A new method of high-latitude navigation based on ECEF system

Abstract

This invention proposes a novel high-latitude navigation method based on the ECEF system, belonging to the field of high-precision navigation technology. This invention addresses the problems of low positioning accuracy and large error fluctuations in traditional grid coordinate system and transverse coordinate system navigation algorithms in high-latitude environments, as well as the navigation interference caused by meridian convergence and high-latitude dynamic effects. The steps of this invention include: establishing a transformation matrix between the geographic coordinate system and the geocentric-fixed coordinate system; establishing discrete navigation solution equations for attitude direction cosine matrix, velocity, and position in the geocentric-fixed coordinate system; establishing error equations for attitude error, velocity error, and position error in the geocentric-fixed coordinate system; performing an S-domain transformation based on the error equations and converting to the time domain to obtain an analytical expression for inertial navigation error in the geocentric-fixed coordinate system; and obtaining optimized high-latitude navigation results based on the oscillation and divergence characteristics of attitude and velocity errors presented by the analytical expression for inertial navigation error.

Description

Technical Field

[0001] This invention relates to a novel high-latitude navigation method based on the ECEF system, belonging to the field of high-precision navigation technology. Background Technology

[0002] Inertial navigation technology in high-latitude polar environments is currently facing multiple challenges and demands for innovative development. The vertical component of the Earth's rotational angular velocity decreases with increasing latitude, leading to singularities in the ENU coordinate system near the poles. Drastically changing magnetic and gravitational fields amplify the error propagation characteristics of inertial sensors, resulting in nonlinear device drift errors. The computational complexity of commonly used geographic coordinate systems surges at extreme high latitudes. Furthermore, the unique polar environment causes nonlinear coupling and variations in the propagation mechanism of error characteristics in submarine sub-inertial navigation systems. Traditional error models and identification methods based on low-latitude assumptions become significantly less applicable in this environment, severely restricting navigation accuracy and system reliability.

[0003] With the increase in high-latitude activities, traditional navigation systems based on mid- and low-latitude assumptions face a series of applicability issues in high-latitude environments. Zhao Yuxin et al., addressing the specific difficulties faced by marine inertial navigation systems in high-latitude applications, systematically reviewed the development history and key technologies of high-latitude inertial navigation systems. They pointed out that traditional "local horizontal fixed north" mechanical choreography suffers from difficulties in finding north, attitude calculation singularities, and computational overflow in high-latitude environments, necessitating a reconstruction of the inertial navigation structure and algorithm system for high-latitude environments. From a broader system perspective, Cheng Jianhua et al. summarized the impact of high-latitude environments on the performance of various marine navigation systems, including inertial, satellite, and acoustic systems, from four aspects: Earth kinematics, geophysical fields, marine environment, and geographical environment. They also reviewed the current status and trends of high-latitude marine navigation and positioning support technologies, providing an overall framework for constructing a comprehensive high-latitude navigation system.

[0004] The rapid convergence of meridians, anomalous gravity fields, intense ionospheric disturbances, widespread ice cover, and complex sea conditions in high-latitude regions severely limit traditional navigation methods widely used in mid- and low-latitude areas. On the one hand, if inertial navigation systems still rely on a geographic coordinate system and a fixed local horizontal north coordinate system, problems such as undefined azimuth, divergence of attitude matrix elements, and singularities in navigation calculations may occur near the poles. On the other hand, GNSS in high latitudes suffers from low visible satellite elevation angles, enhanced multipath effects, and severe ionospheric scintillation, leading to a significant decrease in positioning accuracy and availability, and even situations where calculations are difficult to complete for extended periods. Therefore, constructing inertial navigation algorithms adapted to the characteristics of high-latitude environments—from coordinate system and attitude representation, error modeling and compensation to multi-source information fusion and fault tolerance—and developing deeply integrated integrated navigation technologies based on these algorithms, has become one of the core directions of high-latitude navigation research in China.

[0005] To avoid the singularity problem caused by convergence of high-latitude meridians, domestic scholars have drawn on the concept of lateral navigation and introduced a lateral Earth coordinate system into high-latitude inertial navigation. Zhang Chongmeng et al., using a dual-axis rotation modulation strapdown inertial navigation system as an example, derived a high-latitude mechanical arrangement method based on a lateral wandering azimuth coordinate system under a lateral Earth model, achieving smooth switching of attitude calculation between high and low latitudes. Virtual high-latitude sports car tests showed that the accuracy of this algorithm on a 24-hour navigation timescale is basically consistent with that of the traditional coordinate system, proving that the lateral coordinate system can meet the needs of ships crossing the poles and long-term navigation in high latitudes. Regarding further improvement of lateral inertial navigation theory, Hao Yongshuai et al. systematically analyzed the impact of different Earth models on the high-latitude navigation performance of lateral coordinate inertial navigation, pointing out that accurate modeling of the radius of curvature under an ellipsoidal model is particularly important for ensuring lateral navigation accuracy.

