Initial alignment method based on mahalanobis distance anti-interference

Abstract

The application relates to the field of inertial navigation systems and discloses an initial alignment method based on anti-interference Mahalanobis distance, which comprises the following steps: initialization; updating a first observation vector and a second observation vector at a current time; calculating a residual vector at the current time and further calculating a Mahalanobis distance at the current time; judging whether an abnormal value criterion condition is met; if the abnormal value criterion condition is not met, recursively updating a mean value and a covariance matrix of a residual vector at a next time by using the residual vector and the Mahalanobis distance obtained at the current time; if the abnormal value criterion condition is met, suspending the updating of the mean value and the covariance matrix of the residual vector; updating a flexible weight and an observation matrix, and continuing to complete a moving base alignment by using an attitude determination algorithm. The improved Mahalanobis distance abnormality detection criterion is constructed to judge the abnormality of a residual vector formed by observation vectors, and a weight factor of an observation matrix is introduced, so that abnormal interference in the alignment process is inhibited.

Description

Technical Field

[0001] This invention relates to the field of inertial navigation systems, and more particularly to an initial alignment method based on Mahalanobis distance for interference resistance. Background Technology

[0002] In a moving-base integrated navigation system consisting of a Strapdown Inertial Navigation System (SINS) and a Doppler Velocity Log (DVL), initial alignment is a fundamental step in system startup, and its accuracy has a decisive impact on the stability and accuracy of subsequent navigation calculations. The unique characteristics of the moving-base environment, such as the lack of external absolute position updates during long-duration navigation, cause initial alignment errors to continuously propagate and accumulate, ultimately significantly affecting the success or failure of the entire navigation mission. Therefore, achieving high-precision and robust initial alignment is a prerequisite for ensuring reliable navigation of moving vehicles such as vehicles, aircraft, and underwater vehicles.

[0003] However, as a key sensor providing an external velocity reference, DVL (Device Velocity Level) is susceptible to interference from complex dynamic environments during underwater operation. This interference often results in outliers or non-Gaussian noise in DVL observation data, deviating from the normal distribution. Similar problems exist in velocity sensors used on other moving-base platforms. Traditional initial alignment algorithms based on least-squares estimation or fixed linear weighting typically assume that the observation noise is Gaussian distributed and without significant outliers. When outliers exist in the DVL data, these algorithms deviate significantly from the optimal estimate, leading to a sharp increase in attitude calculation errors and causing attitude drift or even system-wide divergence in subsequent navigation calculations. Therefore, in the complex and dynamically changing moving-base environment, improving the robustness of the initial alignment process and enhancing the algorithm's ability to suppress observation anomalies has become one of the key challenges and hot topics in current research on moving-base navigation systems.

[0004] In SINS / DVL integrated navigation systems, the accuracy of initial alignment directly impacts the accuracy of subsequent navigation. As a velocity reference sensor, DVL is susceptible to various disturbances in complex underwater environments, such as turbulence or multipath effects, often generating outliers. These outliers severely affect the accuracy of the constructed observation data, thus reducing the accuracy of initial alignment. In practical applications, DVL data may introduce anomalous observations due to environmental changes, leading to deviations in residuals and consequently affecting overall alignment accuracy. Existing robust alignment methods fail to adequately consider the uncertainties in the statistical characteristics of observations, resulting in misjudgments and improper handling of outliers, which further affects the stability of the alignment results. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide an initial alignment method based on Mahalanobis distance to resist interference.

[0006] The objective of this invention is achieved through the following technical solution:

[0007] A first aspect of the present invention provides an initial alignment method based on Mahalanobis distance for interference resistance, comprising the following steps:

[0008] S1: Initialization , , , = ,in: The mean of the residual vector. Let covariance be the residual vector. Represents the nominal covariance matrix of the residual vector. This represents the mean of the calculated Mahalanobis distance. This represents the variance of the calculated Mahalanobis distance. This represents the nominal Mahalanobis distance variance;

[0009] S2: Update to get the current time. First observation vector Second observation vector The first observation vector Second observation vector In the sliding window The discretized form is as follows:

[0010] ;

[0011] ;

