A method for tracking a maneuvering target based on underwater acoustic ray correction

Abstract

The application provides a maneuvering target tracking method based on underwater acoustic ray correction, comprising the following steps: for each motion model, the following steps are performed: obtaining an interaction motion state estimation value input into an unscented Kalman filter according to an interaction probability of each motion model, a motion state estimation value and a covariance matrix of a previous moment; obtaining a motion state estimation value and a covariance matrix of a next moment according to the interaction motion state estimation value and the covariance matrix; updating the motion state estimation value of the next moment according to compensated measurement data to obtain an updated motion state estimation value of the next moment; judging whether an iteration termination condition is met, if yes, obtaining a best motion state estimation value; if not, continuing iteration according to the updated motion state estimation value of the next moment and the covariance matrix; and performing weighted fusion according to the interaction probability of each motion model and the best motion state estimation value to obtain a final tracking result.

Description

Technical Field

[0001] This invention belongs to the field of target tracking technology, specifically relating to a method for tracking maneuvering targets based on underwater acoustic ray correction. Background Technology

[0002] The complexity of the underwater environment presents two main challenges to underwater target tracking applications: First, the bending deformation of underwater acoustic rays and the model mismatch caused by target maneuvering. Due to variations in underwater sound speed, acoustic rays bend along directions of lower speed. Continuing to use an ideal straight-line propagation model in this situation introduces a significant systematic error to the sensor's measurements, causing the observed target distance to consistently deviate from the true information. Second, the maneuvering patterns of underwater targets differ from those on land and in the air. Using a fixed tracking model that ignores the actual changes in the target's motion state will amplify filtering errors and reduce the overall performance of the tracking algorithm. To ensure the robustness of underwater maneuvering target tracking, a novel maneuvering target tracking method based on underwater acoustic ray correction is proposed to correct and compensate for existing methods. Summary of the Invention

[0003] Purpose of the invention: To address the common problem of insufficient accuracy in existing underwater target tracking technologies, this invention proposes a maneuvering target tracking method based on underwater acoustic ray correction, using the complex underwater acoustic environment of the deep sea as the research background.

[0004] Technical solution: A method for tracking maneuvering targets based on underwater acoustic ray correction, comprising:

[0005] Step 1: For each motion model, perform the following steps:

[0006] Based on the interaction probability of each motion model, the motion state estimate of the previous time step, and the covariance matrix, the interaction motion state estimate input to the unscented Kalman filter is obtained.

[0007] Based on the interactive motion state estimate and covariance matrix, the motion state estimate and covariance matrix for the next moment are obtained.

[0008] Based on the compensated measurement data, the motion state estimate for the next moment is updated to obtain the updated motion state estimate for the next moment.

[0009] Determine if the iteration termination condition is met. If it is met, the optimal motion state estimate is obtained; if not, continue iterating based on the updated motion state estimate and covariance matrix for the next time step.

[0010] Step 2: Perform weighted fusion based on the interaction probability of each motion model and the best motion state estimate to obtain the final tracking result;

[0011] The compensated measurement data is obtained through the following steps:

[0012] S100: Collect information on underwater sound velocity at different depths; the information includes the sound velocity value, the depth corresponding to the sound velocity value, and the sound velocity gradient;

[0013] S200: Collect underwater target measurement data and establish underwater target measurement equations; the target measurement data includes: target one-way time delay, target azimuth angle, and target pitch angle;

[0014] S300: Based on the sound velocity profile, the underwater environment is divided into layers according to depth;

[0015] S400: Using Snell's law of refraction and initial parameters, acoustic parameters are calculated to obtain compensated measurement data.

[0016] Beneficial effects: Compared with existing technologies, it has the following advantages:

[0017] (1) This invention is used for calibrating the ranging error between underwater targets and friendly observation stations. It divides the underwater sound velocity profile data into multiple water layers along the depth direction using actual measurements. Then, it uses Snell's law of refraction and the initial grazing angle information obtained from sensors to trace the propagation path of the acoustic rays within each water layer segment by segment. This effectively suppresses the significant ranging deviation caused by the path bending of underwater sound rays with the sound velocity gradient. Finally, the error propagation law of the converted horizontal measurement error is analyzed, proving the feasibility of this method. In practical applications, the observation station can complete the distance measurement calibration through the above acoustic ray correction process based on the sound velocity profile data collected in real time at the work site. The tracking filter can then accurately estimate the motion state of the maneuvering target based on the corrected measurement information. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of a maneuvering target tracking method based on underwater acoustic ray correction;

[0019] Figure 2 A deep-sea sound velocity profile model;

[0020] Figure 3 The initial ray tracing results are shown in the diagrams.

