An underwater long baseline positioning continuous wild point online detection and processing method based on Euclidean distance constraint
By combining Euclidean distance constraints and Kalman filters, the problem of detecting and processing continuous outliers in underwater long baseline positioning systems was solved, achieving high-precision and robust underwater target positioning, suitable for complex underwater environments.
Patent Information
- Application Number
- CN202610633653.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-05-09
- Publication Date
- 2026-06-26
AI Technical Summary
Existing underwater long baseline positioning systems struggle to effectively identify and suppress continuous outliers in low-redundancy or non-redundancy observation environments, leading to severe trajectory drift in highly dynamic scenarios and reducing the system's robustness.
A method based on Euclidean distance constraints combined with a Kalman filter is adopted. Continuous outliers are identified by Euclidean distance statistics and detection thresholds. Data processing is performed using a multi-model filter to achieve efficient detection and filtering correction of continuous outliers.
It accurately detects continuous outliers, significantly improving positioning accuracy and robustness. It can adapt to various complex underwater motion scenarios, effectively suppresses positioning trajectory drift, and has a root mean square error superior to traditional methods.
Smart Images
Figure CN122283588A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of underwater target positioning technology, and relates to the positioning technology of continuous field points for underwater long baseline positioning, specifically to an online detection and processing method for continuous field points for underwater long baseline positioning based on Euclidean distance constraints. Background Technology
[0002] The vast ocean contains more than half of the Earth's mineral resources and fosters a rich and diverse marine ecosystem, serving as a crucial strategic space supporting my country's sustainable resource development. As a core strategic pillar of the national maritime security system, underwater positioning systems are not only a key barrier to safeguarding territorial sovereignty and maritime rights, but also a cutting-edge intelligent defense system to ensure the sustainable development of marine resources and support strategic interests in the deep sea. Against this backdrop, underwater positioning technology for safeguarding maritime rights has become an important research direction for numerous research institutions both domestically and internationally.
[0003] In the field of underwater target localization, long baseline positioning systems (LBS) have become a core technology for underwater early warning and monitoring missions due to their high precision and long-range positioning capabilities. The positioning reliability of LBS systems is highly dependent on the number of effective observation bases, i.e., the geometric observation redundancy of the system. Ideally, a four-element LBS system can achieve a unique solution for the target's spatial location by constructing a redundant set of observation equations. When the number of effective observation bases in the system decreases to three, the positioning solution will produce dual solutions due to the nonlinear spherical equations. In this case, depth information or prior trajectory constraints must be introduced to determine a unique solution. Furthermore, when environmental interference intensifies, causing two bases to simultaneously exhibit observational anomalies, the number of effective observation bases drops to two, allowing only two independent distance equations to be constructed. According to the principle of spherical intersection, the trajectory of the intersection of two spheres is a spatial circle, which cannot uniquely determine the target's location in three-dimensional space.
[0004] Existing technologies often suffer from severe algorithmic limitations when facing observation environments with low or no redundancy. Conventional algorithms, when forced to perform position estimation under conditions where observation requirements are not met, will produce positioning results that deviate significantly from the true location. These abrupt positioning jumps caused by missing geometric constraints and insufficient observation information are defined as "outliers."
[0005] Traditional outlier detection methods often rely on static statistical distribution models or simple threshold judgments. Essentially, they are based on the logic of independent single-point observations, making it difficult to identify continuous outliers caused by persistent anomalies. In highly dynamic scenarios involving maintaining maritime security and real-time underwater target positioning, the inability to effectively identify and suppress such outliers will lead to severe trajectory drift in the positioning system within specific time periods, significantly reducing the system's robustness.