[0012] In the formula, Indicates the current time of the system. Relative to the initial time of the system The attitude transformation matrix, express Time-based system Relative to the initial time system The attitude transformation matrix, and They represent Time and Ground speed under the time-carrying system This indicates the start time of the current sliding window; Here is the discretized expression for the first integral term, which is: , express The ratio of the accelerometer output at any given time. This represents the integration time variable in the integral term; The discretized expression corresponding to the second integral term is: , express The projection of the Earth's rotational angular velocity onto the system at any given moment. express Ground speed under the time-carrying system; express Time navigation coordinate system Relative to the initial time vehicle coordinate system The attitude change matrix, Represents the period of discretization. As a unit array, This represents the antisymmetric matrix formed by the rotational angular velocity vectors of the navigation coordinate system relative to the inertial coordinate system. This represents the gravity vector projection in the navigation coordinate system;

[0013] S3: Utilize the first observation vector from step S2 Second observation vector Calculate the current time residual vector :

[0014] ;

[0015] And further calculate the current time. Mahalanobis distance :

[0016] ;

[0017] ;

[0018] ;

[0019] In the formula, Represents the i-th residual scalar;

[0020] S4: Determine whether the outlier criterion is met:

[0021] ;

[0022] in, , ;

[0023] If the outlier criterion is not met, then the residual vector obtained at the current time step is used. and Mahal distance Recursively update the next time step , and cumulative updates , If the outlier criterion is met, updates will be paused. , Directly set the current time , As the next moment , But continue to accumulate updates , ;

[0024] S5: Update flexible weights :

[0025] ;

[0026] In the formula, As a scale factor, The index control coefficient is then used; then flexible weights are applied. renew Observation matrix at time The attitude determination algorithm is then used to continue aligning the moving base.

[0027] ;

[0028] In the formula, express The observation matrix at time, Represents the second observation vector The left-multiplication matrix operator of the quaternions formed; Represents the first observation vector The right-multiplication matrix operator of the quaternions formed.

[0029] Furthermore, in step S4, if the outlier criterion is not met, the residual vector obtained at the current time is used. and Mahal distance Recursively update the next time step , ,include:

[0030] Update data points:

[0031] ;

[0032] Represents the time from the initial moment to the current moment. The total number of non-outlier data points observed. This represents the time from the initial moment to the previous moment. The total number of non-outlier data points observed;

[0033] Update the mean:

[0034] ;

[0035] Indicates based on the previous The mean vector calculated from each data point Indicates based on the previous The mean vector calculated from each data point;

[0036] Update the covariance matrix:

[0037] ;

[0038] Indicates based on the previous The covariance matrix calculated from each data point Indicates based on the previous The covariance matrix is ​​calculated from each data point.

[0039] Furthermore, in step S4, if the outlier criterion is met, then the update is paused. , Directly set the current time , As the next moment , ,include:

[0040] Update data points:

[0041] ;

[0042] Update the mean:

[0043] ;

[0044] Update the covariance matrix:

[0045] .

[0046] The beneficial effects of this invention are:

[0047] In an exemplary embodiment of the present invention, an improved Mahalanobis distance anomaly detection criterion is constructed to determine the anomaly of the residual vector composed of the observation vectors, and a weighting factor of the observation matrix is ​​introduced to suppress abnormal interference in the alignment process; this provides a reliable solution for high-precision initial alignment of the dynamic base navigation system in complex environments, and has good practicality and real-time application potential. Attached Figure Description

[0048] Figure 1A flowchart of an initial alignment method based on Mahalanobis distance for interference resistance provided as an exemplary embodiment of the present invention;

[0049] Figure 2 A schematic diagram of an attitude angle change curve provided for an exemplary embodiment of the present invention;

[0050] Figure 3 A schematic diagram of a velocity variation curve provided for an exemplary embodiment of the present invention;

[0051] Figure 4 A schematic diagram of a trajectory change curve provided for an exemplary embodiment of the present invention;

[0052] Figure 5 A schematic diagram of the roll angle error curve provided for an exemplary embodiment of the present invention;

[0053] Figure 6 A schematic diagram of a pitch angle error curve provided for an exemplary embodiment of the present invention;

[0054] Figure 7 A schematic diagram of a yaw angle error curve provided for an exemplary embodiment of the present invention;

[0055] Figure 8 A schematic diagram of the attitude angle change curve provided in yet another exemplary embodiment of the present invention;

