Method for constructing parameter error model of inertial navigation system based on gravity disturbance
By constructing a gravity disturbance parameter error model for inertial navigation systems, the problem of low accuracy in error calculation caused by gravity disturbances is solved, the error compensation accuracy of navigation systems is improved, and navigation accuracy is enhanced.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- NAT UNIV OF DEFENSE TECH
- Filing Date
- 2024-01-04
- Publication Date
- 2026-05-29
AI Technical Summary
In existing inertial navigation systems, the accuracy of error calculation caused by gravity disturbance is low, and traditional variance analysis method fails to effectively compensate for the error in the initial alignment stage, resulting in low navigation accuracy.
A parameter error model for an inertial navigation system based on gravity disturbance is constructed. The random constant zero bias of the accelerometer and gyroscope is estimated by Kalman filtering. Combined with the gravity disturbance measured by the gravimeter and the disturbance measurement error, velocity, attitude and position error models are constructed, taking into account the influence of gravity disturbance in the navigation and initial alignment stages.
The accuracy of error compensation has been improved. By focusing on the errors caused by gravity disturbances during the navigation and initial alignment stages, an evaluation standard has been established, which enhances the error compensation effect of the navigation system.
Smart Images
Figure CN117848326B_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of navigation technology, and in particular to a method for constructing a parameter error model for an inertial navigation system based on gravity disturbance. Background Technology
[0002] High-precision inertial navigation technology is one of the core technologies for achieving autonomous navigation of ships, vessels, and submersibles during long-endurance ocean navigation. However, due to the influence of gravity disturbances, simply improving the accuracy of inertial devices at the hardware level is insufficient to further enhance navigation accuracy. When the accuracy of the inertial devices carried by the carrier is high, gravity disturbances become an important source of error for the marine inertial navigation system. As the marine carrier accumulates over a long mission cycle, navigation parameter errors that cannot be ignored are generated. Compensation for these errors can improve navigation accuracy. The main error of the inertial navigation system is the navigation parameter error.
[0003] However, the current traditional analysis of variance method only focuses on the error caused by gravity disturbance during the navigation phase, without considering the error generated during the initial alignment phase. This results in low accuracy in error calculation, which in turn leads to low accuracy in error compensation and low navigation precision during the navigation process. Summary of the Invention
[0004] Therefore, it is necessary to provide a method for constructing a parameter error model for an inertial navigation system based on gravity disturbance, which can improve the accuracy of error compensation during navigation, in order to address the above-mentioned technical problems.
[0005] A method for constructing a parameter error model for an inertial navigation system based on gravity perturbation, the method comprising:
[0006] Based on the Kalman filter, the random constant zero bias of the accelerometer and the random constant drift of the gyroscope are estimated. The error models of the accelerometer and the observation error models of the gyroscope are constructed by using the random constant zero bias of the accelerometer and the random constant drift of the gyroscope with zero-mean random white noise, respectively.
[0007] The measured gravity is obtained from the gravimeter and decomposed into gravity disturbance and gravity disturbance measurement error. The velocity error is constructed using the error model of the accelerometer, gravity disturbance and gravity disturbance measurement error.
[0008] Expand the velocity error to obtain the eastward acceleration error and the northward acceleration error; obtain the eastward velocity error and the northward velocity error from the eastward acceleration error and the northward acceleration error; treat the carrier altitude of the inertial navigation system as zero, ignore the altitude error, and calculate the position error using the eastward velocity error and the northward velocity error.
[0009] The attitude error is obtained by using the gyroscope observation error model and the misalignment angle; the navigation system parameter error model is constructed based on the velocity error, position error and attitude error.
[0010] In one embodiment, the zero-mean random white noise includes zero-mean random white noise of angle and zero-mean random white noise of velocity; the accelerometer error model and the gyroscope observation error model are constructed using the accelerometer random constant zero bias and the gyroscope random constant drift, respectively, and the zero-mean random white noise, including:
[0011] An error model for the accelerometer is constructed using the random constant drift of the accelerometer and the zero-mean random white noise of the velocity.