[0006] Regarding the more complex SINS / DVL / GNSS integrated system, although related research is mostly found in project reports and dissertations, its core ideas have been echoed in numerous journal articles: First, addressing the problem of inconsistent spatiotemporal references, joint estimation and compensation of external measurement errors are achieved by uniformly amplifying lever arm effects and time asynchrony errors to the filter state variables; second, for DVL and GNSS measurement anomalies and interruptions, a fault-tolerant federated filtering strategy is constructed using statistical quantities such as Mahalanobis distance to adaptively adjust the weights of each sub-filter in the global estimation, thereby maintaining the robustness of integrated navigation under weak observation or even long-term interruption conditions. Overall, domestic research on high-latitude integrated navigation has evolved from early structural coupling modes such as SINS / GNSS or SINS / DVL to a multi-sensor deep fusion framework that fully considers complex engineering factors such as spatiotemporal reference unification, measurement fault diagnosis, and underwater acoustic link delay. Summary of the Invention

[0007] To address the problems of low positioning accuracy and large error fluctuations in traditional grid coordinate system and horizontal coordinate system navigation algorithms in high-latitude environments, as well as the navigation interference caused by meridian convergence and high-latitude dynamic effects, this invention proposes a new high-latitude navigation method based on the ECEF system.

[0008] The technical solution adopted by the present invention to solve the above problems is as follows: The present invention includes the following steps:

[0009] Step 1: Based on the geometric constraint that the inner product of the grid northward direction and the Y-axis unit vector of the geocentric coordinate system is zero in the geocentric coordinate system, determine the transformation matrix between the geographic coordinate system and the geocentric coordinate system. Step 2: Based on the transformation matrix, establish the discrete navigation solution equations for the attitude direction cosine matrix, velocity, and position in the geocentric coordinate system; Step 3: Based on the discrete navigation solution equations, derive the error equations for attitude error, velocity error, and position error in the geocentric coordinate system; Step 4: Perform an S-domain transformation based on the error equation and convert it to the time domain to obtain the analytical expression of the inertial navigation error in the geocentric-ground-fixed coordinate system; Step 5: Based on the oscillation and divergence characteristics of attitude error and velocity error presented by the analytical expression of inertial navigation error, the attitude non-commutativity error compensation algorithm considering the third-order term of the equivalent rotation vector Picard series is used to compensate for the attitude error, and the velocity non-commutativity error compensation algorithm considering the third-order term of the velocity translation vector Picard series is used to compensate for the velocity error, so as to obtain the optimized high-latitude navigation result.

[0010] Furthermore, step 1 includes: Based on the geometric characteristics of the grid northward direction lying in the parallel plane of the prime meridian, an orthogonal constraint equation is established between the grid northward unit vector and the Y-axis unit vector of the geocentric geofixed coordinate system. Based on the orthogonal constraint equations and in combination with latitude and longitude parameters, the representations of the grid northward, grid eastward, and celestial unit vectors in the geocentric geofixed coordinate system are obtained. Based on the unit vectors of the grid in the north, east, and sky directions, construct the transformation matrix from the geographic coordinate system to the geocentric geofixed coordinate system.

[0011] Furthermore, step 2 specifically includes: With the center of mass of the carrier as the origin, a carrier coordinate system is established. Based on the transformation matrix and the angular increment measurement of the carrier coordinate system relative to the inertial space, the attitude direction cosine matrix is ​​updated using the equivalent rotation vector algorithm. Setting the time starting point to 0, the gyroscope and accelerometer perform equally spaced sampling during the velocity update time period. Assuming the gyroscope angular velocity output is parabolic, the gyroscope angular increment information is calculated, and the force measurement value is compared based on the gyroscope angular increment information. Based on the attitude direction cosine matrix and the specific force measurement, and combined with Earth's rotation and gravitational acceleration compensation, the velocity vector is updated; based on the velocity vector, the position vector in the geocentric-ground-fixed coordinate system is updated through numerical integration.

