Double inertial navigation state monitoring method based on correction model in polar region environment

Abstract

The invention belongs to the field of navigation, discloses a double inertial navigation state monitoring method based on a correction model in a polar region environment, and is suitable for state monitoring of a carrier equipped with multiple inertial navigation systems with indexing mechanisms in a polar region. In order to solve the problem that state monitoring is limited when the inertial navigation systems of the ships sailing in polar regions have no external reference information, a transverse geographic coordinate system under an earth ellipsoid model is used as a navigation coordinate system, and relative postures, relative speeds and relative positions of the two inertial navigation systems under the transverse geographic coordinate system are used as constraints for observation; meanwhile, a speed error equation is corrected, the situation that a specific force term exists in the error equation is avoided, and the problem that a speed error model is inaccurate in calculation in a dynamic environment is solved, so that a double-inertial-navigation-system combined strong tracking filter is established, and error parameters of the inertial navigation system are monitored on line under the condition that no external reference information exists in a polar region. The method is completely independent, does not depend on external reference information, and has important engineering significance.

Description

Technical Field

[0001] The present invention belongs to the technical field of navigation, and relates to a method for monitoring the state of an inertial navigation system, in particular to a method for monitoring the state of a dual-inertial navigation based on a correction model in a polar environment, which is applicable to the state monitoring of two or more inertial navigation systems with a two-axis or three-axis indexing mechanism in the polar region. Background Art

[0002] With the progress of technology, the exploration of polar regions has received increasing attention. Due to the convergence of the Earth's meridians and geomagnetic lines near the poles, as well as phenomena such as frequent magnetic storms and solar storms, the navigation technologies commonly used in low-latitude regions are difficult to be effectively applied in the polar environment. The inertial navigation system has become the main means of polar navigation because it can independently provide continuous attitude, velocity, and position information. However, the inertial navigation system also encounters some challenges in the polar region, such as an increase in computational cumulative errors and a lack of effective heading references. Therefore, it is necessary to switch the navigation coordinate system after entering the polar region. Considering that the Arctic Sea Route is the shortest path connecting East Asia, Europe, and the east coast of North America, and the rich resources contained in this region, the development of high-precision and high-reliability navigation technologies adapted to the polar environment is crucial for supporting various ships to safely cross the polar region.

[0003] Ships with the ability to navigate in polar regions usually have a long navigation time and have high requirements for the reliability of the inertial navigation system. Therefore, the inertial navigation system state monitoring technology is one of the important technologies for polar navigation. The traditional inertial navigation system device state monitoring technology relies on external basic reference information. By combining the external reference benchmark information with the inertial navigation output information, it is determined whether the current inertial navigation system is working properly. However, for some situations lacking external reference information, such as underwater environments and satellite navigation denial environments, the use of inertial navigation system state monitoring technology will be severely restricted.

[0004] Existing long-endurance motion carriers usually carry multiple inertial navigation systems with indexing mechanisms, such as a shipborne redundant configuration of a two-axis rotation modulation inertial navigation system. Utilizing the redundancy feature of the inertial navigation systems in the shipborne configuration, the redundant information of the two inertial navigation systems can be fused to construct an inertial device monitoring algorithm applicable to the polar region, realizing the monitoring of abnormal inertial navigation information, thereby solving the problem that the traditional inertial navigation state monitoring algorithm is restricted by external reference information. In the traditional error model of the inertial navigation system, there is a specific force measurement term in the velocity error equation. However, the specific force term in the navigation system needs to be obtained indirectly through differentiation, which leads to the direct coupling of the accelerometer-related error terms in the velocity error equation. When the specific force estimation is inaccurate, it will affect the effect of state monitoring. In addition, the harsh external conditions in the polar region will cause changes in the operating state of the inertial navigation system, introducing unpredictable environmental noise. The dynamic characteristics of this noise seriously weaken the effectiveness of the traditional fixed-threshold state monitoring method, making it extremely easy to fail, resulting in misjudgment of the true state of the system, manifested as a significant increase in the risk of missed diagnosis or misdiagnosis.

[0005] In view of the existing problems, the present invention proposes a dual-inertial navigation state monitoring method based on a correction model in a polar environment. Based on the navigation information of two two-axis rotation modulation inertial navigation systems, a correction error model is constructed to solve the problem of inaccurate calculation of the velocity error model in a dynamic environment. At the same time, taking the transverse geographical coordinate system under the earth ellipsoid model as the navigation coordinate system, and using the relative attitude, relative position, and relative velocity of the inertial navigation system in the transverse geographical coordinate system as observation constraints, a strong tracking filter based on residual normalization is used to online monitor the gyro drift and accelerometer zero bias of the two systems. Further, according to the error parameters, the threshold is adaptively calculated to monitor and diagnose the state of the inertial devices. This method is completely autonomous, only requires the navigation information of two inertial navigation systems as input, and the entire state monitoring process uses open-loop filtering, and the algorithm does not affect the normal operation of the system. Summary of the Invention

[0006] The present invention proposes a dual-inertial navigation state monitoring method based on a correction model in a polar environment. Taking the transverse geographical coordinate system under the earth ellipsoid model as the navigation coordinate system, it realizes the state monitoring of the two-axis rotation inertial navigation under redundant configuration in the polar environment without external reference information, which has important engineering practical value.

