 5.3: Calculate the Kalman gain matrix based on the predicted state variance covariance matrix and the observation equation;

[0033] Step 5.4: Correct the state prediction value using the Kalman gain matrix and the innovation vector to obtain the state estimate value of the current epoch, which includes the accurately estimated total vertical delay; repeat the above steps using the current epoch state estimate value as the initial value of the next epoch, and recursively complete the accurate estimation of the total vertical delay for all epochs.

[0034] Step 5.5: Substitute the estimated vertical total time delay for each epoch into the transformation function described in Step 3 to obtain the ocean sound speed change and achieve sound speed compensation.

[0035] In a further technical solution, step 5.1 utilizes a rough prior value of the total vertical time delay. and random walk process noise Calculate epochs Vertical total delay prediction at time 1 :

[0036] ;

[0037] In the formula, For an epoch, the symbol " "Indicates state prediction, symbol " "Indicates state estimation; For the calendar The predicted state vector value at time epoch, including epochs Three-dimensional position prediction of the seabed transponder at any given time Vertical total delay prediction ; The corresponding state estimation prior vector contains epochs. Three-dimensional position estimate of the seabed transponder at time 10:00 , calendar Estimated vertical total delay at time t ; It is the calendar The state transition matrix at time t; It is the calendar The state prediction variance-covariance matrix at time 10:00. It is the calendar The state estimation variance-covariance matrix at time t; It is the calendar The noise variance-covariance matrix at time t, where T is the matrix transpose.

[0038] For the initial epoch, the prior value of the vertical total time delay estimate The rough prior value of the total vertical delay The noise variance of the random walk process of the total vertical delay .

[0039] In a further technical solution, step 5.2 involves using underwater acoustic positioning two-way time delay observation data and state vector prediction values. Calculate epochs The new vector at time :

[0040] ;

[0041] In the formula, It is the calendar All two-way time delay observations at time 1 The observation vector formed, The state vector prediction values ​​include the predicted three-dimensional position values ​​of the seabed transponder. Vertical total delay prediction , Design the corresponding observation matrix, based on the epoch. The underwater acoustic positioning observation model at that time is calculated as follows:

[0042] ;

[0043] ;

[0044] In the formula, In the calendar The first moment A set of two-way time delay observations, For the calendar The total number of observations at time 1. The first is calculated by ray tracking. Downlink and uplink propagation times of the group of acoustic signals; In the calendar Predicted 3D position of the seabed transponder at any given time; and They are the first Known three-dimensional positions of the shipborne acoustic transducer at the times of acoustic signal transmission and reception; Is with the first Group sound propagation path glancing angle Related mapping functions; This is the predicted total vertical delay. It is a random error;

[0045] Observation design matrix In the middle, the three-dimensional location prediction value , , , These are the corresponding three-dimensional position prediction components; , , , , , Take 0.001 meters.

[0046] In a further technical solution, in step 5.3, the epoch... The Kalman gain matrix at time t is as follows:

[0047] ;

[0048] In the formula, For the calendar The Kalman gain matrix at time 10:00. It is the calendar The variance-covariance matrix of the state prediction at time step. For the calendar The observation design matrix at each moment, For the calendar The variance and covariance matrix of the two-way delay observation vector at time point.

[0049] In a further technical solution, in step 5.4, the epoch... The state estimates at time t are as follows:

[0050] ;

[0051] In the formula, For the calendar State estimate at time, including epochs Three-dimensional position estimate of the seabed transponder at time 10:00 Vertical total delay estimate , For the calendar The predicted state vector value at time t. For the calendar The Kalman gain matrix at time 10:00. For the calendar The information vector at time, It is the calendar The variance-covariance matrix of the state estimation at each time step. It is the calendar The variance-covariance matrix of the state prediction at time step. For the calendar The observation design matrix at each moment, It is an identity matrix.

[0052] Through the above technical solution, the underwater acoustic positioning sound velocity compensation method based on vertical total time delay random walk provided by the present invention has the following beneficial effects:

[0053] (1) This invention establishes a conversion function between ocean sound speed variation and vertical total time delay, and converts the complex sound speed variation error along the sound propagation path into a two-way time delay along the vertical path, which greatly simplifies the parameterization of the sound speed compensation model and facilitates real-time estimation and compensation under the extended Kalman filter framework.

[0054] (2) The present invention uses a first-order Markov process to calculate the random walk noise of the total vertical time delay. Only the coarse prior values ​​of adjacent epochs are needed to quantify the uncertainty of the time delay change. The computation is low and it is suitable for underwater acoustic rapid real-time positioning scenarios.

