Local horizontal north long-time inertial navigation positioning error extension method and device

Abstract

The application belongs to the technical field of navigation, and specifically discloses a long-time navigation inertial navigation positioning error extension method and device of local horizontal north. Firstly, the north-south, east-west and radial positioning errors are subjected to sliding average to obtain linear components; then the slope parameters are derived from the change trend of the linear components; the slope parameter influence is removed from the error data to obtain a residual part; then the residual part is regarded as an oscillation component in the positioning error to estimate the amplitude parameter and the phase parameter; the linear component of the radial positioning error is regressed and predicted by using the slope parameter; then the linear significance test is carried out based on the regression prediction value and the actual value to ensure that the data meet the linearity; finally, the slope parameter, the amplitude parameter and the phase parameter are substituted into the positioning error extension model to extend the positioning error. The positioning error extension replaces the full-cycle actual measurement of the positioning error, thereby shortening the positioning error test length of the long-time navigation inertial navigation system and improving the test efficiency.

Description

Technical Field

[0001] This application belongs to the field of navigation technology, specifically relating to the field of inertial navigation error extension technology, and more specifically, relating to a long-endurance inertial navigation positioning error extension method and device for local horizontal north. Background Technology

[0002] Inertial navigation systems can experience positioning errors during long-term operation due to sensor errors such as gyroscope drift and accelerometer bias.

[0003] With the continuous advancement of high-precision inertial devices and error compensation technologies, the accuracy-maintaining operating time of inertial navigation systems has been significantly extended. To obtain high-confidence positioning error accuracy assessment results, a large number of positioning error samples are required. However, traditional positioning error acquisition methods require full-cycle measurements for each sample, which has inherent limitations such as excessive time consumption and high cost, becoming a key bottleneck restricting the efficiency of accuracy assessment. Therefore, there is an urgent need for a method to improve the efficiency of acquiring positioning error data for long-endurance inertial navigation systems. Summary of the Invention

[0004] In view of the shortcomings of the prior art, the purpose of this application is to provide a long-endurance inertial navigation positioning error extension method and device for local horizontal north, which aims to solve the technical problem of low efficiency in acquiring existing long-endurance positioning error data by replacing full-cycle actual measurement with positioning error extension.

[0005] The first aspect of this application relates to a long-endurance inertial navigation positioning error extension method for local horizontal north, comprising:

[0006] The north-south and east-west positioning error data are averaged to eliminate oscillation components and obtain linear components; the slope parameters of the north-south and east-west positioning error extension models are derived from the time-domain variation trend of the linear components of the north-south and east-west positioning error data.

[0007] The linear components of the radial positioning error data are regressed and predicted using the slope parameter of the east-west positioning error extension model; the linear significance of the regressed predicted values ​​and actual values ​​of the linear components of the radial positioning error data is then tested.

[0008] If the linear significance test is passed, the slope parameter, amplitude parameter, and phase parameter are substituted into the positioning error extension model to extend the positioning error data; otherwise, the process ends. The method for obtaining the amplitude parameter and phase parameter is as follows: the part affected by the slope parameter is removed from the north-south and east-west positioning error data to obtain the residual part, and the residual part is regarded as an oscillation component to estimate the amplitude parameter and phase parameter.

[0009] Preferably, the north-south and east-west positioning error data are processed by moving average to eliminate oscillation components and obtain linear components. Specifically, a sliding window is used to slide along the sequence number on the positioning error data sequence. During the sliding process, the data located in the middle of the sliding window is replaced with the mean of the data within the sliding window. After the sliding is completed, the final data sequence obtained is the linear component remaining after eliminating oscillation components.

[0010] Preferably, a linear significance test is performed on the regression predicted value and the actual value of the linear component of the radial positioning error data, specifically as follows:

[0011] Obtain the regression sum of squares between the predicted and actual values;

[0012] Obtain the sum of squared residuals between the actual values ​​and the regression predictions;

[0013] The ratio of the mean square of the regression sum of squares to the mean square of the residual sum of squares is obtained. Test statistic;

[0014] Selecting the significance level by The distribution function obtains a critical value;

[0015] Comparison The magnitude of the test statistic and the critical value, if If the test statistic is greater than or equal to the critical value, then the actual value of the linear component of the radial positioning error data is linearly significant.