[0007] To solve the above technical problems, the solution proposed by the present invention is as follows:

[0008] A dual-inertial navigation state monitoring method based on a correction model in a polar environment, the method comprising the following steps:

[0009] (1) Set the indexing order of the two two-axis rotation inertial navigation systems, define the two redundantly configured inertial navigation systems as Inertial Navigation 1 and Inertial Navigation 2 respectively, and their indexing orders are both two-axis 16 orders, using different indexing methods;

[0010] (2) Construct the transverse earth coordinate system and transverse geographic coordinate system based on the earth ellipsoid model;

[0011] The point at 0°N and 90°E is the North Pole in the transverse earth coordinate system, defined as the transverse North Pole. The point at 0°N and 90°W is the South Pole in the transverse earth coordinate system, defined as the transverse South Pole. The elliptical surface surrounded by the 0° meridian and the 180° meridian is the transverse equatorial surface. The half of the large ellipse composed of the transverse North Pole, the transverse South Pole and the North Pole is taken as the 0° transverse meridian, and the plane is the transverse prime meridian. The conversion relationship between the earth coordinate system and the newly defined transverse earth coordinate system is expressed as:

[0012]

[0013] In the formula, the e system represents the earth coordinate system, the e′ system represents the transverse earth coordinate system, The direction cosine matrix representing the transformation between the earth coordinate system and the transverse earth coordinate system;

[0014] The angle between the normal line of the carrier and the transverse equatorial plane is defined as the transverse latitude, and the angle between the normal line and the transverse prime meridian plane is defined as the transverse longitude. The longitude λ, latitude L and transverse longitude λ defined in the earth coordinate system are t , latitude L t The conversion relationship between them is expressed as:

[0015]

[0016] The horizontal geographic coordinate system is defined based on the horizontal longitude and latitude grid. The horizontal north direction points to the horizontal North Pole. The normal line at the location is upward as the celestial direction. The horizontal east direction is defined according to the right-hand coordinate system. The conversion relationship between the geographic coordinate system n system and the horizontal geographic coordinate system t system is It is expressed as:

[0017]

[0018] In the formula, β represents the rotation angle between the geographic coordinate system and the horizontal geographic coordinate system;

[0019] Determine the conversion relationship between β and longitude and latitude, and longitude and latitude:

[0020]

[0021] (3) Using the attitude, velocity, and position information output by the two inertial navigation systems, a state space model in the transverse geographic coordinate system is established. The specific steps are as follows:

[0022] (3.1) Determine the system joint error equation based on the velocity error correction model in the transverse geographic coordinate system:

[0023]

[0024] In the formula, b1 represents the body coordinate system of Inertial Navigation 1, b2 represents the body coordinate system of Inertial Navigation 2, and φ1 t represents the attitude error angle of Inertial Navigation 1 in the transverse geographical coordinate system, δr1 represents the velocity error vector of the corrected Inertial Navigation 1 in the transverse geographical coordinate system, t represents the position error of Inertial Navigation 1 in the transverse geographical coordinate system, represents the velocity in the transverse geographical coordinate system output by Inertial Navigation 1, represents the angular velocity error of the transverse geographical coordinate system relative to the inertial coordinate system related to the position error and velocity error of Inertial Navigation 1, represents the angular velocity error of the Earth's rotation related to the transverse latitude error of Inertial Navigation 1, represents the direction cosine matrix from the body coordinate system of Inertial Navigation 1 to the transverse geographical coordinate system, represents the gyro component error of Inertial Navigation 1, represents the accelerometer component error of Inertial Navigation 1, φ2 t represents the attitude error angle of Inertial Navigation 2 in the transverse geographical coordinate system, represents the velocity error vector of the corrected Inertial Navigation 2 in the transverse geographical coordinate system, represents the position error of Inertial Navigation 2 in the transverse geographical coordinate system, represents the velocity in the transverse geographical coordinate system output by Inertial Navigation 2, represents the angular velocity error of the transverse geographical coordinate system relative to the inertial coordinate system related to the position error and velocity error of Inertial Navigation 2, represents the angular velocity error of the Earth's rotation related to the transverse latitude error of Inertial Navigation 2, represents the direction cosine matrix from the body coordinate system of Inertial Navigation 2 to the transverse geographical coordinate system, is the rotation angular velocity of the transverse geographical coordinate system relative to the inertial coordinate system, is the Earth's rotation angular velocity vector, is the rotation angular velocity of the transverse geographical coordinate system relative to the Earth coordinate system, g t represents the gravity vector at the location of the vehicle, represents the gyro component error of Inertial Navigation 2, represents the accelerometer component error of Inertial Navigation 2;

[0025] (3.2) Determine the combined state equation:

[0026]

[0027] Express the state vector x(t) as:

[0028]

