Joint estimation method and system for one-way long baseline underwater positioning based on graph optimization

Abstract

This application provides a graph optimization-based joint estimation method and system for single-trip long-baseline underwater positioning, relating to the field of underwater acoustic positioning and navigation technology. The method includes acquiring observation data and prior information; constructing an estimation window and state variables; constructing a flight time factor using a flight time observation model of a single-trip long-baseline positioning system containing state variables; constructing a sound speed prior term, a timing state regularization term, and a zero-mean centering term using a sound speed prior and base station timing state centering constraints containing state variables; constructing a depth factor based on depth measurements; constructing a nonlinear least-squares objective function; solving the objective function; and outputting the underwater vehicle trajectory within the estimation window, the window's constant effective sound speed, and the timing state of each base station. This application can achieve high-precision estimation of the underwater vehicle's position even under conditions of propagation model mismatch and base station timing errors, and is applicable to underwater navigation, unmanned platform collaborative operations, and marine observation.

Description

Technical Field

[0001] This application relates to the field of underwater acoustic positioning and navigation technology, and more specifically, to a graph optimization-based method and system for joint estimation of single-trip long baseline underwater positioning. Background Technology

[0002] With the rapid development of marine resource exploration and development, collaborative operations of underwater unmanned platforms, and marine environmental observation, underwater positioning and navigation technology has become a core supporting technology for marine engineering equipment and underwater operation systems. Among them, the long baseline (LBL) acoustic positioning system, with its core advantages of long operating range, high positioning accuracy, and positioning error not accumulating with the travel distance, has become the mainstream technical solution for underwater vehicles, autonomous underwater vehicles (AUVs), remotely operated vehicles (ROVs), and other underwater operation platforms to achieve long-term, long-range, and high-precision positioning.

[0003] Traditional two-way round-trip long baseline positioning systems require the vehicle to send an interrogation signal to an underwater base station and then receive a response signal from the base station. Distance measurement and positioning are achieved through the round-trip time. Although this mode has lower requirements for time synchronization, it has inherent drawbacks: on the one hand, the signal handshake operation mode results in high power consumption at the vehicle end, which is not conducive to the long-term endurance operation of underwater platforms; on the other hand, acoustic channel conflicts and interference are prone to occur in multi-user scenarios, the system has poor scalability, and it is difficult to adapt to the application requirements of large-scale multi-underwater platform collaborative operations.

[0004] To address the aforementioned shortcomings of two-way long baseline systems, single-way long baseline positioning technology has emerged. This technology employs a working mode where an underwater base station broadcasts an acoustic synchronization signal unidirectionally, and the underwater vehicle passively receives and measures the signal's time of flight (TOF). This eliminates the need for round-trip handshake communication between the vehicle and the base station, reducing power consumption and acoustic channel occupancy at the vehicle end. It is easily scalable to multi-platform collaborative scenarios. However, it is more sensitive to time synchronization quality and propagation model accuracy, and suffers from sound speed uncertainty, propagation model mismatch, and timing errors related to the base station.

[0005] Most existing single-path long-baseline positioning schemes employ multilateral measurement methods under the assumption of a fixed sound velocity. These methods set the seawater sound velocity as a constant during positioning calculations, failing to adapt to the sound propagation characteristics of actual marine environments. In the real ocean, the seawater sound velocity exhibits significant spatial and temporal distribution differences due to factors such as temperature, salinity, and hydrostatic pressure. Furthermore, sound rays bend under complex hydrological conditions, leading to a severe mismatch between the straight-line propagation model used for positioning calculations and actual sound propagation patterns. The fixed sound velocity assumption introduces substantial systematic positioning errors, which existing schemes cannot effectively suppress. In medium- to long-range positioning scenarios, errors can reach the hundreds of meters, failing to meet the demands of high-precision underwater operations.