[0006] Therefore, how to combine underwater target Euclidean distance constraints to efficiently detect and eliminate continuous outliers caused by the loss of observation redundancy in long baseline positioning systems has become a key technical challenge to improve the robustness of underwater positioning systems. Summary of the Invention
[0007] Purpose of the invention: To address the shortcomings of existing underwater long baseline positioning system field detection and processing technologies in terms of limited applicability, this invention provides an online detection and processing method for continuous field points in underwater long baseline positioning based on Euclidean distance constraints, which is a complex engineering problem that existing technologies struggle to solve effectively. This method can detect continuous field points using Euclidean distance constraints and then efficiently process them using a Kalman filter.
[0008] Technical Solution: To achieve the above objectives, this invention provides an online detection and processing method for continuous outliers in underwater long baseline positioning based on Euclidean distance constraints, comprising the following steps:
[0009] S1: Define the historical data set based on the working principle of the long baseline positioning system. ,in Indicates time, This indicates the target's three-dimensional coordinate data contained in the vector at that moment;
[0010] S2: Based on the underwater long baseline positioning system If a stable initial positioning point forms a track, then the maximum number of outliers that the system can continuously detect and judge is limited to: The system forms a trajectory during the initial trajectory phase. A stable location point is used as the initial anchor point for outlier detection and judgment;
[0011] S3: Establish spatial Euclidean distance statistics: calculate the current observation vector Compared to the past historical valid observations Euclidean distance between ;
[0012] S4: Establish a criterion threshold based on Euclidean distance constraints: based on the maximum speed of the underwater target. Constrain the instantaneous movement distance of the target and establish a detection threshold. ;
[0013] S5: Based on Euclidean distance and detection threshold Perform outlier identification and analyze the tolerance for consecutive outliers;
[0014] S6: Define the indicator function Used to save the outlier determination results of step S5;
[0015] S7: Set the initial state With measurement data The data is transmitted to unscented Kalman filters under different motion models, and the optimal estimate for each model is calculated. With covariance matrix ;
[0016] S8: Predict the state values and covariance matrix of each model based on the established linear filtering model, and based on the indicator function. The result is the update stage estimate. and covariance Introduce out-of-point correction functions respectively , ;
[0017] S9: Measure and update the state values and covariance matrix of each model based on the linear filtering model and the out-of-point correction function;
[0018] S10: Using the model probability as the weighting coefficient, the output results of each filter are weighted and fused to obtain the overall fusion estimate and covariance matrix;
[0019] S11: Based on the overall fusion estimate and covariance matrix, obtain the actual display result after the final long baseline positioning system continuous field point filtering process.
[0020] Furthermore, the detection threshold in step S4 The expression is as follows:
[0021]
[0022] in, It is the location calculation cycle. It is the trajectory relaxation coefficient.
[0023] Furthermore, the condition for outlier determination in step S5 is as follows:
[0024]
[0025] When a location point meets the criteria for an outlier, the location point is determined to be an outlier.
[0026] Furthermore, in step S6, the indicator function The expression is as follows:
[0027] .
[0028] Further, step S7 includes:
[0029] A1: Based on The state estimates and model probabilities of each model at each time point are used to solve for the interaction state estimates of each filter input.
[0030]
[0031]
[0032] In the formula, This indicates that the target belongs to the model after input interaction. The probability of; The model in the probability transition matrix To the model The probability of transition; Pre-interaction model The probability value; This indicates that the target is assumed to be in the model after interaction. At that time, by model The probability obtained through interaction;
[0033] A2: Obtain the interaction state estimates of the filter inputs for each model. With the interaction covariance matrix ;
[0034]
[0035]
[0036] In the formula, In order to be in Moment-interactive multi-model algorithm model State estimates, In order to be in Time model State estimates, For the model Interactive covariance, In order to be in Time model Error covariance:
[0037] A3: Input the interaction estimates and interaction covariance matrix obtained from the input interaction stage into the multi-model filter; combine with the first... Location data at any time The optimal estimate for each model is calculated. With covariance matrix .
