Linear recursive filtering method considering underwater sound time delay
By introducing a real-time estimation and compensation mechanism for water acoustic delay in the underwater positioning and water acoustic communication system, the impact of water acoustic signal propagation delay on positioning accuracy and signal tracking performance is solved, and the accuracy and adaptability of the system are significantly improved.
Patent Information
- Application Number
- CN202510060495.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-01-15
- Publication Date
- 2025-05-13
AI Technical Summary
The existing underwater positioning and water acoustic communication systems fail to fully consider the impact of the propagation delay of the water acoustic signal, resulting in the impact of positioning accuracy and signal tracking performance under the long delay or severe environmental changes.
A linear recursive filtering method that takes into account the delay of water acoustics is proposed. By establishing a delay model of water acoustics, it is integrated into Kalman filtering or extended Kalman filtering to estimate and compensate the delay of water acoustics in real time to reduce the error caused by delay.
By estimating and compensating the acoustic delay in real time, the positioning accuracy and signal processing robustness are significantly improved, and can adapt to changes in different underwater environments, including water flow, temperature fluctuations, salinity changes and water depth.
Smart Images
Figure CN119995560A_ABST
Abstract
Description
Technical Field
[0001] The invention discloses a linear recursive filtering method taking into account underwater acoustic time delay, belonging to the technical field of underwater acoustic communication and underwater positioning. Background Art
[0002] In underwater positioning, sonar detection and underwater acoustic communication systems, the propagation of underwater acoustic signals is affected by many factors, and the speed of underwater acoustic propagation (i.e., the speed of sound) is closely related to environmental factors such as water temperature, salinity, and depth. Especially in long-distance transmission or deep-sea environments, the propagation delay of underwater acoustic signals has a significant impact on signal processing, target positioning, and navigation accuracy. Traditional underwater positioning systems usually estimate target states based on methods such as Kalman filtering and particle filtering, but these methods do not fully consider the propagation delay effect of underwater acoustic signals. Therefore, in the case of long delays or drastic environmental changes, positioning accuracy and signal tracking performance are easily affected.
[0003] Most existing underwater acoustic communication and positioning systems assume that the delay of underwater acoustic propagation is known and constant, or estimate the delay through external measurement methods. However, in complex underwater environments, the delay of underwater acoustics not only changes with the propagation distance, but is also affected by factors such as water flow, temperature, and salinity, which makes the prediction and compensation of delay a challenge. Therefore, how to accurately model the delay of underwater acoustic propagation and compensate for it during the filtering process is a key issue that needs to be solved in current underwater positioning and underwater acoustic communication technologies.
[0004] Although some studies have attempted to model and compensate for underwater acoustic propagation delay, most methods only consider the impact of delay on underwater target positioning or communication links, and ignore the real-time estimation and compensation of delay factors in recursive filtering algorithms. Therefore, how to effectively introduce underwater acoustic delay in the recursive filtering framework and estimate and compensate for it in real time is an important research direction to improve system performance and accuracy.
[0005] The technical goal of the present invention is to address this background problem and propose a linear recursive filtering method that takes into account the underwater acoustic delay. By improving the existing filtering algorithm and introducing a real-time estimation and compensation mechanism for the underwater acoustic propagation delay, the performance of the underwater positioning and communication system is optimized, and the problems of delay influence and insufficient precision existing in the prior art are overcome. Summary of the invention
[0006] The purpose of the present invention is to provide a linear recursive filtering method taking into account underwater acoustic delay, so as to solve the problems of delay influence and low positioning accuracy in underwater positioning in the prior art.