[0012] Furthermore, step 3 includes: Based on the error definition of the attitude direction cosine matrix, a differential equation for the attitude error vector is established, wherein the attitude error vector represents the misalignment angle between the computation coordinate system and the real coordinate system; Based on the definition of velocity vector error, a velocity error equation is established, which includes the specific force distribution error, gravitational acceleration error and Earth rotation compensation error caused by attitude error. Based on the definition of position vector error, a position error equation is established, which is the integral form of velocity error.

[0013] Furthermore, step 4 includes: Perform a Laplace transform on the differential equations of the attitude error, velocity error, and position error to obtain a system of algebraic equations in the S-domain; solve the system of algebraic equations in the S-domain to obtain the transfer function expressions of each error quantity in the S-domain; By performing an inverse Laplace transform on the transfer function expression, an analytical expression for the error in the time domain is obtained. This analytical expression for the error includes a geooscillation term, a Schuler oscillation term, a constant term, and a time linear divergence term.

[0014] Furthermore, in step 5, based on the oscillation and divergence characteristics of attitude and velocity errors presented in the analytical expression of inertial navigation error, an attitude non-commutativity error compensation algorithm considering the third-order term of the equivalent rotation vector Picard series is used to compensate for the attitude error, including: Based on the assumption that the gyroscope angular velocity output is parabolic, a differential equation for the equivalent rotation vector is established. This differential equation contains first-order, second-order, and third-order terms of a Picard series. Based on the measured angle increment values ​​of the multi-sample sampled at equal intervals, calculate the values ​​of each derivative of the equivalent rotation vector at the start of sampling; establish the algebraic relationship between the angle increment and the equivalent rotation vector based on the values ​​of each derivative and the Taylor series expansion; and solve for the attitude update quaternion or direction cosine matrix containing third-order compensation based on the algebraic relationship.

[0015] Furthermore, an attitude noncommutativity error compensation algorithm considering the third-order terms of the equivalent rotation vector Picard series is adopted, including: A three-sample compensation algorithm is adopted, which calculates the third-order approximation of the equivalent rotation vector based on the angular increment measurement values ​​within three equally spaced sampling time periods.

[0016] Furthermore, an attitude noncommutativity error compensation algorithm considering the third-order terms of the equivalent rotation vector Picard series is adopted, including: A four-sample compensation algorithm is adopted, which calculates the third-order approximation of the equivalent rotation vector based on the angular increment measurement values ​​within four equally spaced sampling time periods.

[0017] Furthermore, in step 5, a velocity noncommutativity error compensation algorithm considering the third-order terms of the velocity translation vector Picard series is used to compensate for the velocity error, including: Based on the assumption that both the gyroscope angular velocity output and the specific force output are parabolic, a differential equation for the velocity translation vector is established, which includes first-order, second-order, and third-order terms of a Picard series. A three-sample or four-sample compensation algorithm is adopted. The three-sample or four-sample compensation algorithm calculates the third-order approximation of the velocity translation vector based on the angular increment and specific force integral measurement values ​​within three or four equally spaced sampling time periods. The third-order coefficients of the velocity translation vector have a dual relationship with the third-order coefficients of the equivalent rotation vector in the attitude compensation algorithm. Based on the measured values ​​of the multi-sample angular increment and specific force integral from equally spaced sampling, the values ​​of each derivative of the velocity translation vector at the start of sampling are calculated; based on the values ​​of each derivative and Taylor series expansion, an algebraic relationship is established between the angular increment, specific force integral, and velocity translation vector; based on the algebraic relationship, the velocity update amount including third-order compensation is obtained.

[0018] The beneficial effects of this invention are: 1. This invention considers third-order and even fourth-order terms of the Picard series of the velocity translation vector in the velocity non-commutativity error compensation design. Compared with the traditional compensation algorithm that only considers second-order terms, it solves the fundamental accuracy loss problem in high dynamic environments. At the same time, it discovers that the attitude and velocity non-commutativity error compensation algorithms have the same duality of coefficients, which improves the theoretical system of error compensation, effectively suppresses the oscillation characteristics of attitude error, and further reduces the solution error of the inertial navigation system.

[0019] 2. This invention addresses the problem that navigation frames in high-latitude regions are prone to frequent switching between the horizontal coordinate system and the north coordinate system due to fluctuations in the carrier's position and GNSS position noise. The designed delayed trigger determination method avoids misjudgment of mode switching by setting dual determination values ​​for penetration and penetration, thus ensuring the continuity and stability of the strapdown inertial navigation system in the transition area between polar and non-polar regions.