[0006] Furthermore, the accuracy of long-baseline positioning is highly dependent on the quality of time synchronization between the base station and the vehicle. Existing technologies struggle to achieve low-cost, highly stable time synchronization and timing error correction. Moreover, clock drift during long-term underwater operations generates timing biases related to the base station, directly leading to systematic shifts in positioning results. When the long-baseline positioning system updates at a low frequency and observation data is sparse, independent calculations at a single moment cannot continuously constrain the vehicle's trajectory, further amplifying positioning errors caused by sound speed mismatch and timing errors. Simultaneously, step-by-step correction of sound speed or timing errors introduces a gradual accumulation of errors. In complex marine environments where propagation model mismatch and base station timing errors coexist, positioning accuracy drops sharply, making it unsuitable for long-term, stable underwater navigation operations. Summary of the Invention

[0007] To address the aforementioned problems, this application employs a graph optimization-based joint estimation method for single-trip long-baseline underwater positioning, comprising the following steps: Acquire observational data and prior information; Construct an estimation window and state variables, including the underwater vehicle trajectory, the window constant effective sound speed, and the timing status of each base station; The flight time factor is constructed by using a flight time observation model of a single-way long baseline positioning system that includes state variables. The sound speed prior, timing state regularization term and zero mean centralization term are constructed by using the sound speed prior and base station timing state centralization constraint that include state variables. The depth factor is constructed based on the depth measurement value. A nonlinear least squares objective function is constructed based on the flight time factor, sound speed prior term, timing state regularization term, zero-mean centering term, and depth factor. The objective function is solved, and the underwater vehicle trajectory, window constant effective sound speed, and timing state of each base station within the estimation window are output.

[0008] Optionally, it also includes introducing relative motion constraints between adjacent long baseline positioning system update times to obtain the Doppler velocity factor; Constructing a nonlinear least squares objective function also involves incorporating Doppler velocity factors into the nonlinear least squares objective function.

[0009] Optionally, the flight time factor is constructed using a single-trip long baseline positioning system flight time observation model, including the time factors from the first... i The base station, at the k The flight time measurement τ obtained at each update time k,i The linear propagation approximation is adopted to establish the observation equation, and the normalized residual term is further constructed as the flight time factor. ; In the formula, Indicates the first The update time is the one-way flight time measurement from the i-th base station. Indicates the first At each update moment, the underwater vehicle's three-dimensional position... This represents the three-dimensional position of the i-th base station. This represents the relative timing deviation of the i-th base station. This represents the constant effective sound velocity of the current estimation window. The noise term represents the time-of-flight measurement; ; In the formula, Represents the time-of-flight factor. This represents the standard deviation of the noise in time-of-flight measurements.

[0010] Optionally, the speed of sound prior term The following formula represents: , In the formula, This represents the constant effective sound velocity of the current estimation window. Indicates the reference speed of sound. It represents the standard deviation of the prior sound speed.

[0011] Optionally, timing state regularization term The following formula represents: In the formula, This represents the relative timing deviation of the i-th base station. This represents the standard deviation of the prior timing bias of the base station.

[0012] Optionally, zero-mean centered term The following formula represents: ; In the formula, This indicates the total number of base stations. This represents the relative timing state of the i-th base station. i This represents the index of an underwater acoustic base station.

[0013] Optionally, obtaining the depth factor based on depth measurement includes: The pressure sensor provides depth measurements at the update time of the long baseline positioning system. The depth residual is constructed as follows: ; In the formula, Represents the depth factor. Indicates the first Spacecraft position vector at time The Z-axis component (depth). Indicates the first The depth measurement value output by the pressure sensor at any given time. This represents the noise standard deviation of pressure depth measurements.

[0014] Optionally, introducing relative motion constraints between adjacent long baseline positioning system update times includes: setting the interval between adjacent times as... The interval average Doppler velocity measurement is Then it is defined as: ; In the formula, This is represented by the timestamp of the k-th update time. Represented as the timestamp of the (k-1)th update time. Represents the original Doppler velocity measurement value at any time t; ; In the formula, Indicates the Doppler velocity factor. This represents the equivalent noise standard deviation of Doppler velocimeters. Indicates the first At each update moment, the underwater vehicle's three-dimensional position... Indicates the first At each update moment, the underwater vehicle's three-dimensional position... An index representing the update time of a long baseline positioning system. This represents the total number of update times for the long baseline positioning system within the optimization window.

[0015] Optionally, solving the objective function includes using the results of fixed sound velocity polygon measurements as initial position values, c eff Initialized to c0, each b i Initialize to 0 and use the trust region reflection algorithm to solve.

