Underwater aided navigation method for measuring carrier velocity using combined multi-order magnetic gradient tensor

Abstract

This invention belongs to the field of underwater positioning and navigation technology, and relates to an underwater auxiliary navigation method for measuring the velocity of a carrier using a multi-order magnetic gradient tensor. The method includes: velocity observation generation based on the multi-order magnetic gradient tensor: raw data acquisition of the multi-order magnetic gradient tensor, tensor time differential processing, and tensor velocity observation calculation; adaptive fusion navigation of multi-source information: system state quantity definition, dual observation channel design, state prediction and measurement update; robustness enhancement and failure handling: online evaluation of observation quality, adaptive weight adjustment and smooth switching. This invention achieves highly robust multi-source information fusion based on the dual observation channel design using extended Kalman filtering, combined with adaptive noise covariance adjustment. This invention constructs a complete failure handling mechanism to ensure continuous and stable operation of the navigation system in complex underwater environments. This method significantly improves the autonomy and mission reliability of long-endurance underwater navigation and achieves true functional redundancy within the system.

Description

Technical Field

[0001] This invention belongs to the field of underwater positioning and navigation technology, specifically relating to an underwater auxiliary navigation method for measuring the velocity of a carrier using a combination of multi-order magnetic gradient tensors. Background Technology

[0002] Currently, underwater positioning and navigation systems are divided into three main categories: autonomous navigation, acoustic positioning and navigation, and geophysical matching navigation. Autonomous navigation primarily relies on the integration of inertial measurement units (IMUs), but its navigation errors accumulate over time, affecting positioning accuracy. Using a strapdown inertial navigation system (SINS) paired with a Doppler velocimeter (DVL) is a common method for underwater autonomous navigation at present. DVL provides high-precision velocity information to suppress the accumulated errors of the inertial navigation system. The publicly available DVL device, NavQuest300, achieves a velocity measurement accuracy of 0.2%v ± 1 mm / s. After 4000 seconds of simulation, the positioning error of SINS combined with DVL is less than 8 meters. However, DVL is prone to failure beyond its operating altitude or in complex geological environments, leading to a loss of its ability to suppress accumulated errors; currently, there is no good solution. Acoustic positioning and navigation relies on geometric acoustic positioning. This error-free acoustic positioning and navigation method is currently the most widely used marine positioning technology. Taking Ultra-Short Baseline (USBL) systems as an example, the latest TrackLink series products launched abroad, such as the TrackLink5000HA, have a range of 10,000 m, a orientation accuracy of 0.15°, and a slant range accuracy of 0.3%D, where D represents the slant range in meters. GAPS products integrate fiber optic inertial devices, omnidirectional acoustic antennas, and USBL systems, achieving a range of up to 4,000 m. With a signal-to-noise ratio of 20 dB, they achieve a ranging accuracy of 0.06%D and an orientation accuracy of 0.03°. The positioning capability of USBL changes with variations in the signal-to-noise ratio. The integration of fiber optic inertial navigation into GAPS significantly increases its size, weight, and power consumption. While USBL systems can measure distances without cumulative error, their measurement accuracy is affected by slant range, acoustic environment, installation accuracy, and carrier speed, leading to significant uncertainty in marine positioning data. Furthermore, this method heavily relies on external beacons, resulting in limited range, poor maneuverability, and poor concealment. Geophysical matching navigation primarily involves measuring geophysical quantities using sensors carried by underwater vehicles and comparing them to pre-drawn maps of these quantities. This method heavily relies on high-precision map databases, resulting in high implementation costs and making it unsuitable as a conventional positioning and navigation method.

[0003] In summary, current mainstream marine navigation technologies all have inherent limitations: autonomous navigation, such as the SINS / DVL combination, while capable of autonomous operation, relies heavily on DVL for velocity correction; if DVL fails in complex sea conditions, system errors accumulate rapidly over time. Acoustic navigation, such as USBL, while not accumulating errors, has a limited range of application, heavily depends on external beacons, and its positioning accuracy is easily affected by acoustic environment, distance, and vehicle motion. Geophysical matching navigation is constrained by the high cost of prior maps, making widespread application difficult. Therefore, developing a new autonomous navigation method that does not rely on external acoustic information and prior topography and can provide an independent velocity reference has become an urgent need for achieving long-endurance underwater covert operations. Summary of the Invention

[0004] The purpose of this invention is to provide an underwater assisted navigation method that uses a multi-order magnetic gradient tensor to measure the velocity of a carrier, in order to solve the problem of drastic deterioration of navigation performance caused by DVL failure in underwater autonomous navigation.