[0021] Figure 4 This is a diagram illustrating the effect of a single target tracking operation in 3D space.

[0022] Figure 5 A comparison chart of the root mean square error of position estimation under 100 Monte Carlo experiments;

[0023] Figure 6 This is a comparison chart of probability predictions for the maneuver model. Detailed Implementation

[0024] The technical features of the present invention will be further described clearly and completely below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments in this specification, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of this specification.

[0025] This invention proposes a method for tracking maneuvering targets based on underwater acoustic ray correction, comprising the following steps:

[0026] Step 1: Initial motion state Compensated measurement data The data is transmitted to unscented Kalman filters under different motion models. Using the filters under each motion model, the motion state at the next moment is predicted based on the motion state estimate from the previous moment. Finally, the optimal estimate for each motion model is calculated. With covariance matrix The variables in the initial motion state represent the target's position, velocity, and spatial rotation angle in three-dimensional coordinates, respectively. Specific operations include:

[0027] S100: Based on Given the state estimates and model probabilities of each motion model at each time step, solve for the interaction state estimates of the filter inputs under each motion model. With the interaction covariance matrix , is represented as:

[0028]

[0029]

[0030] in,

[0031]

[0032] In the formula, This indicates that the target belongs to the model after input interaction. The probability of; The model in the probability transition matrix To the model The probability of transition; Pre-interaction model The probability value; This indicates that the target is assumed to be in the model after interaction. At that time, by model The probability obtained from the interaction In order to be in Time model State estimates, In order to be in Time model State estimates, In order to be in Time model The error covariance.

[0033] S110: Estimate the interaction state With the interaction covariance matrix , combined Time-compensated measurement data The optimal estimate for each motion model is calculated. With covariance matrix The specific steps are as follows:

[0034] Establish a nonlinear model:

[0035]

[0036]

[0037] In the formula, Let this be the system's state vector; For measurement vectors; This represents the nonlinear mapping relationship between the measurement vector and the state vector. and These are process noise and measurement noise, respectively. Both are uncorrelated Gaussian noises with a mean of 0, and their covariance matrix is... and .

[0038] Point sampling can be achieved through a system of nonlinear equations. calculate Points and their weight coefficients:

[0039]

[0040]

[0041]

[0042]

[0043] in, , The number of state vectors. Decide The degree of dispersion of points Set to 0. Used to describe Distribution information, Represents the square root of a matrix. List, To determine the weight coefficients for first-order statistical properties, To determine the weight coefficients when calculating second-order statistical properties; This represents the state transition matrix, which is set according to each motion model of the target.

[0044] Entering the unscented Kalman filtering process, according to State prediction is performed using points and their weight coefficients along with the state equation:

[0045]

[0046] In the formula, Indicates the number of samples taken. indivual Point state vector, Indicates the first prediction after the 1st A state vector, Indicates the process The state prediction value is obtained by weighting the sampling points. This represents the predicted covariance matrix.

[0047] Continue to obtain the measurement predictions along with their covariance matrix, and the cross-covariance between the measurement predictions and the state predictions:

[0048]

[0049] In the formula, Indicates the first indivual The point state vector is the measurement value predicted by the measurement equation. Indicates the process The measurement prediction value is obtained by weighting the sampling points. This represents the autocovariance matrix of the measurement. This is the cross-covariance matrix of the state and the measurement;

[0050] Using the compensated measurement data Prediction, estimation, and covariance matrix:

[0051]

[0052] The likelihood probability of each model is updated based on the predicted state value and predicted covariance of each filter. With the updated Probability values ​​of each model at time step , is represented as:

[0053]

[0054]

[0055]

[0056]

[0057]

[0058] In the formula, The measurement residuals for each model are used to characterize the actual measurement information. With predictive measurement information Deviation between; The covariance matrix of the corresponding residuals. Let be the covariance matrix.