[0016] This application also provides a graph optimization-based joint estimation system for single-trip long-baseline underwater positioning, used to perform any of the aforementioned graph optimization-based joint estimation methods for single-trip long-baseline underwater positioning, including: The data acquisition module is used to acquire flight time measurements, base station locations, pressure depth measurement data, and reference sound velocity from the single-trip long baseline positioning system. The state construction module is used to construct an estimation window based on the update time of the long baseline positioning system, and defines a joint state variable to be estimated, including the underwater vehicle trajectory, the effective sound speed of the window constant, and the timing status of each base station. The factor building module is used to generate time-of-flight factors and pressure-depth factors; The constraint construction module is used to construct soft constraints for the sound speed prior, timing state regularization, and zero-mean centering. The optimization solution module is used to integrate various factors and constraints to construct a nonlinear least squares joint objective function, and uses a batch processing method to perform joint optimization solution for the entire estimation time period. The output module is used to output the underwater vehicle's trajectory, window constant effective sound velocity, and the timing status of each base station.

[0017] The beneficial effects of the graph optimization-based joint estimation method for single-trip long-baseline underwater positioning provided in this application are as follows: This application addresses the unavoidable uncertainties in sound velocity and base station-related timing errors in long-baseline positioning systems. It proposes a unified graph optimization modeling framework capable of simultaneously estimating trajectory, effective sound velocity, and base station timing status. By fusing pressure depth measurement and Doppler velocities into the long-baseline positioning process, it maintains good trajectory constraint capabilities even when the long-baseline positioning system has a low update frequency or when the propagation model is mismatched. By introducing a base station timing status regularization term and a zero-mean centering constraint, the strong coupling between effective sound velocity and timing status is effectively alleviated, improving solution stability. Under the BELLHOP-constructed propagation model mismatch environment, the proposed method can reduce errors from the hundreds of meters to the meters, demonstrating significant engineering application value.

[0018] In summary, the graph optimization-based single-trip long baseline underwater positioning joint estimation method and system provided in this application can achieve high-precision estimation of the position of underwater vehicles under the conditions of propagation model mismatch and base station timing error. It is applicable to underwater navigation, unmanned platform collaborative operation and marine observation and other application scenarios. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below.

[0020] Figure 1 This is a flowchart of the single-trip long baseline underwater positioning joint estimation method based on graph optimization provided in the embodiments of this application; Figure 2 This is a schematic diagram of the factor graph structure of the single-path long baseline positioning system combined with the effective sound velocity and the anchor timing state estimation provided in the embodiments of this application; Figure 3 This is a comparison diagram of horizontal trajectories under the condition of propagation model mismatch provided in the embodiments of this application; Figure 4 This is a comparison diagram of the cumulative distribution function of three-dimensional positioning error under the condition of propagation model mismatch provided in the embodiments of this application; Figure 5These are ablation experiment results under the propagation model mismatch condition provided in the embodiments of this application, where (a) is a comparison of root mean square error and (b) is a comparison of 95th percentile error. Detailed Implementation

[0021] To make the technical problems, technical solutions, and beneficial effects to be solved by this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and are not intended to limit the scope of this application.

[0022] Example 1 This application provides a graph optimization-based joint estimation method for single-trip long-baseline underwater positioning, comprising the following steps: Acquire observational data and prior information; Construct an estimation window and state variables, including the underwater vehicle trajectory, the window constant effective sound speed, and the timing status of each base station; The flight time factor is constructed by using a flight time observation model of a single-way long baseline positioning system that includes state variables. The sound speed prior, timing state regularization term and zero mean centralization term are constructed by using the sound speed prior and base station timing state centralization constraint that include state variables. The depth factor is constructed based on the depth measurement value. A nonlinear least squares objective function is constructed based on the flight time factor, sound speed prior term, timing state regularization term, zero-mean centering term, and depth factor. The objective function is solved, and the underwater vehicle trajectory, window constant effective sound speed, and timing state of each base station within the estimation window are output.

[0023] like Figure 1 As shown, specifically, the graph optimization-based joint estimation method for single-trip long-baseline underwater positioning provided in this application includes: S1 acquires observational data and prior information: acquires long baseline positioning system time-of-flight measurements, base station locations, reference sound speed, depth, and Doppler velocity data.