[0056] Figure 9 A schematic diagram of a velocity variation curve provided as another exemplary embodiment of the present invention;

[0057] Figure 10 A schematic diagram of a trajectory change curve provided as another exemplary embodiment of the present invention;

[0058] Figure 11 A schematic diagram of the roll angle error curve provided for yet another exemplary embodiment of the present invention;

[0059] Figure 12 A schematic diagram of a pitch angle error curve provided for yet another exemplary embodiment of the present invention;

[0060] Figure 13 A schematic diagram of the yaw angle error curve provided for yet another exemplary embodiment of the present invention. Detailed Implementation

[0061] The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. Furthermore, the technical features involved in the different embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0062] In strapdown inertial navigation systems (SINS) and Doppler log (DVL) integrated navigation systems, initial alignment accuracy is crucial for subsequent navigation performance. Because DVL is susceptible to interference in complex underwater environments, traditional initial alignment methods suffer performance degradation under outlier interference, failing to meet high-precision requirements. Specifically:

[0063] For SINS / DVL integrated navigation systems, the ground velocity provided by DVL can be used to assist SINS in initial alignment. First, the attitude matrix is ​​aligned using a chain rule. Decomposed into:

[0064] ;

[0065] in For the current moment, Let be the attitude transformation matrix of the carrying system relative to the navigation system at the current moment. Navigation system for the current moment Navigation system relative to the initial time The attitude transformation matrix, Indicates the current time of the system. Relative to the initial time system The attitude transformation matrix, This is the initial time-loaded system. Navigation system relative to the initial time The attitude matrix is ​​a constant matrix. It contains two time-varying attitude matrices. and It can be updated using the differential equation of the attitude matrix:

[0066] ;

[0067] ;

[0068] In the formula, Represents the attitude matrix The differential, This represents the projection of the rotational angular velocity of the navigation coordinate system relative to the inertial coordinate system onto the navigation coordinate system. express The differential, This represents the angular velocity output by the gyroscope; in the time-varying attitude matrix. and Once obtained, the core of optimized alignment is to determine the constant attitude matrix. .

[0069] Based on the specific force equation, the observation vector equation can be obtained as follows:

[0070] ;

[0071] The first observation vector Second observation vector It can be represented as

[0072] (5);

[0073] ;

[0074] In the above formula, Here, represents the lower bound of integration, and represents the start time of the current sliding window. This represents the current moment, i.e., the maximum score. When... hour( (where the sliding window has a fixed length), the above integral is the result of the time taken within the window length. The sliding integral within. This represents the projection of the current velocity relative to the ground in the carrier coordinate system b. express Time-based system Relative to the initial time system The attitude transformation matrix, express Time-based system Relative to the initial time system The attitude transformation matrix, This indicates the specific force output by the accelerometer. This represents the time variable for integration within the integration interval. The projection of the Earth's rotational angular velocity onto the system of reference. express The projection of the velocity relative to the ground at any given moment onto the vehicle's coordinate system; express The attitude transformation matrix of the navigation coordinate system at time t relative to the initial navigation coordinate system. This represents the projection of the gravitational acceleration vector onto the navigation coordinate system.

[0075] Observation vector and In the sliding window The discretized form is as follows:

[0076] ;

[0077] ;

[0078] in This is the time series at the current moment. The start time of the current sliding window Time series, The length of the sliding window. For the solution period, satisfying . The discretized expression of the first integral term in formula (5) The discretized expression of the second integral term in formula (5). express The attitude transformation matrix of the navigation coordinate system at time t relative to the initial navigation coordinate system. This represents a 3x3 identity matrix. express The rotational angular velocity of the navigation coordinate system relative to the vehicle coordinate system at any given time.

[0079] In SINS / DVL integrated navigation systems, the initial alignment accuracy directly affects the accuracy of subsequent navigation. As a velocity reference sensor, DVL is susceptible to various interferences in complex underwater environments, such as turbulence or multipath effects, often generating outliers. These outliers can severely impact the accuracy of navigation. and The construction precision is reduced, thus decreasing the accuracy of the initial alignment. First observation vector. Second observation vector The construction involves multiple parameters, among which the second observation vector... Depend on and The updated vector is less susceptible to interference from sensor output. And the first observation vector... The alignment is composed of the outputs of the IMU and DVL. In practical applications, DVL data may introduce anomalous observations due to environmental changes, leading to deviations in the residuals and affecting the overall alignment accuracy. Existing robust alignment methods fail to fully consider the uncertainties in the statistical characteristics of observations, resulting in misjudgments and improper handling of outliers, which further affects the stability of the alignment results. Therefore, in the exemplary embodiment below, the outlier discrimination method based on Mahalanobis distance effectively addresses this problem. By recursively calculating the discrimination threshold in real time using all historical Mahalanobis distances, it dynamically detects and suppresses the impact of outliers on alignment accuracy.