[0020] 3. By deriving the arrangement scheme and error model of the ECEF system inertial navigation, this invention clarifies that the attitude error under the static base exhibits the characteristics of Earth oscillation and Schuler oscillation, the velocity error exhibits the characteristics of Earth oscillation, constant value, and time linear divergence, and the position error is generated by the integral of the velocity error and is significantly affected by the attitude error coefficient. This provides a clear theoretical direction for error suppression and parameter optimization design of subsequent high-latitude inertial navigation systems. Attached Figure Description

[0021] Figure 1 This is a flowchart illustrating a novel high-latitude navigation method based on the ECEF system. Figure 2 This is a diagram illustrating the delayed trigger determination process. Figure 3 This is a schematic diagram of an IMU hardware-in-the-loop simulation test platform. Figure 4 The simulation diagram shows the position error in the grid system. Figure 5This is a simulation diagram of the position error in the horizontal coordinate system; Figure 6 The simulation diagram shows the position error in the ECEF system; Figure 7 for =0.01° / h, Schematic diagram of positional error when =100μg; Figure 8 for =0.1° / h Schematic diagram of positional error when =100μg; Figure 9 for =0.5° / h Schematic diagram of positional error when =100μg; Figure 10 for =5° / h Schematic diagram of positional error when =100μg; Figure 11 for =0.01° / h Schematic diagram of positional error at 500μg; Figure 12 The figure shows the simulation results of the positioning error of the inertial navigation system at high latitudes. Detailed Implementation

[0022] like Figure 1 As shown, the steps of a novel high-latitude navigation method based on the ECEF system described in this embodiment include: S1: Establish the transformation matrix between the geographic coordinate system and the geocentric coordinate system; The geocentric-fixed coordinate system is a geocentric coordinate system (also called the Earth coordinate system) with the Earth's center as the origin. The origin O (0,0,0) is the Earth's center of mass. The z-axis is parallel to the Earth's axis and points towards the North Pole, the x-axis points towards the intersection of the Prime Meridian and the equator, and the y-axis is perpendicular to the xOz plane, forming a right-handed coordinate system. The geocentric-fixed coordinate system rotates with the Earth's rotation and can be used to represent the positions of Earth's surface stations and satellites. It is a geocentric-fixed coordinate system (ECEF), fixed to the Earth. Let be the representation of the unit vectors of each axis in the geocentric-fixed coordinate system. Therefore, the transformation matrix between the geographic coordinate system and the geocentric-fixed coordinate system is: (1); Since the northward orientation of the grid lies in a plane parallel to the prime meridian, the northward orientation of the grid is incompatible with the geocentric coordinate system. The axis is perpendicular, and the grid's north-oriented unit vector is perpendicular to the geocentric coordinate system. The dot product of the unit vectors on the x-axis in the geocentric geofixed coordinate system is 0, that is: (2); In the formula, ,and It can be obtained from equations (70) and (71), therefore, we can finally obtain: (3); because: (4); Will Transform into a relational expression containing only latitude and longitude: (5); S2: Establish the discrete navigation solution equations for attitude direction cosine matrix, velocity, and position in the geocentric coordinate system; The following presents the ECEF mechanical arrangement scheme, and the cosine matrix of the ECEF system's inertial navigation attitude direction. ,speed and location The discrete navigation solution equations are as follows: (6); in,

[0023] (7); (8); in, For attitude update cycle, , For the increment of the two-sample gyroscope angle, For the corresponding unit rotation vector, Let be the modulus, with superscripts e and b representing the Earth system and the carrier system, respectively, and m representing the discrete time.

[0024] S3: Based on the discrete navigation solution equations, derive the error equations for attitude error, velocity error, and position error in the geocentric coordinate system; Referring to the derivation process of the inertial navigation error equation, the inertial navigation attitude error of the ECEF frame is: The speed error is The positional error is After further simplification, the error equation can be obtained: (9); In the formula, (10); in, These are the gyroscope and the constant zero bias of the adder, respectively.

[0025] Under static base conditions, with the position accurately known, the error equations of the ECEF system can be simplified to: (11); S4: Perform an S-domain transformation based on the error equation and convert it to the time domain to obtain the analytical expression of the inertial navigation error in the geocentric-ground-fixed coordinate system; Perform an S-domain transformation on the equations in S2: (12); (13); (14); After transforming the S-threshold to the time domain, the inertial navigation error equation in the ECEF system is: (15); (16); (17); in, (18); According to equation (86), the horizontal attitude error and azimuth error exhibit Earth oscillation and Schuler oscillation characteristics. The velocity error mainly exhibits Earth oscillation, constant value, and time linear divergence. Among them, the coefficient of the linear divergence term... It mainly consists of accelerometer measurements and heading error. Common influence; constant term, i.e., positional linear divergence term , , Mainly influenced by Earth system accelerometer measurements , , The position error is mainly caused by the velocity error integral, manifested primarily as constant error, Earth oscillation error, and linear divergence error. A summary of the ECEF system's inertial navigation error characteristics reveals that the attitude error coefficient... , , It is an important parameter affecting inertial navigation error.