[0024] S2 Constructing the estimation window and state variables: The estimation window is constructed using the update time of the long baseline positioning system, denoted as the... The spacecraft's position at each update time is Given the first The location of each base station is After removing the clock term common to all base stations at the receiver, the effective speed of sound is set to a constant window value. and the relative timing status of each base station Introducing the state vector, we obtain the joint estimated variables (i.e., state variables) as follows: ; This application uses the update time of the long baseline positioning system as discrete nodes to locate the vehicle in a local navigation coordinate system. The z-axis of the coordinate system points downwards, so the third dimension in the state vector directly corresponds to the vehicle's depth. All position states within the window, together with the shared effective sound speed and base station timing states, constitute the variable nodes in the factor graph.

[0025] The S3-S6 processes below are just step numbers; the four processes S3-S6 can be performed in parallel.

[0026] S3 constructs a flight time factor using a single-trip long baseline positioning system flight time observation model: For those from the i The base station, at the k The flight time measurement τ obtained at each update time k,i The linear propagation approximation is adopted to establish the observation equation, and the normalized residual term is further constructed as the flight time factor. ; In the formula, This represents the one-way flight time measurement from the i-th base station at the k-th update time. This represents the three-dimensional position of the underwater vehicle at the k-th update time. This represents the three-dimensional position of the i-th base station. This represents the relative timing deviation of the i-th base station. This represents the constant effective sound velocity of the current estimation window. The noise term represents the time-of-flight measurement; ; In the formula, Represents the time-of-flight factor. This represents the standard deviation of the noise in time-of-flight measurements.

[0027] In a one-way scenario, the aircraft does not return a response signal to the base station, but instead directly constructs flight time observations using the arrival times of the broadcast signals from each base station. When residual synchronization error dominates, This can be approximated as a timing deviation related to the base station; when propagation model mismatch dominates, Then the base station related error components that are approximately constant within the absorption estimation window are absorbed.

[0028] S4 constructs depth factors based on depth measurements: The pressure sensor provides depth measurements at the update time of the long baseline positioning system. The depth residual is constructed as follows: ; In the formula, Represents the depth factor. Represents the vehicle's position vector at time k. The Z-axis component (depth). This represents the depth measurement value output by the pressure sensor at time k. This represents the noise standard deviation of pressure depth measurements.

[0029] S5 constructs the Doppler velocity factor: Given Doppler velocity data, relative motion constraints are introduced between adjacent long-baseline positioning system update times. Let the interval between adjacent times be... The interval average Doppler velocity measurement is Then it is defined as: ; In the formula, This is represented by the timestamp of the k-th update time. Represented as the timestamp of the (k-1)th update time. Represents the original Doppler velocity measurement value at any time t; ; In the formula, Indicates the Doppler velocity factor. This represents the equivalent noise standard deviation of Doppler velocimeters. Indicates the first At each update moment, the underwater vehicle's three-dimensional position... Indicates the first At each update moment, the underwater vehicle's three-dimensional position... An index representing the update time of a long baseline positioning system. This represents the total number of update times for the long baseline positioning system within the optimization window.

[0030] Since the attitude projection error and instrument slow drift in the actual system will not completely decay with the increase of the average number of samples, this application adopts a conservative weighting strategy for the Doppler velocity factor in simulation and implementation.

[0031] By introducing depth measurements from pressure sensors at each long baseline positioning system update time and introducing Doppler velocity interval average velocity constraints between adjacent update times, the trajectory continuity and observability are enhanced when long baseline positioning system updates are sparse.

[0032] S6 constructs regularization terms and centralization constraints: A reference sound velocity prior is introduced for the effective sound velocity, and an amplitude regularization term is introduced for the timing states of each base station. A zero-mean soft constraint is applied to fix the reference benchmark for each timing state and alleviate [the impact of the system's limitations]. and The coupling between them. To prevent strong coupling between the effective sound velocity and the base station timing state within a short window, this application addresses the coupling between the effective sound velocity c and the base station timing state. eff Apply a weak prior near the reference speed of sound c0, for each b i Apply regularization and add a zero-mean soft constraint: Sound speed prior The following formula represents: , In the formula, This represents the constant effective sound velocity of the current estimation window. Indicates the reference speed of sound. It represents the standard deviation of the prior sound speed.

[0033] Timing state regularization term The following formula represents: In the formula, This represents the relative timing deviation of the i-th base station. This represents the standard deviation of the prior timing bias of the base station.

[0034] Zero-mean centered term The following formula represents: ; In the formula, This indicates the total number of base stations. This represents the relative timing state of the i-th base station. i This represents the index of an underwater acoustic base station.