[0016] Preferably, the regression prediction value is obtained by multiplying the slope parameter of the east-west positioning error extension model with the current time; the actual value is obtained by performing a moving average on the radial positioning error data to eliminate oscillation components.

[0017] Preferably, the residual part is obtained by removing the part affected by the slope parameter from the north-south and east-west positioning error data. Specifically, the residual part is the positioning error data minus the product of the slope parameter and the current time.

[0018] Preferably, the residual portion is treated as an oscillating component for estimation of amplitude and phase parameters, specifically as follows:

[0019] Design a cosine function as the oscillation component of the positioning error extension model;

[0020] Expand the cosine function into a linear combination of basis functions;

[0021] Construct a design matrix containing basis functions, and obtain the predicted values ​​from the design matrix and linear parameters;

[0022] The linear parameters are solved by fitting the residuals and predicted values ​​using the least squares method.

[0023] The linear parameters are inversely calculated into the amplitude and phase parameters of the cosine function using trigonometric relationships.

[0024] Preferably, the amplitude parameter is:

[0025]

[0026] The phase parameter is:

[0027]

[0028] in, For amplitude parameters, For phase parameters, When it is a moving average, the first A sliding window, For the width of the sliding window, Pi Indicates the first time, Modulo operation function; and The parameter is linear.

[0029] Preferably, the slope parameter, amplitude parameter, and phase parameter are substituted into the positioning error extension model to extend the positioning error data, specifically as follows:

[0030] The amplitude and phase parameters are substituted into the cosine function to form the oscillation component, and the slope parameter is substituted into the linear function to form the linear component.

[0031] The positioning error extension model is composed of the oscillation component and the linear component;

[0032] The positioning error data is predicted by using a positioning error extension model.

[0033] The second aspect of this application relates to a long-endurance inertial navigation positioning error extension device for local horizontal north, said device being used to perform the method described in any one of the first aspects, comprising:

[0034] The slope acquisition module is used to perform a moving average on the north-south and east-west positioning error data to eliminate oscillation components and obtain linear components; the slope parameters of the north-south and east-west positioning error extension model are derived from the time-domain variation trend of the linear components of the north-south and east-west positioning error data.

[0035] The significance test module is used to perform regression prediction on the linear components of the radial positioning error data using the slope parameter of the east-west positioning error extension model; and to perform linear significance test on the regression prediction values ​​and actual values ​​of the linear components of the radial positioning error data.

[0036] The extension module is used to determine whether the linear significance test is passed. If so, the slope parameter, amplitude parameter, and phase parameter are substituted into the positioning error extension model to extend the positioning error data; otherwise, the process ends.

[0037] The amplitude and phase acquisition module is used to remove the slope parameter from the north-south and east-west positioning error data to obtain the residual part, and to estimate the amplitude and phase parameters by treating the residual part as an oscillation component.

[0038] Thirdly, this application provides an electronic device, comprising: at least one memory for storing a program; and at least one processor for executing the program stored in the memory, wherein when the program stored in the memory is executed, the processor is configured to execute the method described in the first aspect or any possible implementation thereof.

[0039] Overall, the technical solutions conceived in this application have the following beneficial effects compared with the prior art:

[0040] This application proposes a method for extending positioning error data of a long-endurance inertial navigation system (INS) with local horizontal north-pointing capability. Utilizing the physical characteristics of north-south, east-west, and radial positioning error data, a time-varying parameter error acquisition method is constructed to estimate the slope, amplitude, and phase parameters in the INS positioning error model. Simultaneously, a linear significance detection method is employed to verify the feasibility of the positioning error model extension, ensuring the accuracy of the extended data acquisition. Using this positioning error extension method significantly improves the efficiency of acquiring long-endurance positioning error data. Attached Figure Description

[0041] Figure 1 This is a flowchart of the long-endurance inertial navigation positioning error extension method for local horizontal north provided in the embodiments of this application.

[0042] Figure 2 This is a schematic diagram comparing the actual data of the long-duration inertial navigation positioning error in the static test provided in the embodiments of this application with the model restoration data.

[0043] Figure 3 This is a schematic diagram comparing the prediction results of long-duration inertial navigation error extension with the actual results in the static test provided in the embodiments of this application, and a schematic diagram showing the changing trend of the deviation ratio of the predicted maximum value.

