Method for detecting the bearing of an underwater target

Abstract

This disclosure relates to an underwater target orientation detection method. It involves underwater autonomous navigation technology and solves the problems of low observation accuracy and difficulty in adapting to complex multi-target scenarios inherent in passive sensing and detection methods for underwater vehicles. The method includes: constructing a passive sonar pure orientation observation model for a high-noise underwater environment and the underwater vehicle; obtaining a virtual observation baseline during the underwater vehicle's cruise process; establishing independent improved UKF trackers based on covariance-forced positive definiteness for each target according to the virtual observation baseline; adaptively updating the state of each improved UKF tracker to obtain state estimates for each target; and extrapolating based on the current state estimates using a first-order kinematic model to obtain the predicted azimuth angle of each target at a future set time. The technical solution provided in this disclosure is applicable to underwater vehicles and achieves high-precision convergent estimation of real-time azimuth angle and azimuth change rate for multiple underwater targets.

Description

Technical Field

[0001] This disclosure relates to underwater autonomous navigation technology, and more particularly to an underwater target orientation detection method. Background Technology

[0002] With the increase in marine development and near-shore operations, underwater vehicles (such as autonomous underwater vehicles, or AUVs) are widely used in scenarios such as marine environmental monitoring, seabed resource exploration, marine engineering inspection, emergency search and rescue, and underwater operations. In these tasks, AUVs typically need to complete autonomous navigation tasks such as reaching target areas, traversing restricted areas, and safely avoiding collisions in complex, dynamic, and information-impaired aquatic environments. Especially in situations with multiple dynamic threats (such as other AUVs, multiple mobile vehicles, multiple operational platforms, escort vehicles, or other mobile risk sources), real-time acquisition of the position, velocity, and other motion status information of unknown surrounding targets is a crucial prerequisite for achieving situational awareness and autonomous navigation.

[0003] In practical underwater applications, constrained by energy consumption, equipment configuration, and stealth requirements, underwater unmanned vehicles typically employ passive acoustic sensing methods for situation assessment, eliminating the need for active acoustic emission. Due to the complexity of the underwater environment, significant interference from background noise and multipath propagation leads to large observation errors for underwater vehicles. Furthermore, underwater targets may exhibit sudden maneuvers, especially in multi-target scenarios, resulting in high algorithm complexity during tracking, which is difficult to adapt to the computational constraints of the embedded platform of the underwater vehicle. These problems, combined, severely impact the situational awareness and autonomous decision-making of underwater vehicles.

[0004] In summary, passive sensing and detection methods for underwater vehicles suffer from low observation accuracy and difficulty in adapting to complex multi-target scenarios. Summary of the Invention

[0005] To overcome the problems existing in related technologies, this disclosure provides an underwater target orientation detection method. In complex and high-noise underwater environments, target orientation detection in multi-target scenarios is completed by relying on a passive sonar pure orientation observation model, which solves the problems of low observation accuracy and difficulty in adapting to complex multi-target scenarios in passive perception and detection methods of underwater vehicles.

[0006] According to a first aspect of the embodiments of this disclosure, an underwater target orientation detection method is provided, comprising:

[0007] A passive sonar pure azimuth observation model for a high-noise underwater environment and an underwater vehicle is constructed. The passive sonar pure azimuth observation model outputs the relative azimuth information of at least one target in the high-noise underwater environment.

[0008] A virtual observation baseline is obtained during the cruise of the underwater vehicle, and the virtual observation baseline contains the observation geometric information obtained by the underwater vehicle during the simulated operation.

[0009] Based on the virtual observation baseline, establish an independent improved unscented Kalman filter UKF tracker for each target;

[0010] Adaptive state updates are performed on each of the improved UKF trackers to obtain state estimates for each of the targets;

[0011] Based on the current state estimates, extrapolation is performed using a first-order kinematic model to obtain the predicted azimuth angles of each target at a future set time.

[0012] Furthermore, the steps for constructing a passive sonar pure azimuth observation model for a high-noise underwater environment and underwater vehicles include:

[0013] The motion state of the underwater vehicle is defined according to the following expression:

[0014] ,

[0015] in, Let k be the state vector of the underwater vehicle at time k. , Let k be the position coordinates of the underwater vehicle at time k. Let k be the heading angle of the underwater vehicle at time k;

[0016] A kinematic model of the underwater vehicle, incorporating composite noise from the underwater environment, is constructed based on the following expression to represent the motion state of the underwater vehicle:

[0017] ,

[0018] in,( )for The position coordinates of the underwater vehicle at any given time. for The heading angle of the underwater vehicle at that moment. for The linear velocity of the underwater vehicle at any given moment. For discrete sampling time intervals, for The angular velocity of the underwater vehicle at any given moment, )for Position drift noise at any given moment for The heading disturbance noise at any given moment;

[0019] The passive sonar pure azimuth observation model of the underwater vehicle is constructed based on the following expression:

[0020] ,

[0021] in, for The observed relative azimuth angle of the target output by the passive sonar of the underwater vehicle at that moment. For pure azimuth observation functions, For the goal The state vector at time t, ( () represents the target's position coordinates. for The azimuth measurement noise at any given time.

[0022] Furthermore, the step of obtaining the virtual observation baseline during the underwater vehicle's cruise includes:

[0023] Controlling the underwater vehicle to perform a zigzag heading sweep based on deviation feedback includes:

[0024] Step 1: Calculate the commanded course of the underwater vehicle according to the following expression:

[0025] ,

[0026] in, The commanded course of the underwater vehicle. The reference heading for the underwater vehicle to point to the estimated position of the target is provided. For sweeping offset angle, , The sweep amplitude of the underwater vehicle.

[0027] Step 2: Calculate the real-time heading deviation using the following expression:

[0028] ,

[0029] in, For real-time heading deviation, This refers to the current actual heading angle of the underwater vehicle.

[0030] If the real-time heading deviation meets the preset flipping conditions, it is determined that a single sweep is completed, the target relative heading deviation angle is flipped, and the next sweep begins;

[0031] The virtual observation baseline is synthesized based on the temporal observation geometric information acquired by the underwater vehicle during its sweeping process.

[0032] Furthermore, the step of establishing an independent improved UKF tracker based on covariance-forced positive definiteness for each target according to the virtual observation baseline includes:

[0033] The state vector of the improved UKF tracker is defined according to the following expression:

[0034] ,

[0035] in, Let be the state vector of the target at time k. Let k be the azimuth angle of the target relative to the underwater vehicle. Normalization to , Let be the rate of change of the target's azimuth at time k;

[0036] Initialize the improved UKF tracker corresponding to each of the targets, including:

[0037] Step 1: Set the initial state estimate, initial error covariance matrix, process noise covariance matrix, and observation noise covariance matrix of the improved UKF tracker.

[0038] Step 2: Set the scaling parameters for Sigma points.

[0039] Step 3: Calculate the mean weight and covariance weight of the sampling results for the Sigma points based on the following set of expressions:

[0040] ,

[0041] ,

[0042] ,

[0043] Among them, the The mean weight of the 0th Sigma point. , where n is the dimension of the target state vector. For scaling parameters, Covariance weight of the 0th Sigma point Let be the mean weight of the i-th Sigma point. Let be the covariance weight of the i-th Sigma point.

[0044] Furthermore, the step of adaptively updating the state of each of the improved UKF trackers to obtain the state estimate of each of the targets includes:

[0045] Generate a set of Sigma points corresponding to each target based on the posterior estimation information of the previous time step, wherein the posterior estimation information includes the posterior state and the posterior covariance matrix;

[0046] Based on the Sigma point set, the improved UKF tracker is updated over time to obtain the prior state estimate and the prior covariance matrix after forced positive definite processing;

[0047] The prior state estimate and the prior covariance matrix after forced positive definite processing are measured and updated to obtain the preliminary corrected prior state estimate and prior covariance matrix;

[0048] An adaptive factor is calculated based on a sliding window of new information, and the process noise matrix is ​​dynamically adjusted using the adaptive factor.

[0049] The prior state estimates after initial correction are normalized, and the prior covariance matrix is ​​forced to positive definite again to complete the single-step filtering loop, including:

[0050] Step 1: Based on the following expression, correct the prior state estimate using Kalman gain and innovation to obtain the posterior state estimate:

[0051] ,

[0052] in, for The posterior state estimate at time t. The value of the prior state at time k is the value at time k-1. for Kalman gain at time step for The new information of the moment

[0053] Step 2: Based on the Kalman gain, obtain the posterior covariance matrix according to the following expression:

[0054] ,

[0055] in, for The posterior covariance matrix at time t. Received for time updates The prior covariance matrix at time t, To observe and predict covariance,

[0056] Step 3: Normalize the azimuth component of the posterior state estimate.

[0057] Step 4: Perform forced positive definite processing on the posterior covariance matrix again to complete the single-step filtering loop;

[0058] The filtering loop is executed iteratively until the state estimates of the targets converge, and the state estimates of each target are output. The state estimates include the real-time azimuth angle and azimuth rate of change of the targets.