[0007] A linear recursive filtering method taking into account underwater acoustic delay, comprising:
[0008] S1. Based on the physical characteristics of underwater acoustic propagation, taking into account the non-uniformity, temperature, salinity and depth of the underwater environment, an underwater acoustic delay model is established to estimate the delay effect on the underwater acoustic signal during the propagation process;
[0009] S2. Based on the Kalman filter or extended Kalman filter (EKF) algorithm, the underwater acoustic delay model is integrated into the filtering process, the influence of the underwater acoustic delay on the current state estimation is calculated, and compensation is performed to reduce the error caused by the delay;
[0010] S3. Using the recursive filtering method, the delay is estimated in real time at each update, and the state estimate is adjusted according to the delay to ensure the accuracy and stability of the filter;
[0011] S4. In the Kalman filter, by introducing the delay compensation term, the filter can adapt to the changes in the underwater acoustic delay and obtain accurate target state estimation.
[0012] S1 includes the calculation of the speed of underwater sound propagation:
[0013] v(T,S,D)=1500+4.6T-0.0055S+0.00029D;
[0014] Where v is the speed of sound in water, T is the water temperature, S is the salinity, and D is the water depth;
[0015] The distance from the transmitter to the receiver affects the propagation delay. The speed of sound in water varies with underwater environmental factors, including hydrology, salinity, and water depth. The relationship between underwater sound propagation delay, propagation distance, and sound speed is:
[0016]
[0017] Where Δt is the underwater acoustic propagation delay, and d is the actual distance the signal propagates.
[0018] S1 includes the time measurement error τ caused by the vertical sound velocity stratification:
[0019]
[0020] In the formula, z p and z q is the depth of the upper and lower boundaries of the layer, δs(z) is the slowness deviation between the reference sound velocity profiles, c(z) is the sound velocity at depth z, s(z) is the sound velocity slowness, s n is s(z) of the nth layer, dividing the sound velocity profile into N layers, z n is the depth of the nth layer, δ is the cosine of the grazing angle;
[0021] Assume that in each sound speed layer s n It varies linearly with the horizontal distance x, is a constant, z n The horizontal displacement dx of the sound path caused by the horizontal gradient of the sound velocity structure of the nth layer is:
[0022]
[0023] Where Δx is the horizontal distance and Δz is the depth difference;
[0024] The propagation time delay t caused is:
[0025]
[0026] The error in the vertical direction is the sound line bending error caused by the change in sound speed. The sound line bending error prevents the sound line from arriving vertically, resulting in time delay.
[0027] S2 includes using Kalman filtering to process linear systems and using extended Kalman filtering to process nonlinear systems.
[0028] In the underwater positioning system, the state variable x k for:
[0029] x k =[x 1,k x 2,k x 3,k …x n,k ] T ;
[0030] In the formula, x n,k is the value of the nth state variable at time step k, where n is the dimension of the state variable;
[0031] Control input u k for:
[0032] u k =[u 1,k u 2,k u 3,k …u m,k ] T ;
[0033] In the formula, u m,k is the value of the mth control input at time step k, where m is the dimension of the control input;
[0034] Observable quantity z k for:
[0035] z k =[z 1,k z 2,k z 3,k …z p,k ] T ;
[0036] In the formula, z p,k is the value of the pth observation at time step k, where p is the dimension of the observation.
[0037] S2 includes assuming that the system is linear and using a linear model to describe the state transition process. The state equation is expressed as:
[0038] x k =Ax k-1 +Bu k +w k ;
[0039] Where A is the state transfer matrix, which represents the transition relationship of the system from time k-1 to time k, B is the control input matrix, which represents the influence of the control input on the state, and w k is the process noise, which is zero-mean, Gaussian white noise with covariance Q;
[0040] The observation equation is:
[0041] z k =Hx k +v k ;
[0042] Where H is the observation matrix, which maps the system state to the observation space, v k is the observation noise, which is zero-mean, Gaussian white noise with covariance R;
[0043] Assuming that the underwater acoustic propagation delay is calculated from environmental factors, taking into account the underwater acoustic propagation delay, the observation equation is changed to:
[0044] z k =Hx k +v k -Δt k ;
[0045] In the formula, Δt k is the delay compensation item at the current moment;
[0046] Taking into account the delay compensation term, the optimal state estimation iterative update is:
[0047]
[0048] In the formula, is the posterior state estimate at time step k, is the prior state estimate at time step k, K k is the Kalman gain.