[0029] In the formula, Indicates the attitude errors of INS 1 in the transverse eastward, transverse northward, and upward directions. Respectively represent the velocity errors of INS 1 after correction in the transverse eastward, transverse northward, and upward directions. Indicates the errors of INS 1 in the transverse eastward, transverse northward, and upward directions. Indicates the attitude errors of INS 2 in the transverse eastward, transverse northward, and upward directions. Respectively represent the velocity errors of INS 2 after correction in the transverse eastward, transverse northward, and upward directions. Indicates the errors of INS 2 in the transverse eastward, transverse northward, and upward directions. Indicates the x-axis gyro drift of INS 1. Indicates the y-axis gyro drift of INS 1. Indicates the z-axis gyro drift of INS 1. Indicates the x-axis accelerometer zero bias of INS 1. Indicates the y-axis accelerometer zero bias of INS 1. Indicates the z-axis accelerometer zero bias of INS 1. Indicates the x-axis gyro drift of INS 2. Indicates the y-axis gyro drift of INS 2. Indicates the z-axis gyro drift of INS 2. Indicates the x-axis accelerometer zero bias of INS 2. Indicates the y-axis accelerometer zero bias of INS 2. Indicates the z-axis accelerometer zero bias of INS 2.

[0030] Express the noise distribution matrix G(t) and the noise matrix w(t) as:

[0031]

[0032] Where, Indicates the gyro noise vector of INS 1. Indicates the accelerometer noise vector of INS 1. Indicates the gyro noise vector of INS 1. Indicates the accelerometer noise vector of INS 2.

[0033] (3.3) Determine the state constraint observation equation:

[0034] Define the body coordinate systems of INS 1 and INS 2 when the indexing mechanism is at the zero position as the b 10 system and the b 20 system, the vehicle body coordinate system is the b system, and the attitude matrices and output by the two sets of two-axis rotating INSs are expressed as:

[0035]

[0036] In the formula, I 3×3 represents a 3×3 identity matrix, is the direction cosine matrix from the zero position b of the indexing mechanism 10 to the t system, represents the direction cosine matrix from the b1 system to b 10 system, represents the direction cosine matrix from the b2 system to b 20 system, represents the attitude matrix between the b 20 system and the b 10 system;

[0037] Determine the difference expression of the attitude errors of two sets of two-axis rotating inertial navigation:

[0038]

[0039] Considering the lever arm, the velocity and position outputs of inertial navigation 1 and inertial navigation 2 are respectively expressed as:

[0040]

[0041] In the formula, v t represents the carrier velocity vector in the transverse geographical coordinate system, r t represents the position radius vector in the transverse geographical coordinate system, and respectively represent the position information output by inertial navigation 1 and inertial navigation 2, represents the difference in the velocities of the two sets of inertial navigation systems caused by the outer lever arm, l r12 represents the relative position between inertial navigation 2 and inertial navigation 1;

[0042] Since the two systems reflect the velocity information and position information of the same carrier, the observed quantities essentially constitute the constraints on the velocity errors and position errors of inertial navigation 1 and inertial navigation 2 respectively. Express the observed quantities as:

[0043]

[0044] Express the observation equation as:

[0045] z(t) = H(t)x(t) + υ(t)

[0046] where,

[0047]

[0048] In the formula, z(t) represents the observation vector of the system, H(t) represents the observation matrix of the system, υ(t) is the noise vector corresponding to the observed quantity, and H1 represents the first two rows of the skew-symmetric matrix of The first two rows of the skew-symmetric matrix, I 2×2 represents the 2x2 identity matrix;

[0049] (4) Establish an adaptive error parameter estimation filter;

[0050] Use a strong tracking filter based on residual normalization to track and estimate the error state. The one-step prediction of the filter covariance matrix is expressed as:

[0051]

[0052] where,

[0053]

[0054] and there is

[0055]

[0056] where, λ k is the fading factor, P k / k-1 is the one-step prediction covariance matrix, Φ k / k-1 represents the state one-step transition matrix, P k-1 is the covariance matrix at time k-1, G k-1 is the noise distribution matrix at time k-1,, Q k-1 is the system noise matrix at time k-1, tr(·) is the matrix trace operator, H k is the system observation matrix at time k, R k is the observation noise matrix at time k, l k is the weakening factor, λ 0,k is the fading factor calculated at time k, represents the innovation covariance matrix of the actual filtering. ρ is the forgetting factor, taking 0.95 ≤ ρ ≤ 0.995, γ0 represents the innovation at time 0, γ k represents the innovation at time k, and η is the normalization parameter, which is used to eliminate the problem of information asymmetry caused by the difference in the values of the residuals themselves, resulting in a reduction in the response speed of the error state estimation;

[0057] (5) Based on the error parameters output by the filter, perform state monitoring in real time;

[0058] When the state of the inertial device is abnormal, the corresponding gyro drift or accelerometer zero bias changes. The real-time health state monitoring of the inertial device is realized by analyzing the output of the monitoring filter;

[0059] Set a data window that slides with time, with a length of N. The filter output information included in the sliding window at time k is Calculate the data statistical characteristics as follows:

[0060]

[0061] Wherein, μ k and respectively represent the mean and variance of the real-time estimated parameters of the filter within the sliding window at time k, and the dimensions of both are the same as those of ;

[0062] Set the weighting coefficient α and perform iterative calculation on the mean of the historical sliding window:

[0063] Σ k =α·μ k +(1 - α)Σ k-1

[0064] Wherein, Σ k represents the mean of the sliding window after iteration at time k, and determine the following high and low thresholds:

[0065] T - =Σ k +k1σ k

[0066] T + =k2Σ k

[0067] Wherein, k1 and k2 are parameters to be adjusted, and k1≥1, k2>1, T + is the high threshold, and T - is the low threshold;

[0068] Establish a health status monitoring criterion as:

[0069]

[0070] Wherein, represents the i-th component of the filter estimated output at time k + 1, T + (i) and T - (i) respectively represent the i-th components of the real-time high threshold and low threshold to be obtained. According to the sliding window, the monitoring thresholds of each inertial device are updated in real time. When all the error parameter values estimated by the filter are less than the low threshold, it is output that the system has no fault; when the i-th error parameter value estimated by the filter is greater than the low threshold and less than the high threshold, a fault warning is given; when the i-th error parameter value estimated by the filter is greater than the high threshold, it is output that device i has a fault.

[0071] Based on the given joint indexing mode in step (1), make INS1 and INS2 in the normal navigation state, and construct a dual-INS state space model under the polar region through step (2), step (3) and step (4); based on the error parameters output by the filter, the state monitoring of the INS can be realized through step (5).

[0072] Further, in the step (1), the inertial navigation 1 and the inertial navigation 2 rotate at different times according to the same indexing sequence, that is, the two inertial navigations rotate in an asynchronous manner according to the same rotation scheme.

[0073] Further, in the step (1), the inertial navigation 1 and the inertial navigation 2 adopt different indexing sequences and rotate synchronously.

[0074] Further, the coordinate system adopted in the step (2) includes but is not limited to the transverse geographical coordinate system, and the grid coordinate system and other coordinate systems applicable to the polar region all fall within the scope of the present invention.

[0075] Further, the relative attitude of the indexing mechanisms of the inertial navigation 1 and the inertial navigation 2 when in the zero position in the step (3) is determined after the two sets of inertial navigations are installed and aligned by the two systems respectively, or determined with the aid of an external attitude reference.

[0076] Further, the lever arm between the inertial navigation 1 and the inertial navigation 2 in the step (3) is calibrated and determined after the two sets of inertial navigations are installed.

[0077] Further, the method of the present invention is not only applicable to the case where both the inertial navigation 1 and the inertial navigation 2 are two-axis rotationally modulated inertial navigations, but also applicable to the cases where both the inertial navigation 1 and the inertial navigation 2 are three-axis rotationally modulated inertial navigations, the inertial navigation 1 is a two-axis rotationally modulated inertial navigation or a three-axis rotationally modulated inertial navigation, the inertial navigation 2 is a single-axis rotationally modulated inertial navigation, the inertial navigation 1 is a single-axis rotationally modulated inertial navigation, the inertial navigation 2 is a two-axis rotationally modulated inertial navigation or a three-axis rotationally modulated inertial navigation, and the redundant configurations of multiple sets of two-axis rotational inertial navigations and multiple sets of three-axis rotational inertial navigations.

[0078] In summary, the advantages and positive effects of the present invention are as follows: The present invention establishes a combined state Kalman filter based on the transverse geographical coordinate system of the earth ellipsoid model, solves the problem that the traditional inertial navigation system with the local horizontal coordinate system as the navigation coordinate system fails in the polar region; modifies the velocity error equation to avoid the presence of the specific force term in the error equation, and solves the problem that the velocity error model calculation is inaccurate in the dynamic environment; utilizes the redundant information of the two sets of inertial navigation systems to realize the device-level state monitoring of the inertial navigation system in the polar region environment. The method proposed by the present invention is completely autonomous, does not rely on any external reference information, is not restricted by the use environment, and has important engineering significance. BRIEF DESCRIPTION OF THE DRAWINGS

[0079] Figure 1 is a flowchart provided by an embodiment of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0080] In order to make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below in conjunction with embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0081] Due to the rapid convergence of the meridians at the poles, there will be a large error in the inertial navigation system with the local horizontal geographic coordinate system as the navigation coordinate system. Due to the interference of magnetic storms, ionosphere, etc., there is a lack of reliable external reference information in the polar regions, and navigation and positioning in the polar regions mainly rely on the inertial navigation system. However, the inertial navigation system needs to perform real-time status monitoring in the polar environment to ensure that the navigation information provided by the inertial navigation is accurate and reliable, meeting the requirements of ship long-distance navigation. In addition, the specific force term in the traditional velocity error equation cannot be directly measured, and inaccurate differential calculation of the specific force during motion will affect the accuracy of status monitoring. To address these problems, the present invention proposes a dual-inertial navigation status monitoring method based on a correction model in the polar environment, and the status monitoring method is as Figure 1 shown. The specific implementation is as follows:

[0082] (1) Set the rotation order of two sets of two-axis rotating inertial navigation systems. Define the two redundantly configured inertial navigation systems as inertial navigation 1 and inertial navigation 2 respectively, and their rotation orders are both the two-axis 16 order, and different rotation methods are adopted;

[0083] (2) Construct a transverse earth coordinate system and a transverse geographic coordinate system based on the earth ellipsoid model;

[0084] Take the point at 0° north latitude and 90° east longitude as the north pole in the transverse earth coordinate system, defined as the transverse north pole, the point at 0° north latitude and 90° west longitude as the south pole in the transverse earth coordinate system, defined as the transverse south pole, the elliptical surface surrounded by the 0° meridian and the 180° meridian as the transverse equatorial plane, and take the half major ellipse composed of the transverse north pole, the transverse south pole and the north pole as the 0° transverse meridian, and the plane where it is located as the transverse prime meridian. Represent the conversion relationship between the earth coordinate system and the newly defined transverse earth coordinate system as:

[0085]

[0086] In the formula, the e system represents the earth coordinate system, the e' system represents the transverse earth coordinate system, represents the direction cosine matrix of the conversion between the earth coordinate system and the transverse earth coordinate system;

[0087] The angle between the normal of the carrier's location and the transverse equatorial plane is defined as the transverse latitude, and the angle with the transverse prime meridian plane is defined as the transverse longitude. Represent the conversion relationship between the longitude λ and latitude L defined in the earth coordinate system and the transverse longitude λ t and the transverse latitude L t as:

[0088]

[0089] Define the transverse geographic coordinate system based on the transverse longitude and latitude grid. The transverse north direction points to the transverse north pole, the normal vector at the location points upward as the sky direction, and the transverse east direction is defined according to the right - hand coordinate system. The conversion relationship between the geographic coordinate system n and the transverse geographic coordinate system t is expressed as:

[0090]

[0091] In the formula, β represents the rotation angle between the geographic coordinate system and the transverse geographic coordinate system;

[0092] Determine the conversion relationship between β, longitude and latitude, and transverse longitude and latitude:

[0093]

[0094] (3) Use the attitude, velocity, and position - related information output by two inertial navigation systems to establish a state - space model in the transverse geographic coordinate system. The specific steps are as follows:

[0095] (3.1) Determine the system combined error equation based on the velocity error correction model in the transverse geographic coordinate system:

[0096]

[0097] In the formula, b1 represents the body coordinate system of inertial navigation 1, b2 represents the body coordinate system of inertial navigation 2, φ1 t represents the attitude error angle of inertial navigation 1 in the transverse geographic coordinate system, δr1 represents the velocity error vector of the corrected inertial navigation 1 in the transverse geographic coordinate system, t represents the position error of inertial navigation 1 in the transverse geographic coordinate system, represents the velocity output by inertial navigation 1 in the transverse geographic coordinate system, represents the angular velocity error of the transverse geographic coordinate system relative to the inertial coordinate system related to the position error and velocity error of inertial navigation 1, represents the angular velocity error of the Earth's rotation related to the transverse latitude error of inertial navigation 1, represents the direction cosine matrix from the body coordinate system of inertial navigation 1 to the transverse geographic coordinate system, represents the gyro component error of inertial navigation 1, represents the accelerometer component error of inertial navigation 1, φ2 t represents the attitude error angle of inertial navigation 2 in the transverse geographic coordinate system, represents the velocity error vector of the corrected inertial navigation 2 in the transverse geographic coordinate system, represents the position error of inertial navigation 2 in the transverse geographic coordinate system, represents the velocity output by inertial navigation 2 in the transverse geographic coordinate system, Indicates the angular velocity error of the transverse geographical coordinate system relative to the inertial coordinate system related to the position error and velocity error of INS 2, Indicates the angular velocity error of the earth's rotation related to the transverse latitude error of INS 2, Indicates the direction cosine matrix from the body coordinate system of INS 2 to the transverse geographical coordinate system, Is the rotational angular velocity of the transverse geographical coordinate system relative to the inertial coordinate system, Is the angular velocity vector of the earth's rotation, Is the rotational angular velocity of the transverse geographical coordinate system relative to the earth coordinate system, g t Indicates the gravity vector at the position of the vehicle, Indicates the gyro assembly error of INS 2, Indicates the accelerometer assembly error of INS 2;

[0098] (3.2) Determine the combined state equation:

[0099]

[0100] Express the state vector x(t) as:

[0101]