[0059] Furthermore, the posterior estimation information includes the posterior covariance matrix, and the step of generating the Sigma point set corresponding to each target based on the posterior estimation information of the previous time step includes:

[0060] The posterior covariance matrix from the previous time step is forced to be symmetric according to the following expression:

[0061] ,

[0062] in, Let be the posterior covariance matrix of the previous time step. for The transpose of the matrix, To take the average;

[0063] The eigenvalues ​​of the posterior covariance matrix at the previous time step are decomposed according to the following expression:

[0064] ,

[0065] in, The eigenvector matrix, It is an eigenvalue diagonal matrix. , and These are the eigenvalues ​​of the posterior covariance matrix. yes The transpose of the matrix;

[0066] The eigenvalues ​​in the posterior covariance matrix are corrected according to the following expression:

[0067] ,

[0068] in, for The i-th original feature value, where i takes the value 1 or 2. These are the corrected eigenvalues. This is a preset positive definite threshold;

[0069] The positive definite covariance matrix can be reconstructed based on the following expression:

[0070] ,

[0071] in, For the reconstructed positive definite covariance matrix, It is a diagonal matrix composed of the corrected eigenvalues;

[0072] Based on the reconstructed positive definite matrix, a set of Sigma points corresponding to each of the improved UKF trackers is constructed according to the following expression:

[0073] ,

[0074] in, Let be the i-th Sigma point at time k-1. For the posterior state estimation of the target at time k-1, For the reconstructed positive definite covariance matrix, To control the scaling parameter of the Sigma point distribution range, n is the dimension of the target state vector. For matrix The i-th column, where i takes values ​​from 0 to 2n, contains 2n+1 Sigma points.

[0075] Furthermore, the step of updating the improved UKF tracker based on the Sigma point set to obtain the prior state estimate and the prior covariance matrix after forced positive definite processing includes:

[0076] The azimuth rate of change is limited for each of the Sigma points according to the following expression:

[0077] ,

[0078] in, The azimuth change rate at the i-th Sigma point after amplitude limiting. The azimuth change rate at the i-th Sigma point before amplitude limiting. This represents the maximum physical limit for the rate of change of orientation.

[0079] Based on the following expression, a Gaussian random perturbation is introduced to generate the predicted azimuth change rate covering the unknown maneuver of the target:

[0080] ,

[0081] in, Let be the predicted azimuth change rate of the i-th Sigma point after adding the perturbation. The azimuth change rate at the i-th Sigma point after amplitude limiting.

[0082] For Gaussian random perturbation terms, Used to cover the unknown maneuvers of the target. express It follows the principle of zero mean and variance. Gaussian distribution, Let V be the variance of the Gaussian perturbation;

[0083] The predicted azimuth change rate is integrally expressed using the following formula:

[0084] ,

[0085] in, The predicted azimuth angle is obtained through i Sigma points. The azimuth component of the i-th Sigma point at the previous time step. This is the filter sampling time interval;

[0086] The predicted azimuth angle is normalized according to the following expression:

[0087] ,

[0088] in, Modulo operation;

[0089] The prior state estimate is calculated according to the following expression:

[0090] ,

[0091] in, Let be the prior state estimate at time k based on time k-1, and n be the dimension of the target state vector. Let be the mean weight of the i-th Sigma point. To predict the state of the i-th Sigma point after the state transition;

[0092] The prior covariance matrix is ​​calculated according to the following expression, and the calculated prior covariance matrix is ​​then forced to positive definite again:

[0093] ,

[0094] in, Let be the prior covariance matrix at time k. Let be the covariance weight of the i-th Sigma point. Let be the deviation vector between the predicted state and the prior state estimate at the i-th Sigma point. It is the transpose matrix. Let be the process noise matrix at time k-1.

[0095] Furthermore, the step of measuring and updating the prior state estimate and the prior covariance matrix after forced positive definite processing to obtain the preliminarily corrected prior state estimate and the prior covariance matrix includes:

[0096] Based on the following expression, extract the azimuth component of the predicted Sigma point as the observation projection:

[0097] ,

[0098] in, For the first The projection values ​​of Sigma points in the observation space, wherein the projection values ​​include azimuth components. For the first Azimuth components of the predicted Sigma point

[0099] Calculate the observed prediction mean using the following expression:

[0100] ,

[0101] in, for The observed and predicted mean at time [time]. For the first The mean weight of each Sigma point;

[0102] Based on the following set of expressions, calculate the observation-predicted covariance and the cross-covariance between state variables and observations using covariance weights:

[0103] ,

[0104] in, To observe and predict covariance, For the first Covariance weights of Sigma points

[0105] Let be the difference between the projection value of the i-th Sigma point in the observation space and the mean of the observation prediction, that is, the observation prediction bias of the i-th Sigma point.

[0106] Let be the observation noise covariance matrix at time k, which mainly represents the variance of the passive sonar azimuth measurement noise.

[0107] The cross-variance between state variables and observations.

[0108] To complete the predicted state of the i-th Sigma point after the state transition,

[0109] The value of the prior state at time k is the value estimated based on time k-1.

[0110] The Kalman gain is calculated based on the observed prediction covariance and the cross-covariance between the state variables and the observed variables, according to the following expression:

[0111] ,

[0112] in, for Kalman gain at time step This is the inverse matrix for predicting covariance.

[0113] Furthermore, the step of calculating the adaptive factor based on the innovation sliding window and dynamically adjusting the process noise matrix using the adaptive factor includes:

[0114] Retrieve the new information using the following expression:

[0115] ,

[0116] in, for The new information of the moment for The actual azimuth angle observation value of the passive sonar at that moment. for The average of the observed predictions at any given time;

[0117] Calculate the adaptive factor within the innovation sliding window using the following expression:

[0118] ,

[0119] in, As an adaptive factor, The actual variance of the information within the sliding window. The theoretical variance of the new information;

[0120] The process noise matrix is ​​dynamically updated according to the following expression:

[0121] ,

[0122] in, for The process noise matrix updated at each time step. for The process noise matrix at time step, Forgetting factor, This is the adaptive adjustment factor after amplitude limiting. This is the initially set process noise covariance matrix.

[0123] Furthermore, the step of extrapolating the state estimates using a first-order kinematic model to obtain the predicted azimuth angles of each target at a future set time includes:

[0124] The predicted azimuth angle is calculated according to the following expression:

[0125] ,

[0126] in, To set the predicted azimuth angle of the target at a future time, The current posterior azimuth estimate of the target. The rate of change of the target's current azimuth is extracted based on the state estimate. The set prediction extrapolation duration.

[0127] The technical solutions provided by the embodiments of this disclosure may include the following beneficial effects: constructing a passive sonar pure azimuth observation model for a high-noise underwater environment and an underwater vehicle, wherein the passive sonar pure azimuth observation model outputs the relative azimuth information of at least one target in the high-noise underwater environment; then acquiring a virtual observation baseline during the underwater vehicle's cruise process, wherein the virtual observation baseline contains the observation geometric information acquired by the underwater vehicle during simulated operation; then establishing an independent improved UKF tracker based on covariance-forced positive definiteness for each target according to the virtual observation baseline, performing adaptive state updates on each improved UKF tracker, and obtaining state estimates for each target; finally, based on the current state estimates, extrapolating using a first-order kinematic model to obtain the predicted azimuth of each target at a future set time. In complex and noisy underwater environments, the passive sonar pure azimuth observation model is used to complete target aspect detection in multi-target scenarios and predict the future azimuth of targets. This solves the problems of low observation accuracy and difficulty in adapting to complex multi-target scenarios in passive perception and detection methods of underwater vehicles. It achieves high-precision convergence estimation of real-time azimuth and azimuth change rate of underwater multi-targets, and provides reliable state basis for situational awareness, safe collision avoidance and autonomous decision-making of underwater vehicles.

[0128] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and are not intended to limit this disclosure. Attached Figure Description

[0129] The accompanying drawings, which are incorporated in and form a part of this specification, illustrate embodiments consistent with this disclosure and, together with the description, serve to explain the principles of this disclosure.

[0130] Figure 1 This is a flowchart illustrating an underwater target orientation detection method according to an exemplary embodiment.

[0131] Figure 2 This is a flowchart illustrating yet another underwater target orientation detection method according to an exemplary embodiment.

[0132] Figure 3 This is a flowchart illustrating yet another underwater target orientation detection method according to an exemplary embodiment.

[0133] Figure 4 This is a flowchart illustrating yet another underwater target orientation detection method according to an exemplary embodiment.

[0134] Figure 5 This is a schematic diagram illustrating the relative positions of the reference course and the virtual observation baseline when an underwater vehicle is sweeping, according to an exemplary embodiment.

[0135] Figure 6 This is a schematic diagram illustrating an underwater vehicle navigating along a virtual observation baseline according to an exemplary embodiment.

[0136] Figure 7 This is a flowchart illustrating yet another underwater target orientation detection method according to an exemplary embodiment.

[0137] Figure 8 This is a flowchart illustrating yet another underwater target orientation detection method according to an exemplary embodiment.