[0005] This invention is achieved through the following technical solution:

[0006] An underwater-assisted navigation method for measuring vehicle velocity using a combined multi-order magnetic gradient tensor includes the following steps:

[0007] A. Generation of velocity observations based on multi-order magnetic gradient tensors:

[0008] A1. Acquisition of raw data for multi-order magnetic gradient tensors:

[0009] The multi-order magnetic gradient tensor measuring instrument modulates the spatial magnetic field information into a frequency domain signal by driving its internal sensor to move continuously along a preset closed butterfly spatial trajectory. After demodulation, the magnetic gradient tensor measuring instrument can synchronously and continuously output the magnetic field vector, second-order magnetic gradient tensor G, and third-order magnetic gradient tensor H in the carrier coordinate system to the industrial control computer.

[0010] A2. Tensor-time differential processing:

[0011] The industrial control computer receives a real-time sequence of second-order magnetic gradient tensors G, performs smooth differentiation on the continuous sequence of second-order magnetic gradient tensors G, and calculates its second-order tensor time change rate. ;

[0012] A3. Solving for tensor velocity observations:

[0013] Will The third-order magnetic gradient tensor H and the current-moment carrier attitude matrix obtained from SINS. Substituting into the observation equation, solve for the vehicle velocity vector V in the navigation coordinate system. n This speed is the tensor measurement speed V2;

[0014] B. Multi-source information adaptive fusion navigation:

[0015] B1. System state variable definition: The navigation data processing unit operates an extended Kalman filter that uses error states as state variables;

[0016] B2. The filter is configured with two parallel and independent observation channels;

[0017] B3. State Prediction and Measurement Update:

[0018] C. Robustness enhancement and failure handling:

[0019] C1. Online assessment of observation quality: Real-time monitoring of DVL signal strength, bottom tracking lock status, and residual size of tensor measurement speed solution; calculation and dynamic updating of observation noise covariance estimates for the two observation channels; quantification of the reliability of each observation quantity.

[0020] C2. Adaptive weight adjustment and smooth switching: When the evaluation module determines that the DVL signal is faulty or its quality is severely degraded, the navigation filter automatically increases the observation noise covariance of the DVL channel, reducing its weight in the fusion to near zero; and maintains or increases the weight of the tensor measurement velocity channel, so that the system smoothly transitions to the working mode dominated by SINS / tensor fusion.

[0021] Further, step A2: use a smooth estimation algorithm based on the state-space model to perform smooth differentiation on the continuous second-order magnetic gradient tensor G sequence.

[0022] Furthermore, step A2:

[0023] ;

[0024] in, ,

[0025] It is the velocity vector of the vehicle in the navigation coordinate system. This is the time-varying part of the magnetic field gradient, which is usually very small and can be simplified as follows:

[0026] (1).

[0027] Furthermore, in step A3, the third-order magnetic gradient tensor H is the spatial rate of change of the second-order tensor. Its component form is:

[0028] ;

[0029] According to the chain rule, the time derivative of the gradient tensor is:

[0030] (2)

[0031] This can be written in matrix form as follows:

[0032] (3)

[0033] in, This represents the contraction of the third-order tensor and the velocity vector.

[0034] Expanding the equation by its components yields nine equations, for each i, j∈{x, y, z}:

[0035] ;

[0036] Since the magnetic field is sourceless and irrotational, the magnetic gradient tensor G is symmetric:

[0037] ,and ;

[0038] At the same time, the third-order tensor also has symmetry:

[0039] ;

[0040] Write the independent equations in matrix form:

[0041] ;

[0042] in, , is the speed to be determined;

[0043] b is independent Component composition;

[0044] A is the corresponding Component composition;

[0045] The specific form is as follows:

[0046] ;

[0047] Reorganize into the form of independent variables:

[0048] ;

[0049] Solve using the least squares method:

[0050] ;

[0051] The speed of the transport platform in the carrier coordinate system can then be obtained;

[0052] Furthermore, in practical navigation, considering the transformation between the vehicle coordinate system and the navigation coordinate system, the coordinate transformation of the second-order tensor is as follows:

[0053] ;

[0054] Coordinate transformation of a third-order tensor:

[0055] ;

[0056] in, It is the attitude matrix Element;

[0057] In the navigation system, the time derivative of the second-order tensor is:

[0058] ;

[0059] in, With angular velocity Related:

[0060] ;

[0061] Substituting into formula (3), the final tensor-velocity solution formula is obtained as follows:

[0062] (4)

[0063] in, It is the cross product matrix of angular velocities;

[0064] The velocity V of the vehicle in the navigation coordinate system is obtained by using the least squares method. n Let V2 be the tensor measurement velocity.

[0065] Further, in step B1, the state vector X contains the error states of SINS, namely position error, velocity error, and attitude error.