[0026] S5: Based on the oscillation and divergence characteristics of attitude and velocity errors presented by the analytical expression of inertial navigation error, obtain the optimized high-latitude navigation results.

[0027] To address the oscillating characteristics of attitude errors, this proposal suggests an attitude error compensation algorithm that considers the third-order term of the equivalent rotation vector Picard series. The equivalent rotating vector differential equation considering the third-order terms of the Picard series is written as follows: (19); To make the derived expression look a little simpler, let The starting time is 0. The derivation is performed using the three-sample error compensation algorithm as an example, where the gyroscope operates within the attitude update time period. The angular increment sampling is performed at equal intervals. Assuming the gyroscope angular velocity output is parabolic, then... (20); Then the gyroscope angle increment It can be represented as (twenty one); According to equations (89) and (90), the values ​​of angular velocity and angular increment at time 0 and their derivatives can be obtained.

[0028] (twenty two); Will Expanding the series by Taylor series at time 0, we get: (twenty three); To make the derivation process more concise and clear, the following definition is made. (twenty four); Then in equation (23) The derivatives of each order can be expressed as follows (25); (26); Substituting equations (22) and (23) into equation (24) and rearranging, we get: (27); Therefore, we can obtain for (28); The angular increment information over the three time periods can be represented as (29); and They are and The angular increment during the sampling time.

[0029] (30); Then the parameter in equation (28) and This can be expressed in terms of angular increments as follows: (31); Therefore, we can conclude that: (32); Substituting equations (31) and (32) into (28) and rearranging, we can obtain the error compensation algorithm for the noncommutativity of the three-sample attitude considering the third-order terms of the Picard series: (33); The velocity translation vector differential equation considering the third-order term of the Picard series is rewritten as follows: (34); In the formula, (35); First, we will derive the algorithm using the three-sample compensation method as an example. To simplify the derived expression, we will set the time starting point to 0. The gyroscope and accelerometer will sample at equal intervals during the velocity update period. Assuming the angular velocity and specific force outputs are parabolic, then... (36); Then the angular increment and the integral of the specific force acceleration can be expressed as: (37); Then, according to equations (36) and (37), we can obtain (38); (39); The parameters in the above formula and This can be represented using angular increments. The angular increment information over three time periods can be represented as: (40); (41); By rearranging equation (41), we can obtain: (42); Similarly, parameters by It can also be obtained by integrating the specific force acceleration: (43); For the second-order term of the Picard series of the velocity translation vector By performing a Taylor series expansion and combining equations (38) and (39), we can obtain... (44); (45); Equation (45) is an extended form of the velocity noncommutativity error compensation algorithm, which only considers the second-order term of the Picard series of the velocity translation vector. Although the accuracy is improved in high dynamic environments compared with the traditional compressed form of the velocity compensation algorithm, there is still a fundamental loss of accuracy. Therefore, this chapter considers the third-order and fourth-order terms of the velocity translation vector for the first time in the algorithm optimization design process. In order to make the derivation process more concise and clear, the following definition is made: Substituting equations (42) and (43) into equation (44), we can obtain the following: (46); (47); (48); The third-order term of the Picard series for the velocity translation vector By performing a Taylor series expansion and combining equations (38) and (39), we can obtain: (49); (50); (51); (52); (53); (54); (55); (56); (57); (58); (59); (60); From the above formula, we can obtain: (61); (62);

[0030]

[0031]

[0032]

[0033]

[0034]

[0035]

[0036] Substituting equations (85) and (86) into equation (95) and rearranging, we get: (63); Comparing equations (122) and (101), we find that the coefficients of the attitude non-commutative error compensation algorithm are exactly the same as those of the velocity compensation algorithm, and their forms are similar. What is the intrinsic connection between the two compensation algorithms, and why is there duality between them? This paper will explore this in the following section. Equation (122) is a three-sample velocity non-commutative error compensation algorithm considering the third-order term of the Picard series of the velocity translation vector. Similarly, by transforming the equation into the following form, the four-sample velocity non-commutative error compensation algorithm can be derived using a similar method described above.