[0138] Figure 9 This is a flowchart illustrating yet another underwater target orientation detection method according to an exemplary embodiment.

[0139] Figure 10 This is a flowchart illustrating yet another underwater target orientation detection method according to an exemplary embodiment.

[0140] Figure 11 This is a flowchart illustrating yet another underwater target orientation detection method according to an exemplary embodiment.

[0141] Figure 12 This is a flowchart illustrating yet another underwater target orientation detection method according to an exemplary embodiment.

[0142] Figure 13 This is a flowchart illustrating yet another underwater target orientation detection method according to an exemplary embodiment.

[0143] Figure 14 This is a flowchart illustrating yet another underwater target orientation detection method according to an exemplary embodiment. Detailed Implementation

[0144] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numerals in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this disclosure. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this disclosure as detailed in the appended claims.

[0145] In practical underwater applications, constrained by energy consumption, equipment configuration, and stealth requirements, underwater unmanned vehicles typically employ passive acoustic sensing methods for situation assessment, eliminating the need for active acoustic emission. Due to the complexity of the underwater environment, significant interference from background noise and multipath propagation leads to large observation errors for underwater vehicles. Furthermore, underwater targets may exhibit sudden maneuvers, especially in multi-target scenarios, resulting in high algorithm complexity during tracking, which is difficult to adapt to the computational constraints of the embedded platform of the underwater vehicle. These problems, combined, severely impact the situational awareness and autonomous decision-making of underwater vehicles.

[0146] In summary, passive sensing and detection methods for underwater vehicles suffer from low observation accuracy and difficulty in adapting to complex multi-target scenarios.

[0147] To address the aforementioned issues, embodiments of this disclosure provide an underwater target orientation detection method. In complex, high-noise underwater environments, target orientation detection in multi-target scenarios is achieved using a passive sonar pure orientation observation model. This solves the problems of low observation accuracy and difficulty in adapting to complex multi-target scenarios inherent in passive sensing and detection methods for underwater vehicles.

[0148] This disclosure provides an underwater target orientation detection method. In complex, high-noise underwater environments, where multiple target orientation detection and state estimation rely solely on passive sonar pure orientation observation, this method effectively solves technical problems such as unmeasurable distance, filter divergence, and tracking lag due to sudden target maneuvers under pure orientation observation. It achieves high-precision convergent estimation of real-time azimuth angles and azimuth change rates for multiple underwater targets, providing reliable state information for underwater vehicles' situational awareness, collision avoidance, and autonomous decision-making. The process of automatically detecting underwater targets using this method during autonomous navigation is as follows: Figure 1 As shown, it includes:

[0149] Step 101: Construct a passive sonar pure azimuth observation model for high-noise underwater environments and underwater vehicles.

[0150] The passive sonar pure azimuth observation model outputs the relative azimuth information of at least one target in the high-noise underwater environment.

[0151] In this step, a real marine environment is simulated, including the combined noise effects of underwater acoustic background noise, multipath propagation, obstruction, ocean current interference, and equipment errors. A kinematic model of the underwater vehicle and a passive sonar pure azimuth observation model that closely match the actual underwater operating scenario are constructed. The passive sonar pure azimuth observation model outputs the target's relative azimuth information.

[0152] According to one exemplary implementation, the passive sonar pure azimuth observation model does not output observation data such as range and radial velocity, but only outputs the target's relative azimuth angle information. This can reduce the energy consumption of underwater vehicles and reduce the computing burden on the embedded systems of underwater vehicles.

[0153] According to one exemplary embodiment, the underwater vehicles and targets involved in the embodiments of this disclosure include, but are not limited to:

[0154] AUV, Remotely Operated Underwater Vehicle (ROV).

[0155] This step is as follows: Figure 2 As shown, it includes:

[0156] Step 201: Define the motion state of the underwater vehicle.

[0157] In this step, the motion state of the underwater vehicle is defined according to the following expression:

[0158] ,

[0159] in, Let k be the state vector of the underwater vehicle at time k. , Let k be the position coordinates of the underwater vehicle at time k. Let k be the heading angle of the underwater vehicle at time k.

[0160] According to one exemplary embodiment, the heading angle of the underwater vehicle represents the angle between the underwater vehicle's direction of travel and a preset reference coordinate axis.

[0161] Step 202: Construct a kinematic model of the underwater vehicle that includes the composite noise of the underwater environment to represent the motion state of the underwater vehicle.

[0162] In this step, a kinematic model of the underwater vehicle, incorporating the composite noise of the underwater environment, is constructed based on the following expression:

[0163] ,

[0164] in,( )for The position coordinates of the underwater vehicle at any given time.

[0165] for The linear velocity of the underwater vehicle at any given time can be a fixed value or dynamically adjusted according to the navigation strategy. For example, it can be set to 12 m / s.

[0166] for The heading angle of the underwater vehicle at that moment. for The heading angle of the underwater vehicle at that moment.

[0167] The discrete sampling time interval represents the time step between motion state updates and observation data acquisition.

[0168] for The angular velocity of the underwater vehicle at any given moment.

[0169] ( )for The position drift noise at any given time follows a zero-mean Gaussian distribution, i.e. This is used to simulate the random displacement effect of ocean currents and water currents on underwater vehicles. According to one exemplary embodiment, .

[0170] for The heading disturbance noise at any given time follows a zero-mean Gaussian distribution, i.e. This is used to simulate the interference of factors such as gyroscope drift, equipment vibration, and water flow disturbance on the heading control of a vehicle. According to an exemplary embodiment, a configuration is set... .

[0171] In this embodiment, the introduction of composite noise consisting of drift noise and heading disturbance noise is consistent with the actual underwater operating environment. Both position drift noise and heading disturbance noise are simulated using Gaussian distribution, which conforms to the statistical characteristics of random disturbances in the marine environment.

[0172] Step 203: Construct the passive sonar pure azimuth observation model of the underwater vehicle.

[0173] In this step, the passive sonar pure azimuth observation model of the underwater vehicle is constructed according to the following expression:

[0174] ,

[0175] in, for The observed relative azimuth angle of the target output by the passive sonar of the underwater vehicle at that moment. For pure azimuth observation functions, For the goal The state vector at time t, ( ( ) represents the target's position coordinates. for The azimuth measurement noise at any given time.

[0176] According to one exemplary implementation, The range of values ​​is It represents the azimuth deviation of the target relative to the heading of the vehicle. It is a nonlinear function, determined by the relative position of the target and the underwater vehicle, as well as the course of the underwater vehicle.

[0177] for The azimuth measurement noise at any given time follows a zero-mean Gaussian distribution, i.e. In this embodiment, it can be set It is used to simulate the interference of factors such as underwater acoustic background noise and the measurement error of the passive sonar equipment itself on the azimuth observation.

[0178] In this embodiment, the passive sonar employs a butterfly-shaped detection area configuration. According to an exemplary implementation, the detection area configuration of the passive sonar pure azimuth observation model is as follows:

[0179] Forward detection sector: detection radius 9000m, detection half angle 30°;

[0180] Lateral detection sector: detection radius 13500m, detection half angle 60°.

[0181] Passive sonar only outputs the relative azimuth angle of the target within the detection area. There is no observation data output when the target is outside the detection area, and the target's distance and other information are never output within the detection area, which meets the application constraints of pure azimuth observation.

[0182] In pure azimuth observation function The term represents the absolute azimuth of the target relative to the geographic coordinate system, minus After, add This yields the relative azimuth angle actually measured by the passive sonar.

[0183] Step 102: Obtain the virtual observation baseline during the underwater vehicle's cruise process. The virtual observation baseline contains the observation geometry information obtained by the underwater vehicle during the simulated operation.

[0184] In this step, the underwater vehicle is controlled to perform a zigzag heading sweep based on bias feedback, actively changing its observation position and viewing angle. An equivalent triangulation virtual observation baseline is constructed in the time domain as the virtual observation baseline. This proactive introduction of observational geometric changes enhances target identifiability and accelerates the convergence speed of subsequent filtering estimation. The virtual observation baseline contains observational geometric information such as the vehicle's position coordinates, heading angle, and target relative azimuth angle at different times during the sweep, serving as a crucial foundation for subsequent multi-target state estimation.

[0185] This step is as follows: Figure 3 As shown, it includes:

[0186] Step 301: Control the underwater vehicle to perform a zigzag heading sweep based on deviation feedback.

[0187] In this step, a course roll control strategy is used to enable the underwater vehicle to perform periodic zigzag sweeps based on deviation feedback while advancing towards the estimated target position. This generates lateral displacement, avoiding the problem of limited observation geometry caused by straight-line cruising, and also solving the problem of untimely early warning for distant targets caused by the small radius of the forward detection sector of passive sonar.

[0188] Step 301 is as follows: Figure 4 As shown, it includes:

[0189] Step 401: Calculate the commanded course of the underwater vehicle.