[0066] Further, in step B2, channel one is the DVL velocity channel, and the observed value is the DVL-measured velocity V1 relative to the ground in the carrier coordinate system; after coordinate transformation, it forms a measurement residual with the SINS velocity prediction value; channel two is the tensor velocity channel, and the observed value is the tensor-measured velocity V2 generated in step A3; it directly forms a measurement residual with the SINS velocity prediction value in the navigation coordinate system.

[0067] Further, step B3 includes the following steps:

[0068] B31. State Prediction: Using the three-axis specific force and angular velocity information obtained by SINS, the navigation state, including position, velocity and attitude, is predicted in one step to obtain the prior state estimate.

[0069] B32. Measurement Update: The filter performs optimal weighted fusion of information from two observation channels based on the preset or online estimated observation noise covariance matrix of each channel; completes the update of the state vector X, and then performs real-time correction on the navigation solution results of SINS, including position, velocity and attitude.

[0070] Further, in step C2, the evaluation module determines that the bottom tracking is lost and the signal strength is too low. The navigation filter automatically increases the observation noise covariance of the DVL channel, reducing its weight in the fusion to near zero. At the same time, the weight of the tensor measurement velocity channel is maintained or increased, so that the system smoothly transitions to a working mode dominated by SINS / tensor fusion.

[0071] Compared with the prior art, the beneficial effects of the present invention are:

[0072] 1. This invention provides an autonomous and covert velocity observation method that does not rely on external information sources, fundamentally enhancing the reliability and survivability of navigation systems. Existing underwater navigation systems primarily rely on a combination of SINS / DVL after GPS failure. However, DVL is prone to failure in complex sea conditions, leading to error accumulation; while external auxiliary methods such as acoustic navigation have limitations in their range and are easily detected. This invention, by processing the magnetic field changes induced by the carrier's own motion, can measure independent "magnetic tensor-velocity" information from the geomagnetic field in real time. This information does not rely on any external beacons, acoustic signals, or prior databases. Therefore, in underwater missions where DVL fails, acoustic denial occurs, or radio silence is required, it can provide continuous and covert velocity correction for inertial navigation systems, effectively suppressing error divergence and significantly improving the autonomy and mission reliability of long-endurance underwater navigation.

[0073] 2. This invention introduces novel physical observations into integrated navigation systems, constructing deep information redundancy and functional backup, thereby enhancing system robustness. Traditional underwater integrated navigation observations primarily rely on DVL (Depth-to-ground velocity) and periodic external position corrections, such as GPS and acoustics. These methods offer limited information dimensions and are susceptible to common failure risks. The "magnetic tensor-velocity" observation designed in this invention operates on a sensing principle—magnetic field gradient measurement—and its information source—magnetic anomalies—is entirely independent of existing technologies. When DVL fails due to complex seabed conditions or excessive altitude, this observation can seamlessly take over as the core velocity reference, forming a new and stable "SINS / magnetic tensor" integrated navigation mode with SINS (Synchronous Inertial Navigation System). This achieves true functional redundancy within the system and solves the long-standing bottleneck problem of "DVL failure causing a sharp deterioration in navigation performance" in underwater navigation. Attached Figure Description

[0074] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0075] Figure 1 Integrated schematic diagram of core components of a navigation system;

[0076] Figure 2 Schematic diagram of the principle of using multi-order magnetic gradient tensor to measure carrier velocity for auxiliary SINS integrated navigation;

[0077] Figure 3 The motion trajectory of the underwater ROV in the simulation experiment;

[0078] Figure 4 The comparison between the actual velocity of the ROV and the velocity measured based on the multi-order magnetic gradient tensor in the simulation experiment is shown in the figure. (a) is the comparison between the actual velocity and the measured velocity in the X direction, (b) is the comparison between the actual velocity and the measured velocity in the Y direction, and (c) is the comparison between the actual velocity and the measured velocity in the Z direction.

[0079] Figure 5 Comparison of the actual trajectory of the ROV in the simulation experiment and the trajectory after velocity integration based on multi-order magnetic gradient tensor measurement.

[0080] Figure 6 Flowchart of underwater assisted navigation method for measuring carrier velocity using a combination of multi-order magnetic gradient tensors. Detailed Implementation

[0081] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, the accompanying drawings show only the parts relevant to the present invention, and not all of the structures.