[0055] (3) This invention introduces the total vertical time delay as a state variable into the extended Kalman filter, and combines it with conventionally collected two-way time delay observation data to accurately calculate the total vertical time delay while estimating the position of the seabed transponder. Then, it uses the transformation function to invert the ocean sound speed change, thereby realizing online compensation for sound speed error without the need for additional sound speed profile measurement equipment.

[0056] (4) The method of the present invention can effectively improve the real-time processing efficiency of underwater acoustic positioning, and significantly enhance the time resolution capability of ocean sound speed changes. It provides key technical support for applications such as seabed crustal movement monitoring, seismic activity tracking, detection of rapid changes in marine hydrology, and dynamic updating of geodetic benchmarks, and has important engineering practical value. Attached Figure Description

[0057] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below.

[0058] Figure 1 This is a schematic diagram of a method for underwater acoustic positioning sound velocity compensation based on vertical total time delay random walk, as disclosed in an embodiment of the present invention.

[0059] Figure 2 This is a diagram showing the ocean sound velocity compensation results disclosed in an embodiment of the present invention. Detailed Implementation

[0060] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.

[0061] This invention provides an underwater acoustic positioning sound velocity compensation method based on vertical total time delay random walk. This method equates the complex changes in ocean sound velocity to the vertical total time delay (NTD) parameter and uses extended Kalman filtering (EKF) to estimate and compensate for it in real time, thereby achieving high-precision and high-efficiency underwater positioning without the need for additional sound velocity measurement equipment.

[0062] The specific implementation of this embodiment is based on the following real observation data scenario: the seabed transponder stations are fixed on the seabed at a depth of approximately 1670 meters, with the three-dimensional positions of the four stations being [788.4m, -199.4m, -1676.4m], [31.3m, -932.5m, -1675.3m], [-859.9m, -138.4m, -1668.1m], and [-4.1m, 898.1m, -1659.4m]. The shipborne acoustic transducer navigates on the sea surface, transmitting a set of acoustic interrogation signals every 10 seconds and recording the two-way propagation time of the response signals, collecting 4317 observation epochs.

[0063] Specifically, the following steps are included:

[0064] Step 1: Collect two-way time delay observation data for underwater acoustic positioning.

[0065] During ship navigation, the shipborne acoustic transducers continuously transmit acoustic signals according to a preset trajectory and transmission cycle (10 seconds), and receive response signals from the seabed transponders. A high-precision timer records the transmission and reception times of the acoustic signals at each epoch, calculating the raw two-way delay observations for each transponder. Simultaneously, the shipborne GNSS equipment precisely records the three-dimensional position of the transducers at each transmission and reception moment. The data collected in this step forms the basis for all subsequent compensation and positioning calculations.

[0066] Step 2: Establish the ocean sound speed compensation formula, and quantify the sound speed compensation as the two-way time delay of the sound propagation path caused by the change of ocean sound speed.

[0067] This step aims to quantify the impact of changes in sound speed as a delay in sound propagation time. In this embodiment, a formula for ocean sound speed compensation is first established.

[0068] In the calendar At any given moment, the slowness of sound is defined as the reciprocal of the speed of sound, relative to a reference speed of sound. Using slow speed Sound propagation path The integral parameterizes the sound speed compensation into the ocean sound speed variation. Caused two-way time delay in sound propagation path The formula is as follows:

[0069] ;

[0070] ;

[0071] In the formula, and They are located in the horizontal position and depth Changes in ocean sound speed and slowness, This refers to the sound propagation path.

[0072] This formula establishes a direct physical link between the change in sound speed and the observation time delay, parameterizing the complex change in the sound speed field into an integral quantity along the path.

[0073] Step 3: Define the total vertical time delay, convert the two-way time delay of the sound propagation path into an equivalent quantity of the two-way time delay of the vertical propagation path, and establish a conversion function between the change of ocean sound speed and the total vertical time delay.

[0074] To facilitate modeling in the filter, this step equivalently transforms the path integral along the curved sound ray into the integral along the vertical path, defining the "total vertical delay" (NTD).

[0075] First, the total vertical time delay is defined as the equivalent of the two-way time delay along the vertical path caused by the change in ocean sound speed:

[0076] ;

[0077] In the formula, It is the total vertical delay. Sound propagation path The grazing angle, using trigonometric functions to determine the sound propagation path Switch to vertical path .