[0012]
[0013] in, Zero-mean random white noise representing velocity. The accelerometer's random constant bias is zero.
[0014] A gyroscope observation error model is constructed using the gyroscope's random constant zero bias and the angle's zero-mean random white noise.
[0015]
[0016] in, Zero-mean random white noise representing the angle, ε b This represents the random constant drift of the gyroscope.
[0017] In one embodiment, a velocity error is constructed using an accelerometer error model, gravity disturbance, and gravity disturbance measurement error, including:
[0018] The velocity error is constructed using the accelerometer error model, gravity disturbance, and gravity disturbance measurement error.
[0019]
[0020] Where, φ n Indicates the misalignment angle, f n v is the projection of the specific force measured by the accelerometer onto the n-coordinate system. n For velocity, the subscript 2 indicates that the physical quantity is considered only in relation to the horizontal plane. To account for the calculation errors of Coriolis acceleration and centrifugal acceleration, This indicates the error in the Earth's rotation angular rate. ω represents the angular rate error of the navigation system's rotation caused by the curvature of the Earth's surface, resulting from the movement of the inertial navigation system carrier on the surface. ie ω represents the angular rate of Earth's rotation. en This represents the angular rate of rotation of the navigation system caused by the curvature of the Earth's surface, resulting from the movement of the inertial navigation system carrier on the surface. For the velocity error on the horizontal plane, The velocity on the horizontal surface, This is the projection of the force measurement error on the horizontal plane onto the n-system. This represents the horizontal component of the gravitational disturbance. This represents the horizontal component of the measurement error due to gravity disturbance.
[0021] In one embodiment, the velocity error is expanded to obtain the eastward velocity error and the northward velocity error, including:
[0022] Expanding the velocity error, we obtain the eastward acceleration error as follows:
[0023]
[0024] Among them, f U Indicates the force relative to the celestial direction, φ N Indicates a northward orientation, f N Indicates the northward specific force, φ U Indicates an upward-facing posture, v N Indicates the northward velocity, δv E Indicates the eastward velocity error, δv N δL represents the northward velocity error, and δL represents the latitude error. This indicates that the random constant of the accelerometer pointing east has zero bias. This represents the horizontal component of the eastward gravity disturbance measurement error, where L is the geographic latitude, h is the geographic altitude, and R... E Let be the radius of the curved surface of the zonal loop.
[0025] In one embodiment, the method further includes:
[0026] Expanding the velocity error, we obtain the northward acceleration error as follows:
[0027]
[0028] Where, φ E Indicates an eastward orientation, f E Indicates the force to the east. This represents the horizontal component of the measurement error for northward gravity disturbance. This indicates that the random constant of the accelerometer pointing north is zero bias.
[0029] In one embodiment, the position error includes geographic latitude error, geographic longitude error, and geographic altitude error; the carrier altitude of the inertial navigation system is equivalent to zero, and altitude error is ignored. The position error is calculated using eastward velocity error and northward velocity error, including:
[0030] By treating the altitude of the inertial navigation system as zero and neglecting altitude error, the geographical latitude error, geographical longitude error, and geographical altitude error are calculated using the eastward and northward velocity errors, respectively.
[0031]
[0032]
[0033]
[0034] Among them, R E R is the radius of the surface of the zonal loop. N Let λ be the radius of the meridian circle, λ be the geographic longitude, L be the geographic latitude, h be the geographic altitude, and δv be the geographic altitude. N Indicates the northbound velocity error, δv E Indicates the eastward velocity error, δv U This indicates the upward velocity error.
[0035] In one embodiment, the attitude error is calculated using a gyroscope observation error model and the misalignment angle, including:
[0036] The attitude error was calculated using the gyroscope observation error model and the misalignment angle.