[0044] Figure 4 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. Detailed Implementation

[0045] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0046] In this application, the terms "first" and "second," etc., are used to distinguish different objects, not to describe a specific order of objects. For example, "first positioning error data" and "second positioning error data," etc., are used to distinguish different positioning error data, not to describe a specific order of positioning error data.

[0047] In this application, the term "electrical connection" can refer to a direct circuit connection or a signal transmission via a communication protocol.

[0048] In the embodiments of this application, the terms "exemplary" or "for example" are used to indicate that something is an example, illustration, or description. Any embodiment or design that is described as "exemplary" or "for example" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or design. Specifically, the use of the terms "exemplary" or "for example" is intended to present the relevant concepts in a specific manner.

[0049] In the description of the embodiments of this application, unless otherwise stated, "multiple" means two or more, for example, multiple parameters means two or more parameters, multiple predicted values ​​means two or more predicted values, etc.

[0050] The embodiments of this application are described below with reference to the accompanying drawings.

[0051] like Figure 1 As shown, this application provides a long-endurance inertial navigation positioning error extension method for local horizontal north, specifically including the following steps:

[0052] (1) Short-time positioning error data of the inertial navigation system were obtained through actual measurement, including:

[0053] The north-south positioning error data is as follows:

[0054]

[0055] The east-west positioning error data is as follows:

[0056]

[0057] The radial positioning error data are as follows:

[0058]

[0059] The unit is meters or nautical miles.

[0060] (2) Define the positioning error model of the inertial navigation system. The model is defined as follows:

[0061] North-South Positioning Error Model:

[0062]

[0063] East-west positioning error model:

[0064]

[0065] Radial positioning error model:

[0066]

[0067] The north-south and east-west positioning error models are designed as a combination of oscillating and linear components, i.e., a combination of cosine and linear functions. These are the amplitude parameters of the north-south positioning error model. These are the phase parameters of the north-south positioning error model. The slope parameter of the north-south positioning error model; The amplitude parameters of the east-west positioning error model. These are the phase parameters of the east-west positioning error model. The slope parameter of the east-west positioning error model; This is the Earth's rotational angular velocity. This is the extended value of the north-south positioning error. This is the extended value of the east-west positioning error. This is the extended value of the radial positioning error.

[0068] (3) The oscillation components are eliminated by moving average of the north-south, east-west and radial positioning errors to obtain the linear components.

[0069] In some embodiments, a sliding window is used to slide along the sequence number on the data sequence of positioning error. During the sliding process, the data in the middle of the sliding window is replaced with the mean of all data in the sliding window. After the sliding is completed, the final data sequence is the linear component remaining after eliminating the oscillation component.

[0070] In some embodiments, the width of the sliding window is set to the amount of data acquired in 24 hours, and the step size S is set to the amount of data acquired in 1 hour.

[0071] After moving average processing, the linear components of the north-south positioning error are obtained as follows:

[0072]

[0073] The linear component of the east-west positioning error is:

[0074]

[0075] The linear component of the radial positioning error is:

[0076]

[0077] (4) The slope parameters of the positioning error extension model are derived from the time-domain variation trend of the linear components of the north-south and east-west positioning errors.

[0078] In some embodiments, the slope parameter of the north-south positioning error extension model for:

[0079]

[0080] In some embodiments, the slope parameter of the east-west positioning error extension model for:

[0081]

[0082] in, When it is a moving average, the first A sliding window, The width of the sliding window. For the first The sequence number of the first data in the sliding window. express The linear components of the north-south positioning error data at any given time. express The linear component of the east-west positioning error data at any given time.

[0083] (5) Remove the portion affected by the slope parameter from the north-south and east-west positioning error data to obtain the residual portion; treat the residual portion as an oscillation component to estimate the amplitude and phase parameters in the positioning error extension model;

[0084] (51) The residual part is the positioning error data minus the product of the slope parameter and the current time:

[0085] The residual portion of the north-south positioning error:

[0086]

[0087] The residual portion of the east-west positioning error:

[0088] in, This refers to the current moment.