[0080] To address issues such as misjudgment of outliers during detection and suboptimal weighting during the weighting process, the following exemplary embodiment presents a novel detection method. Mahalanobis distance is a distance metric that considers the correlation and scale differences between data features and effectively reflects the dispersion between data outliers and the sample mean. However, when using Mahalanobis distance, the sample data needs to follow a normal distribution, which the data obtained during the initial alignment process does not meet. The following exemplary embodiment is based on the first observation vector. Second observation vector The residual vector was constructed. As a data vector in Mahalanobis distance:

[0081] ;

[0082] set up For the first scalar of observation residuals , This is the time series at the current moment. Therefore, based on... The square of the Mahalanobis distance can be expressed as:

[0083] ;

[0084] ;

[0085] ;

[0086] In the above formula It is the mean of the residual vector. This is the covariance matrix of the residual vector. In practical applications, when the observed vector... and When the value is an outlier, if formulas (11) and (12) are used to directly update the value at the next time step... and This will inevitably affect the accuracy of subsequent Mahalanobis distance updates.

[0087] Therefore, in the following exemplary embodiments, an outlier criterion based on cumulative statistics is established as follows:

[0088] ;

[0089] ;

[0090] ;

[0091] If the Mahalanobis distance is updated at the current moment If a sample point satisfies formula (13), it is considered an outlier relative to the entire sample. This sample will not participate in the update of the sample mean and covariance to prevent the statistical value from being updated. , Although contaminated, updates are still being made at this time to improve the stability of the testing process. , .

[0092] Based on the outlier criterion of formula (13), the following exemplary embodiment constructs a flexible weight update formula for the observation vector:

[0093] ;

[0094] in As the exponential control coefficient, experiments have shown that when The optimal value is when... As a scaling factor, it controls the mapping relationship between residual magnitude and weight decay. To achieve consistency with the statistical criteria of Mahalanobis distance, it is preferably set to... This value is for a degree of freedom of The critical value of the chi-square distribution at a confidence level of 0.975.

[0095] Based on the outlier criterion of formula (13), the weight coefficients obtained from formula (16) under different conditions are... Action on attitude observation matrix During the construction phase, the weight of each set of new information terms is set to... This can further enhance the robustness of the optimized alignment model to anomaly observations.

[0096] The update formula for the observation matrix can be obtained as follows:

[0097] ;

[0098] According to formulas (4), (7)-(17), the initial alignment method based on Mahalanobis distance for anti-interference provided by an exemplary embodiment of the present invention is obtained. See [link to relevant documentation]. Figure 1 This includes the following steps:

[0099] S1: Initialization , , , = ,in: The mean of the residual vector. Let covariance be the residual vector. Represents the nominal covariance matrix of the residual vector. This represents the mean of the calculated Mahalanobis distance. This represents the variance of the calculated Mahalanobis distance. This represents the nominal Mahalanobis distance variance;

[0100] S2: Update and obtain the current time according to formulas (7) and (8). First observation vector Second observation vector The first observation vector Second observation vector In the sliding window The discretized form is as follows:

[0101] ;

[0102] ;

[0103] In the formula, Indicates the current time of the system. Relative to the initial time system The attitude transformation matrix, express Time-based system Relative to the initial time system The attitude transformation matrix, and They represent Time and Ground speed under the time-carrying system This indicates the start time of the current sliding window; Here is the discretized expression for the first integral term, which is: , express The ratio of the accelerometer output at any given time. This represents the integration time variable in the integral term; The discretized expression corresponding to the second integral term is: , express The projection of the Earth's rotational angular velocity onto the system at any given moment. express Ground speed under the time-carrying system; express Time navigation coordinate system Relative to the initial time vehicle coordinate system The attitude change matrix, Represents the period of discretization. As a unit array, This represents the antisymmetric matrix formed by the rotational angular velocity vectors of the navigation coordinate system relative to the inertial coordinate system. This represents the gravity vector projection in the navigation coordinate system;