[0078] Then, based on the trigonometric relationship between the sound propagation path and the vertical path, a conversion function between the change in ocean sound speed and the total vertical time delay is established. Considering the curvature of sound rays in the ocean, a function related to the grazing angle is introduced. Related mapping functions It can be used This indicates that an approximate straight-line sound propagation path is used to express a generalized... .

[0079] Considering only a uniform water layer, the two-way propagation time delay This can be simplified as follows:

[0080] ;

[0081] In the formula, It is the two-way sound path length. It is the average speed of sound, and in a marine hydrological environment. It is a very small amount.

[0082] Combining the above formulas, the total vertical delay Changes in ocean sound speed The conversion function between them can be expressed as:

[0083] ;

[0084] In the formula, It is the two-way sound path length. It is the average speed of sound. It is related to the sound propagation path glancing angle Related mapping functions, It refers to changes in the speed of sound in the ocean.

[0085] Step 4: Calculate the coarse prior value of the total vertical delay based on the transformation function, and use a first-order Markov process to calculate the random walk noise of the total vertical delay.

[0086] Based on the transformation function, from the reference sound speed A rough prior value for calculating the total vertical time delay. .

[0087] Then, based on the coarse prior value of the total vertical delay... The random walk noise with vertical total time delay is constructed using a first-order Markov process. The formula is as follows:

[0088] ;

[0089] In the formula, yes The time interval between Represents the mathematical expectation. , They represent , The approximate prior value of the total vertical delay at each moment.

[0090] Step 5: Using the two-way time delay observation data, the coarse prior value of the total vertical time delay, and the noise of the random walk process, the extended Kalman filter is used to accurately estimate the total vertical time delay of the random walk. Then, the accurately estimated total vertical time delay is substituted into the transformation function to obtain the change in ocean sound speed, thereby achieving sound speed compensation.

[0091] The specific method is as follows:

[0092] Step 5.1: Using the rough prior value of the total vertical delay obtained in Step 4 and the noise of the random walk process, predict the state prediction value of the current epoch based on the state estimate value of the previous epoch.

[0093] Using the rough prior value of total vertical delay and random walk process noise Calculate epochs Vertical total delay prediction at time 1 :

[0094] ;

[0095] In the formula, For an epoch, the symbol " "Indicates state prediction, symbol " "Indicates state estimation; For the calendar The predicted state vector value at time epoch, including epochs Three-dimensional position prediction of the seabed transponder at any given time Vertical total delay prediction ; The corresponding state estimation prior vector contains epochs. Three-dimensional position estimate of the seabed transponder at time 10:00 , calendar Estimated vertical total delay at time t ; It is the calendar The state transition matrix at time t; It is the calendar The state prediction variance-covariance matrix at time 10:00. It is the calendar The state estimation variance-covariance matrix at time t; It is the calendar The noise variance-covariance matrix at time t, where T is the matrix transpose.

[0096] For the initial epoch, the prior value of the vertical total time delay estimate The rough prior value for the total vertical delay The noise variance of the random walk process in terms of total vertical delay .

[0097] Step 5.2: Calculate the innovation vector at the current epoch based on underwater acoustic positioning two-way time delay observation data and state vector prediction values.

[0098] Based on underwater acoustic positioning two-way time delay observation data and state vector prediction values Calculate epochs The new vector at time :

[0099] ;

[0100] In the formula, It is the calendar All two-way time delay observations at time 1 The observation vector formed, The state vector prediction values ​​include the predicted three-dimensional position values ​​of the seabed transponder. Vertical total delay prediction , Design the corresponding observation matrix, based on the epoch. The underwater acoustic positioning observation model at that time is calculated as follows:

[0101] ;

[0102] ;

[0103] In the formula, In the calendar The first moment A set of two-way time delay observations, For the calendar The total number of observations at time 1. The first is calculated by ray tracking. Downlink and uplink propagation times of the group of acoustic signals; In the calendar Predicted 3D position of the seabed transponder at any given time; and They are the first Known three-dimensional positions of the shipborne acoustic transducer at the times of acoustic signal transmission and reception; Is with the first Group sound propagation path glancing angle Related mapping functions; This is the predicted total vertical delay. It is a random error;

[0104] Observation design matrix In the middle, the three-dimensional location prediction value , , , These are the corresponding three-dimensional position prediction components; , , , , , Take 0.001 meters.

[0105] Step 5.3: Calculate the Kalman gain matrix based on the predicted state variance covariance matrix and the observation equation.