[0089] (52) The cosine function is used as the oscillation component of the positioning error extension model. The residual part is regarded as the oscillation component. Here, the residual part of the north-south positioning error is used to illustrate:

[0090]

[0091] In the cosine function, Represents the Earth's angular velocity; the amplitude is estimated using the above formula. and phase ;

[0092] Expand the cosine function into a linear combination of basis functions, and construct a design matrix containing the basis functions. :

[0093]

[0094] The predicted value is obtained by multiplying the design matrix and the linear parameters. The least squares method is used to fit the residual part and the predicted value, and the linear parameters are solved. and :

[0095]

[0096] The linear parameters are then inversely calculated into the amplitude and phase parameters of the cosine function using trigonometric relationships:

[0097] The amplitude parameter is:

[0098]

[0099] The phase parameter is:

[0100]

[0101] in, For amplitude parameters, For phase parameters, When it is a moving average, the first A sliding window, For the width of the sliding window, Pi Indicates the first time, Modulo operation function; and The parameter is linear.

[0102] (6) Using the slope parameter of the model to extend the east-west positioning error Regression prediction of the linear component of the radial positioning error:

[0103] The regression prediction value of the linear component of the radial positioning error is:

[0104]

[0105] The actual value of the linear component of the radial positioning error is:

[0106]

[0107] Obtain the sum of squares of the regression predicted and actual values. :

[0108]

[0109]

[0110] in, This represents the total amount of data related to radial positioning error.

[0111] Obtain the sum of squared residuals between the actual values ​​and the regression predictions. :

[0112]

[0113] Obtained from the ratio of the mean square of the regression sum of squares to the mean square of the residual sum of squares Test statistic:

[0114]

[0115] Selecting the significance level by The distribution function obtains a critical value, which is then compared with the stated value. The magnitude of the test statistic and the critical value, if If the test statistic is greater than or equal to the critical value, then the actual value of the linear component of the radial positioning error is linearly significant.

[0116] The significance level was set at 0.01, and the critical value was:

[0117]

[0118] If satisfied If the actual value of the linear component of the radial positioning error is determined to be linearly significant, proceed to step (7). Indicates a degree of freedom of 1 and of Distribution function Quantiles.

[0119] (7) Substitute the slope parameter, amplitude parameter and phase parameter into the positioning error extension model to extend the positioning error.

[0120] (71) Calculate the parameters of the north-south positioning error extension model by averaging:

[0121]

[0122]

[0123]

[0124] (72) Calculate the parameters of the east-west positioning error extension model by averaging:

[0125]

[0126]

[0127]

[0128] (73) Substitute parameters into the model:

[0129] North-South Positioning Error Extension Model:

[0130]

[0131] in, express time, express Predicted north-south positioning error at any given time. It represents the Earth's angular velocity.

[0132] East-west positioning error extension model:

[0133]

[0134] in, express Predicted east-west positioning error at any given time.

[0135] Radial positioning error extension model:

[0136]

[0137] in, express Predicted radial positioning error at any given time.

[0138] (74) The time when the positioning error needs to be predicted Input into the above model, model output The positioning error at any given time satisfies .

[0139] The effectiveness of the positioning error extension method proposed in this application will be verified by the following experiment:

[0140] Static experimental verification:

[0141] Figure 2 The actual positioning error data from the static test is compared with the model-reconstructed data, showing that the linear component is the main component of the positioning error. The model-reconstructed data and the actual data show a high degree of consistency, verifying the effectiveness of the positioning error model and parameter calculation method proposed in this application. This result confirms that the positioning error model can accurately reflect the dynamic error of the inertial navigation system in terms of the amplitude and phase characteristics of the cosine component, as well as the linear component.

[0142] The validity of the extended positioning error data from the first four days was determined. The test statistic is 2834, which is much greater than This indicates that the positioning error data for the first four days exhibits significant linearity. The mean eigenvalues ​​from day 2 to day 4 were used as key parameters of the model, and their extension was applied to the entire experimental period (12 days). Figure 3 The comparison between the error extension prediction and the actual results is presented. Analysis shows that the actual positioning error is mainly dominated by the linear component, and the growth rate of this component accelerates over time, becoming the main source of the extension error. For the more relevant maximum positioning error indicator, the figure shows the deviation ratio curve between the predicted maximum and the actual maximum, which shows a slow increasing trend over time. Based on the error results of the first 4 days, extension prediction (extended to 3 times) was performed. Throughout the entire process up to day 12, the deviation ratio of the predicted maximum did not exceed 18%. The specific change in this deviation ratio depends on the time-varying trend of the slope of the actual linear component.