[0035] Linearizing the time-of-flight model yields: ; In the formula, This is the standard notation for linearization approximation in numerical computation, representing small perturbations. From the above equation, it can be seen that when the estimation window is short and the geometric change is small, c... eff With b i There is a clear coupling between them. Therefore, depth measurement, Doppler velocimetry velocity constraints, and prior regularization together constitute important conditions for improving the identifiability of the problem.

[0036] S7 constructs and solves a joint objective function: The flight time factor, depth factor, Doppler velocity factor, sound speed prior term, timing state regularization term, and zero mean centering term are uniformly written into the nonlinear least squares objective function, and the lsqnonlin trust region reflection algorithm in MATLAB is used to solve it. The output is the vehicle trajectory, effective sound speed, and timing status of each base station within the estimation window.

[0037] Joint Objective Function and Solution: By combining all factors, the following nonlinear least squares objective function is established: ; During the solution process, the results of fixed sound velocity polygon measurements are used as the initial position value, c. eff Initialized to c0, each b i Initialized to 0. In the simulation implementation corresponding to this application, a batch processing method is used to jointly optimize the entire estimation time period.

[0038] Time-of-flight observation data with propagation model mismatch were generated using the Bellhop ray tracer and compared with fixed sound velocity multilateral measurement methods and fixed... The proposed method is compared with other methods to verify its effectiveness in improving positioning accuracy in complex propagation environments.

[0039] The S8 outputs the vehicle's trajectory, effective sound speed, and timing status of each base station.

[0040] Simulation experiment design: 1. Scene and Sensor Setup: A 2km × 2km single-trip long baseline positioning system (LBS) measurement area is constructed. Four base stations are deployed at (0,0,10)m, (2000,0,30)m, (2000,2000,50)m, and (0,2000,20)m, respectively. The vehicle moves in a horizontal circular trajectory with a center of (1000,1000)m and a radius of 800m, at a constant depth of 80m. The simulation duration is 300s, with a time step of 1s. The LBS flight time measurement is generated every 5s, resulting in 61 LBS update times. Doppler velocity is sampled every 0.2s and averaged over adjacent LBS update intervals. Depth measurements are generated at the simulation time step and are used for estimation at the LBS update times.

[0041] The reference speed of sound is set to c0 = 1500 m / s, and the timing deviation of each base station meets the following requirements. ,in s. The observation noise parameters are set as follows: s, m / s, m.

[0042] 2. Construction of Propagation Model Mismatch: To construct a controllable propagation model mismatch environment, a Bellhop ray tracer is used to generate true time-of-flight values ​​under a depth-dependent sound velocity profile, while the estimator still uses a linear propagation model for interpretation. The sound velocity profile is represented as: ; Where H = 150m. Three profile offsets are set. m / s is used to represent mild, moderate, and strong propagation model mismatches, respectively. Under this condition, the prior standard deviation of the effective sound velocity is taken as... m / s, and c eff The range of values ​​is constrained as follows: m / s.

[0043] 3. Comparison Method Design: To verify the effectiveness of the method in this application, the following two types of comparison methods are set up. The first is a fixed sound velocity polygonal measurement baseline method, where pseudorange is used independently for positioning at each long baseline positioning system time. The second is a fixed c0 map optimization method, which uses the same trajectory parameterization, Doppler velocity factor, and depth factor as this application, but with a fixed c0 map. eff =c0 and b i =0.

[0044] ; For each propagation mismatch condition, 20 independent Monte Carlo experiments were conducted. In each experiment, base station timing bias, flight time, Doppler velocity, and depth noise were resampled, while the flight path remained consistent with the propagation environment.

[0045] Simulation analysis: The method described in this application demonstrates stable and high-precision positioning capabilities under three propagation model mismatch conditions. The fixed sound velocity polygon measurement method, along with... The increase in c0 exhibits a significant systematic bias and large error dispersion; the fixed c0 graph optimization method significantly improves trajectory stability after introducing Doppler velocity measurement and depth constraints; further joint estimation of c eff With b i Afterwards, most of the residual system bias can be eliminated.

[0046] The Monte Carlo statistical results are shown in Tables 1 and 2. The results show that the root mean square error of the proposed method remains around 2.1 m under all three mismatch conditions, significantly better than the two comparative methods. Especially in… Under the severe mismatch condition of m / s, the root mean square error of the fixed c0 graph optimization method is still 20.7m, while the method in this application can be reduced to 2.1m, indicating that the joint estimation of effective sound velocity and base station timing state plays an important role in suppressing propagation mismatch bias.