[0104] S3: According to formula (9), use the first observation vector in step S2 Second observation vector Calculate the current time residual vector :

[0105] ;

[0106] Furthermore, based on formula (10), the current time is calculated. Mahalanobis distance :

[0107] ;

[0108] ;

[0109] ;

[0110] In the formula, Represents the i-th residual scalar;

[0111] S4: Based on formula (13), determine whether the outlier criterion is met:

[0112] ;

[0113] in, , ;

[0114] If the outlier criterion is not met, then the residual vector obtained at the current time step is used according to formulas (11) and (12). and Mahal distance Recursively update the next time step , and cumulative updates , If the outlier criterion is met, updates will be paused. , Directly set the current time , As the next moment , But continue to accumulate updates , ;

[0115] S5: Update the flexible weights according to formula (16). :

[0116] ;

[0117] In the formula, As a scale factor, The index control coefficient is used; then, according to formula (17), flexible weights are applied. renew Observation matrix at time The attitude determination algorithm is then used to continue aligning the moving base.

[0118] ;

[0119] In the formula, express The observation matrix at time, Represents the second observation vector The left-multiplication matrix operator of the quaternions formed; Represents the first observation vector The right-multiplication matrix operator of the quaternions formed.

[0120] In summary, the initial alignment method based on Mahalanobis distance for anti-interference proposed in this exemplary embodiment determines the anomalies in the residual vector formed by the observation vectors by constructing an improved Mahalanobis distance anomaly detection criterion and introduces a weighting factor for the observation matrix, thereby suppressing abnormal interference in the alignment process.

[0121] More preferably, in an exemplary embodiment, in order to improve computational efficiency, in step S4, formulas (11) and (12) can be calculated using a recursive update method. In step S4, if the outlier criterion is not met, the residual vector obtained at the current time is used. and Mahal distance Recursively update the next time step , ,include:

[0122] Update data points:

[0123] ;

[0124] Represents the time from the initial moment to the current moment. The total number of non-outlier data points observed. This represents the time from the initial moment to the previous moment. The total number of non-outlier data points observed;

[0125] Update the mean:

[0126] ;

[0127] Indicates based on the previous The mean vector calculated from each data point Indicates based on the previous The mean vector calculated from each data point;

[0128] Update the covariance matrix:

[0129] ;

[0130] Indicates based on the previous The covariance matrix calculated from each data point Indicates based on the previous The covariance matrix is ​​calculated from each data point.

[0131] Specifically, in this exemplary embodiment, the mean and covariance can be updated according to the above recursive formula, assuming there are no abnormal observation points.

[0132] More preferably, in an exemplary embodiment, in step S4, the update is paused if the outlier criterion is met. , Directly set the current time , As the next moment , ,include:

[0133] Update data points:

[0134] ;

[0135] Update the mean:

[0136] ;

[0137] Update the covariance matrix:

[0138] .

[0139] Specifically, in this exemplary embodiment, the above formula is used so that when there are abnormal observation points, the mean and variance are retained from the previous time point, thus avoiding contamination by abnormal observation points and affecting the judgment at the next time point.

[0140] More preferably, in an exemplary embodiment, for step S4, the flexible weights are used according to formula (17). renew Observation matrix at time The attitude determination algorithm is then used to complete the alignment of the moving base. The specific implementation method can be as follows:

[0141] Due to the attitude matrix With quaternions If they can be converted to each other, then the corresponding observation formulas are... This can be represented using quaternions:

[0142] ;

[0143] To perform quaternion multiplication, we can rearrange the above expression to obtain...

[0144] ;

[0145] Based on the new observation vector equation, a loss function for the observation equation can be constructed:

[0146] ;

[0147] Where the matrix for:

[0148] ;

[0149] The attitude quaternion can be determined The problem is transformed into a constrained optimization problem:

[0150] ;

[0151] By updating the observation matrix Determine the optimal pose quaternion Thus, the attitude matrix is ​​obtained. .