[0049] S2 includes assuming that the system is nonlinear and using extended Kalman filtering to linearize the state equation and observation equation. The nonlinear state equation is expressed as:
[0050] xk =f(x k-1 ,u k );
[0051] Where f() is the nonlinear state transfer function;
[0052] Perform Taylor expansion to obtain the state transfer matrix F k :
[0053]
[0054] In the formula, It is based on u k Calculate the state estimate at time k-1;
[0055] The nonlinear observation equation is:
[0056] z k =h(x k )+v k ;
[0057] In the formula, h(x k ) is a nonlinear observation function;
[0058] Perform Taylor expansion to obtain the state transfer matrix H k :
[0059]
[0060] According to the linearized state equation and observation equation, prediction and update are performed according to the steps of Kalman filtering. The delay compensation term needs to be corrected in the update step.
[0061] The covariance matrix of process noise and observation noise is adjusted through experiments or simulations to improve the robustness and accuracy of the filter. The delay compensation term is dynamically updated according to real-time changes in water temperature, salinity, and water depth, and fed back to the filter to improve the adaptability of the system.
[0062] S3 includes obtaining the real-time status data of the target through a positioning sensor such as suona or GPS, the real-time status data including position and speed data, obtaining underwater environmental data through underwater sensors or from external data, and using the underwater environmental data to calculate the water sound propagation speed, and then calculating the water sound propagation delay.
[0063] S3 includes using a recursive filtering method of a Kalman filter or an extended Kalman filter to estimate the target state in real time, including predicting the current state and updating it based on new observation data, and when the observation is updated, compensating for the underwater acoustic propagation delay is added to the measurement data;
[0064] The accuracy of state estimation is optimized by calculating the underwater acoustic delay in real time and compensating it into the observation data. In the observation update at each moment, the calculated underwater acoustic delay is subtracted from the observation value to perform delay compensation:
[0065] z k 1 =z k -Δt k ;
[0066] In the formula, z k 1 is z minus the water sound delay k ; When updating the target state estimate, the modified observations are used for calculation:
[0067]
[0068] The target state after real-time estimation and compensation is provided as the output result of the system to the downstream modules, which include the positioning system, navigation control system and signal processing system.
[0069] S4 includes regularly collecting environmental data and recalculating the underwater acoustic propagation speed and underwater acoustic delay. The system needs to achieve real-time feedback and automatically adjust delay compensation, including real-time updating of environmental data, dynamic calculation of propagation delay and feedback of delay changes;
[0070] Real-time updating of environmental data is done by using sensors to regularly collect water temperature, salinity and depth data;
[0071] Dynamically calculate the propagation delay based on the latest environmental data and current position to calculate the latest underwater acoustic propagation delay;
[0072] Delay change feedback is the updating process of feeding back the delay change to the filter, so that the filter can adapt to the delay change in time.
[0073] Compared with the prior art, the present invention has the following beneficial effects: by introducing a real-time estimation and compensation mechanism for underwater acoustic propagation delay in a recursive filtering algorithm, the system can dynamically adjust the delay parameters and correct the error caused by the delay in real time. This dynamic compensation method can more accurately cope with the delay fluctuations caused by environmental changes during underwater acoustic propagation, thereby significantly improving the positioning accuracy and the robustness of signal processing; it can adapt to changes in different underwater environments, including factors such as water flow, temperature fluctuations, salinity changes, and water depth; through the delay compensation item in the recursive filtering, it is possible to adjust the parameters in real time in a dynamic environment, thereby improving the adaptability of the system. BRIEF DESCRIPTION OF THE DRAWINGS
[0074] Figure 1 It is a technical flow chart of the present invention;
[0075] Figure 2 This is the effect diagram of underwater acoustic delay compensation. DETAILED DESCRIPTION
[0076] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention is described clearly and completely below. Obviously, the described embodiments are part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.