[0102] Where, Indicates the attitude errors of INS 1 in the transverse eastward, transverse northward, and upward directions, Respectively indicate the velocity errors of INS 1 after correction in the transverse eastward, transverse northward, and upward directions, Indicates the errors of INS 1 in the transverse eastward, transverse northward, and upward directions, Indicates the attitude errors of INS 2 in the transverse eastward, transverse northward, and upward directions, Respectively indicate the velocity errors of INS 2 after correction in the transverse eastward, transverse northward, and upward directions, Indicates the errors of INS 2 in the transverse eastward, transverse northward, and upward directions, Indicates the x-axis gyro drift of INS 1, Indicates the y-axis gyro drift of INS 1, Indicates the z-axis gyro drift of INS 1, Indicates the x-axis accelerometer zero bias of INS 1, Indicates the y-axis accelerometer zero bias of INS 1, Indicates the z-axis accelerometer zero bias of INS 1, Indicates the x-axis gyro drift of INS 2, Indicates the y-axis gyro drift of INS 2, Indicates the z-axis gyro drift of INS 2, Indicates the x-axis accelerometer zero bias of INS 2, Indicates the y-axis accelerometer zero bias of INS 2, Denote the zero bias of the z-axis accelerometer of the inertial navigation 2;

[0103] Express the noise distribution matrix G(t) and the noise matrix w(t) as:

[0104]

[0105] where denotes the gyro noise vector of the inertial navigation 1, denotes the accelerometer noise vector of the inertial navigation 1, denotes the gyro noise vector of the inertial navigation 1, denotes the accelerometer noise vector of the inertial navigation 2;

[0106] (3.3) Determine the state constraint observation equation:

[0107] Define the body coordinate systems of the inertial navigation 1 and the inertial navigation 2 when the indexing mechanism is at the zero position as the b 10 system and the b 20 system, the vehicle coordinate system is the b system, and the attitude matrices and output by the two sets of two-axis rotating inertial navigations are expressed as:

[0108]

[0109] where I 3×3 denotes the 3-row and 3-column identity matrix, is the direction cosine matrix from the b 10 system to the t system when the indexing mechanism is at the zero position, denotes the direction cosine matrix from the b1 system to the b 10 system, denotes the direction cosine matrix from the b2 system to the b 20 system, denotes the attitude matrix between the b 20 system and the b 10 system;

[0110] Determine the difference expression of the attitude errors of the two sets of two-axis rotating inertial navigations:

[0111]

[0112] Considering the lever arm, determine that the velocity and position outputs of the inertial navigation 1 and the inertial navigation 2 are respectively expressed as:

[0113]

[0114] where v t denotes the vehicle velocity vector in the transverse geographical coordinate system, r t denotes the position radius vector in the transverse geographical coordinate system, and respectively represent the position information output by INS 1 and INS 2, represents the difference in the speeds of the two INS systems caused by the external lever arm, l r12 represents the relative position between INS 2 and INS 1;

[0115] Since the two systems reflect the speed information and position information of the same carrier, the observed quantities essentially constitute the constraints on the respective speed errors and position errors of INS 1 and INS 2. Express the observed quantities as:

[0116]

[0117] Express the observation equation as:

[0118] z(t) = H(t)x(t) + υ(t)

[0119] where,

[0120]

[0121] In the formula, z(t) represents the observation vector of the system, H(t) represents the observation matrix of the system, υ(t) is the noise vector corresponding to the observed quantity, and H1 represents the first two rows of the skew-symmetric matrix of, H2 represents the first two rows of the skew-symmetric matrix of, I 2×2 represents the 2×2 identity matrix;

[0122] (4) Establish an adaptive error parameter estimation filter;

[0123] Adopt a strong tracking filter based on residual normalization to track and estimate the error state. The one-step prediction of the filter covariance matrix is expressed as:

[0124]

[0125] In the formula,

[0126]

[0127] And there is

[0128]

[0129] where, λ k is the fading factor, P k / k-1 is the one-step prediction covariance matrix, Φ k / k-1 represents the state one-step transition matrix, P k-1 is the covariance matrix at time k - 1, G k-1 is the noise distribution matrix at time k - 1,, Q k-1is the system noise matrix at time k-1, tr(·) is the matrix trace operator, H k is the system observation matrix at time k, R k is the observation noise matrix at time k, l k is the weakening factor, λ 0,k is the fading factor calculated at time k, represents the innovation covariance matrix of the actual filtering, ρ is the forgetting factor, taking 0.95 ≤ ρ ≤ 0.995, γ0 represents the innovation at time 0, γ k represents the innovation at time k, η is the normalization parameter, which is used to eliminate the problem that the information asymmetry caused by the difference in the numerical value of the residual itself leads to a reduction in the response speed of the error state estimation; (5) Based on the error parameters output by the filter, the state monitoring is carried out in real time;

[0130] When the state of the inertial device is abnormal, the corresponding gyro drift or accelerometer zero bias changes, and the real-time health state monitoring of the inertial device is realized by analyzing the output of the monitoring filter;

[0131] Set a data window that slides with time, its length is N, and the filter output information included in the sliding window at time k is Calculate the data statistical characteristics as follows:

[0132]

[0133] In the formula, μ k and respectively represent the mean and variance of the real-time estimation parameters of the filter within the sliding window at time k, and the dimensions of both are the same as those of ;

[0134] Set the weighting coefficient α and perform iterative calculation on the mean of the historical sliding window:

[0135] Σ k = α·μ k +(1-α)Σ k-1

[0136] In the formula, Σ k represents the sliding window mean after iteration at time k, and determine the upper and lower thresholds as follows:

[0137] T - = Σ k + k1σ k

[0138] T + = k2Σ k

[0139] In the formula, k1, k2 are parameters to be adjusted, and k1 ≥ 1, k2 > 1, T +is the high threshold, T - is the low threshold;

[0140] The health status monitoring criterion is established as:

[0141]

[0142] wherein, represents the i-th component of the filter estimated output at the (k + 1)-th moment, T + (i) and T - (i) respectively represent the i-th components of the required real-time high threshold and low threshold. According to the sliding window, the monitoring thresholds of each inertial device are updated in real time. When all the error parameter values estimated by the filter are less than the low threshold, it is output that the system has no fault; when the i-th error parameter value estimated by the filter is greater than the low threshold and less than the high threshold, a fault warning is given; when the i-th error parameter value estimated by the filter is greater than the high threshold, it is output that device i has a fault.

[0143] Based on the given combined indexing method in step (1), make Inertial Navigation 1 and Inertial Navigation 2 in the normal navigation state, and construct the state space model of the dual inertial navigation in the polar region through step (2), step (3) and step (4); based on the error parameters output by the filter, the state monitoring of the inertial navigation system can be realized through step (5).

[0144] As an improvement, in step (1), Inertial Navigation 1 and Inertial Navigation 2 rotate at different times according to the same indexing order, that is, the two inertial navigations rotate in an asynchronous manner according to the same rotation scheme.

[0145] As an improvement, in step (1), Inertial Navigation 1 and Inertial Navigation 2 adopt different indexing orders and rotate synchronously.

[0146] As an improvement, the coordinate system adopted in step (2) includes but is not limited to the transverse geographic coordinate system. The use of the grid coordinate system and other coordinate systems suitable for the polar region all fall within the scope of the present invention.

[0147] As an improvement, the relative attitude when the indexing mechanisms of Inertial Navigation 1 and Inertial Navigation 2 are in the zero position in step (3) is determined after the alignment of the two sets of inertial navigations after the installation of the two sets of inertial navigations, or determined with the help of an external attitude reference.

[0148] As an improvement, the lever arm between Inertial Navigation 1 and Inertial Navigation 2 in step (3) is calibrated and determined after the installation of the two sets of inertial navigations.

[0149] As an improvement, the method of the present invention is applicable not only to the case where both inertial navigation 1 and inertial navigation 2 are two-axis rotation modulation inertial navigations, but also to the cases where both inertial navigation 1 and inertial navigation 2 are three-axis rotation modulation inertial navigations, inertial navigation 1 is a two-axis rotation modulation inertial navigation or a three-axis rotation modulation inertial navigation and inertial navigation 2 is a single-axis rotation modulation inertial navigation, inertial navigation 1 is a single-axis rotation modulation inertial navigation and inertial navigation 2 is a two-axis rotation modulation inertial navigation or a three-axis rotation modulation inertial navigation, and the redundant configurations of multiple sets of two-axis rotation inertial navigations and multiple sets of three-axis rotation inertial navigations.

[0150] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. All technical solutions falling within the concept of the present invention belong to the protection scope of the present invention. Several improvements and refinements made without departing from the principle of the present invention should also be regarded as within the protection scope of the present invention.