[0190] The commanded course of the underwater vehicle is calculated according to the following expression:

[0191] ,

[0192] in, The commanded course of the underwater vehicle. The reference heading for the underwater vehicle to point to the estimated position of the target is provided. The sweeping offset angle is... , The sweep amplitude of the underwater vehicle.

[0193] According to an exemplary implementation, the sweeping amplitude is set in this embodiment. The sweep amplitude can also be dynamically adjusted according to the underwater environment and detection requirements.

[0194] Reference heading The calculations follow the real-time changes in the vehicle's position and the updated estimated target position, ensuring that the sweeping process is always target-oriented and avoiding the extra costs caused by ineffective sweeps. Sweeping amplitude The settings are dynamically adjusted according to the underwater environment and detection requirements, ensuring sufficient changes in observation geometry while avoiding problems such as unstable vehicle maneuvering and excessive energy consumption caused by excessive sweep amplitude.

[0195] Step 402: Calculate the real-time heading deviation.

[0196] In this step, the real-time heading deviation is calculated according to the following expression:

[0197] ,

[0198] in, For real-time heading deviation, This represents the current actual heading angle of the underwater vehicle.

[0199] Step 403: If the real-time heading deviation meets the preset flipping conditions, determine that a single sweep is completed, flip the target relative heading deviation angle, and enter the next sweep.

[0200] In this step, if the real-time heading deviation meets the preset flipping conditions, it is determined that a single sweep is completed, the target relative heading deviation angle is flipped, and the next sweep begins.

[0201] According to one exemplary implementation, the rollover condition is preset as a real-time heading deviation. This value represents the heading tolerance, indicating that the vehicle's actual heading is close to the commanded heading, and a single sweep is complete. The flip rule is... That is, after a single forward sweep is completed, the relative heading deviation angle changes from... Flip to The underwater vehicle performs a reverse sweep to achieve a periodic sinusoidal heading sweep.

[0202] In addition, to comply with the physical maneuvering constraints of underwater vehicles, a single-step turning angle limit is set, meaning that the maximum turning angle of the underwater vehicle does not exceed the single-step turning angle limit, in order to avoid problems such as loss of vehicle attitude and equipment damage caused by excessive turning angle.

[0203] According to one exemplary implementation, to enhance the discernibility of target relative motion under pure azimuth observation conditions, a zigzag sinusoidal sweeping strategy based on heading deviation feedback control is employed. First, the guiding heading from the current position towards the target is calculated. :

[0204] ,

[0205] in,( ) represents the current position coordinates pointing to the target, and t represents the current time.

[0206] To prevent untimely detection due to the short-sightedness of forward sonar detection, thereby passively shortening the reaction time, and to avoid the observation geometry being singular due to straight-line navigation, this embodiment controls the underwater vehicle to perform zigzag sweeping navigation.

[0207] Based on the heading angle calculated using the following sine function, the heading of the underwater vehicle can be continuously controlled in a sinusoidal manner, allowing for continuous, smooth, and small-amplitude adjustments to the underwater vehicle's angle:

[0208] ,

[0209] in, Based on the cruise heading, To sweep the amplitude, This is the sweep frequency.

[0210] Considering the maximum physical turning rate limit and further increasing the amplitude of lateral sweep, according to an exemplary implementation, the specific set reference cruise heading is as follows: Set the maximum sweep amplitude to Set the heading tolerance to be Initialize the current sweep bias direction The current command heading is calculated in real time based on the following expression:

[0211] .

[0212] And monitor the current course of the underwater vehicle. Deviation from the commanded course When the deviation is less than the positioning tolerance When a single sweep is completed, the bias direction is reversed. Then, it enters the next reverse sweep. This maneuvering strategy introduces geometric observability into a pure azimuth observation system by actively and periodically changing the lateral position of the observation platform, thereby accelerating the convergence of the UKF tracker to the target's hidden state. To comply with physical maneuvering constraints, a single-step angle limit is imposed on the commanded course:

[0213] ,

[0214] in, This is a single-step rotation angle limit.

[0215] Step 302: Based on the temporal observation geometric information acquired by the underwater vehicle during the sweeping process, synthesize the virtual observation baseline.

[0216] In this step, during the underwater vehicle's zigzag traverse, each sampling time interval... A set of observational geometric information will be collected, including: the position coordinates of the spacecraft at time k ( , Actual heading angle Target relative azimuth observation value Command heading Real-time heading deviation By systematically integrating the aforementioned temporal observation geometric information according to time steps, a virtual observation baseline can be constructed.

[0217] Virtual observation baselines overcome the limitation of unmeasurable distance in pure azimuth observations from a single platform by utilizing the relative azimuth changes of the target at different observation locations. The synthesized virtual observation baseline will serve as input data for subsequent improvements to the UKF tracker, providing rich observational geometric information for multi-target state estimation, effectively enhancing the identifiability of target states, and solving the problem of weak observability under pure azimuth observations.

[0218] Figure 5 An example of the relative positions of a reference course and a virtual observation baseline during an underwater vehicle's sweep is shown. The reference course is based on... The determination is the basic heading from the current position of the underwater vehicle to the target, which provides a reference for the generation of the virtual observation baseline.

[0219] Figure 6 An example of an underwater vehicle navigating along a virtual observation baseline is shown, with the underwater vehicle's low-level controller based on... Continuously adjust posture.

[0220] exist Figure 5 and Figure 6 In the example, ignoring the length of the hull, taking the center as the origin, the forward and backward detection radius is 6000m with an opening angle of 60°, and the left and right detection radius is 9000m with an opening angle of 120°.

[0221] Step 103: Based on the virtual observation baseline, establish an independent improved UKF tracker for each target based on covariance-forced positive definiteness.

[0222] In this step, an independent improved UKF tracker is established for each detected target. Numerical instability is eliminated from the algorithm's underlying layer by covariance-forced positive definiteness processing. At the same time, a low-dimensional state vector definition is adopted to reduce computational complexity and adapt to the embedded platform of the underwater vehicle. The improved UKF trackers for each target are independent of each other, and a decoupled multi-target state estimation architecture is adopted. The time complexity of the algorithm is linearly related to the number of targets, and it can handle the state estimation of multiple underwater dynamic targets simultaneously.

[0223] Step 103 is as follows: Figure 7 As shown, it includes:

[0224] Step 701: Define the state vector of the improved UKF tracker.

[0225] In this step, the state vector of the improved UKF tracker is defined according to the following expression:

[0226] ,

[0227] in, Let be the state vector of the target at time k. Let k be the azimuth angle of the target relative to the underwater vehicle. Normalization to , Let be the rate of change of the target's azimuth at time k.

[0228] The state vector contains only the target's azimuth and azimuth rate of change. By defining the state in a low dimension, it adapts to the information constraints of pure azimuth observation, while significantly reducing the computational complexity and memory usage of the filtering algorithm.

[0229] Step 702: Initialize the improved UKF tracker corresponding to each of the targets.

[0230] In this step, the improved UKF tracker for each target is initialized and configured, setting the initial parameters and weight coefficients required for the filtering iteration. Step 702 is detailed as follows: Figure 8 As shown, it includes:

[0231] Step 801: Set the improvement

[0232] The initial state estimate, initial error covariance matrix, process noise covariance matrix, and observation noise covariance matrix of the UKF tracker.

[0233] 1. Initial state estimate: denoted as ,in The initial azimuth angle of the target is estimated using the observation value when the passive sonar first detects the target as the initial value; This is an estimate of the initial azimuth rate of change of the target. It is assumed that the target is initially stationary, and it will be gradually corrected by subsequent filtering iterations.

[0234] 2. Initial error covariance matrix: denoted as , is a diagonal matrix, representing the uncertainty of the initial state estimate. .

[0235] 3. Process noise covariance matrix: denoted as It characterizes the uncertainty of the target's motion state changes and describes the state changes of the target during motion caused by factors such as sudden maneuvers and environmental interference.

[0236] 4. Observation noise covariance matrix: denoted as , is a one-dimensional scalar (because the observed value is a single azimuth angle). ,in It is consistent with the standard deviation of azimuth measurement noise set in step 203.

[0237] Step 802: Set the scaling parameters for the Sigma points.

[0238] In this step, three scaling parameters for the Sigma point are set:

[0239] Set to 0.1 to control the degree of diffusion of Sigma points around the mean, thereby controlling the distribution range of sampling points to adapt to strong nonlinearity;

[0240] Set to 2.0 to minimize higher-order term errors and improve the accuracy of filter estimation;

[0241] Set to 1.0 for calculating scaling parameters. , where n is the dimension of the target state vector. According to one exemplary implementation, n=2.

[0242] Step 803: Calculate the mean weight and covariance weight of the sampling results of the Sigma points.

[0243] In this step, the mean weight and covariance weight of the sampling results at the Sigma point are calculated according to the following set of expressions:

[0244] ,

[0245] ,

[0246] ,

[0247] Among them, the The mean weight of the 0th Sigma point. , where n is the dimension of the target state vector. For scaling parameters, Covariance weight of the 0th Sigma point Let be the mean weight of the i-th Sigma point. Let be the covariance weight of the i-th Sigma point.