[0037]
[0038]
[0039] Among them, the misalignment angle φ n , This represents the projection of the gyroscope output error onto the n-frame. This represents the gyroscope observation error model. Zero-mean random white noise representing the angle, ε b For random constant drift of the gyroscope, Let n be the rotation of the navigation frame n relative to the inertial frame i. This represents the rotation calculation error of the navigation frame n relative to the inertial frame i. This represents the attitude transition matrix from the b-system to the n-system.
[0040] The above-mentioned method for constructing the parameter error model of an inertial navigation system based on gravity disturbance, starting from the basic principles of inertial navigation solution, establishes a navigation parameter error equation considering gravity disturbance, clarifies the influence of gravity disturbance and inertial device errors on inertial navigation accuracy and their corresponding magnitude relationships, as well as the coupling relationship between gravity disturbance and inertial device errors. By calculating the relationship between gravity disturbance and navigation parameter errors, the error propagation process is analyzed from the perspective of error propagation relationship and inertial navigation solution premise, clarifying the mechanism and magnitude relationship of the influence of gravity disturbance on inertial navigation. In addition to focusing on the error caused by gravity disturbance in the navigation stage, the error generated in the initial alignment stage is also considered, providing an evaluation standard for the compensation effect, thereby improving the error compensation accuracy. Attached Figure Description
[0041] Figure 1 This is a flowchart illustrating a method for constructing a parameter error model for an inertial navigation system based on gravity disturbance in one embodiment. Detailed Implementation
[0042] 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.
[0043] In one embodiment, such as Figure 1 As shown, a method for constructing a parameter error model for an inertial navigation system based on gravity perturbation is provided, including the following steps:
[0044] Step 102: Estimate the random constant zero bias of the accelerometer and the random constant drift of the gyroscope using Kalman filtering. Construct the error model of the accelerometer and the observation error model of the gyroscope using the random constant zero bias of the accelerometer and the random constant drift of the gyroscope, respectively, and zero-mean random white noise.
[0045] Step 104: Based on the measured gravity obtained from the gravimeter, the measured gravity is decomposed into gravity disturbance and gravity disturbance measurement error. The velocity error is constructed using the accelerometer error model, gravity disturbance, and gravity disturbance measurement error.
[0046] The actual gravity disturbance vector obtained from the gravimeter during gravity measurement. To measure the sum of gravity disturbance and gravity disturbance measurement error:
[0047]
[0048] Similarly, when using a spherical harmonic model to extract model gravity, the true gravity perturbation vector is the sum of the model gravity perturbation and the gravity perturbation model error:
[0049]
[0050] The measurement error of gravity disturbance and the error of gravity disturbance model are collectively referred to as the gravity disturbance acquisition error.
[0051] Step 106: Expand the velocity error to obtain the eastward acceleration error and the northward acceleration error; obtain the eastward velocity error and the northward velocity error from the eastward acceleration error and the northward acceleration error; treat the carrier altitude of the inertial navigation system as zero, disregard the altitude error, and calculate the position error using the eastward velocity error and the northward velocity error.
[0052] Step 108: Calculate the attitude error using the gyroscope observation error model and the misalignment angle; construct the navigation system parameter error model based on the velocity error, position error, and attitude error.