[0106] Era The Kalman gain matrix at time t is as follows:

[0107] ;

[0108] In the formula, For the calendar The Kalman gain matrix at time 10:00. It is the calendar The variance-covariance matrix of the state prediction at time step. For the calendar The observation design matrix at each moment, For the calendar The variance and covariance matrix of the two-way delay observation vector at time point.

[0109] Step 5.4: Correct the state prediction value using the Kalman gain matrix and the innovation vector to obtain the state estimate value for the current epoch, which includes the accurately estimated total vertical delay. Repeat the above steps using the current epoch state estimate value as the initial value for the next epoch, and recursively complete the accurate estimation of the total vertical delay for all epochs.

[0110] Era The state estimates at time t are as follows:

[0111] ;

[0112] In the formula, For the calendar State estimate at time, including epochs Three-dimensional position estimate of the seabed transponder at time 10:00 Vertical total delay estimate , For the calendar The predicted state vector value at time t. For the calendar The Kalman gain matrix at time 10:00. For the calendar The information vector at time, It is the calendar The variance-covariance matrix of the state estimation at each time step. It is the calendar The variance-covariance matrix of the state prediction at time step. For the calendar The observation design matrix at each moment, It is an identity matrix.

[0113] Step 5.5, estimate the total vertical delay for each epoch. Substituting the transformation function from step three, we obtain the change in ocean sound speed. To achieve sound speed compensation, such as Figure 2 As shown, the implementation example of this invention calculates the ocean sound velocity compensation results for all epochs. The estimated ocean sound velocity compensation for different stations is represented by purple, orange, light blue, and dark blue squares, respectively. It can be seen that the estimated ocean sound velocity compensation ranges from -0.7 to 0.2 m / s, spanning approximately two days. During this period, the ocean sound velocity compensation at different stations exhibits a continuous change curve over time, and the curve waveforms are consistent. This demonstrates that the method of this invention can extract ocean sound velocity changes at each epoch without requiring additional sound velocity profile measurement equipment, effectively improving the temporal resolution of ocean sound velocity changes. However, for some time periods, two-way delay data was not collected, resulting in no corresponding ocean sound velocity compensation.

[0114] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for underwater acoustic positioning sound velocity compensation based on vertical total time delay random walk, characterized in that, Includes the following steps: Step 1: Collect two-way time delay observation data for underwater acoustic positioning; Step 2: Establish the ocean sound speed compensation formula, and quantify the sound speed compensation as the two-way time delay of the sound propagation path caused by the change of ocean sound speed. Step 3: Define the total vertical time delay, convert the two-way time delay of the sound propagation path into an equivalent quantity of the two-way time delay of the vertical propagation path, and establish a conversion function between the change of ocean sound speed and the total vertical time delay. Step 4: Calculate a rough prior value of the total vertical delay based on the transformation function, and use a first-order Markov process to calculate the random walk noise of the total vertical delay; Step 5: Using the two-way time delay observation data, the coarse prior value of the total vertical time delay, and the noise of the random walk process, the total vertical time delay of the random walk is accurately estimated by extended Kalman filtering. Then, the accurately estimated total vertical time delay is substituted into the transformation function to obtain the ocean sound speed change, thereby achieving sound speed compensation. The specific method for step two is as follows: In the calendar Time, relative to the reference speed of sound Using slow speed Sound propagation path The integral parameterizes the sound speed compensation into the ocean sound speed variation. Caused two-way time delay in sound propagation path The formula is as follows: ； ； In the formula, and They are located in the horizontal position and depth Changes in ocean sound speed and slowness, The path of sound propagation; In step three, the total vertical delay is defined as follows: ； In the formula, It is the total vertical delay. Sound propagation path The grazing angle, using trigonometric functions to determine the sound propagation path Switch to vertical path ; In step three, the conversion function between the change in ocean sound speed and the total vertical time delay is established as follows: ； In the formula, It is the two-way sound path length. It is the average speed of sound. It is related to the sound propagation path glancing angle Related mapping functions, It refers to changes in the speed of sound in the ocean.

2. The underwater acoustic positioning sound velocity compensation method based on vertical total time delay random walk according to claim 1, characterized in that, In step four, based on the transformation function, the reference sound speed... A rough prior value for calculating the total vertical time delay. ; Then, based on the coarse prior value of the total vertical delay... The random walk noise with vertical total time delay is constructed using a first-order Markov process. The formula is as follows: ； In the formula, yes The time interval between Represents the mathematical expectation. , They represent , The approximate prior value of the total vertical delay at each moment.