[0248] Step 104: Perform adaptive state updates on each of the improved UKF trackers to obtain the state estimates of each target.

[0249] In this step, the improved UKF tracker undergoes filtering iterations. Addressing the issues of non-positive definite covariance matrix caused by strong underwater noise and tracking lag due to sudden target maneuvers, key technologies such as forced positive definite covariance processing and adaptive process noise adjustment based on innovation statistics are employed to achieve high-precision and high-stability estimation of the state of each target. The improved UKF tracker for each target independently executes the filtering iterations in this step until the state estimate converges, ultimately outputting the target's real-time azimuth and rate of change of azimuth.

[0250] Step 104 is as follows: Figure 9 As shown, it includes:

[0251] Step 901: Generate the Sigma point set corresponding to each target based on the posterior estimation information of the previous time step.

[0252] The posterior estimation information includes the posterior state and the posterior covariance matrix.

[0253] In this step, 2n+1 Sigma points are generated by sampling in the state space to replace the linearization process of traditional Kalman filtering, thus adapting to the highly nonlinear nature of the pure azimuth observation model. Before generating the Sigma points, the posterior covariance matrix is ​​forced to be positive definite to ensure the smooth progress of Cholesky decomposition and eliminate numerical instability from the algorithm's underlying layer.

[0254] Step 901 is as follows: Figure 10 As shown, it includes:

[0255] Step 1001: Force symmetry on the posterior covariance matrix of the previous time step.

[0256] In this step, the posterior covariance matrix from the previous time step is forced to be symmetric according to the following expression:

[0257] ,

[0258] in, Let be the posterior covariance matrix of the previous time step. for The transpose of the matrix, To take the average.

[0259] In noisy underwater environments, numerical calculation errors during the filtering iteration process can cause the covariance matrix to lose its symmetry, and a symmetric matrix is ​​a necessary condition for a positive definite matrix. This step ensures the symmetry of the covariance matrix through forced symmetry processing, laying the foundation for subsequent eigenvalue decomposition and positive definite reconstruction.

[0260] Step 1002: Perform eigenvalue decomposition on the posterior covariance matrix from the previous time step.

[0261] In this step, the eigenvalues ​​of the posterior covariance matrix from the previous time step are decomposed according to the following expression:

[0262] ,

[0263] in, The eigenvector matrix, It is an eigenvalue diagonal matrix. , and These are the eigenvalues ​​of the posterior covariance matrix. yes The transpose of .

[0264] Eigenvalue decomposition is the process of decomposing the covariance matrix into eigenvectors and eigenvalues. Positive definite reconstruction of the covariance matrix is ​​achieved by modifying the eigenvalues.

[0265] Step 1003: Correct each eigenvalue in the posterior covariance matrix.

[0266] In this step, the eigenvalues ​​in the posterior covariance matrix are corrected according to the following expression:

[0267] ,

[0268] in, for The i-th original feature value, where i takes the value 1 or 2. These are the corrected eigenvalues. This is a preset positive definite threshold.

[0269] In this step, by using a threshold less than the positive definite threshold The eigenvalues ​​are forcibly corrected to This ensures that all corrected eigenvalues ​​are greater than 0, providing a guarantee for subsequent reconstruction of the positive definite covariance matrix. Positive definite threshold. The setting of this value needs to balance numerical stability and estimation accuracy. A value that is too small may lead to numerical calculation errors, while a value that is too large may excessively amplify the uncertainty of the covariance matrix. According to an exemplary implementation, .

[0270] Step 1004: Reconstruct the positive definite covariance matrix.

[0271] In this step, the positive definite covariance matrix is ​​reconstructed according to the following expression:

[0272] ,

[0273] in, For the reconstructed positive definite covariance matrix, It is a diagonal matrix composed of the corrected eigenvalues.

[0274] Step 1005: Based on the reconstructed positive definite matrix, construct a set of Sigma points corresponding to each of the improved UKF trackers.

[0275] Based on the reconstructed positive definite matrix, a set of Sigma points corresponding to each of the improved UKF trackers is constructed according to the following expression:

[0276] ,

[0277] in, Let be the i-th Sigma point at time k-1. For the posterior state estimation of the target at time k-1, For the reconstructed positive definite covariance matrix, To control the scaling parameter of the Sigma point distribution range, n is the dimension of the target state vector. For matrix The i-th column, where i takes values ​​from 0 to 2n, contains 2n+1 Sigma points.

[0278] The generation of the Sigma point set is based on the reconstructed positive definite covariance matrix, ensuring the reasonable distribution of sampling points, effectively adapting to the highly nonlinear characteristics of the pure azimuth observation model, and reducing the truncation error of the filtering iteration. The five generated Sigma points will serve as inputs for subsequent time update steps to complete the nonlinear transfer of state.

[0279] Step 902: Based on the Sigma point set, update the improved UKF tracker over time to obtain the prior state estimate and the prior covariance matrix after forced positive definite processing.

[0280] In this step, the prediction phase begins. The Sigma point at time k-1 is transferred to time k via a nonlinear state transition function to obtain the predicted Sigma point at time k. Then, a weighted summation is used to obtain the prior state estimate and prior covariance matrix at time k, achieving a one-step prediction of the target state. This step incorporates azimuth rate of change limiting and Gaussian random perturbations to address the target's sudden maneuvers and physical motion constraints, ensuring the physical feasibility of the predicted state and its coverage of unknown target maneuvers.

[0281] Step 902 is as follows: Figure 11 As shown, it includes:

[0282] Step 1101: Limit the azimuth rate of change for each Sigma point according to the following expression.

[0283] ,

[0284] in, The azimuth change rate at the i-th Sigma point after amplitude limiting. The azimuth change rate at the i-th Sigma point before amplitude limiting. This represents the maximum physical limit for the rate of change of orientation.

[0285] According to one exemplary implementation, the setting is configured. .

[0286] Step 1102: Introduce Gaussian random perturbation to generate a predicted azimuth change rate covering the unknown maneuver of the target.

[0287] In this step, a Gaussian random perturbation is introduced according to the following expression to generate the predicted azimuth change rate covering the unknown maneuver of the target:

[0288] ,

[0289] in, Let be the predicted azimuth change rate of the i-th Sigma point after adding the perturbation. This represents the rate of change of orientation at the i-th Sigma point after amplitude limiting;

[0290] For Gaussian random perturbation terms, Used to cover the unknown maneuvers of the target. express It follows the principle of zero mean and variance. Gaussian distribution, Let V be the variance of the Gaussian perturbation.

[0291] Since targets often possess autonomous maneuvering capabilities, their sudden maneuvering behaviors are difficult to describe using a fixed motion model. This step broadens the distribution range of the predicted state by introducing a Gaussian random perturbation term, effectively covering the unknown maneuvering characteristics of the target and avoiding tracking lag problems caused by motion model mismatch.

[0292] Step 1103: Perform state integration on the predicted azimuth rate of change of the Sigma point.

[0293] In this step, the state integral is performed on the predicted azimuth rate of change at the Sigma point according to the following expression:

[0294] ,

[0295] in, The predicted azimuth angle is obtained through i Sigma points. The azimuth component of the i-th Sigma point at the previous time step. This is the filter sampling time interval.

[0296] Step 1104: Normalize the predicted azimuth angle.

[0297] In this step, the predicted azimuth angle is normalized according to the following expression:

[0298] ,

[0299] in, Modulo operation. This step normalizes the predicted azimuth angle to a modulo value using modulo operation. This ensures the consistency of state variable values ​​and improves the accuracy of filtering estimation.

[0300] Step 1105: Calculate the prior state estimate.

[0301] In this step, the prior state estimate is calculated according to the following expression:

[0302] ,

[0303] in, Let be the prior state estimate at time k based on time k-1, and n be the dimension of the target state vector. Let be the mean weight of the i-th Sigma point. This is the predicted state of the i-th Sigma point after the state transition.

[0304] By weighted summing of the five predicted Sigma points, the prior estimate of the target state at time k is obtained. The setting of the weight coefficients ensures the accuracy of the estimate.

[0305] Step 1106: Calculate the prior covariance matrix, and then perform forced positive definite processing on the calculated prior covariance matrix again.

[0306] In this step, the prior covariance matrix is ​​calculated according to the following expression, and the calculated prior covariance matrix is ​​then subjected to forced positive definite processing again:

[0307] ,

[0308] in, Let be the prior covariance matrix at time k. Let be the covariance weight of the i-th Sigma point. Let be the deviation vector between the predicted state and the prior state estimate at the i-th Sigma point. It is the transpose matrix. Let be the process noise matrix at time k-1.

[0309] This step incorporates the process noise matrix when calculating the prior covariance matrix. This is used to describe the uncertainty of changes in the target's motion state. To prevent the calculated prior covariance matrix from losing its positive definiteness again, steps 1001-1004 are repeated to force positive definiteness on the prior covariance matrix, resulting in a forced positive definite prior covariance matrix. This ensures the smooth progress of subsequent measurement update steps.