[0059] Step 2: Determine if the iteration termination condition is met. If it is, perform weighted fusion of the motion state estimates output by each motion model to obtain the final tracking result, represented as:

[0060]

[0061]

[0062] In the formula, This represents the model probability and is used as the weight coefficient. This represents the overall fusion estimate. Represents the covariance matrix. Indicates the number of models.

[0063] If the conditions are not met, proceed to step 1. In this embodiment of the invention, the compensated measurement data is obtained according to the following steps:

[0064] The observation station uses a sound velocity profiler to collect real-time information on the underwater sound velocity at different depths z. Based on the requirements of the target tracking filter, the one-way time delay of the target is collected by the active detection sonar on the observation station. Target azimuth and target pitch angle Obtain measurement data containing target motion information. ;

[0065] Based on the sound velocity profile, underwater layers are stratified according to depth, and any complex vertical sound velocity distribution is approximately divided into multiple constant gradient medium layers, totaling... Segment, denoted as If the target is not in the first The segment then needs to be analyzed based on the propagation time while performing ray tracing. Real-time inference of the target's layer number Set the initial sweep angle of the sound trail to the target pitch angle. The speed of sound at the observation station is The thickness of the layer is denoted as The sound velocity gradient in the layer is This allows us to deduce the speed of sound in each layer. .

[0066] Using Snell's law of refraction and the initial grazing angle and Acoustic parameters are estimated based on the depth of the dielectric layer to determine the depth within the layer. Corresponding glancing angle Horizontal distance and transmission time , is represented as:

[0067]

[0068]

[0069]

[0070] In the formula, Indicates depth Given the speed of sound, calculate the propagation time of the last layer:

[0071] Target one-way delay obtained This corresponds to the direct sound ray, and besides the seabed target, it is necessary to determine the last layer actually reached. The vocal timbre is specially processed, and the propagation time of the last layer is calculated:

[0072]

[0073] Utilizing the propagation time of the last layer Calculate the horizontal distance increment of the actual arrival point level. and depth increment ;

[0074] Summing up the horizontal distances across all water layers yields the total horizontal distance the sound ray actually travels, i.e., the compensated horizontal distance. Similarly, the total propagation time of the sound ray can be obtained. :

[0075]

[0076]

[0077] When the total propagation time Ray tracing terminates upon completion. Horizontal distance before compensation. for:

[0078]

[0079] in, , These represent the horizontal distance between the target and the sonar, respectively. coordinate axes and Relative distances on the coordinate axes.

[0080] Based on the compensated horizontal distance measurement Target azimuth and target pitch angle Constructing new measurement equations .

[0081] The horizontal propagation distance after compensation in the embodiments of the present invention is now discussed. The law of error propagation is explained, including:

[0082] The target delay and elevation angle measurements acquired by active detection sonar both follow a Gaussian distribution, denoted as . ,in, This represents the actual value of the delay. This represents the true value of the target pitch angle; the solution for horizontal distance in ray tracking can be expressed as an implicit equation. The expectation is obtained by performing a second-order Taylor expansion on the nonlinear function. The horizontal propagation distance can be obtained by ray tracing calculation. The laws governing error propagation. Specifically, these include:

[0083] The time delay before conversion and the error distribution that the pitch angle measurement data follow:

[0084]

[0085] In the formula, , This indicates that the time delay measurement and pitch angle measurement errors respectively follow zero-mean Gaussian noise. and These represent the variances corresponding to the errors.

[0086] Implicit equations In true value Perform a second-order multivariate Taylor expansion at this point:

[0087]

[0088] Find the expected value of both sides of the above equation. The deviation term after measurement conversion is obtained:

[0089]

[0090] Analysis of measurement data after horizontal distance compensation The error propagation law shows that the measurement error after conversion is a higher-order term, and its impact on subsequent target tracking is almost negligible.