[0037] (64); The derivation process is exactly the same, so I won't repeat it here. The error compensation algorithm for the non-commutative velocity of the four samples is as follows: (65); in The expression is: (66);

[0038]

[0039]

[0040]

[0041]

[0042]

[0043]

[0044]

[0045]

[0046]

[0047]

[0048]

[0049] ;

[0050]

[0051]

[0052] To verify the navigation effect of the present invention in high-dimensional regions, the following verification was performed in this embodiment: In practical work, the motion state of the carrier is complex and diverse. If a simple latitude circle is set as the switching threshold for mode switching, the strapdown inertial navigation system will repeatedly switch between the horizontal coordinate system navigation frame and the north coordinate system navigation frame when the carrier repeatedly enters and exits near the latitude circle. Especially when a GNSS-assisted inertial navigation system is working, the introduced position signal has a certain amount of noise, and the calculated position information will jump up and down near the switching trigger edge, affecting the switching judgment work.

[0053] To avoid misjudgments caused by entering or exiting the working area of ​​the horizontal coordinate system, two judgment values ​​can be set for entry and exit. The difference between these two judgment values ​​should be much larger than the positioning error of the inertial navigation system over a short period of time, thus avoiding frequent switching of navigation working modes caused by the above situation. Based on this idea, a delayed trigger judgment method can be designed, such as... Figure 2 As shown.

[0054] The middle latitude line is the preset line for the working mode. The red line above is the line that enters the polar region boundary, and the blue line below is the line that exits the polar region boundary.

[0055] Simulation analysis will be used to compare the polar navigation performance of pseudo-geographic coordinate systems and classical coordinate systems. And, using methods such as... Figure 3 The hardware-in-the-loop simulation experiment scheme shown is used for hardware-in-the-loop simulation.

[0056] 1. Polar Navigation Algorithm Simulation: The experiment was set with a gyroscope zero bias of 0.03° / h, an accelerometer zero bias of 100 μg, a gyroscope random walk of 0.003° / √h, and an accelerometer random walk of 10 μg / √Hz. The initial position was set in a high-latitude near-polar region at 89.9818°N, near the Prime Meridian (0° longitude), and the simulation duration was 300 seconds. By comparing the position calculation errors of three algorithms—grid coordinate system, horizontal coordinate system, and ECEF system—the system evaluated the anti-interference capability and navigation accuracy advantages of the ECEF algorithm under strong meridian convergence and high-latitude dynamic effects, thus providing a theoretical basis for the design of high-precision inertial navigation systems in polar regions.

[0057] Figure 4 , Figure 5 , Figure 6The figures show examples of position errors under the three methods. Simulation experiments show that the ECEF algorithm has the smallest position error fluctuation and has better positioning accuracy compared to the horizontal coordinate system and grid system algorithms.

[0058] Table 1

[0059] In this comparative experiment of polar navigation algorithms, ten independent tests were conducted on three algorithms—grid coordinate system, abscissa coordinate system, and ECEF coordinate system—and the root mean square value of the three-dimensional position error of each algorithm was calculated. As shown in Table 1, the average position error of the ECEF coordinate system algorithm is 35.77m, significantly lower than that of the grid coordinate system (37.82m) and the abscissa system (37.72m), demonstrating an accuracy improvement of approximately 5.2% to 5.4%. Furthermore, the error distribution of the ECEF algorithm is more concentrated and the overall fluctuation is smaller, indicating better adaptability and stability in the high-latitude polar environment. Therefore, under the conditions set in this experiment, the ECEF coordinate system performs best in terms of position calculation accuracy and is more suitable for polar navigation tasks requiring high positioning accuracy.

[0060] 2. Experimental Analysis of the Impact of Device Drift on Inertial Navigation Accuracy in Polar Environments: To investigate the impact of device drift on the accuracy of navigation and positioning in polar regions, this implementation method designed a set of systematic numerical simulation experiments. Five different combinations of gyroscope and accelerometer zero-bias parameters were set up, with their random walk coefficients all corresponding to one-tenth of the zero bias. The initial simulation position was set in the high-latitude region near the poles at 89.9818°N, the Prime Meridian (0° longitude). The simulation duration was 300 seconds, and the ECEF (Earth-centered Earth-fixed) coordinate system algorithm was used for calculation to quantitatively evaluate the specific impact of different device error levels on the accuracy of polar navigation. Rigorous numerical simulation experiments were designed to study and analyze the impact of device drift on the positioning accuracy of polar navigation algorithms. The experiment was set up with gyroscope zero bias and accelerometer zero bias as different parameter controls. The random walk of the gyroscope was set to one-tenth of the zero bias, and the random walk of the accelerometer was set to one-tenth of the zero bias. The initial position was set to the high latitude near-polar region of 89.9818° North latitude and the Prime Meridian (0° longitude). The simulation duration was 300 seconds, and the ECEF system algorithm was used for the simulation experiment.