[0047] Table 1. Statistical results of root mean square error under mismatch conditions for the three propagation models (unit: m)

[0048] Table 2. Statistical results of P95 under mismatch conditions for the three propagation models (unit: m)

[0049] like Figure 2As shown in the figure, this illustrates the graph optimization modeling approach of this application. The positioning state, effective sound velocity state, and timing state corresponding to each base station are jointly optimized within the same estimation window, and a depth factor and a Doppler velocimetry velocity factor are introduced simultaneously to enhance the estimation stability under the condition of sparse updates in long baseline positioning systems.

[0050] like Figure 3 As shown in the figure, each dot represents the localization result at a discrete sampling time. The black curve represents the true trajectory (which coincides with the trajectory obtained by the method in this application), the red dashed line represents the fixed sound velocity polygon localization result, and the blue curve represents the joint estimation result proposed in this application. It can be seen that the fixed sound velocity baseline method has obvious systematic bias, while the method in this application is closer to the true trajectory.

[0051] like Figure 4 As shown in the figure, this statistical distribution illustrates the error levels of different methods. Compared to the baseline method, the error distribution of the joint estimation method proposed in this application is generally concentrated in the small error region, indicating that it has better robustness under the condition of propagation model mismatch.

[0052] Table 3. Monte Carlo statistical results of the propagation model mismatch experiment (unit: m)

[0053] As shown in Table 3, under the three propagation model mismatch intensities, the joint estimation method proposed in this application can stably control the root mean square error to the order of approximately 2 m. In contrast, the root mean square error of fixed sound velocity multilateral positioning ranges from 109.9 m to 186.4 m, which is significantly larger. This result demonstrates that the method proposed in this application can effectively suppress systematic errors caused by sound velocity uncertainty, propagation model mismatch, and anchor timing deviation.

[0054] Figure 5 (a) in the figure represents the comparison of root mean square error. Figure 5 (b) in the figure represents the comparison at P95 (95th percentile error). Figure 5 (a) and Figure 5 In (b), "baseline method" refers to the fixed sound velocity multilateral measurement method as the baseline model, "fixed sound velocity + auxiliary" refers to the fixed c0 combined with auxiliary sensor constraint method, "method of this application" refers to the complete joint estimation method (i.e. the graph optimization-based single-trip long baseline underwater positioning joint estimation method provided in this application), and "this application-Doppler" and "this application-depth factor" refer to the methods of removing the Doppler velocity factor and depth factor based on the complete joint estimation method, respectively.

[0055] The results show that the error increases significantly after removing the depth constraint, and the error also increases significantly after removing the Doppler velocity constraint. This indicates that both the depth factor and the Doppler velocity factor play an important role in improving positioning accuracy, with the depth factor having a more prominent stabilizing effect under the current simulation geometry.

[0056] Ablation experiments show that, in a representative single experiment, the root mean square error (RMSE) of the fixed c0 combined with auxiliary sensor constraint method is 20.7 m; the RMSE of the complete joint estimation method is 1.7 m; after removing the Doppler velocity factor, it rises to 6.1 m; and after removing the depth factor, it rises sharply to 140.6 m. This indicates that, under the geometric configuration and update frequency corresponding to this application, the depth factor is a key constraint to prevent timing errors from being erroneously absorbed into the vertical motion, while the Doppler velocity factor further improves the trajectory continuity between update times of adjacent long baseline positioning systems.

[0057] Comprehensive analysis shows that Doppler velocities and depth constraints provide the main stabilization effect, while the joint estimation of effective sound velocity and base station timing states further eliminates the residual system bias under the fixed sound velocity model. In this application, b i It is more appropriate to understand it as the effective base station timing state that absorbs the modeling error of approximate constant value within the estimation window, rather than simply equating it with the fixed hardware delay.