[0053] The essence of the impact of gravity disturbance on inertial navigation is that the gravity disturbance acts on the inertial device, is transmitted through the inertial navigation calculation process, and is reflected in the navigation calculation result. Therefore, this application analyzes the error propagation process from the perspective of error propagation relationship and inertial navigation calculation premise. In the error propagation process, velocity error is affected by the specific force measurement accuracy and gravity disturbance; position error is affected by velocity error; attitude error is affected by velocity error, position error, and gyroscope drift. The attitude accuracy of inertial navigation during the navigation phase is affected by gyroscope drift, accelerometer zero bias, and gravity disturbance, while horizontal accelerometer zero bias and gravity disturbance have a greater impact on attitude. The velocity and position errors during the navigation phase are mainly affected by accelerometer zero bias and gravity disturbance. Unlike the traditional variance analysis method, in addition to In order to address the errors caused by gravity disturbances during the navigation phase, errors generated during the initial alignment phase are also considered. Therefore, the measured gravity is obtained from the gravimeter and decomposed into gravity disturbance and gravity disturbance measurement error. The velocity error is constructed using the accelerometer error model, gravity disturbance, and gravity disturbance measurement error. The velocity error is then expanded to obtain the eastward velocity error and the northward velocity error. The carrier altitude of the inertial navigation system is equivalent to zero, and the altitude error is ignored. The position error is calculated using the eastward velocity error and the northward velocity error. Then, the attitude error is calculated using the gyroscope observation error model and the misalignment angle. Finally, the process of constructing the navigation system parameter error model based on the velocity error, position error, and attitude error is existing technology and will not be elaborated on in this application. By calculating the relationship between gravity disturbance and navigation parameter error, this paper analyzes the error propagation process from the perspectives of error propagation and inertial navigation solution premises. It clarifies the mechanism and magnitude of the influence of gravity disturbance on inertial navigation. It not only focuses on the error caused by gravity disturbance in the navigation stage, but also considers the error generated in the initial alignment stage. The established navigation parameter error equation considering gravity disturbance provides an evaluation standard for the compensation effect. When using the error calculated by the navigation parameter error equation to compensate for navigation system parameter errors, the accuracy of error compensation can be greatly improved.
[0054] In the aforementioned method for constructing the parameter error model of an inertial navigation system based on gravity disturbance, this application, starting from the basic principles of inertial navigation calculation, establishes a navigation parameter error equation considering gravity disturbance, clarifies the influence of gravity disturbance and inertial device errors on inertial navigation accuracy and their corresponding magnitude relationships, as well as the coupling relationship between gravity disturbance and inertial device errors. By calculating the relationship between gravity disturbance and navigation parameter errors, the error propagation process is analyzed from the perspective of error propagation relationship and inertial navigation calculation premises. The mechanism and magnitude relationship of the influence of gravity disturbance on inertial navigation are clarified. In addition to focusing on the error caused by gravity disturbance in the navigation stage, the error generated in the initial alignment stage is also considered, providing an evaluation standard for the compensation effect, thereby improving the error compensation accuracy.
[0055] In one embodiment, the zero-mean random white noise includes zero-mean random white noise of angle and zero-mean random white noise of velocity; the accelerometer error model and the gyroscope observation error model are constructed using the accelerometer random constant zero bias and the gyroscope random constant drift, respectively, and the zero-mean random white noise, including:
[0056] An error model for the accelerometer is constructed using the random constant drift of the accelerometer and the zero-mean random white noise of the velocity.
[0057]
[0058] in, Zero-mean random white noise representing velocity. The accelerometer's random constant bias is zero.
[0059] A gyroscope observation error model is constructed using the gyroscope's random constant zero bias and the angle's zero-mean random white noise.
[0060]
[0061] in, Zero-mean random white noise representing the angle, ε b This represents the random constant drift of the gyroscope.
[0062] In a specific embodiment, the error model of the gyroscope can be expressed in the following form:
[0063]
[0064] in, This refers to the gyroscope observation error; subscript g b represents a gyroscope; g For gyroscope drift; k g This is the scale factor error of the gyroscope; The error in angular velocity measurement is caused by the installation error of the gyroscope; w g It is random noise.
[0065] Gyro Drift b g Includes constant drift, random drift, and random constant drift ε b The constant drift and installation error can be obtained through calibration in the laboratory and directly compensated during navigation. Random drift is mainly temperature-related and can be effectively suppressed through a precision temperature control system. For ocean-going vehicles, the inertial navigation system has high calibration accuracy and temperature control precision, and the vehicle's maneuverability is not significant. To simplify the model, the influence of the scale factor error is temporarily disregarded. Therefore, the gyroscope observation error model is updated as follows:
[0066]
[0067] Among them, zero-mean random white noise Integration causes the angle to wander randomly. Let ε be the variance of the random noise of the gyroscope. b The random constant drift of the gyroscope is estimated using Kalman filtering.