[0061] Figure 7 , Figure 8 , Figure 9 , Figure 10 This is a simulation experiment using the ECEF system method, with the accelerometer zero bias kept constant and the gyroscope zero bias varying.

[0062] Figure 11 Is and Figure 12 Simulation experiments comparing the ECEF algorithm under the same gyroscope zero bias with different accelerometer zero bias.

[0063] This experiment systematically evaluated the impact of different inertial device errors on polar navigation and positioning accuracy in the ECEF coordinate system. The results show that the highest navigation accuracy is achieved when the gyroscope zero bias is 0.01° / h and the accelerometer zero bias is 100μg, with an average position error of 37.69. Keeping the accelerometer zero bias constant, gradually increasing the gyroscope zero bias to 0.1° / h, 0.5° / h, and 5° / h increases the average error to 38.71, 76.01, and 763.06, respectively. Particularly when the gyroscope zero bias reaches 5° / h, the error exhibits an order-of-magnitude increase, indicating that the impact of gyroscope error on polar navigation accuracy is non-linearly and significantly worsens. With the gyroscope zero bias fixed at 0.01° / h, increasing the accelerometer zero bias from 100μg to 500μg causes a sharp increase in average error from 37.69 to 189.87, demonstrating that accelerometer error also has a crucial impact on positioning accuracy.

[0064] Inertial navigation high-latitude simulation experiments were conducted in MATLAB, such as... Figure 11 The simulation duration was 3660s, and the positioning error was 1609.1m, meeting the positioning requirement of 1 nautical mile / h. The comparison of position errors under the influence of device drift is shown in Table 2. For zero bias of the gyroscope, This is for zero bias of the accelerometer.

[0065] Table 2

[0066] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent substitutions, and improvements made to the above embodiments without departing from the scope of the present invention, based on the technical essence of the present invention and within the spirit and principles of the present invention, shall still fall within the protection scope of the present invention.

Claims

1. A novel high-latitude navigation method based on the ECEF system, characterized in that, include: Step 1: Based on the geometric constraint that the inner product of the grid northward direction and the Y-axis unit vector of the geocentric coordinate system is zero in the geocentric coordinate system, determine the transformation matrix between the geographic coordinate system and the geocentric coordinate system. Step 2: Based on the transformation matrix, establish the discrete navigation solution equations for the attitude direction cosine matrix, velocity, and position in the geocentric coordinate system; Step 3: Based on the discrete navigation solution equations, derive the error equations for attitude error, velocity error, and position error in the geocentric coordinate system; Step 4: Perform an S-domain transformation based on the error equation and convert it to the time domain to obtain the analytical expression of the inertial navigation error in the geocentric-ground-fixed coordinate system; Step 5: Based on the oscillation and divergence characteristics of attitude error and velocity error presented by the analytical expression of inertial navigation error, the attitude non-commutativity error compensation algorithm considering the third-order term of the equivalent rotation vector Picard series is used to compensate for the attitude error, and the velocity non-commutativity error compensation algorithm considering the third-order term of the velocity translation vector Picard series is used to compensate for the velocity error, so as to obtain the optimized high-latitude navigation result.

2. The novel high-latitude navigation method based on the ECEF system according to claim 1, characterized in that, Step 1 includes: Based on the geometric characteristics of the grid northward direction lying in the parallel plane of the prime meridian, an orthogonal constraint equation is established between the grid northward unit vector and the Y-axis unit vector of the geocentric geofixed coordinate system. Based on the orthogonal constraint equations and in combination with latitude and longitude parameters, the representations of the grid northward, grid eastward, and celestial unit vectors in the geocentric geofixed coordinate system are obtained. Based on the unit vectors of the grid in the north, east, and sky directions, construct the transformation matrix from the geographic coordinate system to the geocentric geofixed coordinate system.