[0091]

[0092] To verify the performance of the underwater acoustic ray correction-based maneuvering target tracking method proposed in this embodiment of the invention, corresponding performance simulation experiments were conducted. The ground truth of the time delay data was extracted from the .arr file of the underwater acoustic software Bellhop. The other specific simulation parameters were set as follows:

[0093] 1. Define the target's motion as a turning maneuver satisfying a certain turning rate (the turning time and turning rate are unknown; it is only assumed that the underwater target is maneuvering on a horizontal surface). The simulation parameters of the target are shown in the table below:

[0094]

[0095] 2. The target's movement types are divided into straight-line and maneuvering turns, and its specific movement mode is spiral maneuvering, as shown in the following scenarios;

[0096] The first phase (1-30s) involves the target moving at a constant velocity in a straight line from the starting point; the second phase (31-270s) involves the target beginning to rotate at an angle of... The coordinated maneuvering and turning; in the third stage, 271-300s, the target resumes uniform linear motion.

[0097] 3. To quantitatively evaluate the tracking performance of each model, this embodiment of the invention derives the Cramérold lower bound based on the acoustic propagation observation model, serving as a theoretical benchmark for algorithm performance. State vector The unbiased estimator is Its corresponding covariance matrix is ​​expressed as Then the lower bound of Clamerau satisfies the following relationship:

[0098]

[0099] in, Represents the information matrix;

[0100]

[0101] The iterative equation for this information matrix can be expressed as:

[0102]

[0103] in Represents the matrix of the first line, number The elements corresponding to the column, This represents a calculation rule. Represents the first-order partial derivative, defined as:

[0104]

[0105]

[0106]

[0107] in and The Jacobian matrix for the state transition equation and the measurement equation:

[0108]

[0109] The final Cramélau lower bound of the algorithm can be expressed as:

[0110]

[0111] in The information matrix represents the first... line, number The elements corresponding to the column.

[0112] 4. This simulation employs three motion models: one constant-velocity CV model and two improved constant-angle CT models. The two improved CT models are configured with high and low angular velocity process noise respectively to achieve rapid detection of the target's maneuvering moments. The prior probability of the CV model is 0.5, and the prior probability of both improved CT models is 0.25. The initial model probability transition matrix is ​​as follows:

[0113]

[0114] Figure 3 This is a comparison chart of the ray-tracing simulation performance of the maneuvering target tracking method based on underwater acoustic ray correction described in this invention. The simulation results show that under the same measurement error and... Figure 2 Under the conditions of deep-sea sound velocity profiles, the ray tracing method based on horizontal layering used in this paper is more accurate and more applicable to underwater environments with varying sound velocity.

[0115] To demonstrate the maneuver tracking performance of the maneuver target tracking method based on underwater acoustic ray correction described in this invention, a maneuver target tracking method with horizontal layered ray tracing compensation, a maneuver target tracking method without compensation, and a maneuver target tracking method under single-step ray tracing were employed. Figure 4 The comparison of the three-dimensional space single target tracking effect of the present invention shows that the estimation effect of the present invention is closest to the actual target trajectory. Figure 5 The comparison of the root mean square error of the position estimation under 100 Monte Carlo experiments of the present invention shows that the root mean square error of the position estimation of the present invention is closest to the theoretical lower bound. Figure 6 The diagram shows a comparison of the probability predictions for the maneuver model in this invention. It can be seen that the probability predictions for the maneuver model in this invention are in line with expectations.

[0116] In summary, the maneuvering target tracking method of the present invention is applicable to complex environments where underwater sound rays constantly bend with depth, and can stably and accurately estimate the motion state of maneuvering targets, exhibiting strong robustness. Therefore, it can be used for maneuvering target tracking in complex underwater environments.

Claims

1. A method for maneuvering target tracking based on underwater acoustic ray correction, characterized in that: include: Step 1: For each motion model, perform the following steps: Based on the interaction probability of each motion model, the motion state estimate of the previous time step, and the covariance matrix, the interaction motion state estimate input to the unscented Kalman filter is obtained. Based on the interactive motion state estimate and covariance matrix, the motion state estimate and covariance matrix for the next moment are obtained. Based on the compensated measurement data, the motion state estimate for the next moment is updated to obtain the updated motion state estimate for the next moment. Determine if the iteration termination condition is met. If it is met, the optimal motion state estimate is obtained; if not, continue iterating based on the updated motion state estimate and covariance matrix for the next time step. Step 2: Perform weighted fusion based on the interaction probability of each motion model and the best motion state estimate to obtain the final tracking result; The compensated measurement data is obtained through the following steps: S100: Collects information on underwater sound velocity at different depths; the information includes the sound velocity value, the depth corresponding to the sound velocity value, and the sound velocity gradient; S200: Collect underwater target measurement data and establish underwater target measurement equations; the target measurement data includes: target one-way time delay, target azimuth angle, and target pitch angle; S300: Based on the sound velocity profile, the underwater environment is divided into layers according to depth; S400: Using Snell's law of refraction and initial parameters, acoustic parameters are calculated to obtain compensated measurement data.