[0068] The error model of an accelerometer can be expressed in the following form:
[0069] δf b =b a +diag(f b )k a +N a f b +w a
[0070] Where, δf b To account for the observation error, the superscript is used. b Indicates the carrier coordinate system; subscript a b indicates accelerometer; a For accelerometer zero bias error; k a For the accelerometer's calibration factor error; N a f b Accelerometer measurement error caused by installation error; w a It is random noise.
[0071] Accelerometer zero bias b a Includes constant zero bias, random zero bias, and random constant zero bias. The constant zero bias can be obtained through laboratory calibration. The random zero bias is mainly temperature-dependent and can be effectively suppressed through a precise temperature control system. Installation errors can also be obtained through laboratory calibration and are directly compensated for by the constant zero bias during navigation calculations. Similar to gyroscopes, for marine vessels, the inertial navigation system has high calibration accuracy and minimal maneuverability. To simplify the model, the scale factor error is ignored; therefore, the force observation error model is updated as follows:
[0072]
[0073] Among them, zero-mean random white noise Integral results in a random walk of speed. For the accelerometer random noise variance, The accelerometer's random constant bias is zero, estimated using Kalman filtering.
[0074] In one embodiment, a velocity error is constructed using an accelerometer error model, gravity disturbance, and gravity disturbance measurement error, including:
[0075] The velocity error is constructed using the accelerometer error model, gravity disturbance, and gravity disturbance measurement error.
[0076]
[0077] Where, φ n Indicates the misalignment angle, f n v is the projection of the specific force measured by the accelerometer onto the n-coordinate system. n For velocity, the subscript 2 indicates that the physical quantity is considered only in relation to the horizontal plane. To account for the calculation errors of Coriolis acceleration and centrifugal acceleration, This indicates the error in the Earth's rotation angular rate. ω represents the angular rate error of the navigation system's rotation caused by the curvature of the Earth's surface, resulting from the movement of the inertial navigation system carrier on the surface. ie ω represents the angular rate of Earth's rotation. en This represents the angular rate of rotation of the navigation system caused by the curvature of the Earth's surface, resulting from the movement of the inertial navigation system carrier on the surface. For the velocity error on the horizontal plane, The velocity on the horizontal surface, This represents the projection of the force measurement error on the horizontal plane onto the n-system. This represents the horizontal component of the gravitational disturbance. This represents the horizontal component of the measurement error due to gravity disturbance.
[0078] In specific embodiments, due to the poor stability of the altitude channel in inertial navigation systems, which generally diverges exponentially, its reliability is poor when used alone for extended periods. Altitude damping is typically achieved through other sensors, and in applications such as oceans where precise altitude navigation results are less critical, the altitude is usually set to zero. In this application, gravity compensation aims to improve the horizontal accuracy of the inertial navigation system using gravity measurements in the horizontal direction. Therefore, when modeling the error of accelerometer zero bias, the velocity, position, and celestial component of gravity disturbance in the altitude channel will not be considered.
[0079] In one embodiment, the velocity error is expanded to obtain the eastward velocity error and the northward velocity error, including:
[0080] Expanding the velocity error, we obtain the eastward acceleration error as follows:
[0081]
[0082] Among them, f U Indicates the force relative to the celestial direction, φ N Indicates a northward orientation, f N Indicates the northward specific force, φ U Indicates an upward-facing posture, vN Indicates the northward velocity, δv E Indicates the eastward velocity error, δv N δL represents the northward velocity error, and δL represents the latitude error. This indicates that the random constant of the accelerometer pointing east has zero bias. This represents the horizontal component of the eastward gravity disturbance measurement error, where L is the geographic latitude, h is the geographic altitude, and R... E Let be the radius of the curved surface of the yoke.