[0038] Furthermore, the linear filtering model in step S8 is expressed as follows:
[0039]
[0040]
[0041] In the formula, Let this be the system's state vector; For measurement vectors; It is the linear transition matrix between the measurement vector and the state vector; and These are process noise and measurement noise, respectively. Both are uncorrelated Gaussian noises with a mean of 0, and their covariance matrix is... and .
[0042] Furthermore, in step S8, the linear filtering model uses Kalman filtering to predict the state values and covariance matrix of each model:
[0043] .
[0044] Furthermore, the out-of-point correction function in step S8 , The expression is as follows:
[0045]
[0046] in, The dimension is A square matrix of all zeros Represents the identity matrix. It is the dimension of the state.
[0047] Furthermore, the measurement update in step S9 includes:
[0048] Indicator function output by the continuous outlier detection method The filter adaptively determines its output mode during the update phase.
[0049]
[0050] The likelihood probability of each model is updated based on the predicted state value and predicted covariance of each filter. With the updated Probability values of each model at time step ;
[0051]
[0052]
[0053]
[0054]
[0055] In the formula, The measurement residuals for each model are used to characterize the actual measurement information. With predictive measurement information Deviation between; This is the covariance matrix of the corresponding residuals. Let be the covariance matrix.
[0056] Furthermore, the weighted fusion in step S10 is expressed as follows:
[0057]
[0058] .
[0059] Furthermore, the actual result displayed in step S11 is as follows:
[0060] .
[0061] This invention comprises two aspects: continuous outlier detection and continuous outlier filtering. The continuous outlier detection technique is used to detect persistent outliers in target positioning data of an underwater long baseline positioning system. This technique constructs an initial target trajectory using initial stable positioning data as anchor points, and combines target Euclidean distance constraints with historical positioning data to complete anomaly detection, efficiently and accurately identifying the occurrence time and duration of continuous outliers. The continuous outlier filtering technique is used to filter, correct, and replace positioning data identified as continuous outliers in the underwater long baseline positioning system. This technique achieves synchronous positioning filtering with the positioning system through a Kalman filter. When a positioning point at a single moment or multiple consecutive moments is detected as an outlier, the positioning output automatically switches to the prediction result of the Kalman filter.
[0062] In practical engineering applications, this invention directly embeds the continuous field detection and judgment logic into the real-time Kalman filter framework, enabling the filter to synchronously output the field judgment result and the positioning filter correction result at each moment, ultimately realizing the full-process online detection and closed-loop processing of continuous field points in the underwater long baseline positioning system.
[0063] Beneficial effects: Compared with the prior art, the present invention has the following advantages:
[0064] 1. Capable of accurately detecting consecutive outliers. The method of this invention, based on Euclidean distance constraints combined with initial stable anchor points, overcomes the limitation of traditional methods that can only detect single outliers, and can accurately determine the occurrence time and duration of consecutive outliers.
[0065] 2. Significantly improved positioning accuracy and robustness. The method of this invention can effectively suppress positioning trajectory drift, and the root mean square error is better than that of traditional single field point processing methods; compared with existing continuous field point known methods, it has stronger adaptability and can adapt to various complex underwater motion scenarios such as straight lines, uniform acceleration, and maneuvering turns. Attached Figure Description
[0066] Figure 1 This is a schematic flowchart of the method of the present invention;
[0067] Figure 2 A comparison chart of the single-test results and localization results for Scene 1;
[0068] Figure 3 A comparison chart of the scene outlier handling method and the root mean square error of long baseline positioning.
[0069] Figure 4 This is a comparison chart of the single-test results and positioning results in scenario two;
[0070] Figure 5 This is a magnified view of the single-test results and positioning effects in Scene 2;
[0071] Figure 6 A comparison chart of the scene field point processing method and the root mean square error of long baseline positioning;
[0072] Figure 7 This is a comparison chart of the root mean square error under different positioning standard deviations. Detailed Implementation
[0073] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. After reading this invention, any modifications of the invention in various equivalent forms by those skilled in the art will fall within the scope defined by the appended claims.