[0082] Research has revealed the following shortcomings in existing underwater navigation technologies: 1. Mainstream autonomous navigation, the SINS / DVL combination, suffers from rapid error accumulation when DVL fails due to altitude exceeding limits or complex seabed conditions, lacking reliable autonomous backup observation methods; 2. Acoustic navigation, such as USBL, heavily relies on external beacons, has limited range, and its accuracy is easily affected by the underwater acoustic environment, resulting in poor maneuverability; 3. Geophysical matching navigation, such as terrain matching, heavily relies on costly prior mapping, making it difficult to apply universally. Underwater vehicles have long relied on the combined SINS and DVL navigation, but DVL is prone to failure beyond operating altitudes or in complex seabed environments, leading to the accumulation and divergence of navigation errors over time. Commonly used acoustic correction methods face the dilemma of high cost and difficult deployment, while geophysical field matching navigation relies on prior high-precision digital maps, with complex matching algorithms and poor real-time performance. Therefore, this invention utilizes the spatial characteristics of the magnetic gradient tensor to measure the vehicle's velocity, providing an autonomous velocity observation method that does not rely on external acoustic signals or terrain assistance. This velocity-assisted information based on geomagnetic spatial structure can effectively suppress the error divergence between SINS and DVL, significantly improving the autonomy, stealth, and reliability of underwater long-endurance navigation.

[0083] This invention relates to an underwater-assisted navigation method that combines multi-order magnetic gradient tensor measurement of carrier velocity. The navigation system comprises a multi-order magnetic gradient tensor measuring instrument, a strapdown inertial navigation system (SINS), a Doppler velocimeter (DVL), and an industrial control computer for navigation data processing. Figure 1 , Figure 2 As shown, the multi-order magnetic gradient tensor measurement instrument, SINS, DVL, and industrial control computer are all fixedly installed on the same underwater platform. The multi-order magnetic gradient tensor measurement instrument is mounted at the front end of the platform via a long lever arm, with its X-axis aligned with the platform's forward direction. The SINS and DVL are jointly mounted on the left front of the bottom support of the platform, also with their X-axis aligned with the platform's forward direction. The industrial control computer is mounted at the rear end of the platform via a long lever arm, and the installation deviations of the lever arm and the SINS and DVL have been precisely calibrated. The industrial control computer is responsible for running the data fusion and navigation solution algorithms, processing the navigation data. To ensure navigation continuity in abnormal situations such as DVL failure, the navigation system incorporates an online observation quality assessment and an adaptive weight adjustment and smooth switching mechanism. The navigation system uses SINS to output the three-axis specific force, angular velocity and other state information of the carrier in real time for state prediction; it uses a multi-order magnetic gradient tensor measuring instrument to collect the raw data of multi-order magnetic gradient tensors of the underwater environment; and it uses DVL to output the carrier's ground velocity V1, while reporting the DVL's own working status, including normal / fault / bottom tracking loss, etc.

[0084] like Figure 6As shown, this invention combines a multi-order magnetic gradient tensor to measure the velocity of a carrier in underwater assisted navigation. This includes using initial state information from the SINS (Sensory Inertial Navigation System), including specific force and angular velocity, as algorithm input; performing SINS state prediction; and, based on the initial state, predicting position, velocity, and attitude through inertial navigation calculations, providing a basic state vector for subsequent data fusion. Multi-sensor data acquisition and preprocessing are completed through two paths: Path 1 (DVL data link): The DVL (Doppler Velocity Analyzer) outputs the carrier velocity V1 and state information. Combined with the attitude matrix predicted by SINS, the velocity data coordinates are transformed to the navigation coordinate system to obtain usable velocity observations. Path 2 (Magnetic Gradient Tensor Data Link): The multi-order magnetic gradient tensor acquires second- and third-order magnetic gradient tensor data, processes it through time differentiation, and combines it with the SINS attitude matrix to obtain the tensor-measured velocity V2. Extended Kalman Filter (EKF) fusion input: The DVL output carrier velocity V1, tensor-measured velocity V2, and the SINS-predicted state vector in the navigation coordinate system are input together into the extended Kalman filter. Online Observation Quality Assessment: The validity and observation quality of the DVL signal are assessed online, with two branch processing methods: Branch A (DVL signal normal): The observation noise covariance matrix of each channel is dynamically estimated; Branch B (DVL signal failure): The observation noise covariance matrix of the DVL channel is automatically increased, reducing the weight of failed data in the fusion. Adaptive Weighted Fusion and State Update: Based on the output observation noise covariance matrix, the system state error is updated through an adaptive weighted fusion algorithm.

[0085] SINS solution result correction: Correct the navigation solution results (position, velocity, attitude) using the updated state error. High-precision navigation information output: Output the corrected high-precision attitude, velocity, and position information to complete a single navigation solution process. Subsequent iterations will enable continuous navigation.