[0077] A linear recursive filtering method taking into account underwater acoustic delay, comprising:
[0078] S1. Based on the physical characteristics of underwater acoustic propagation, taking into account the non-uniformity, temperature, salinity and depth of the underwater environment, an underwater acoustic delay model is established to estimate the delay effect on the underwater acoustic signal during the propagation process;
[0079] S2. Based on the Kalman filter or extended Kalman filter (EKF) algorithm, the underwater acoustic delay model is integrated into the filtering process, the influence of the underwater acoustic delay on the current state estimation is calculated, and compensation is performed to reduce the error caused by the delay;
[0080] S3. Using the recursive filtering method, the delay is estimated in real time at each update, and the state estimate is adjusted according to the delay to ensure the accuracy and stability of the filter;
[0081] S4. In the Kalman filter, by introducing the delay compensation term, the filter can adapt to the changes in the underwater acoustic delay and obtain accurate target state estimation.
[0082] S1 includes the calculation of the speed of underwater sound propagation:
[0083] v(T,S,D)=1500+4.6T-0.0055S+0.00029D;
[0084] Where v is the speed of sound in water, T is the water temperature, S is the salinity, and D is the water depth;
[0085] The distance from the transmitter to the receiver affects the propagation delay. The speed of sound in water varies with underwater environmental factors, including hydrology, salinity, and water depth. The relationship between underwater sound propagation delay, propagation distance, and sound speed is:
[0086]
[0087] Where Δt is the underwater acoustic propagation delay, and d is the actual distance the signal propagates.
[0088] S1 includes the time measurement error τ caused by the vertical sound velocity stratification:
[0089]
[0090] In the formula, z p and z q is the depth of the upper and lower boundaries of the layer, δs(z) is the slowness deviation between the reference sound velocity profiles, c(z) is the sound velocity at depth z, s(z) is the sound velocity slowness, s n is s(z) of the nth layer, dividing the sound velocity profile into N layers, z n is the depth of the nth layer, δ is the cosine of the grazing angle;
[0091] Assume that in each sound speed layer s n It varies linearly with the horizontal distance x, is a constant, z n The horizontal displacement dx of the sound path caused by the horizontal gradient of the sound velocity structure of the nth layer is:
[0092]
[0093] Where Δx is the horizontal distance and Δz is the depth difference;
[0094] The propagation time delay t caused is:
[0095]
[0096] The error in the vertical direction is the sound line bending error caused by the change in sound speed. The sound line bending error prevents the sound line from arriving vertically, resulting in time delay.
[0097] S2 includes using Kalman filtering to process linear systems and using extended Kalman filtering to process nonlinear systems.
[0098] In the underwater positioning system, the state variable x k for:
[0099] x k =[x 1,k x 2,k x 3,k …x n,k ] T ;
[0100] In the formula, x n,k is the value of the nth state variable at time step k, where n is the dimension of the state variable;
[0101] Control input u k for:
[0102] u k =[u 1,k u 2,k u 3,k …um,k ] T ;
[0103] In the formula, u m,k is the value of the mth control input at time step k, where m is the dimension of the control input;
[0104] Observable quantity z k for:
[0105] z k =[z 1,k z 2,k z 3,k …z p,k ] T ;
[0106] In the formula, z p,k is the value of the pth observation at time step k, where p is the dimension of the observation.
[0107] S2 includes assuming that the system is linear and using a linear model to describe the state transition process. The state equation is expressed as:
[0108] x k =Ax k-1 +Bu k +w k ;
[0109] Where A is the state transfer matrix, which represents the transition relationship of the system from time k-1 to time k, B is the control input matrix, which represents the influence of the control input on the state, and w k is the process noise, which is zero-mean, Gaussian white noise with covariance Q;
[0110] The observation equation is:
[0111] z k =Hx k +v k ;
[0112] Where H is the observation matrix, which maps the system state to the observation space, v k is the observation noise, which is zero-mean, Gaussian white noise with covariance R;
[0113] Assuming that the underwater acoustic propagation delay is calculated from environmental factors, taking into account the underwater acoustic propagation delay, the observation equation is changed to:
[0114] z k =Hx k +v k -Δt k ;
[0115] In the formula, Δt k is the delay compensation item at the current moment;
[0116] Taking into account the delay compensation term, the optimal state estimation iterative update is:
[0117]
[0118] In the formula, is the posterior state estimate at time step k, is the prior state estimate at time step k, K k is the Kalman gain.