[0074] Example 1:
[0075] like Figure 1 As shown in the figure, this embodiment provides an online detection and processing method for continuous field points in underwater long baseline positioning based on Euclidean distance constraints, including the following steps:
[0076] S1: Define the historical data set based on the working principle of the long baseline positioning system. ,in Indicates time, This indicates the target's three-dimensional coordinate data contained in the vector at that moment;
[0077] S2: Based on the underwater long baseline positioning system If a stable initial positioning point forms a track, then the maximum number of outliers that the system can continuously detect and judge is limited to: The system forms a trajectory during the initial trajectory phase. A stable location point is used as the initial anchor point for outlier detection and judgment;
[0078] S3: Establish spatial Euclidean distance statistics: calculate the current observation vector Compared to the past historical valid observations Euclidean distance between :
[0079]
[0080] S4: Establish a criterion threshold based on Euclidean distance constraints: based on the maximum speed of the underwater target. Constrain the instantaneous movement distance of the target and establish a detection threshold. ;
[0081] Detection threshold The expression is as follows:
[0082]
[0083] in, It is the location calculation cycle. It is the trajectory relaxation coefficient.
[0084] When the pace of history When the target size is large, the actual target trajectory usually involves turning maneuvers, and its spatial straight-line chord length will necessarily be less than the theoretical maximum range arc length. To prevent the threshold from being set too leniently with large step sizes, thus leading to missed outlier values, Should follow The increase should be appropriately reduced.
[0085] S5: Based on Euclidean distance and detection threshold Perform outlier identification and analyze the tolerance for consecutive outliers;
[0086] The conditions for determining outliers are:
[0087]
[0088] When a location point meets the criteria for an outlier, the location point is determined to be an outlier.
[0089] The tolerance of this outlier criterion to consecutive outliers is limited by the initial anchor point and the criterion dimension. If there exists a continuous For each outlier point, to ensure that subsequent normal points are not misjudged, it must satisfy the following conditions: .like When the first When each point is a normal point, due to its reference anchor point... If all historical points are outliers, then that point will satisfy all... The conditions of a criterion are incorrectly identified as outliers, causing the detection logic to continuously fail. Therefore, the criterion dimension... It should be at least 1 greater than the expected maximum number of consecutive wild points.
[0090] S6: Define the indicator function Used to save the outlier determination results of step S5;
[0091] Indicator function The expression is as follows:
[0092]
[0093] S7: Set the initial state With measurement data The data is transmitted to unscented Kalman filters under different motion models, and the optimal estimate for each model is calculated. With covariance matrix ;
[0094] Step S7 includes:
[0095] A1: Based on The state estimates and model probabilities of each model at each time point are used to solve for the interaction state estimates of each filter input.
[0096]
[0097]
[0098] In the formula, This indicates that the target belongs to the model after input interaction. The probability of; The model in the probability transition matrix To the model The probability of transition; Pre-interaction model The probability value; This indicates that the target is assumed to be in the model after interaction. At that time, by model The probability obtained through interaction;
[0099] A2: Obtain the interaction state estimates of the filter inputs for each model. With the interaction covariance matrix ;
[0100]
[0101]
[0102] In the formula, In order to be in Moment-interactive multi-model algorithm model State estimates, In order to be in Time model State estimates, For the model Interactive covariance, In order to be in Time model Error covariance:
[0103] A3: The estimated interaction state obtained from the input interaction process. With the interaction covariance matrix The array is input into the multi-model filter; combined with the first... Location data at any time The optimal estimate for each model is calculated. With covariance matrix .