[0152] The following content will use experiments to demonstrate its effectiveness:

[0153] Designing simulation experiments in a dynamic marine environment: ( Figure 2 Attitude angle change curve; Figure 3 Velocity change curve; Figure 4 (Trajectory change curve) The vehicle executes a pre-generated, 300-second high-maneuver trajectory. This trajectory simulates typical motion in a dynamic marine environment, and its characteristics include... Figure 2 and Figure 3 As shown, the trajectory includes acceleration, turning, and pitch and roll maneuvers with an amplitude of approximately ±30°. The initial position of the trajectory is latitude 34.5°, longitude 118.8°, and altitude 50m. The sensor configuration is shown in Table 1, including an IMU (100 Hz, gyroscope bias 0.01° / h, accelerometer bias 100μg) and a DVL (5 Hz, velocity noise standard deviation 0.05m / s, randomly injected outliers with a probability of 2% and a noise level of 200 times). The comparison methods include conventional optimized alignment (OBA), OBA without additional outliers (OBAr), existing robust alignment (Robust OBA), and the Mahalanobis distance-based OBA method (MOBA) proposed in the above exemplary embodiment.

[0154] Table 1 Sensor Configuration

[0155]

[0156] Figure 5 –7 shows the root mean square error (RMSE) curve for the attitude angle. Figures 5-7 The error curves for roll angle, pitch angle, and yaw angle are shown in Table 2. When DVL outliers occur, they degrade the performance of the OBA method, causing significant error fluctuations. The OBAM and ROBA methods, however, are not significantly affected. The average RMSE over the last 50 seconds is shown in Table 2. OBAM's root mean square error for heading angle is 0.8890°, superior to all other methods. This is because OBAM calculates the Mahalanobis distance threshold in real-time using a sliding window. When an outlier occurs, the Mahalanobis distance D exceeds the threshold, triggering a statistics freeze mechanism, effectively blocking error propagation and contamination. Under strong maneuvering and anomalous data interference, MOBA, with its strong mechanism to block error propagation, suppresses heading angle fluctuations to within 1°. Furthermore, its parameter configuration is simple, and its computational efficiency is comparable to classic optimized alignment methods. This provides a reliable solution for high-precision initial alignment of unmanned vehicles in complex environments, offering both milliradian-level accuracy and strong anti-interference capabilities.

[0157] Table 2 Comparison of Average RMSE of Attitude Angles

[0158]

[0159] To verify the practical performance of the initial alignment method based on Mahalanobis distance for interference resistance, initial alignment was performed using sea trial experimental data. The data duration was 300 seconds, and the attitude angle change curve, velocity change curve, and motion trajectory change curve are shown below. Figure 8-10 As shown in Table 3. Data acquisition was performed using a fiber optic strapdown inertial navigation system (FSINS), DVL, and a high-precision integrated navigation system. The specific configuration is shown in Table 3. The FSINS consists of a gyroscope (zero-bias stability). random walk ) and accelerometer (zero bias stability is Speed ​​random walk The system consists of a 98Hz output frequency and a 1Hz Doppler velocimeter (DVL) with a velocity measurement noise standard deviation of 0.1m / s. The output of the high-precision integrated navigation system is used as a data reference. To simulate occasional abnormal observations in the actual system, outliers are randomly injected into the DVL output with a 2% probability to verify the robustness of the algorithm under non-ideal observation conditions. The alignment results of MOBA are compared with those of OBA, OBA, and ROBA. The experimental results are as follows: Figure 11-13 As shown in Table 3.

[0160] Table 3 Sensor Configuration

[0161]

[0162] Figure 11 Table 13 shows the roll, pitch, and yaw error curves, and Table 4 presents the RMSE error statistics 50 seconds after alignment. It can be seen that both robust methods (ROBA and MOBA) exhibit good suppression of outliers, and the MOBA method proposed in the above exemplary embodiment has the highest accuracy in yaw angle estimation, with an error of 0.4225°, significantly better than other methods. In terms of horizontal attitude estimation, the errors of all methods remain at a low level, indicating that the methods in the above exemplary embodiment do not sacrifice horizontal attitude estimation performance while ensuring heading accuracy. The results show that the robust optimization alignment method based on Mahalanobis distance proposed in the above exemplary embodiment exhibits significant superiority in a moving-base marine environment. By calculating the Mahalanobis distance adaptive threshold in real time through cumulative statistical recursion, it accurately isolates sudden outliers and continuous interference in DVL velocity measurement. The heading angle alignment accuracy is the best compared to existing methods, and the pitch and roll angle errors are also small.