[0310] Step 903: Perform measurement updates on the prior state estimate and the prior covariance matrix after forced positive definite processing to obtain the preliminary corrected prior state estimate and the prior covariance matrix.

[0311] In this step, the measurement is updated during the calibration phase. The prior state estimate at time k is fused with the actual observations from the passive sonar, and the prior estimate is corrected using Kalman gain to obtain a more accurate posterior state estimate.

[0312] Step 903 is as follows: Figure 12 As shown, it includes:

[0313] Step 1201: Extract the azimuth component of the predicted Sigma point as the observation projection.

[0314] In this step, the azimuth component of the predicted Sigma point is extracted as the observation projection according to the following expression:

[0315] ,

[0316] in, For the first The projection values ​​of Sigma points in the observation space, wherein the projection values ​​include azimuth components. For the first The azimuth components of the predicted Sigma point.

[0317] In this step, since the passive sonar of the underwater vehicle only outputs azimuth observation values, it is only necessary to extract the azimuth component of the Sigma point for observation projection.

[0318] Step 1202: Calculate the mean of the observed predictions.

[0319] In this step, the observed prediction mean is calculated according to the following expression:

[0320] ,

[0321] in, for The observed and predicted mean at time [time]. For the first The mean weight of each Sigma point.

[0322] Step 1203: Calculate the observation prediction covariance and the cross-covariance between the state variables and the observations using covariance weights.

[0323] In this step, the observed prediction covariance and the cross-covariance between the state variables and the observed variables are calculated using the following set of expressions and covariance weights:

[0324] ,

[0325] in, To observe and predict covariance, For the first Covariance weights of Sigma points

[0326] Let be the difference between the projection value of the i-th Sigma point in the observation space and the mean of the observation prediction, that is, the observation prediction bias of the i-th Sigma point.

[0327] Let be the observation noise covariance matrix at time k, which mainly represents the variance of the passive sonar azimuth measurement noise.

[0328] The cross-variance between state variables and observations.

[0329] To complete the predicted state of the i-th Sigma point after the state transition,

[0330] The value is the prior state estimate at time k based on time k-1.

[0331] Step 1204: Calculate the Kalman gain based on the predicted covariance and the cross-covariance between the state variables and the observations.

[0332] In this step, the Kalman gain is calculated based on the predicted covariance and the cross-covariance between the state variables and the observations, according to the following expression:

[0333] ,

[0334] in, for Kalman gain at time step This is the inverse matrix for predicting covariance.

[0335] If the observation-prediction covariance is small (i.e., the observation accuracy is high), the Kalman gain is large, and the degree of correction of the observation to the prior estimate is high; if the observation-prediction covariance is large (i.e., the observation accuracy is low), the Kalman gain is small, and the degree of correction of the observation to the prior estimate is low, thus ensuring the rationality of filtering and fusion.

[0336] Step 904: Calculate the adaptive factor based on the new information sliding window, and dynamically adjust the process noise matrix using the adaptive factor.

[0337] To prevent the target from switching between stable cruise and violent maneuvers, the traditional UKF process noise matrix Q is set to a constant. If the Q value remains small, the filter may mistakenly interpret the deviation as measurement noise and refuse to correct it, leading to tracking lag or even loss of tracking, and making it unable to adapt to sudden target maneuvers. In this step, an adaptive adjustment factor is generated by calculating the statistical characteristics of the innovation sequence in real time, and the process noise matrix Q is dynamically scaled to achieve a rapid response to sudden target maneuvers. When the target undergoes a sudden maneuver, the process noise gain is automatically amplified to increase the filter's sensitivity to new observation data; when the target is moving smoothly, a small process noise gain is maintained to suppress interference from strong underwater noise and achieve smooth tracking.

[0338] Step 904 is as follows: Figure 13 As shown, it includes:

[0339] Step 1301: Obtain the latest information.

[0340] In this step, the new information is obtained according to the following expression:

[0341] ,

[0342] in, for The new information of the moment for The actual azimuth angle observation value of the passive sonar at that moment. for The average of the observed predictions at each time point.

[0343] When the target moves steadily, the innovation is small and follows a zero-mean Gaussian distribution; when the target undergoes a sudden maneuver, the innovation increases significantly and deviates from the zero-mean Gaussian distribution.

[0344] Step 1302: Calculate the adaptive factor within the new information sliding window.

[0345] In this step, the adaptive factor within the news sliding window is calculated according to the following expression:

[0346] ,

[0347] in, As an adaptive factor, The actual variance of the information within the sliding window. This represents the theoretical variance of the new information. If the target is determined to be in a hunting state, this is further amplified. If the target moves steadily, the adaptive factor... .

[0348] Step 1303: Dynamically update the process noise matrix.

[0349] In this step, the process noise matrix is ​​dynamically updated according to the following expression:

[0350] ,

[0351] in, for The process noise matrix updated at each time step. for The process noise matrix at time step, Forgetting factor, This is the adaptive adjustment factor after amplitude limiting. The initial process noise matrix is ​​set in step 801.

[0352] According to one exemplary implementation, the forgetting factor takes the value of 0.1 to 0.3.

[0353] In this step, the influence of the current adaptive factor is considered while retaining the information of the historical process noise matrix, ensuring the smoothness and stability of the update. The dynamically updated process noise matrix will serve as the input to step 906 in the next filtering iteration, achieving adaptive matching to changes in the target's motion state.

[0354] Step 905: Normalize the preliminary corrected prior state estimate and force the prior covariance matrix to be positive definite again to complete the single-step filtering loop.

[0355] This step is the last step of the single-step filtering iteration. The prior state estimate and prior covariance matrix are corrected by Kalman gain and innovation to obtain the posterior state estimate and posterior covariance matrix at time k. These are then normalized and forced to be positive definite to ensure the consistency of the state variable values ​​and the positive definiteness of the covariance matrix, thus providing reliable posterior estimation information for the next filtering iteration.

[0356] This step is as follows: Figure 14 As shown, it includes:

[0357] Step 1401: Correct the prior state estimate based on Kalman gain and innovation to obtain the posterior state estimate.

[0358] In this step, the prior state estimate is corrected based on Kalman gain and innovation according to the following expression to obtain the posterior state estimate:

[0359] ,

[0360] in, for The posterior state estimate at time t. The value of the prior state at time k is the value at time k-1. for Kalman gain at time step for The new information of the moment.

[0361] Step 1402: Based on the Kalman gain, obtain the posterior covariance matrix.

[0362] In this step, the posterior covariance matrix is ​​obtained based on the Kalman gain according to the following expression:

[0363] ,

[0364] in, for The posterior covariance matrix at time t. Received for time updates The prior covariance matrix at time t.

[0365] Step 1403: Normalize the azimuth component of the posterior state estimate.

[0366] In this step, the updated posterior state estimate will be... Substitute the values ​​into the normalization formula in step 1104 to perform normalization processing, ensuring the consistency of the azimuth angle values.

[0367] Step 1404: Perform forced positive definite processing on the posterior covariance matrix again to complete the single-step filtering loop.

[0368] In this step, the forced positive definite processing is performed again. The resulting positive definite posterior covariance matrix can be used as the input of step 901 in the next filtering iteration. Thus, the single-step filtering loop at time k is completed.

[0369] Step 906: Iteratively execute the filtering loop until the state estimates of the targets converge, and output the state estimates of each target.

[0370] The state estimate includes the target's real-time azimuth angle and azimuth rate of change.

[0371] In this step, the state estimate and / or positive definite posterior covariance matrix at time k are used as the input for the filtering iteration at time k+1. Steps 901 to 905 are repeated to achieve continuous iteration of the filtering algorithm.

[0372] According to one exemplary implementation, the convergence criterion is set as follows: the change in the state estimate over M consecutive time steps is less than a preset convergence threshold. When the convergence criterion is met, the state estimate of the target is determined to have converged, and the filter enters the steady-state tracking stage; if the condition is not met, the iteration continues until convergence.

[0373] The state estimate output in this step can be directly used as input for underwater vehicles to perform situational awareness, risk assessment and collision avoidance decisions: the real-time azimuth angle can be used to determine the target's real-time azimuth, and the azimuth change rate can be used to determine the target's approach trend and motion state.

[0374] Step 105: Based on the current state estimate, extrapolate using a first-order kinematic model to obtain the predicted azimuth angle of each target at a future set time.

[0375] The step of extrapolating from the current state estimate using a first-order kinematic model to obtain the predicted azimuth angles of each target at a future set time includes:

[0376] ,

[0377] in, To set the predicted azimuth angle of the target at a future time, The current posterior azimuth estimate of the target. The rate of change of the target's current azimuth is extracted based on the state estimate. The set prediction extrapolation duration, for example, can be set to 5 seconds.