[0104] S8: Predict the state values and covariance matrix of each model based on the established linear filtering model, and based on the indicator function. The result is the update stage estimate. and covariance Introduce out-of-point correction functions respectively , ;
[0105] The linear filtering model is expressed as follows:
[0106]
[0107]
[0108] In the formula, Let this be the system's state vector; For measurement vectors; It is the linear transition matrix between the measurement vector and the state vector; and These are process noise and measurement noise, respectively. Both are uncorrelated Gaussian noises with a mean of 0, and their covariance matrix is... and ;
[0109] The linear filtering model uses Kalman filtering to predict the state values and covariance matrix of each model:
[0110]
[0111] Wild point correction function , The expression is as follows:
[0112]
[0113] in, The dimension is A square matrix of all zeros Represents the identity matrix. It is the dimension of the state.
[0114] S9: Measure and update the state values and covariance matrix of each model based on the linear filtering model and the out-of-point correction function;
[0115] Indicator function output by the continuous outlier detection method The filter adaptively determines its output mode during the update phase.
[0116]
[0117] The likelihood probability of each model is updated based on the predicted state value and predicted covariance of each filter. With the updated Probability values of each model at time step ;
[0118]
[0119]
[0120]
[0121]
[0122] In the formula, The measurement residuals for each model are used to characterize the actual measurement information. With predictive measurement information Deviation between; This is the covariance matrix of the corresponding residuals. Let be the covariance matrix.
[0123] S10: Based on model probability As weighting coefficients, the outputs of each filter are weighted and fused to obtain the overall fused estimate. With covariance matrix ;
[0124] The weighted fusion is expressed as follows:
[0125]
[0126]
[0127] S11: Based on the overall fusion estimate and covariance matrix, obtain the actual display results after continuous field point filtering of the final long baseline positioning system:
[0128]
[0129] When the system determines that the location point is an outlier, it uses the prediction result of the Kalman filter instead; otherwise, it directly uses the location result of the long baseline.
[0130] The above steps S1~S6 correspond to the continuous outlier detection and determination method for the long baseline positioning system, and steps S7~S11 correspond to the continuous outlier processing method for the long baseline positioning system. In this embodiment, the continuous outlier detection and determination logic is directly embedded in the real-time Kalman filter framework, so that the filter can synchronously output the outlier determination result and the positioning filter correction result at each moment, and finally realize the full-process online detection and closed-loop processing of continuous outliers in the underwater long baseline positioning system.
[0131] In this embodiment, the initial stable long baseline positioning data is used as anchor points and combined with the target Euclidean distance constraint to perform continuous outlier detection and determination. A Kalman filter is introduced during the long baseline system positioning to perform real-time data processing on the positioning points. The results of the continuous outlier detection and determination are used to decide whether to replace the positioning points estimated by the filter, resulting in a superior underwater long baseline target positioning outlier processing method.
[0132] Example 2:
[0133] To verify the effectiveness and impact of this invention, a corresponding performance simulation experiment was conducted in this embodiment, as detailed below:
[0134] The specific simulation parameters are set as follows:
[0135] 1. Define different types of outlier generation methods and conduct experiments in two different scenarios. The simulation parameters are shown in Table 1.
[0136] Table 1 Simulation parameters for Scenario 1 / 2
[0137]
[0138] 2. The target's motion types are categorized into linear motion, uniform acceleration, and maneuvering turns, with specific scenarios as follows;
[0139] Scenario 1: Phase 1 (1-15s): The target remains stationary at the starting point. Phase 2 (18-30s): The target begins uniformly accelerated linear motion. Phase 3 (33-60s): The target moves at a constant speed in a straight line. Phase 4 (63-180s): The target makes a uniform turn to the left. The total duration is... The fifth stage, from 168 to 285 seconds, involves the target making a uniform turning motion to the right, during which a total of... The sixth stage, from 288 to 300 seconds, involves the target moving at a constant speed in a straight line.