[0143] The following describes a long-endurance inertial navigation system (INS) positioning error extension device for local horizontal north-pointing provided in this application. The device described below corresponds to the method described above. The long-endurance INS positioning error extension device for local horizontal north-pointing includes:

[0144] The slope acquisition module is used to perform a moving average on the north-south and east-west positioning error data to eliminate oscillation components and obtain linear components; the slope parameters of the north-south and east-west positioning error extension model are derived from the time-domain variation trend of the linear components of the north-south and east-west positioning error data.

[0145] The significance test module is used to perform regression prediction on the linear components of the radial positioning error data using the slope parameter of the east-west positioning error extension model; and to perform linear significance test on the regression prediction values ​​and actual values ​​of the linear components of the radial positioning error data.

[0146] The extension module is used to determine whether the linear significance test is passed. If so, the slope parameter, amplitude parameter, and phase parameter are substituted into the positioning error extension model to extend the positioning error data; otherwise, the process ends.

[0147] The amplitude and phase acquisition module is used to remove the slope parameter from the north-south and east-west positioning error data to obtain the residual part, and to estimate the amplitude and phase parameters by treating the residual part as an oscillation component.

[0148] It should be understood that the above-described device is used to execute the methods in the above embodiments. The implementation principle and technical effect of the corresponding program modules in the device are similar to those described in the above methods. The working process of the device can be referred to the corresponding process in the above methods, and will not be repeated here.

[0149] Based on the methods in the above embodiments, this application provides an electronic device, such as... Figure 4 As shown, the electronic device may include a processor 10, a communications interface 20, a memory 30, and a communication bus 40, wherein the processor 10, the communications interface 20, and the memory 30 communicate with each other via the communication bus 40. The processor 10 can call logical instructions in the memory 30 to execute the methods described in the above embodiments.

[0150] Furthermore, the logical instructions in the aforementioned memory 30 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application.

[0151] Based on the methods in the above embodiments, this application provides a computer-readable storage medium storing a computer program that, when run on a processor, causes the processor to execute the methods in the above embodiments.

[0152] Based on the methods in the above embodiments, this application provides a computer program product that, when run on a processor, causes the processor to execute the methods in the above embodiments.

[0153] It is understood that the processor in the embodiments of this application can be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, transistor logic devices, hardware components, or any combination thereof. A general-purpose processor can be a microprocessor or any conventional processor.

[0154] The method steps in this application embodiment can be implemented in hardware or by a processor executing software instructions. The software instructions can consist of corresponding software modules, which can be stored in random access memory (RAM), flash memory, read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), registers, hard disks, portable hard disks, CD-ROMs, or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor, enabling the processor to read information from and write information to the storage medium. Of course, the storage medium can also be a component of the processor. The processor and the storage medium can reside in an ASIC.

[0155] In the above embodiments, implementation can be achieved entirely or partially through software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented entirely or partially as a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted through the computer-readable storage medium. The computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid-state disk (SSD)).

[0156] It is understood that the various numerical designations used in the embodiments of this application are merely for the convenience of description and are not intended to limit the scope of the embodiments of this application.

[0157] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A long-endurance inertial navigation positioning error extension method for local horizontal north, characterized in that, include: The north-south and east-west positioning error data are averaged to eliminate oscillating components and obtain linear components; The slope parameters of the north-south and east-west positioning error extension models are derived from the temporal variation trends of the linear components of the north-south and east-west positioning error data. The slope parameter of the east-west positioning error extension model is used to perform regression prediction on the linear components of the radial positioning error data; Linear significance test was performed on the regression predicted values ​​and actual values ​​of the linear components of the radial positioning error data; If the linear significance test is passed, the slope parameter, amplitude parameter, and phase parameter are substituted into the positioning error extension model to extend the positioning error data; otherwise, the process ends. The method for obtaining the amplitude and phase parameters is as follows: remove the portion affected by the slope parameter from the north-south and east-west positioning error data to obtain the residual portion, and use the residual portion as an oscillation component to estimate the amplitude and phase parameters.