[0086] Specifically, the following steps are included:

[0087] A. Generation of velocity observations based on multi-order magnetic gradient tensors:

[0088] A1. Acquisition of raw data for multi-order magnetic gradient tensors:

[0089] The multi-order magnetic gradient tensor measuring instrument modulates spatial magnetic field information into a frequency domain signal by driving its internal sensor to move continuously along a preset closed butterfly spatial trajectory. After demodulation, the magnetic gradient tensor measuring instrument can synchronously and continuously output high-precision magnetic field vector, second-order magnetic gradient tensor G, and third-order magnetic gradient tensor H in the carrier coordinate system to the industrial control computer.

[0090] A2. Tensor-time differential processing:

[0091] The industrial control computer receives a real-time sequence of the second-order magnetic gradient tensor G, and uses a smoothing estimation algorithm based on a state-space model to perform smooth differentiation on the continuous second-order magnetic gradient tensor G sequence, thereby calculating its second-order tensor time change rate. .

[0092] A3. Solving for tensor velocity observations:

[0093] Will The third-order magnetic gradient tensor H and the current-moment carrier attitude matrix obtained from SINS. Substituting into the observation equations, solve for the carrier velocity vector V in the navigation coordinate system (n-frame). n This speed is the tensor measurement speed V2.

[0094] B. Multi-source information adaptive fusion navigation:

[0095] B1. Definition of system state variables:

[0096] The navigation data processing unit operates an extended Kalman filter (EKF) with error states as state variables; where the state vector X contains the error states of SINS, namely position error, velocity error, and attitude error.

[0097] B2. Dual observation channel design:

[0098] The filter is configured with two parallel and independent observation channels.

[0099] Channel 1 (DVL velocity channel) measures the ground velocity V1 in the DVL-measured carrier coordinate system (b-frame). After coordinate transformation, this value forms the measurement residual with the SINS velocity prediction value.

[0100] Channel 2 (Tensor Velocity Channel) uses the tensor velocity V2 generated in step A3 as the observation. This directly forms the measurement residual with the SINS velocity prediction value in the navigation coordinate system.

[0101] B3. State Prediction and Measurement Update:

[0102] B31. State Prediction: Using the three-axis specific force, angular velocity and other information obtained by SINS, the navigation state, including position, velocity and attitude, is predicted in one step to obtain the prior state estimate.

[0103] B32. Measurement Update: The filter performs optimal weighted fusion of information from two observation channels based on the preset or online estimated observation noise covariance matrix of each channel; completes the update of the state vector X, and then performs real-time correction on the navigation solution results of SINS, including position, velocity and attitude.

[0104] C. Robustness enhancement and failure handling:

[0105] C1. Online assessment of observation quality: Real-time monitoring of DVL signal strength, bottom tracking lock status, and residual size of tensor measurement speed solution; calculation and dynamic updating of observation noise covariance estimates for the two observation channels; quantification of the reliability of each observation quantity.

[0106] C2. Adaptive Weight Adjustment and Smooth Switching: When the evaluation module determines that the DVL signal is faulty or its quality is severely degraded, such as bottom tracking loss or excessively low signal strength, the navigation filter automatically increases the observation noise covariance of the DVL channel, reducing its weight in the fusion to near zero. At the same time, it maintains or increases the weight of the tensor measurement velocity channel, enabling the system to smoothly transition to a working mode dominated by SINS / tensor fusion, avoiding jumps in navigation calculations due to sudden changes in observations, and ensuring the continuity and stability of navigation output.

[0107] In this invention, SINS is used to provide triaxial specific force / angular velocity information, a multi-order magnetic gradient tensor system provides G / H data, and DVL provides the carrier's ground velocity V1 and state monitoring information. Smooth differentiation of G yields... The tensor measurement velocity V2 is calculated by combining H and the attitude matrix. EKF, with the error state as its core, fuses the ground velocity V1 and tensor measurement velocity V2 provided by DVL in parallel to complete state correction. Online evaluation of observation quality and dynamic adjustment of observation noise covariance enable smooth switching in the event of DVL failure, ensuring navigation robustness. This invention uses a multi-order magnetic gradient tensor calculation velocity as a redundant backup for DVL, solving the problem of easy lock-up in underwater DVL. Based on an extended Kalman filter dual-observation channel design, combined with adaptive noise covariance adjustment, this invention achieves highly robust multi-source information fusion. This invention constructs a complete failure handling mechanism to ensure continuous and stable operation of the navigation system in complex underwater environments.

[0108] Example 1

[0109] An underwater-assisted navigation method for measuring vehicle velocity using a combined multi-order magnetic gradient tensor includes the following steps:

[0110] 1. Generation of velocity observations based on multi-order magnetic gradient tensors:

[0111] In this embodiment, a multi-order magnetic gradient tensor measurement instrument is mounted on the front end of the remotely operated vehicle (ROV) platform, with its X-axis aligned with the vehicle's forward direction. When the vehicle moves in a magnetic field, the measured changes in the magnetic field depend not only on its position but also on its attitude and velocity. By analyzing the rate of change of the magnetic field in space, the vehicle's motion information can be deduced.