[0119] S2 includes assuming that the system is nonlinear and using extended Kalman filtering to linearize the state equation and observation equation. The nonlinear state equation is expressed as:
[0120] x k =f(x k-1 ,u k );
[0121] Where f() is the nonlinear state transfer function;
[0122] Perform Taylor expansion to obtain the state transfer matrix F k :
[0123]
[0124] In the formula, It is based on u k Calculate the state estimate at time k-1;
[0125] The nonlinear observation equation is:
[0126] z k =h(x k )+v k ;
[0127] In the formula, h(x k ) is a nonlinear observation function;
[0128] Perform Taylor expansion to obtain the state transfer matrix H k :
[0129]
[0130] According to the linearized state equation and observation equation, prediction and update are performed according to the steps of Kalman filtering. The delay compensation term needs to be corrected in the update step.
[0131] The covariance matrix of process noise and observation noise is adjusted through experiments or simulations to improve the robustness and accuracy of the filter. The delay compensation term is dynamically updated according to real-time changes in water temperature, salinity, and water depth, and fed back to the filter to improve the adaptability of the system.
[0132] S3 includes obtaining the real-time status data of the target through a positioning sensor such as suona or GPS, the real-time status data including position and speed data, obtaining underwater environmental data through underwater sensors or from external data, and using the underwater environmental data to calculate the water sound propagation speed, and then calculating the water sound propagation delay.
[0133] S3 includes using a recursive filtering method of a Kalman filter or an extended Kalman filter to estimate the target state in real time, including predicting the current state and updating it based on new observation data, and when the observation is updated, compensating for the underwater acoustic propagation delay is added to the measurement data;
[0134] The accuracy of state estimation is optimized by calculating the underwater acoustic delay in real time and compensating it into the observation data. In the observation update at each moment, the calculated underwater acoustic delay is subtracted from the observation value to perform delay compensation:
[0135] z k 1 =z k -Δt k ;
[0136] In the formula, z k 1 is z minus the water sound delay k ; When updating the target state estimate, the modified observations are used for calculation:
[0137]
[0138] The target state after real-time estimation and compensation is provided as the output result of the system to the downstream modules, which include the positioning system, navigation control system and signal processing system.
[0139] S4 includes regularly collecting environmental data and recalculating the underwater acoustic propagation speed and underwater acoustic delay. The system needs to achieve real-time feedback and automatically adjust delay compensation, including real-time updating of environmental data, dynamic calculation of propagation delay and feedback of delay changes;
[0140] Real-time updating of environmental data is done by using sensors to regularly collect water temperature, salinity and depth data;
[0141] Dynamically calculate the propagation delay based on the latest environmental data and current position to calculate the latest underwater acoustic propagation delay;
[0142] Delay change feedback is the updating process of feeding back the delay change to the filter, so that the filter can adapt to the delay change in time. Figure 1As shown. In the simulation of the underwater positioning system, the target moves from position P1 to position P2, and the target position is measured by the hydroacoustic signal. For simplicity, it is assumed in the simulation process that the actual trajectory of the target is a straight line in two-dimensional space, and the real position changes with time; the delay of hydroacoustic propagation is affected by the environment, and the underwater environment includes water temperature, salinity and water depth; the environmental parameters are known, and the delay is calculated using the formula.
[0143] The effect of underwater acoustic delay compensation is shown in the figure below: Figure 2 As shown in the figure, the blue represents the real trajectory of the target, which moves along the accelerated straight line; the red represents the original observation position data (including delay), and due to the influence of delay, the observation position deviates from the real position; the green square represents the observation position after delay compensation. The compensated observation data will be restored to the real trajectory. The real trajectory moves along a straight line with acceleration; due to the delay of underwater sound propagation, there is a significant offset between the observation position and the real trajectory, especially when the time is long, the delay effect is more obvious; after delay compensation, the observation data completely overlaps with the real trajectory, indicating that the delay has been effectively compensated.