[0163] Table 4 Comparison of Average RMSE of Attitude Angles

[0164]

[0165] The initial alignment method based on Mahalanobis distance for interference resistance proposed in the above exemplary embodiments has demonstrated its effectiveness and superiority in a moving-base marine environment. Through adaptive Mahalanobis distance threshold adjustment based on cumulative statistics, this method can identify and suppress sudden outliers and interferences in DVL measurements in real time, ensuring stable convergence of attitude errors. Experimental results show that, compared with traditional static methods and other robust alignment methods, the method in the above exemplary embodiments exhibits significant performance improvements in heading angle accuracy, pitch angle, and roll angle errors. Therefore, this method provides a reliable solution for high-precision initial alignment of moving-base navigation systems in complex environments, possessing good practicality and real-time application potential.

[0166] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art can make other variations or modifications based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. An initial alignment method based on Mahalanobis distance for interference resistance, characterized in that: Includes the following steps: S1: Initialization , , , = ,in: The mean of the residual vector. Let covariance be the residual vector. Represents the nominal covariance matrix of the residual vector. This represents the mean of the calculated Mahalanobis distance. This represents the variance of the calculated Mahalanobis distance. This represents the nominal Mahalanobis distance variance; S2: Update to get the current time. First observation vector Second observation vector The first observation vector Second observation vector In the sliding window The discretized form is as follows: ； ； In the formula, Indicates the current time of the system. Relative to the initial time system The attitude transformation matrix, express Time-based system Relative to the initial time system The attitude transformation matrix, and They represent Time and Ground speed under the time-carrying system This indicates the start time of the current sliding window; Here is the discretized expression for the first integral term, which is: , express The ratio of the accelerometer output at any given time. This represents the integration time variable in the integral term; The discretized expression corresponding to the second integral term is: , express The projection of the Earth's rotational angular velocity onto the system at any given moment. express Ground speed under the time-carrying system; express Time navigation coordinate system relative to the initial navigation coordinate system The attitude change matrix, Represents the period of discretization. As a unit array, This represents the antisymmetric matrix formed by the rotational angular velocity vectors of the navigation coordinate system relative to the inertial coordinate system. This represents the gravity vector projection in the navigation coordinate system; S3: Utilize the first observation vector from step S2 Second observation vector Calculate the current time residual vector : ； And further calculate the current time. Mahalanobis distance : ； ； ； In the formula, Represents the i-th residual scalar; S4: Determine whether the outlier criterion is met: ； in, , ; If the outlier criterion is not met, then the residual vector obtained at the current time step is used. and Mahal distance Recursively update the next time step , and cumulative updates , If the outlier criterion is met, updates will be paused. , Directly set the current time , As the next moment , But continue to accumulate updates , ; S5: Update flexible weights : ； In the formula, As a scale factor, The index control coefficient is then used; then flexible weights are applied. renew Observation matrix at time The attitude determination algorithm is then used to continue aligning the moving base. ； In the formula, express The observation matrix at time, Represents the second observation vector Left-multiplication matrix operator for quaternions; Represents the first observation vector The right-multiplication matrix operator of the quaternions formed.

2. The initial alignment method based on Mahalanobis distance for interference resistance according to claim 1, characterized in that: In step S4, if the outlier criterion is not met, the residual vector obtained at the current time is used. and Mahal distance Recursively update the next time step , ,include: Update data points: ； Represents the time from the initial moment to the current moment. The total number of non-outlier data points observed. This represents the time from the initial moment to the previous moment. The total number of non-outlier data points observed; Update the mean: ； Indicates based on the previous The mean vector calculated from each data point Indicates based on the previous The mean vector calculated from each data point; Update the covariance matrix: ； Indicates based on the previous The covariance matrix calculated from each data point Indicates based on the previous The covariance matrix is ​​calculated from each data point.

3. The initial alignment method based on Mahalanobis distance for interference resistance according to claim 2, characterized in that: In step S4, if the outlier criterion is met, then the update is paused. , Directly set the current time , As the next moment , ,include: Update data points: ； Update the mean: ； Update the covariance matrix: 。

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