[0058] This application focuses on the problems of sound velocity uncertainty, propagation model mismatch, and base station-related timing errors in single-journey long baseline positioning of underwater vehicles. It provides an underwater positioning method based on graph optimization, which jointly estimates sound velocity and base station timing status in a single-journey long baseline positioning system, belonging to the field of underwater acoustic positioning and navigation technology. In a single-journey long baseline positioning system, the base station broadcasts a signal unidirectionally to the underwater vehicle, and the vehicle positions itself based on its flight time. This method eliminates the need for round-trip handshakes and is easily scalable to multi-platform collaborative scenarios, but it is more sensitive to time synchronization quality and propagation model accuracy. This application constructs a factor graph model based on an estimation window, using the vehicle trajectory, the window's constant effective sound velocity, and the relative timing status of each base station as joint estimation variables. It also integrates pressure depth measurement and Doppler velocimetry velocity constraints and uses a nonlinear least squares method for solution. Monte Carlo experiments conducted in a 2km×2km simulated sea area show that the root mean square error (RMSE) of the fixed sound velocity polygonal measurement baseline method ranges from 110m to 186m. After introducing Doppler velocity and depth constraints, this error can be reduced to 5.5m to 20.7m. Furthermore, by jointly estimating the effective sound velocity and base station timing, the error can be stably reduced to approximately 2.1m. This application can significantly suppress system bias under propagation model mismatch conditions, improving the positioning accuracy and robustness of single-path long baseline positioning systems.

[0059] This application addresses the unavoidable uncertainties in sound velocity and base station-related timing errors in single-path long baseline positioning systems by proposing a unified graph optimization modeling framework that can simultaneously estimate the trajectory, effective sound velocity, and base station timing status.

[0060] This application integrates pressure depth measurement and Doppler velocity information into the positioning process of a long baseline positioning system, which can still maintain good trajectory constraint capability even when the long baseline positioning system has a low update frequency or the propagation model has mismatch.

[0061] This application effectively alleviates the strong coupling between the effective sound velocity and the timing state by introducing a base station timing state regularization term and a zero-mean centralization constraint, thereby improving the solution stability.

[0062] In the case of a mismatch in the propagation model constructed by Bellhop, the method in this application can reduce the error from the order of hundreds of meters to the order of meters, which has high engineering application value.

[0063] The method proposed in this application has a clear structure and is easy to extend to online estimation with sliding windows, time-varying sound velocity modeling, and robust localization tasks in complex sea trial scenarios.

[0064] In summary, the underwater positioning method proposed in this application, which combines sound speed and base station timing state estimation for a single-trip long baseline positioning system based on graph optimization, can achieve high-precision estimation of the position of underwater vehicles under the conditions of propagation model mismatch and base station timing error. It is applicable to underwater navigation, collaborative operation of unmanned platforms, and marine observation.

[0065] This application also provides a graph optimization-based joint estimation system for single-trip long-baseline underwater positioning, used to perform any of the aforementioned graph optimization-based joint estimation methods for single-trip long-baseline underwater positioning, including: The data acquisition module is used to acquire flight time measurements, base station locations, pressure depth measurement data, and reference sound velocity from the single-trip long baseline positioning system. The state construction module is used to construct an estimation window based on the update time of the long baseline positioning system, and defines a joint state variable to be estimated, including the underwater vehicle trajectory, the effective sound speed of the window constant, and the timing status of each base station. The factor building module is used to generate time-of-flight factors and pressure-depth factors; The constraint construction module is used to construct soft constraints for the sound speed prior, timing state regularization, and zero-mean centering. The optimization solution module is used to integrate various factors and constraints to construct a nonlinear least squares joint objective function, and uses a batch processing method to perform joint optimization solution for the entire estimation time period. The output module is used to output the underwater vehicle's trajectory, window constant effective sound velocity, and the timing status of each base station.