2. The long-endurance inertial navigation positioning error extension method according to claim 1, characterized in that, To eliminate oscillation components and obtain linear components, a moving average is performed on the north-south and east-west positioning error data. Specifically, a sliding window is used to slide along the sequence number on the positioning error data. During the sliding process, the data located in the middle of the sliding window is replaced with the mean of the data within the sliding window. After the sliding is completed, the final data sequence obtained is the linear component remaining after eliminating oscillation components.

3. The long-endurance inertial navigation positioning error extension method according to claim 1, characterized in that, A linear significance test is performed on the regression predicted values ​​and actual values ​​of the linear components of the radial positioning error data, specifically as follows: Obtain the regression sum of squares between the predicted and actual values; Obtain the sum of squared residuals between the actual values ​​and the regression predictions; The ratio of the mean square of the regression sum of squares to the mean square of the residual sum of squares is obtained. Test statistic; Selecting the significance level by The distribution function obtains a critical value; Comparison The magnitude of the test statistic and the critical value, if If the test statistic is greater than or equal to the critical value, then the actual value of the linear component of the radial positioning error data is linearly significant.

4. The long-endurance inertial navigation positioning error extension method according to claim 1 or 3, characterized in that, The regression prediction value is obtained by multiplying the slope parameter of the east-west positioning error extension model with the current time; the actual value is obtained by performing a moving average on the radial positioning error data to eliminate oscillation components.

5. The long-endurance inertial navigation positioning error extension method according to claim 1, characterized in that, The residual is obtained by removing the portion affected by the slope parameter from the north-south and east-west positioning error data. Specifically, the residual is the positioning error data minus the product of the slope parameter and the current time.

6. The long-endurance inertial navigation positioning error extension method according to claim 1, characterized in that, The residual portion is treated as an oscillating component for estimation of amplitude and phase parameters, specifically as follows: Design a cosine function as the oscillation component of the positioning error extension model; Expand the cosine function into a linear combination of basis functions; Construct a design matrix containing basis functions, and obtain the predicted values ​​from the design matrix and linear parameters; The linear parameters are solved by fitting the residuals and predicted values ​​using the least squares method. The linear parameters are inversely calculated into the amplitude and phase parameters of the cosine function using trigonometric relationships.

7. The long-endurance inertial navigation positioning error extension method according to claim 1 or 6, characterized in that, The amplitude parameter is: The phase parameter is: in, For amplitude parameters, For phase parameters, When it is a moving average, the first A sliding window, For the width of the sliding window, Pi Indicates the first time, Modulo operation function; and The parameter is linear.

8. The long-endurance inertial navigation positioning error extension method according to claim 1, characterized in that, The slope parameter, amplitude parameter, and phase parameter are substituted into the positioning error extension model to extend the positioning error data, specifically as follows: The amplitude and phase parameters are substituted into the cosine function to form the oscillation component, and the slope parameter is substituted into the linear function to form the linear component. The positioning error extension model is composed of the oscillating components and the linear components; The positioning error data is predicted by using a positioning error extension model.

9. A long-endurance inertial navigation positioning error extension device for local horizontal north, characterized in that, The apparatus is used to perform the method according to any one of claims 1-8, comprising: The slope acquisition module is used to perform a moving average on the north-south and east-west positioning error data to eliminate oscillation components and obtain linear components; the slope parameters of the north-south and east-west positioning error extension model are derived from the time-domain variation trend of the linear components of the north-south and east-west positioning error data. The significance test module is used to perform regression prediction on the linear components of the radial positioning error data using the slope parameter of the east-west positioning error extension model; and to perform linear significance test on the regression prediction values ​​and actual values ​​of the linear components of the radial positioning error data. The extension module is used to determine whether the linear significance test is passed. If so, the slope parameter, amplitude parameter, and phase parameter are substituted into the positioning error extension model to extend the positioning error data; otherwise, the process ends. The amplitude and phase acquisition module is used to remove the slope parameter from the north-south and east-west positioning error data to obtain the residual part, and to estimate the amplitude and phase parameters by treating the residual part as an oscillation component.

10. An electronic device, characterized in that, Includes memory and one or more processors; The memory is coupled to the one or more processors, and the memory is used to store computer program code, the computer program code including computer instructions; The one or more processors invoke the computer instructions to cause the electronic device to perform the method as described in any one of claims 1-8.

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