[0112] Rate of change of second-order tensor in time on a moving vehicle It consists of two parts:

[0113] (1) Due to the movement of the carrier, it passes through regions with different magnetic field strengths.

[0114] (2) The change of the magnetic field itself over time, i.e. the time-varying part of the geomagnetic field. .

[0115] According to the concept of the material derivative in fluid mechanics, the rate of total change is:

[0116] ;

[0117] in, It is the second-order tensor of the magnetic field.

[0118] , is the velocity vector of the carrier in the navigation coordinate system.

[0119] It is the local time derivative of the magnetic field, which is usually very small and can be ignored.

[0120] It is a key component, containing a third-order tensor and velocity information.

[0121] After simplification, we get the following form:

[0122] (1)

[0123] The third-order magnetic gradient tensor H is the spatial rate of change of the second-order tensor. Its component form is:

[0124] ;

[0125] According to the chain rule, the time derivative of the gradient tensor is:

[0126] (2)

[0127] This can be written in matrix form as follows:

[0128] (3)

[0129] in, This represents the contraction of the third-order magnetic gradient tensor and the velocity vector.

[0130] Expanding the equation by its components yields nine equations (corresponding to the nine elements of G).

[0131] For each i, j∈{x, y, z}:

[0132] ;

[0133] Since the magnetic field is sourceless and irrotational, the magnetic gradient tensor G is symmetric:

[0134] ,and ;

[0135] At the same time, the third-order tensor also has symmetry:

[0136] ;

[0137] Therefore, the number of equations for solving the independent components is reduced to 5.

[0138] Write the independent equations in matrix form:

[0139] ;

[0140] in, , is the speed to be determined;

[0141] b is independent Component composition;

[0142] A is the corresponding Components.

[0143] The specific form is as follows:

[0144] ;

[0145] Reorganize into the form of independent variables:

[0146] ;

[0147] Since there are 5 equations and 3 unknowns, the least squares method is used to solve them:

[0148] ;

[0149] Thus, the speed of the transport platform in the carrier coordinate system can be obtained.

[0150] In practical navigation, the transformation between the vehicle coordinate system (b-frame) and the navigation coordinate system (n-frame) needs to be considered.

[0151] Coordinate transformation of a second-order tensor:

[0152] ;

[0153] Coordinate transformation of a third-order tensor:

[0154] ;

[0155] in, It is the attitude matrix Element.

[0156] In the navigation system, the time derivative of the second-order tensor is:

[0157] ;

[0158] in, With angular velocity Related:

[0159] ;

[0160] Substituting into formula (3), the final tensor-velocity solution formula is obtained as follows:

[0161] (4)

[0162] in, It is the cross product matrix of angular velocities.

[0163] The velocity V of the vehicle in the navigation coordinate system is obtained by using the least squares method. n Let V2 be the tensor measurement velocity.

[0164] 2. Multi-source information adaptive fusion navigation:

[0165] The system's navigation system (SINS) and dynamic range filter (DVL) are integrated into the industrial control computer (ICSC). SINS provides initial state prediction, while DVL outputs the vehicle's ground velocity V1. Based on this, the ICCC runs an Extended Kalman Filter (EKF) that uses the error state as the state variable. The filter has two parallel and independent observation channels. In the state prediction phase, the filter uses the real-time triaxial force and angular velocity information output by SINS to make a one-step prediction of the vehicle's position, velocity, and attitude, obtaining a priori state estimates. In the measurement update phase, the filter performs weighted fusion of the information from the two channels based on the observation noise covariance matrix of each channel, updating the state vector X and correcting the navigation solution results of SINS in real time, outputting the corrected position, velocity, and attitude information.

[0166] 3. Robustness enhancement and failure handling:

[0167] To address potential loss of lock or failure of DVL under complex seabed or ultra-high altitude conditions, this embodiment constructs an online assessment mechanism for observation quality and an adaptive weight adjustment mechanism. The industrial control computer monitors the signal strength and bottom tracking lock status of the DVL in real time, while simultaneously calculating the residual statistical characteristics of the tensor measurement velocity channel. Based on this information, the observation noise covariance of the two observation channels is dynamically estimated, quantifying the real-time reliability of each observation. When the assessment module determines that the DVL signal has failed or its quality has severely degraded, the filter automatically increases the observation noise covariance of the DVL channel, bringing its weight in the fusion process close to zero; simultaneously, the weight of the tensor measurement velocity channel is maintained or increased, allowing the system to smoothly transition to a working mode primarily based on SINS / tensor fusion.