[0066] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application 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 of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A method for joint estimation of one-way long baseline underwater positioning based on graph optimization, characterized in that, Includes the following steps: Acquire observational data and prior information; Construct an estimation window and state variables, the state variables including the underwater vehicle trajectory, the window constant effective sound speed, and the timing status of each base station; A flight time factor is constructed using a flight time observation model of a single-way long baseline positioning system that includes the state variables. A sound speed prior, a timing state regularization term, and a zero-mean centralization term are constructed using a sound speed prior and a base station timing state centralization constraint that include the state variables. A depth factor is constructed based on depth measurement values. A nonlinear least squares objective function is constructed based on the flight time factor, sound speed prior term, timing state regularization term, zero mean centering term and depth factor. The objective function is solved, and the underwater vehicle trajectory, window constant effective sound speed and timing state of each base station are output within the estimation window. It also includes obtaining the Doppler velocity factor by introducing relative motion constraints between update times of adjacent long baseline positioning systems; The construction of the nonlinear least squares objective function also includes incorporating the Doppler velocity factors into the nonlinear least squares objective function; The construction of the time-of-flight factor includes for the data from the first... i The base station, at the k The flight time measurement τ obtained at each update time k,i The linear propagation approximation is adopted to establish the observation equation, and the normalized residual term is further constructed as the flight time factor. ； In the formula, Indicates the first The update time is the one-way flight time measurement from the i-th base station. Indicates the first At each update moment, the underwater vehicle's three-dimensional position... This represents the three-dimensional position of the i-th base station. This represents the relative timing deviation of the i-th base station. This represents the constant effective sound velocity of the current estimation window. The noise term represents the time-of-flight measurement; ； wherein denotes the time of flight factor, denotes the standard deviation of the time of flight measurement noise; The relative motion constraint introduced between adjacent long baseline positioning system update instants comprises: setting the interval between adjacent instants as , and the interval average Doppler velocity as , and the definition is as follows: ； wherein denotes a timestamp of the kth update, denotes a timestamp of the k-1th update, denotes a raw Doppler velocity measurement at an arbitrary time t; ； In the formula, Indicates the Doppler velocity factor. This represents the equivalent noise standard deviation of Doppler velocimeters. Indicates the first At each update moment, the underwater vehicle's three-dimensional position... Indicates the first At each update moment, the underwater vehicle's three-dimensional position... An index representing the update time of a long baseline positioning system. This represents the total number of update times for the long baseline positioning system within the optimization window.

2. The graph optimization based cooperative estimation method for one-way long baseline underwater positioning according to claim 1, wherein: The a priori term of the speed of sound The following formula represents: ， In the formula, This represents the constant effective sound velocity of the current estimation window. Indicates the reference speed of sound. It represents the standard deviation of the prior sound speed.

3. The graph optimization-based joint estimation method for single-trip long baseline underwater positioning according to claim 2, characterized in that: the timing state regularizer The following formula is represented: In the formula, This represents the relative timing deviation of the i-th base station. This represents the standard deviation of the prior timing bias of the base station.

4. The joint estimation method for single-trip long baseline underwater positioning based on graph optimization according to claim 3, characterized in that: the zero-mean centering term The following formula is represented: ； In the formula, This indicates the total number of base stations. Indicates the first i The relative timing status of each base station i This represents the index of an underwater acoustic base station.

5. The joint estimation method for single-trip long baseline underwater positioning based on graph optimization according to claim 1, characterized in that: The method of obtaining the depth factor based on depth measurement includes: The pressure sensor provides depth measurements at the update time of the long baseline positioning system. The depth residual is constructed as follows: ； In the formula, Represents the depth factor. Represents the vehicle's position vector at time k. Z-axis component, This represents the depth measurement value output by the pressure sensor at time k. This represents the noise standard deviation of pressure depth measurements.

6. The graph optimization based cooperative estimation method for one-way long baseline underwater positioning according to claim 1, wherein: The solving target function includes taking the fixed sound velocity multi-measurement result as a position initial value, c eff initialized as c0, each b i initialized as 0, and solved by using a trust region reflection algorithm.

7. A single pass long baseline underwater positioning joint estimation system based on graph optimization, characterized in that, To perform the graph optimization-based joint estimation method for single-trip long baseline underwater positioning as described in any one of claims 1-6, comprising: The data acquisition module is used to acquire flight time measurements, base station locations, pressure depth measurement data, and reference sound velocity from the single-trip long baseline positioning system. The state construction module is used to construct an estimation window based on the update time of the long baseline positioning system, and defines a joint state variable to be estimated, including the underwater vehicle trajectory, the effective sound speed of the window constant, and the timing status of each base station. The factor building module is used to generate time-of-flight factors and pressure-depth factors; The constraint construction module is used to construct soft constraints for the sound speed prior, timing state regularization, and zero-mean centering. The optimization solution module is used to integrate various factors and constraints to construct a nonlinear least squares joint objective function, and uses a batch processing method to perform joint optimization solution for the entire estimation time period. The output module is used to output the underwater vehicle's trajectory, window constant effective sound velocity, and the timing status of each base station.

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