[0140] Scenario 2: Phase 1 (1-15s): The target remains stationary at the starting point. Phase 2 (18-30s): The target begins uniformly accelerated linear motion. Phase 3 (33-60s): The target moves at a constant speed in a straight line. Phase 4 (63-165s): The target makes a uniform turn to the left. The total duration is... The fifth stage, from 183 to 390 seconds, involves the target making a uniform turning motion to the right, during which a total of... The sixth stage, from 393 to 450 seconds, involves the target moving at a constant speed in a straight line.
[0141] 3. Outliers are generated by adding Gaussian noise with a large standard deviation to the true values. The occurrence of consecutive outliers is random. The specific generation methods for the two scenarios are as follows:
[0142] In scenario one, to test the stability of the proposed method, two sets of a maximum of four consecutive outliers are generated, with only one normal localization point between these two sets of outliers.
[0143] In scenario two, to test the applicability of the proposed method, three sets of outliers were generated: the first set had three consecutive outliers, the second set had three consecutive outliers, and the third set had a single outlier.
[0144] Figure 2 The simulation performance comparison in a specific scenario is shown. The simulation results show that under the same positioning error and Euclidean distance constraint, the continuous field point detection and processing method used in this invention is closer to the target location and performs better than the traditional single field point detection and processing method. The logic of field point judgment is completely accurate. Figure 4 and Figure 5 The simulation performance comparison in scenario two is shown. The simulation results show that the continuous field detection and processing method used in this invention can effectively deal with various numbers of continuous field points at the same time, which is significantly better than the traditional single field detection and processing method.
[0145] To demonstrate the robustness of the method of the present invention, a comparison is made between the method of the present invention, the traditional single field point detection and processing method, and the root mean square error of unprocessed target localization data. Figure 3Comparing the root mean square error of position estimation under 100 Monte Carlo experiments in scenario one, it can be seen that the root mean square error of the position estimation of the present invention is the smallest, and the number of outlier identifications is completely correct. Figure 6 The comparison of the root mean square error of position estimation under the condition of 100 Monte Carlo experiments in scenario 2 shows that the detection and processing of outliers with redundant mixed numbers in this invention is equally effective. Figure 7 A comparison of the average root mean square error of position estimation under different positioning standard deviations in 100 Monte Carlo experiments shows that the present invention has a smaller error than the traditional single field point detection and processing method.
[0146] In summary, the continuous outlier online detection and processing method provided by this invention is applicable to various complex underwater scenarios, and can stably and accurately detect the number of outliers, exhibiting strong robustness. Therefore, it can be used in long baseline positioning systems in complex underwater environments.
Claims
1. An online detection and processing method for continuous wild points of underwater long baseline positioning based on Euclidean distance constraint, characterized in that, Includes the following steps: S1: Define the historical data set based on the working principle of the long baseline positioning system. ,in Indicates time, This indicates the target's three-dimensional coordinate data contained in the vector at that moment; S2: Based on the underwater long baseline positioning system If a stable initial positioning point forms a track, then the maximum number of outliers that the system can continuously detect and judge is limited to: The system forms a trajectory during the initial trajectory phase. A stable location point is used as the initial anchor point for outlier detection and judgment; S3: Establish spatial Euclidean distance statistics: calculate the current observation vector Compared to the past historical valid observations Euclidean distance between ; S4: Establish a criterion threshold based on Euclidean distance constraints: based on the maximum speed of the underwater target. Constrain the instantaneous movement distance of the target and establish a detection threshold. ; S5: Based on Euclidean distance and detection threshold Perform wilderness point identification and analyze the tolerance for consecutive wilderness points; S6: Define the indicator function Used to save the outlier determination results of step S5; S7: Set the initial state With measurement data The data is transmitted to unscented Kalman filters under different motion models, and the optimal estimate for each model is calculated. With covariance matrix ; S8: Predict the state values and covariance matrix of each model based on the established linear filtering model, and based on the indicator function. The result is the update stage estimate. and covariance Introduce out-of-point correction functions respectively , ; S9: Measure and update the state values and covariance matrix of each model based on the linear filtering model and the out-of-point correction function; S10: Using the model probability as the weighting coefficient, the output results of each filter are weighted and fused to obtain the overall fusion estimate and covariance matrix; S11: Based on the overall fusion estimate and covariance matrix, obtain the actual display result after the final long baseline positioning system continuous field point filtering process.