[0144] The method proposed in the present invention enhances the influence of time delay, especially in the case of long time and long distance, the compensation effect becomes more obvious, and through simulation, the role of the time delay compensation mechanism is more intuitive, and the difference in trajectory before and after compensation can be clearly demonstrated.
[0145] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, a person skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some or all of the technical features may be replaced by equivalents, and these modifications or replacements 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. A linear recursive filtering method taking into account underwater acoustic delay, characterized in that: include: S1. Based on the physical characteristics of underwater acoustic propagation, taking into account the non-uniformity, temperature, salinity and depth of the underwater environment, an underwater acoustic delay model is established to estimate the delay effect on the underwater acoustic signal during the propagation process; S2. Based on the Kalman filter or extended Kalman filter (EKF) algorithm, the underwater acoustic delay model is integrated into the filtering process, the influence of the underwater acoustic delay on the current state estimation is calculated, and compensation is performed to reduce the error caused by the delay; S3. Using the recursive filtering method, the delay is estimated in real time at each update, and the state estimate is adjusted according to the delay to ensure the accuracy and stability of the filter; S4. In the Kalman filter, by introducing the delay compensation term, the filter can adapt to the changes in the underwater acoustic delay and obtain accurate target state estimation.
2. A linear recursive filtering method taking into account underwater acoustic delay according to claim 1, characterized in that: S1 includes the calculation of the speed of underwater sound propagation: v(T,S,D)=1500+4.6T-0.0055S+0.00029D; Where v is the speed of sound in water, T is the water temperature, S is the salinity, and D is the water depth; The distance from the transmitter to the receiver affects the propagation delay. The speed of sound in water varies with underwater environmental factors, including hydrology, salinity, and water depth. The relationship between underwater sound propagation delay, propagation distance, and sound speed is: Where Δt is the underwater acoustic propagation delay, and d is the actual distance the signal propagates.
3. A linear recursive filtering method taking into account underwater acoustic delay according to claim 2, characterized in that: S1 includes the time measurement error τ caused by the vertical sound velocity stratification: In the formula, z p and z q is the depth of the upper and lower boundaries of the layer, δs(z) is the slowness deviation between the reference sound velocity profiles, c(z) is the sound velocity at depth z, s(z) is the sound velocity slowness, s n is s(z) of the nth layer, dividing the sound velocity profile into N layers, z n is the depth of the nth layer, δ is the cosine of the grazing angle; Assume that in each sound speed layer s n It varies linearly with the horizontal distance x, is a constant, z n The horizontal displacement dx of the sound path caused by the horizontal gradient of the sound velocity structure of the nth layer is: Where Δx is the horizontal distance and Δz is the depth difference; The propagation time delay t caused is: The error in the vertical direction is the sound line bending error caused by the change in sound speed. The sound line bending error prevents the sound line from arriving vertically, resulting in time delay.
4. A linear recursive filtering method taking into account underwater acoustic delay according to claim 3, characterized in that: S2 includes using Kalman filtering to process linear systems and using extended Kalman filtering to process nonlinear systems.
5. A linear recursive filtering method taking into account underwater acoustic delay according to claim 4, characterized in that: In the underwater positioning system, the state variable x k for: x k =[x 1,k x 2,k x 3,k … x n,k ] T ; In the formula, x n,k is the value of the nth state variable at time step k, where n is the dimension of the state variable; Control input u k for: in k =[in 1,k in 2,k in 3,k ... in m,k ] T ; In the formula, u m,k is the value of the mth control input at time step k, where m is the dimension of the control input; Observable quantity z k for: With k =[of 1,k With 2,k With 3,k … With p,k ] T ; In the formula, z p,k is the value of the pth observation at time step k, where p is the dimension of the observation.