[0168] To verify the effectiveness of the method in this embodiment, the following simulation experiment was conducted. The underwater ROV was set to perform a closed-loop, figure-eight-shaped, periodic translational motion starting from the origin. Its trajectory can be described by the following equation:

[0169] Linear velocity v(t) = 10 + 10sin(t);

[0170] Angular velocity ω(t) = 10cos(t);

[0171] The initial state is (x, y, z) = (0m, 0m, 0m).

[0172] By integrating the kinematic equations, we obtain the direction angle θ(t) = 10sin(t), and its trajectory is as follows: Figure 3 As shown.

[0173] Within this motion space, a magnetic dipole is placed at the coordinates (500m, 500m, 500m) as a magnetic source. The magnetic moment of the magnetic dipole is 3 A·m. 2 The magnetic declination is 60° and the magnetic inclination is -30°. The second and third order tensors of the magnetic field at any location in space can be calculated using the following formulas:

[0174] (5)

[0175] (6)

[0176] Among them, the magnetic permeability in vacuum =4π ×10 -7 N / A 2 , =( il , jl , kl() is the Kronecker function, which outputs a value of 1 when the two subscripts are equal, and 0 otherwise. l = 1, 2, 3 represent the x, y, z axes in the Cartesian coordinate system, and r (r x ,r y ,r z ) is the position vector from the measuring point to the magnetic source, and M represents the magnetic moment vector of the magnetic source. Represents the components of a second-order tensor. This represents the components of a third-order tensor.

[0177] Therefore, the second and third order tensors of the magnetic field at the ROV position in the carrier coordinate system can be obtained. Then, by combining the motion attitude of the ROV with formula (4), the velocity V2 of the ROV in the navigation coordinate system can be solved.

[0178] Assuming that the signal quality gradually deteriorates and the error gradually increases during the operation of DVL, the filter automatically adjusts the observation noise covariance of the two channels and fuses the two speed solutions to calculate the final output speed. This output speed is then compared with the simulated actual speed, and the results are as follows: Figure 4 (a)- Figure 4 As shown in (c). The results show that the maximum relative error of the speed measured by this method is 2.41%, which is comparable to the speed measurement accuracy of the SINS / DVL mode under normal operating conditions.

[0179] Furthermore, based on the initial position and velocity in the navigation coordinate system, the ROV's motion trajectory is simulated and calculated in the SINS / tensor fusion mode. The calculated navigation trajectory is compared with the actual trajectory, for example... Figure 5 As shown in the figure. The results indicate that the positioning error of this method is less than 0.5m within 250s.

[0180] It will be understood by those skilled in the art that the present invention is not limited to the specific embodiments described herein, and that various obvious changes, readjustments, and substitutions can be made by those skilled in the art without departing from the scope of protection of the present invention. Therefore, although the present invention has been described in detail through the above embodiments, the present invention is not limited to the above embodiments, and may include more other equivalent embodiments without departing from the concept of the present invention, and the scope of the present invention is determined by the scope of the appended claims.

Claims

1. An underwater auxiliary navigation method for measuring carrier velocity using a combination of multi-order magnetic gradient tensors, characterized in that, Includes the following steps: A. Generation of velocity observations based on multi-order magnetic gradient tensors: A1. Acquisition of raw data for multi-order magnetic gradient tensors: The multi-order magnetic gradient tensor measuring instrument modulates the spatial magnetic field information into a frequency domain signal by driving its internal sensor to move continuously along a preset closed butterfly spatial trajectory. After demodulation, the magnetic gradient tensor measuring instrument can synchronously and continuously output the magnetic field vector, second-order magnetic gradient tensor G, and third-order magnetic gradient tensor H in the carrier coordinate system to the industrial control computer. A2. Tensor-time differential processing: The industrial control computer receives a real-time sequence of second-order magnetic gradient tensors G, performs smooth differentiation on the continuous sequence of second-order magnetic gradient tensors G, and calculates its second-order tensor time change rate. ; A3. Solving for tensor velocity observations: Will The third-order magnetic gradient tensor H and the current-moment carrier attitude matrix obtained from SINS. Substituting into the observation equation, solve for the vehicle velocity vector V in the navigation coordinate system. n This speed is the tensor measurement speed V2; B. Multi-source information adaptive fusion navigation: B1. The navigation data processing unit operates an extended Kalman filter that uses the error state as the state variable. B2. The filter is configured with two parallel and independent observation channels; B3. State Prediction and Measurement Update: C. Robustness enhancement and failure handling: C1. Online assessment of observation quality: Real-time monitoring of DVL signal strength, bottom tracking lock status, and residual size of tensor measurement velocity solution; calculation and dynamic updating of observation noise covariance estimates for the two observation channels respectively. C2. Adaptive weight adjustment and smooth switching: When the evaluation module determines that the DVL signal is faulty or its quality is severely degraded, the navigation filter automatically increases the observation noise covariance of the DVL channel, reducing its weight in the fusion to near zero. It also maintains or increases the weight of the tensor measurement speed channel, enabling the system to smoothly transition to a working mode primarily based on SINS / tensor fusion.