[0083] In one embodiment, the method further includes:
[0084] Expanding the velocity error, we obtain the northward acceleration error as follows:
[0085]
[0086] Where, φ E Indicates an eastward orientation, f E Indicates the force to the east. This represents the horizontal component of the measurement error for northward gravity disturbance. This indicates that the random constant of the accelerometer pointing north is zero bias.
[0087] In one embodiment, the position error includes geographic latitude error, geographic longitude error, and geographic altitude error; the carrier altitude of the inertial navigation system is equivalent to zero, and altitude error is ignored. The position error is calculated using eastward velocity error and northward velocity error, including:
[0088] By treating the altitude of the inertial navigation system as zero and neglecting altitude error, the geographical latitude error, geographical longitude error, and geographical altitude error are calculated using the eastward and northward velocity errors, respectively.
[0089]
[0090]
[0091]
[0092] Among them, R E R is the radius of the surface of the zonal loop. N Let λ be the radius of the meridian circle, λ be the geographic longitude, L be the geographic latitude, h be the geographic altitude, and δv be the geographic altitude. N Indicates the northbound velocity error, δv E Indicates the eastward velocity error, δv U This indicates the upward velocity error.
[0093] In one embodiment, the attitude error is calculated using a gyroscope observation error model and the misalignment angle, including:
[0094] The attitude error was calculated using the gyroscope observation error model and the misalignment angle.
[0095]
[0096]
[0097] Among them, the misalignment angle φ n , This represents the projection of the gyroscope output error onto the n-frame. This represents the gyroscope observation error model. Zero-mean random white noise representing the angle, ε b For random constant drift of the gyroscope, Let n be the rotation of the navigation frame n relative to the inertial frame i. This represents the rotation calculation error of the navigation frame n relative to the inertial frame i. This represents the attitude transition matrix from the b-system to the n-system.
[0098]
[0099]
[0100] In a specific embodiment,
[0101] Where, ω ie This is the Earth's rotational angular rate.
[0102] The attitude error is expanded into components as follows:
[0103]
[0104]
[0105]
[0106] Where ε represents the gyroscope drift. Velocity and position are affected by gravitational disturbances.
[0107] It should be understood that, although Figure 1 The steps in the flowchart are shown sequentially as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified herein, there is no strict order in which these steps are executed, and they can be performed in other orders. Figure 1At least some of the steps in the process may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily executed at the same time, but may be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but may be executed in turn or alternately with other steps or at least some of the sub-steps or stages of other steps.
[0108] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), Rambus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.
[0109] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.
[0110] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.
Claims
1. A method for constructing a parameter error model for an inertial navigation system based on gravity perturbation, characterized in that, The method includes: Based on the Kalman filter estimation of the accelerometer random constant zero bias and the gyroscope random constant drift, the accelerometer error model and the gyroscope observation error model are constructed by using the accelerometer random constant zero bias and the gyroscope random constant drift with zero-mean random white noise, respectively. The measured gravity is obtained from the gravimeter, and the measured gravity is decomposed into gravity disturbance and gravity disturbance measurement error. The velocity error is constructed using the error model of the accelerometer, gravity disturbance, and gravity disturbance measurement error. Expand the velocity error to obtain the eastward acceleration error and the northward acceleration error; obtain the eastward velocity error and the northward velocity error from the eastward acceleration error and the northward acceleration error; treat the carrier altitude of the inertial navigation system as zero and ignore the altitude error, and calculate the position error using the eastward velocity error and the northward velocity error; The attitude error is calculated using the gyroscope observation error model and the misalignment angle; a navigation system parameter error model is constructed based on the velocity error, position error, and attitude error. The velocity error is constructed using the accelerometer's error model, gravity disturbance, and gravity disturbance measurement error, including: Using the accelerometer's error model, gravity disturbance, and gravity disturbance measurement error, a velocity error is constructed as follows: in, Indicates the misalignment angle. The specific force measured by the accelerometer Projection in coordinate system For speed, subscript This indicates that only physical quantities on the horizontal plane are considered. To account for the calculation errors of Coriolis acceleration and centrifugal acceleration, This indicates the error in the Earth's rotation angular rate. This represents the angular rate error of the navigation system's rotation caused by the curvature of the Earth's surface, resulting from the movement of the inertial navigation system's carrier on the surface. Represents the Earth's rotational angular rate. This represents the angular rate of rotation of the navigation system caused by the curvature of the Earth's surface, resulting from the movement of the inertial navigation system carrier on the surface. For the velocity error on the horizontal plane, The velocity on the horizontal surface, For the measurement error of the specific force on the horizontal plane The projection under the system, This represents the horizontal component of the gravitational disturbance. This represents the horizontal component of the measurement error due to gravity disturbance.