2. The method for online detection and processing of continuous outliers in underwater long baseline positioning based on Euclidean distance constraints as described in claim 1, characterized in that, The detection threshold in step S4 The expression is as follows: ； in, It is the location calculation cycle. It is the trajectory relaxation coefficient.
3. The method for online detection and processing of continuous outliers in underwater long baseline positioning based on Euclidean distance constraints as described in claim 2, characterized in that, The conditions for outlier detection in step S5 are as follows: ； When a location point meets the criteria for an outlier, the location point is determined to be an outlier.
4. The method for online detection and processing of continuous outliers in underwater long baseline positioning based on Euclidean distance constraints as described in claim 3, characterized in that, Indicative function in step S6 The expression is as follows: 。 5. The method for online detection and processing of continuous outliers in underwater long baseline positioning based on Euclidean distance constraints as described in claim 4, characterized in that, Step S7 includes: A1: Based on The state estimates and model probabilities of each model at each time point are used to solve for the interaction state estimates of each filter input. ； ； In the formula, This indicates that the target belongs to the model after input interaction. The probability of; The model in the probability transition matrix To the model The probability of transition; Pre-interaction model The probability value; This indicates that the target is assumed to be in the model after interaction. At that time, by model The probability obtained through interaction; A2: Obtain the interaction state estimates of the filter inputs for each model. With the interaction covariance matrix ; ； ； In the formula, In order to be in Moment-to-Moment Interactive Multi-Model Algorithm Model State estimates, In order to be in Time model State estimates, For the model Interactive covariance, In order to be in Time model Error covariance: A3: Input the interaction estimates and interaction covariance matrix obtained from the input interaction stage into the multi-model filter; combine with the first... Location data at any time The optimal estimate for each model is calculated. With covariance matrix .
6. The method for online detection and processing of continuous outliers in underwater long baseline positioning based on Euclidean distance constraints as described in claim 5, characterized in that, The linear filtering model in step S8 is expressed as follows: ； ； In the formula, Let this be the system's state vector; For measurement vectors; It is the linear transition matrix between the measurement vector and the state vector; and These are process noise and measurement noise, respectively. Both are uncorrelated Gaussian noises with a mean of 0, and their covariance matrix is... and .
7. The method for online detection and processing of continuous outliers in underwater long baseline positioning based on Euclidean distance constraints as described in claim 6, characterized in that, In step S8, the linear filtering model uses Kalman filtering to predict the state values and covariance matrix of each model: 。 8. The method for online detection and processing of continuous outliers in underwater long baseline positioning based on Euclidean distance constraints as described in claim 7, characterized in that, Out-point correction function in step S8 , The expression is as follows: ； in, The dimension is A square matrix of all zeros. Represents the identity matrix. It is the dimension of the state.
9. The method for online detection and processing of continuous outliers in underwater long baseline positioning based on Euclidean distance constraints as described in claim 8, characterized in that, The measurement update in step S9 includes: Indicator function output by the continuous outlier detection method The filter adaptively determines its output mode during the update phase. ； The likelihood probability of each model is updated based on the predicted state value and predicted covariance of each filter. With the updated Probability values of each model at time step ; ； ； ； ； In the formula, The measurement residuals for each model are used to characterize the actual measurement information. With predictive measurement information Deviation between; This is the covariance matrix of the corresponding residuals. Let be the covariance matrix.
10. The method for online detection and processing of continuous outliers in underwater long baseline positioning based on Euclidean distance constraints as described in claim 9, characterized in that, The weighted fusion in step S10 is expressed as follows: ； 。