6. A linear recursive filtering method taking into account underwater acoustic delay according to claim 5, characterized in that: S2 includes assuming that the system is linear and using a linear model to describe the state transition process. The state equation is expressed as: x k =Ax k-1 +Bu k +w k ; Where A is the state transfer matrix, which represents the transition relationship of the system from time k-1 to time k, B is the control input matrix, which represents the influence of the control input on the state, and w k is the process noise, which is zero-mean, Gaussian white noise with covariance Q; The observation equation is: z k =Hx k +v k ; Where H is the observation matrix, which maps the system state to the observation space, v k is the observation noise, which is zero-mean, Gaussian white noise with covariance R; Assuming that the underwater acoustic propagation delay is calculated from environmental factors, taking into account the underwater acoustic propagation delay, the observation equation is changed to: z k =Hx k +v k -Δt k ; In the formula, Δt k is the delay compensation item at the current moment; Taking into account the delay compensation term, the optimal state estimation iterative update is: In the formula, is the posterior state estimate at time step k, is the prior state estimate at time step k, K k is the Kalman gain.
7. A linear recursive filtering method taking into account underwater acoustic delay according to claim 6, characterized in that: S2 includes assuming that the system is nonlinear and using extended Kalman filtering to linearize the state equation and observation equation. The nonlinear state equation is expressed as: x k =f(x k-1 ,u k ); Where f() is the nonlinear state transfer function; Perform Taylor expansion to obtain the state transfer matrix F k : In the formula, u k It is based on u k Calculate the state estimate at time k-1; The nonlinear observation equation is: z k =h(x k )+v k ; In the formula, h(x k ) is a nonlinear observation function; Perform Taylor expansion to obtain the state transfer matrix H k : According to the linearized state equation and observation equation, prediction and update are performed according to the steps of Kalman filtering. The delay compensation term needs to be corrected in the update step. The covariance matrix of process noise and observation noise is adjusted through experiments or simulations to improve the robustness and accuracy of the filter. The delay compensation term is dynamically updated according to real-time changes in water temperature, salinity, and water depth, and fed back to the filter to improve the adaptability of the system.
8. A linear recursive filtering method taking into account underwater acoustic delay according to claim 7, characterized in that: S3 includes obtaining the real-time status data of the target through a positioning sensor such as suona or GPS, the real-time status data including position and speed data, obtaining underwater environmental data through underwater sensors or from external data, and using the underwater environmental data to calculate the water sound propagation speed, and then calculating the water sound propagation delay.
9. A linear recursive filtering method taking into account underwater acoustic delay according to claim 8, characterized in that: S3 includes using a recursive filtering method of a Kalman filter or an extended Kalman filter to estimate the target state in real time, including predicting the current state and updating it based on new observation data, and when the observation is updated, compensating for the underwater acoustic propagation delay is added to the measurement data; The accuracy of state estimation is optimized by calculating the underwater acoustic delay in real time and compensating it into the observation data. In the observation update at each moment, the calculated underwater acoustic delay is subtracted from the observation value to perform delay compensation: With k 1 =from k -Δt k ; In the formula, z k 1 is z minus the water sound delay k ; When updating the target state estimate, the modified observations are used for calculation: The target state after real-time estimation and compensation is provided as the output result of the system to the downstream modules, which include the positioning system, navigation control system and signal processing system.
10. A linear recursive filtering method taking into account underwater acoustic delay according to claim 9, characterized in that: S4 includes regularly collecting environmental data and recalculating the underwater acoustic propagation speed and underwater acoustic delay. The system needs to achieve real-time feedback and automatically adjust delay compensation, including real-time updating of environmental data, dynamic calculation of propagation delay and feedback of delay changes; Real-time updating of environmental data uses sensors to regularly collect water temperature, salinity and depth data; Dynamically calculate the propagation delay based on the latest environmental data and current position to calculate the latest underwater acoustic propagation delay; Delay change feedback is the updating process of feeding back the delay change to the filter, so that the filter can adapt to the delay change in time.