2. The method according to claim 1, characterized in that, The zero-mean random white noise includes zero-mean random white noise of angle and zero-mean random white noise of velocity; the accelerometer error model and gyroscope error model are constructed using the accelerometer's random constant zero bias and the gyroscope's random constant drift, respectively, and the zero-mean random white noise, including: An error model for the accelerometer is constructed using the random constant drift of the accelerometer and the zero-mean random white noise of the velocity. in, Zero-mean random white noise representing velocity. The accelerometer's random constant bias is zero. A gyroscope observation error model is constructed using the gyroscope's random constant zero bias and the zero-mean random white noise of the angle. in, Zero-mean random white noise representing the angle. This represents the random constant drift of the gyroscope.
3. The method according to claim 1, characterized in that, Expanding the velocity error yields the eastward acceleration error and the northward acceleration error, including: Expanding the velocity error, we obtain the eastward acceleration error as follows: in, Indicates the heavens are in opposition to the heavens. Indicating a northward orientation, Indicates northward comparison, Indicates the attitude towards the sky. Indicates northbound speed. Indicates the eastward velocity error. Indicates the northbound velocity error. Indicates latitude error. This indicates that the random constant of the accelerometer pointing east has zero bias. This represents the horizontal component of the measurement error for eastward gravity disturbance. Geographical latitude, For geographical altitude, Let be the radius of the curved surface of the yoke.
4. The method according to claim 3, characterized in that, The method further includes: Expanding the velocity error, we obtain the northward acceleration error as follows: in, Indicating an eastward orientation, Indicates the force to the east. This represents the horizontal component of the measurement error for northward gravity disturbance. This indicates that the random constant of the accelerometer pointing north is zero bias.
5. The method according to claim 1, characterized in that, The position error includes geographical latitude error, geographical longitude error, and geographical altitude error; the inertial navigation system's carrier altitude is equivalent to zero, and altitude error is ignored. The position error is calculated using the eastward velocity error and northward velocity error, including: By treating the carrier altitude of the inertial navigation system as zero and disregarding altitude error, the geographical latitude error, geographical longitude error, and geographical altitude error are calculated using the aforementioned eastward and northward velocity errors. in, Let be the radius of the curved surface of the y-y circle. Let be the radius of the surface of the meridian circle. Geographical longitude, Geographical latitude, For geographical altitude, Indicates the northbound velocity error. Indicates the eastward velocity error. This indicates the upward velocity error.
6. The method according to claim 1, characterized in that, The attitude error is calculated using the gyroscope observation error model and the misalignment angle, including: The attitude error was calculated using the gyroscope observation error model and the misalignment angle. Among them, the misalignment angle , For the gyroscope output error in The projection under the system, This represents the gyroscope observation error model. Zero-mean random white noise representing the angle. For random constant drift of the gyroscope, For navigation system Frame of reference relative to inertial frame The rotation of the system Navigation system Frame of reference relative to inertial frame The rotation calculation error of the system, express Tie The attitude transition matrix of the system.