2. The method of claim 1, wherein: The interaction motion state estimate input to the unscented Kalman filter is obtained based on the interaction probability of each motion model, the motion state estimate of the previous time step, and the covariance matrix, and is expressed as follows: ； ； In the formula, Represents the motion model before interaction The probability of interaction, Motion model in a pre-defined probability transition matrix Towards the motion model The probability of transition, in general, the probability transition matrix is ​​a preset fixed value. This indicates that the target belongs to the motion model after input interaction. The probability of; This indicates that the target is assumed to be in motion mode after interaction. At that time, by the motion model The probability obtained from the interaction Indicates the number of models; Based on the motion state estimate from the previous moment and The estimated value of the interactive motion state is obtained. With the interaction covariance matrix , is represented as: ； ； In the formula, In order to be in Motion Model at a Moment The estimated motion state, In order to be in Motion Model at a Moment The estimated motion state, In order to be in Motion Model at a Moment The error covariance.

3. The method for tracking maneuvering targets based on underwater acoustic ray correction according to claim 2, characterized in that: The step of obtaining the motion state estimate and covariance matrix at the next moment based on the interactive motion state estimate and covariance matrix specifically includes: Establish a nonlinear model: ； ； In the formula, Let this be the system's state vector; For measurement vectors; This represents the nonlinear mapping relationship between the measurement vector and the state vector. and These are process noise and measurement noise, respectively. Both are uncorrelated Gaussian noises with a mean of 0, and their covariance matrix is... and ; Point sampling can be achieved through a system of nonlinear equations. calculate Points and their weight coefficients: ； ； ； ； in, , The number of state vectors. Decide The degree of dispersion of points Set to 0. Used to describe Distribution information, Represents the square root of a matrix. List, To determine the weight coefficients for first-order statistical properties, To determine the weight coefficients when calculating second-order statistical properties; This represents the state transition matrix, which is set according to each motion model of the target. Entering the unscented Kalman filtering process, according to State prediction is performed using points and their weight coefficients along with the state equation: ； In the formula, Indicates the number of samples taken. indivual Point state vector, Indicates the first prediction after the 1st A state vector, Indicates the process The state prediction value is obtained by weighting the sampling points. Represents the predicted covariance matrix; Continue to obtain the measurement predictions along with their covariance matrix, and the cross-covariance between the measurement predictions and the state predictions: ； In the formula, Indicates the first indivual The point state vector is the measurement value predicted by the measurement equation. Indicates the process The measurement prediction value is obtained by weighting the sampling points. This represents the autocovariance matrix of the measurement. This is the cross-covariance matrix of the state and the measurement; Using the compensated measurement data From the prediction, estimation, and covariance matrix, we obtain the motion state estimate and covariance matrix for the next time step: ； in, This represents the Kalman gain.

4. The method for tracking maneuvering targets based on underwater acoustic ray correction according to claim 3, characterized in that: The calculation of acoustic parameters using Snell's law of refraction and initial parameters yields compensated measurement data, including: Assuming the vertical distribution of sound velocity is divided into multiple constant gradient medium layers, the total number of layers is... Segment, denoted as If the target is not in the first The segment then needs to be analyzed based on the propagation time while performing ray tracing. Real-time inference of the target's layer number ; Using Snell's law of refraction and the initial grazing angle and Acoustic parameters are estimated based on the depth of the dielectric layer to determine the depth within the layer. Corresponding glancing angle Horizontal distance and transmission time , is represented as: ； ； ； In the formula, Indicates depth Given the speed of sound, calculate the propagation time of the last layer: ； Utilizing the propagation time of the last layer Calculate the horizontal distance increment of the actual arrival point level. and depth increment ; Summing up the horizontal distances across all water layers yields the total horizontal distance the sound ray actually travels. : ； Based on total horizontal distance Target azimuth and target pitch angle Constructing new measurement equations .

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