[0378] To quantify the continuous tracking risk of dynamic targets, a "continuous tracking duration" indicator can be set as a constraint, for example, 120 seconds. For any dynamic target, if the cumulative duration of its continuous tracking of the underwater vehicle exceeds a preset threshold, the mission is deemed a failure; otherwise, the mission objective is to reach the target point while meeting safety constraints. The "continuous tracking status" can be directly provided by the target sensor / tracking model in the simulation environment; in actual deployment or when the target's status information is unavailable, the underwater vehicle can also construct a "tracked risk" indicator based on available pure azimuth observations for approximate assessment. Based on the above scenario, the technical solution disclosed herein, under conditions of lack of distance observation and incomplete observation, performs stable azimuth and situation estimation for multiple dynamic targets, providing preliminary conditions for subsequent risk assessment and generation of safe evasion control commands that meet maneuver constraints, guiding navigation to the target point to complete the mission.

[0379] According to one exemplary implementation, the filtering iteration frequency of the improved UKF tracker is consistent with the observation data acquisition frequency of the passive sonar.

[0380] An exemplary embodiment of this disclosure also provides a computer apparatus, including:

[0381] processor;

[0382] Memory used to store processor-executable instructions;

[0383] The processor is configured to execute the underwater target orientation detection method provided in the embodiments of this disclosure.

[0384] An exemplary embodiment of this disclosure also provides a non-transitory computer-readable storage medium, wherein when instructions in the storage medium are executed by a computer processor, the computer is able to perform the underwater target orientation detection method provided by the embodiments of this disclosure.

[0385] This disclosure provides an underwater target azimuth detection method. It constructs a passive sonar pure azimuth observation model for a high-noise underwater environment and an underwater vehicle. The passive sonar pure azimuth observation model outputs the relative azimuth information of at least one target in the high-noise underwater environment. Then, it acquires a virtual observation baseline during the underwater vehicle's cruise process, which includes observational geometric information acquired by the underwater vehicle during simulated operation. Next, based on the virtual observation baseline, it establishes an independent improved UKF tracker for each target using covariance-forced positive definiteness, performs adaptive state updates on each improved UKF tracker, and obtains state estimates for each target. Finally, based on the current state estimates, it extrapolates using a first-order kinematic model to obtain the predicted azimuth angle of each target at a future set time. In complex and noisy underwater environments, the passive sonar pure azimuth observation model is used to complete target aspect detection in multi-target scenarios and predict the future azimuth of targets. This solves the problems of low observation accuracy and difficulty in adapting to complex multi-target scenarios in passive perception and detection methods of underwater vehicles. It achieves high-precision convergence estimation of real-time azimuth and azimuth change rate of underwater multi-targets, and provides reliable state basis for situational awareness, safe collision avoidance and autonomous decision-making of underwater vehicles.

[0386] The technical solution disclosed herein improves the identifiability and evasion availability under pure azimuth conditions. Addressing the physical limitation of passive sonar's inability to measure range, a virtual observation baseline is actively constructed through a zigzag maneuver based on bias feedback. This artificially introduces geometric changes in the observation, significantly enhancing the observability of the UKF filter for the hidden state of target distance. This increases the information about the target within the system, facilitating the judgment and prediction of its state for appropriate response measures.

[0387] The filter stability is enhanced under conditions of noise interference and incomplete observations. The proposed covariance matrix forced positive definiteness and adaptive Q-adjustment mechanism effectively overcome the divergence problem of standard UKF filter caused by strong underwater noise, and can still maintain fast convergence when non-cooperative targets suddenly maneuver.

[0388] It features low computational load and high real-time performance, making it suitable for resource-constrained underwater embedded platforms. It employs a decoupled multi-target state estimation architecture. Compared to complex algorithms based on deep reinforcement learning or global path search, the time complexity in the embodiments of this disclosure is only linearly related to the number of targets. Furthermore, UKF has a low state dimension, requiring minimal memory and computing resources. This allows the algorithm to be deployed on embedded control chips for underwater unmanned vehicles with limited computing power and sensitive power consumption, meeting the stringent requirements of millisecond-level decision-making response in underwater combat environments.

[0389] Extrapolation using a first-order kinematic model adapts to the high inertia of underwater vehicles such as AUVs, avoiding the risk of collisions caused by delayed avoidance actions due to ad-hoc generation. The extrapolation primarily relies on state estimates, requiring no additional observation information, and provides a data foundation for avoidance in multi-target fusion scenarios, enhancing the ability to handle complex situations.

[0390] Those skilled in the art will also understand that the various illustrative logical blocks and steps listed in the embodiments of this disclosure can be implemented by electronic hardware, computer software, or a combination of both. Whether such functionality is implemented in hardware or software depends on the specific application and the overall system design requirements. Those skilled in the art can implement the described functionality using various methods for each specific application, but such implementation should not be construed as exceeding the scope of protection of the embodiments of this disclosure.

[0391] Furthermore, the term “exemplary” is used herein to mean serving as an example, instance, or illustration. Any aspect or design described herein as “exemplary” is not necessarily to be construed as advantageous compared to other aspects or designs. Rather, the use of the term “exemplary” is intended to present the concept in a concrete manner. As used herein, the term “or” is intended to mean an inclusive “or” rather than an exclusive “or.” That is, unless otherwise specified or clear from the context, “X applies A or B” is intended to mean any of the natural inclusive arrangements. That is, “X applies A or B” satisfies any of the foregoing instances if X applies A; X applies B; or both X applies A and B. Additionally, unless otherwise specified or clear from the context to refer to the singular form, the articles “a” and “an” as used in this application and the appended claims are generally understood to mean “one or more.”

[0392] Similarly, although this disclosure has been shown and described with respect to one or more implementations, equivalent variations and modifications will occur to those skilled in the art upon reading and understanding this specification and the accompanying drawings. This disclosure includes all such modifications and variations and is limited only by the scope of the claims. In particular, with respect to the various functions performed by the components described above (e.g., elements, resources, etc.), unless otherwise indicated, the terminology used to describe such components is intended to correspond to any component (functionally equivalent) that performs the specific function of the described component, even if structurally not equivalent to the disclosed structure. Furthermore, although specific features of this disclosure may have been disclosed with respect to only one of several implementations, such features may be combined with one or more other features of other implementations, as may be desired and advantageous to any given or particular application. Moreover, with regard to the terms “comprising,” “owning,” “having,” “having,” or variations thereof as used in the detailed description or claims, such terms are intended to be inclusive in a manner similar to the term “including.”

[0393] Other embodiments of this disclosure will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This disclosure is intended to cover any variations, uses, or adaptations of this disclosure that follow the general principles of this disclosure and include common knowledge or customary techniques in the art not disclosed herein. The specification and examples are to be considered exemplary only, and the true scope and spirit of this disclosure are indicated by the following claims.

[0394] It should be understood that this disclosure is not limited to the precise structures described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of this disclosure is limited only by the appended claims.

Claims

1. A method for detecting the location of an underwater target, characterized in that, include: A passive sonar pure azimuth observation model for a high-noise underwater environment and an underwater vehicle is constructed. The passive sonar pure azimuth observation model outputs the relative azimuth information of at least one target in the high-noise underwater environment. A virtual observation baseline is obtained during the underwater vehicle's cruise process. This virtual observation baseline includes the observation geometry information acquired by the underwater vehicle during simulated operation, including: Step 1: Control the underwater vehicle to perform a zigzag heading sweep based on deviation feedback, including steps 1 and 2: Step 1: Calculate the commanded course of the underwater vehicle according to the following expression: ， in, The commanded course of the underwater vehicle. The reference heading for the underwater vehicle to point to the estimated position of the target is provided. For sweeping offset angle, , The sweep amplitude of the underwater vehicle. Step 2: Calculate the real-time heading deviation using the following expression: ， in, For real-time heading deviation, This refers to the current actual heading angle of the underwater vehicle. Step 2: If the real-time heading deviation meets the preset flip conditions, determine that a single sweep is complete, flip the target's relative heading deviation angle, and proceed to the next sweep. Step 3: Based on the temporal observation geometric information acquired by the underwater vehicle during the sweeping process, synthesize the virtual observation baseline; Based on the virtual observation baseline, establish an independent improved unscented Kalman filter UKF tracker for each target; Adaptive state updates are performed on each of the improved UKF trackers to obtain state estimates for each of the targets; Based on the current state estimates, extrapolation is performed using a first-order kinematic model to obtain the predicted azimuth angles of each target at a future set time.

2. The underwater target orientation detection method according to claim 1, characterized in that, The steps for constructing a passive sonar pure azimuth observation model for high-noise underwater environments and underwater vehicles include: The motion state of the underwater vehicle is defined according to the following expression: ， in, Let k be the state vector of the underwater vehicle at time k. , Let k be the position coordinates of the underwater vehicle at time k. Let k be the heading angle of the underwater vehicle at time k; A kinematic model of the underwater vehicle, incorporating composite noise from the underwater environment, is constructed based on the following expression to represent the motion state of the underwater vehicle: ， in,( )for The position coordinates of the underwater vehicle at any given time. for The heading angle of the underwater vehicle at that moment. for The linear velocity of the underwater vehicle at any given moment. For discrete sampling time intervals, for The angular velocity of the underwater vehicle at any given moment, )for Position drift noise at any given moment for The heading disturbance noise at any given moment; The passive sonar pure azimuth observation model of the underwater vehicle is constructed based on the following expression: ， in, for The observed relative azimuth angle of the target output by the passive sonar of the underwater vehicle at that moment. For pure azimuth observation functions, For the goal The state vector at time t, ( () represents the target's position coordinates. for The azimuth measurement noise at any given time.