2. The underwater auxiliary navigation method for measuring carrier velocity using a combined multi-order magnetic gradient tensor as described in claim 1, characterized in that, Step A2: Use a smooth estimation algorithm based on the state-space model to perform smooth differentiation on the continuous second-order magnetic gradient tensor G sequence.

3. The underwater auxiliary navigation method for measuring carrier velocity using a combined multi-order magnetic gradient tensor as described in claim 2, characterized in that, Step A2: ； in, , It is the velocity vector of the vehicle in the navigation coordinate system. The time-varying part of the magnetic field gradient can be simplified as follows: （1）。 4. The underwater auxiliary navigation method for measuring carrier velocity using a combined multi-order magnetic gradient tensor as described in claim 3, characterized in that, Step A3, the third-order magnetic gradient tensor H is the spatial rate of change of the second-order tensor. Its component form is: ； According to the chain rule, the time derivative of the gradient tensor is: （2） This can be written in matrix form as follows: （3） in, This represents the contraction of a third-order tensor and a velocity vector; Expanding the equation by its components, for each i, j∈{x, y, z}: ； Since the magnetic field is sourceless and irrotational, the magnetic gradient tensor G is symmetric: ,and ; At the same time, the third-order tensor also has symmetry: ； Write the independent equations in matrix form: ； in, , is the speed to be determined; b is independent Component composition; A is the corresponding Component composition; The specific form is as follows: ； Reorganize into the form of independent variables: ； Solve using the least squares method: ； The speed of the carrier platform in the carrier coordinate system can then be obtained.

5. The underwater auxiliary navigation method for measuring carrier velocity using a combined multi-order magnetic gradient tensor as described in claim 4, characterized in that: In practical navigation, considering the transformation between the vehicle coordinate system and the navigation coordinate system, the coordinate transformation of the second-order tensor is as follows: ； Coordinate transformation of a third-order tensor: ； in, It is the attitude matrix Element; In the navigation system, the time derivative of the second-order tensor is: ； in, With angular velocity Related: ； Substituting into formula (3), the final tensor-velocity solution formula is obtained as follows: （4） in, It is the cross product matrix of angular velocities; The velocity V of the vehicle in the navigation coordinate system is obtained by using the least squares method. n Let V2 be the tensor measurement velocity.

6. The underwater auxiliary navigation method for measuring carrier velocity using a combined multi-order magnetic gradient tensor as described in claim 1, characterized in that: Step B1: The state vector X contains the error states of SINS, namely position error, velocity error, and attitude error.

7. The underwater auxiliary navigation method for measuring carrier velocity using a combined multi-order magnetic gradient tensor as described in claim 1, characterized in that: Step B2: Channel 1 is the DVL velocity channel, and the observed value is the DVL-measured velocity V1 relative to the ground in the carrier coordinate system. After coordinate transformation, it forms a measurement residual with the SINS velocity prediction value. Channel 2 is the tensor velocity channel, and the observed value is the tensor-measured velocity V2 generated in step A3. It directly forms a measurement residual with the SINS velocity prediction value in the navigation coordinate system.

8. The underwater auxiliary navigation method for measuring carrier velocity using a combined multi-order magnetic gradient tensor as described in claim 1, characterized in that, Step B3 includes the following steps: B31. State Prediction: Using the three-axis specific force and angular velocity information obtained by SINS, the navigation state, including position, velocity and attitude, is predicted in one step to obtain the prior state estimate. B32. Measurement Update: The filter performs optimal weighted fusion of information from two observation channels based on the preset or online estimated observation noise covariance matrix of each channel; completes the update of the state vector X, and then performs real-time correction on the navigation solution results of SINS, including position, velocity and attitude.

9. The underwater auxiliary navigation method for measuring carrier velocity using a combined multi-order magnetic gradient tensor as described in claim 1, characterized in that: In step C2, the evaluation module determines that the bottom tracking is lost and the signal strength is too low. The navigation filter automatically increases the observation noise covariance of the DVL channel, reducing its weight in the fusion to near zero. At the same time, the weight of the tensor measurement velocity channel is maintained or increased, so that the system smoothly transitions to the working mode dominated by SINS / tensor fusion.

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