3. A novel high-latitude navigation method based on the ECEF system according to claim 1, characterized in that, Step 2 specifically includes: With the center of mass of the carrier as the origin, a carrier coordinate system is established. Based on the transformation matrix and the angular increment measurement of the carrier coordinate system relative to the inertial space, the attitude direction cosine matrix is ​​updated using the equivalent rotation vector algorithm. Setting the time starting point to 0, the gyroscope and accelerometer perform equally spaced sampling during the velocity update time period. Assuming the gyroscope angular velocity output is parabolic, the gyroscope angular increment information is calculated, and the force measurement value is compared based on the gyroscope angular increment information. Based on the attitude direction cosine matrix and the specific force measurement, and combined with Earth's rotation and gravitational acceleration compensation, the velocity vector is updated; based on the velocity vector, the position vector in the geocentric-ground-fixed coordinate system is updated through numerical integration.

4. A novel high-latitude navigation method based on the ECEF system according to claim 1, characterized in that, Step 3 includes: Based on the error definition of the attitude direction cosine matrix, a differential equation for the attitude error vector is established, wherein the attitude error vector represents the misalignment angle between the computation coordinate system and the real coordinate system; Based on the definition of velocity vector error, a velocity error equation is established, which includes the specific force distribution error, gravitational acceleration error and Earth rotation compensation error caused by attitude error. Based on the definition of position vector error, a position error equation is established, which is the integral form of velocity error.

5. A novel high-latitude navigation method based on the ECEF system according to claim 1, characterized in that, Step 4 includes: Perform a Laplace transform on the differential equations of the attitude error, velocity error, and position error to obtain a system of algebraic equations in the S-domain; solve the system of algebraic equations in the S-domain to obtain the transfer function expressions of each error quantity in the S-domain; By performing an inverse Laplace transform on the transfer function expression, an analytical expression for the error in the time domain is obtained. This analytical expression for the error includes a geooscillation term, a Schuler oscillation term, a constant term, and a time linear divergence term.

6. A novel high-latitude navigation method based on the ECEF system according to claim 1, characterized in that, In step 5, based on the oscillation and divergence characteristics of attitude and velocity errors presented in the analytical expression of inertial navigation error, an attitude non-commutativity error compensation algorithm considering the third-order term of the equivalent rotation vector Picard series is used to compensate for the attitude error, including: Based on the assumption that the gyroscope angular velocity output is parabolic, a differential equation for the equivalent rotation vector is established. This differential equation contains first-order, second-order, and third-order terms of a Picard series. Based on the measured angle increment values ​​of the multi-sample sampled at equal intervals, calculate the values ​​of each derivative of the equivalent rotation vector at the start of sampling; establish the algebraic relationship between the angle increment and the equivalent rotation vector based on the values ​​of each derivative and Taylor series expansion; and solve for the attitude update quaternion or direction cosine matrix containing third-order compensation based on the algebraic relationship.

7. A novel high-latitude navigation method based on the ECEF system according to claim 6, characterized in that, The attitude noncommutativity error compensation algorithm, which considers the third-order terms of the equivalent rotation vector Picard series, includes: A three-sample compensation algorithm is adopted, which calculates the third-order approximation of the equivalent rotation vector based on the angular increment measurement values ​​within three equally spaced sampling time periods.

8. A novel high-latitude navigation method based on the ECEF system according to claim 6, characterized in that, The attitude noncommutativity error compensation algorithm, which considers the third-order terms of the equivalent rotation vector Picard series, includes: A four-sample compensation algorithm is adopted, which calculates the third-order approximation of the equivalent rotation vector based on the angular increment measurement values ​​within four equally spaced sampling time periods.

9. A novel high-latitude navigation method based on the ECEF system according to claim 1, characterized in that, Step 5 employs a velocity noncommutativity error compensation algorithm that considers the third-order terms of the velocity translation vector Picard series to compensate for the velocity error, including: Based on the assumption that both the gyroscope angular velocity output and the specific force output are parabolic, a differential equation for the velocity translation vector is established, which includes first-order, second-order, and third-order terms of a Picard series. A three-sample or four-sample compensation algorithm is adopted. The three-sample or four-sample compensation algorithm calculates the third-order approximation of the velocity translation vector based on the angular increment and specific force integral measurement values ​​within three or four equally spaced sampling time periods. The third-order coefficients of the velocity translation vector have a dual relationship with the third-order coefficients of the equivalent rotation vector in the attitude compensation algorithm. Based on the measured values ​​of the multi-sample angular increment and specific force integral from equally spaced sampling, the values ​​of each derivative of the velocity translation vector at the start of sampling are calculated; based on the values ​​of each derivative and Taylor series expansion, an algebraic relationship is established between the angular increment, specific force integral, and velocity translation vector; based on the algebraic relationship, the velocity update amount including third-order compensation is obtained.

Images