3. The underwater target orientation detection method according to claim 1, characterized in that, The steps of establishing an independent improved UKF tracker based on covariance-forced positive definiteness for each target according to the virtual observation baseline include: The state vector of the improved UKF tracker is defined according to the following expression: ， in, Let be the state vector of the target at time k. Let k be the azimuth angle of the target relative to the underwater vehicle. Normalization to , Let be the rate of change of the target's azimuth at time k; Initialize the improved UKF tracker corresponding to each of the targets, including: Step 1: Set the initial state estimate, initial error covariance matrix, process noise covariance matrix, and observation noise covariance matrix of the improved UKF tracker. Step 2: Set the scaling parameters for Sigma points. Step 3: Calculate the mean weight and covariance weight of the sampling results for the Sigma points based on the following set of expressions: ， ， ， Among them, the The mean weight of the 0th Sigma point. , where n is the dimension of the target state vector. For scaling parameters, Covariance weight of the 0th Sigma point Let be the mean weight of the i-th Sigma point. Let be the covariance weight of the i-th Sigma point.

4. The underwater target orientation detection method according to claim 1, characterized in that, The step of adaptively updating the state of each of the improved UKF trackers to obtain the state estimate of each of the targets includes: Generate a set of Sigma points corresponding to each target based on the posterior estimation information of the previous time step, wherein the posterior estimation information includes the posterior state and the posterior covariance matrix; Based on the Sigma point set, the improved UKF tracker is updated over time to obtain the prior state estimate and the prior covariance matrix after forced positive definite processing; The prior state estimate and the prior covariance matrix after forced positive definite processing are measured and updated to obtain the preliminary corrected prior state estimate and prior covariance matrix; An adaptive factor is calculated based on a sliding window of new information, and the process noise matrix is ​​dynamically adjusted using the adaptive factor. The prior state estimates after initial correction are normalized, and the prior covariance matrix is ​​forced to positive definite again to complete the single-step filtering loop, including: Step 1: Based on the following expression, correct the prior state estimate using Kalman gain and innovation to obtain the posterior state estimate: ， in, for The posterior state estimate at time t. The value of the prior state at time k is the value at time k-1. for Kalman gain at time step for The new information of the moment Step 2: Based on the Kalman gain, obtain the posterior covariance matrix according to the following expression: ， in, for The posterior covariance matrix at time t. Received for time updates The prior covariance matrix at time t, To observe and predict covariance, Step 3: Normalize the azimuth component of the posterior state estimate. Step 4: Perform forced positive definite processing on the posterior covariance matrix again to complete the single-step filtering loop; The filtering loop is executed iteratively until the state estimates of the targets converge, and the state estimates of each target are output. The state estimates include the real-time azimuth angle and azimuth rate of change of the targets.

5. The underwater target orientation detection method according to claim 4, characterized in that, The posterior estimation information includes the posterior covariance matrix, and the step of generating the Sigma point set corresponding to each target based on the posterior estimation information of the previous time step includes: The posterior covariance matrix from the previous time step is forced to be symmetric according to the following expression: ， in, Let be the posterior covariance matrix of the previous time step. for The transpose of the matrix, To take the average; The eigenvalues ​​of the posterior covariance matrix at the previous time step are decomposed according to the following expression: ， in, The eigenvector matrix, It is an eigenvalue diagonal matrix. , and These are the eigenvalues ​​of the posterior covariance matrix. yes The transpose of the matrix; The eigenvalues ​​in the posterior covariance matrix are corrected according to the following expression: ， in, for The i-th original feature value, where i takes the value 1 or 2. These are the corrected eigenvalues. This is a preset positive definite threshold; The positive definite covariance matrix can be reconstructed based on the following expression: ， in, For the reconstructed positive definite covariance matrix, It is a diagonal matrix composed of the corrected eigenvalues; Based on the reconstructed positive definite matrix, a set of Sigma points corresponding to each of the improved UKF trackers is constructed according to the following expression: ， in, Let be the i-th Sigma point at time k-1. For the posterior state estimation of the target at time k-1, For the reconstructed positive definite covariance matrix, To control the scaling parameter of the Sigma point distribution range, n is the dimension of the target state vector. For matrix The i-th column, where i takes values ​​from 0 to 2n, contains 2n+1 Sigma points.

6. The underwater target orientation detection method according to claim 4, characterized in that, The step of updating the improved UKF tracker based on the Sigma point set to obtain the prior state estimate and the prior covariance matrix after forced positive definite processing includes: The azimuth rate of change is limited for each of the Sigma points according to the following expression: ， in, The azimuth change rate at the i-th Sigma point after amplitude limiting. The azimuth change rate at the i-th Sigma point before amplitude limiting. This represents the maximum physical limit for the rate of change of azimuth; Based on the following expression, a Gaussian random perturbation is introduced to generate the predicted azimuth change rate covering the unknown maneuver of the target: ， in, Let be the predicted azimuth change rate of the i-th Sigma point after adding the perturbation. The azimuth change rate at the i-th Sigma point after amplitude limiting. For Gaussian random perturbation terms, Used to cover the unknown maneuvers of the target. express It follows the principle of zero mean and variance. Gaussian distribution, Let V be the variance of the Gaussian perturbation; The predicted azimuth change rate is integrally expressed using the following formula: ， in, The predicted azimuth angle is obtained through i Sigma points. The azimuth component of the i-th Sigma point at the previous time step. This is the filter sampling time interval; The predicted azimuth angle is normalized according to the following expression: ， in, Modulo operation; The prior state estimate is calculated according to the following expression: ， in, Let be the prior state estimate at time k based on time k-1, and n be the dimension of the target state vector. Let be the mean weight of the i-th Sigma point. To predict the state of the i-th Sigma point after the state transition; The prior covariance matrix is ​​calculated according to the following expression, and the calculated prior covariance matrix is ​​then subjected to forced positive definite processing again: ， in, Let be the prior covariance matrix at time k. Let be the covariance weight of the i-th Sigma point. Let be the deviation vector between the predicted state and the prior state estimate at the i-th Sigma point. It is the transpose matrix. Let be the process noise matrix at time k-1.

7. The underwater target orientation detection method according to claim 4, characterized in that, The step of measuring and updating the prior state estimate and the prior covariance matrix after forced positive definite processing to obtain the pre-corrected prior state estimate and prior covariance matrix includes: Based on the following expression, extract the azimuth component of the predicted Sigma point as the observation projection: ， in, For the first The projection values ​​of Sigma points in the observation space, wherein the projection values ​​include azimuth components. For the first Azimuth components of the predicted Sigma point Calculate the observed prediction mean using the following expression: ， in, for The observed and predicted mean at time [time]. For the first The mean weight of each Sigma point; Based on the following set of expressions, calculate the observation-predicted covariance and the cross-covariance between state variables and observations using covariance weights: ， Where n is the dimension of the target state vector. To observe and predict covariance, For the first Covariance weights of Sigma points Let be the difference between the projection value of the i-th Sigma point in the observation space and the mean of the observation prediction, that is, the observation prediction bias of the i-th Sigma point. Let be the observation noise covariance matrix at time k, which mainly represents the variance of the passive sonar azimuth measurement noise. The cross-variance between state variables and observations. To complete the predicted state of the i-th Sigma point after the state transition, The value of the prior state at time k is the value estimated based on time k-1. The Kalman gain is calculated based on the observed prediction covariance and the cross-covariance between the state variables and the observed variables, according to the following expression: ， in, for Kalman gain at time step This is the inverse matrix for predicting covariance.

8. The underwater target orientation detection method according to claim 4, characterized in that, The step of calculating the adaptive factor based on the information sliding window, and dynamically adjusting the process noise matrix using the adaptive factor, includes: Retrieve the new information using the following expression: ， in, for The new information of the moment for The actual azimuth angle observation value of the passive sonar at that moment. for The average of the observed predictions at any given time; Calculate the adaptive factor within the innovation sliding window using the following expression: ， in, As an adaptive factor, The actual variance of the information within the sliding window. The theoretical variance of the new information; The process noise matrix is ​​dynamically updated according to the following expression: ， in, for The process noise matrix updated at each time step. for The process noise matrix at time step, Forgetting factor, This is the adaptive adjustment factor after amplitude limiting. This is the initially set process noise covariance matrix.

9. The underwater target orientation detection method according to claim 1, characterized in that, The step of extrapolating the state estimates using a first-order kinematic model to obtain the predicted azimuth angles of each target at a future set time includes: The predicted azimuth angle is calculated according to the following expression: ， in, To set the predicted azimuth angle of the target at a future time, The current posterior azimuth estimate of the target. The rate of change of the target's current azimuth is extracted based on the state estimate. The set prediction extrapolation duration.

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