3. The underwater acoustic positioning sound velocity compensation method based on vertical total time delay random walk according to claim 2, characterized in that, The specific method for step five is as follows: Step 5.1: Using the rough prior value of the total vertical delay obtained in Step 4 and the noise of the random walk process, predict the state prediction value of the current epoch based on the state estimate value of the previous epoch. Step 5.2: Calculate the innovation vector at the current epoch based on underwater acoustic positioning two-way time delay observation data and state vector prediction values; Step 5.3: Calculate the Kalman gain matrix based on the predicted state variance covariance matrix and the observation equation; Step 5.4: Correct the state prediction value using the Kalman gain matrix and the innovation vector to obtain the state estimate value of the current epoch, which includes the accurately estimated total vertical delay; repeat the above steps using the current epoch state estimate value as the initial value of the next epoch, and recursively complete the accurate estimation of the total vertical delay for all epochs. Step 5.5: Substitute the estimated vertical total time delay for each epoch into the transformation function described in Step 3 to obtain the ocean sound speed change and achieve sound speed compensation.

4. The underwater acoustic positioning sound velocity compensation method based on vertical total time delay random walk according to claim 3, characterized in that, In step 5.1, a rough prior value of the total vertical time delay is used. and random walk process noise Calculate epochs Vertical total delay prediction at time 1 : ； In the formula, For an epoch, the symbol " "Indicates state prediction, symbol " "Indicates state estimation; For the calendar The predicted state vector value at time epoch, including epochs Three-dimensional position prediction of the seabed transponder at any given time Vertical total delay prediction ; The corresponding state estimation prior vector contains epochs. Three-dimensional position estimate of the seabed transponder at time 10:00 , calendar Estimated vertical total delay at time t ; It is the calendar The state transition matrix at time t; It is the calendar The state prediction variance-covariance matrix at time 10:

00. It is the calendar The state estimation variance-covariance matrix at time t; It is the calendar The noise variance-covariance matrix at time t, where T is the matrix transpose; For the initial epoch, the prior value of the vertical total time delay estimate The rough prior value of the total vertical delay The noise variance of the random walk process of the total vertical delay .

5. The underwater acoustic positioning sound velocity compensation method based on vertical total time delay random walk according to claim 4, characterized in that, In step 5.2, based on the underwater acoustic positioning two-way time delay observation data and the state vector prediction value... Calculate epochs The new vector at time : ； In the formula, It is the calendar All two-way time delay observations at time 1 The observation vector formed, The state vector prediction values ​​include the predicted three-dimensional position values ​​of the seabed transponder. Vertical total delay prediction , Design the corresponding observation matrix, based on the epoch. The underwater acoustic positioning observation model at that time is calculated as follows: ； ； In the formula, In the calendar The first moment A set of two-way time delay observations, For the calendar The total number of observations at time 1. The first is calculated by ray tracking. Downlink and uplink propagation times of the group of acoustic signals; In the calendar Predicted 3D position of the seabed transponder at any given time; and They are the first Known three-dimensional positions of the shipborne acoustic transducer at the times of acoustic signal transmission and reception; Is with the first Group sound propagation path glancing angle Related mapping functions; This is the predicted total vertical delay. It is a random error; Observation design matrix In the middle, the three-dimensional location prediction value , , , These are the corresponding three-dimensional position prediction components; , , , , , Take 0.001 meters.

6. The underwater acoustic positioning sound velocity compensation method based on vertical total time delay random walk according to claim 5, characterized in that, In step 5.3, the epoch The Kalman gain matrix at time t is as follows: ； In the formula, For the calendar The Kalman gain matrix at time t. It is the calendar The variance-covariance matrix of the state prediction at time step. For the calendar The observation design matrix at each moment, For the calendar The variance and covariance matrix of the two-way delay observation vector at time point.

7. The underwater acoustic positioning sound velocity compensation method based on vertical total time delay random walk according to claim 6, characterized in that, In step 5.4, the epoch The state estimates at time t are as follows: ； In the formula, For the calendar State estimate at time, including epochs Three-dimensional position estimate of the seabed transponder at time 10:00 Vertical total delay estimate , For the calendar The predicted state vector value at time t. For the calendar The Kalman gain matrix at time 10:

00. For the calendar The information vector at time, It is the calendar The variance-covariance matrix of the state estimation at each time step. It is the calendar The variance-covariance matrix of the state prediction at time step. For the calendar The observation design matrix at each moment, It is an identity matrix.

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