Claims

1. A dual-inertial navigation state monitoring method based on a correction model in a polar environment, characterized in that The method includes the following steps: (1) Set the indexing order of two sets of two-axis rotating inertial navigation systems. Define the two inertial navigation systems with redundant configuration as Inertial Navigation 1 and Inertial Navigation 2 respectively. The indexing order of both is the two-axis 16-order, and different indexing methods are adopted. (2) Construct a transverse earth coordinate system and a transverse geographic coordinate system based on the earth ellipsoid model. Take the point at 0° north latitude and 90° east longitude as the north pole in the transverse earth coordinate system, defined as the transverse north pole, and the point at 0° north latitude and 90° west longitude as the south pole in the transverse earth coordinate system, defined as the transverse south pole. The elliptical surface surrounded by the 0° meridian and the 180° meridian is the transverse equatorial plane. Take the half major ellipse composed of the transverse north pole, the transverse south pole and the north pole as the 0° transverse meridian, and the plane where it is located is the transverse prime meridian. The conversion relationship between the earth coordinate system and the newly defined transverse earth coordinate system is expressed as: In the formula, the e system represents the Earth coordinate system, and the e' system represents the transverse Earth coordinate system. represents the direction cosine matrix for the conversion between the Earth coordinate system and the transverse Earth coordinate system; The angle between the normal line of the carrier and the transverse equatorial plane is defined as the transverse latitude, and the angle between the normal line and the transverse prime meridian plane is defined as the transverse longitude. The longitude λ, latitude L and transverse longitude λ defined in the earth coordinate system are t , latitude L t The conversion relationship between them is expressed as: Define the transverse geographic coordinate system based on the transverse longitude and latitude grid, with the transverse north direction pointing to the transverse north pole, the normal direction at the location pointing upward as the celestial direction, and define the transverse east direction according to the right-hand coordinate system. The conversion relationship between the geographic coordinate system n and the transverse geographic coordinate system t is expressed as: In the formula, β represents the rotation angle between the geographic coordinate system and the transverse geographic coordinate system. Determine the conversion relationship between β and longitude and latitude, transverse longitude and latitude. (3) Use the attitude, velocity, and position-related information output by the two sets of inertial navigation systems to establish a state space model in the transverse geographic coordinate system. The specific steps are as follows: (3.1) Determine the system combined error equation based on the velocity error correction model in the transverse geographic coordinate system. Where, b1 represents the body coordinate system of inertial navigation 1, and b2 represents the body coordinate system of inertial navigation 2. represents the attitude error angle of inertial navigation 1 in the transverse geographical coordinate system. represents the velocity error vector of the corrected inertial navigation 1 in the transverse geographical coordinate system. represents the position error of inertial navigation 1 in the transverse geographical coordinate system. represents the velocity output by inertial navigation 1 in the transverse geographical coordinate system. represents the angular velocity error of the transverse geographical coordinate system relative to the inertial coordinate system related to the position error and velocity error of inertial navigation 1. represents the angular velocity error of the Earth's rotation related to the transverse latitude error of inertial navigation 1. represents the direction cosine matrix from the body coordinate system of inertial navigation 1 to the transverse geographical coordinate system. represents the gyro assembly error of inertial navigation 1. represents the accelerometer assembly error of inertial navigation 1. represents the attitude error angle of inertial navigation 2 in the transverse geographical coordinate system. represents the velocity error vector of the corrected inertial navigation 2 in the transverse geographical coordinate system. represents the position error of inertial navigation 2 in the transverse geographical coordinate system. represents the velocity output by inertial navigation 2 in the transverse geographical coordinate system. represents the angular velocity error of the transverse geographical coordinate system relative to the inertial coordinate system related to the position error and velocity error of inertial navigation 2. represents the angular velocity error of the Earth's rotation related to the transverse latitude error of inertial navigation 2. represents the direction cosine matrix from the body coordinate system of inertial navigation 2 to the transverse geographical coordinate system. is the rotational angular velocity of the transverse geographical coordinate system relative to the inertial coordinate system. is the angular velocity vector of the Earth's rotation. is the rotational angular velocity of the transverse geographical coordinate system relative to the Earth coordinate system, g t represents the gravity vector at the position of the vehicle. represents the gyro assembly error of inertial navigation 2. represents the accelerometer assembly error of inertial navigation 2; (3.2) Determine the combined state equation. Express the state vector x(t) as: In the formula, represents the attitude errors of inertial navigation 1 in the transverse eastward, transverse northward, and upward directions, respectively represent the velocity errors of inertial navigation 1 after correction in the transverse eastward, transverse northward, and upward directions, represents the errors of inertial navigation 1 in the transverse eastward, transverse northward, and upward directions, represents the attitude errors of inertial navigation 2 in the transverse eastward, transverse northward, and upward directions, respectively represent the velocity errors of inertial navigation 2 after correction in the transverse eastward, transverse northward, and upward directions, represents the errors of inertial navigation 2 in the transverse eastward, transverse northward, and upward directions, represents the x-axis gyro drift of inertial navigation 1, represents the y-axis gyro drift of inertial navigation 1, represents the z-axis gyro drift of inertial navigation 1, represents the zero bias of the x-axis accelerometer of inertial navigation 1, represents the zero bias of the y-axis accelerometer of inertial navigation 1, represents the zero bias of the z-axis accelerometer of inertial navigation 1, represents the x-axis gyro drift of inertial navigation 2, represents the y-axis gyro drift of inertial navigation 2, represents the z-axis gyro drift of inertial navigation 2, represents the zero bias of the x-axis accelerometer of inertial navigation 2, represents the zero bias of the y-axis accelerometer of inertial navigation 2, represents the zero bias of the z-axis accelerometer of inertial navigation 2; Express the noise distribution matrix G(t) and the noise matrix w(t) as: In the formula, represents the gyro noise vector of inertial navigation 1, represents the accelerometer noise vector of inertial navigation 1, represents the gyro noise vector of inertial navigation 1, represents the accelerometer noise vector of inertial navigation 2; (3.3) Determine the state constraint observation equation. Define the body coordinate systems of inertial navigation 1 and inertial navigation 2 when the indexing mechanism is at the zero position as the b 10 system and the b 20 system. The vehicle coordinate system is the b system. The attitude matrices and output by the two sets of two-axis rotating inertial navigations are expressed as: where, I 3×3 represents a 3×3 identity matrix, is the direction cosine matrix from the b system to the t system when the indexing mechanism is at the zero position b, 10 is the direction cosine matrix from the b1 system to the b system, 10 is the direction cosine matrix from the b2 system to the b system, 20 is the direction cosine matrix from the b system to the b 20 system, 10 and is the attitude matrix between the b Determine the difference expression of the attitude errors of the two sets of two-axis rotating inertial navigations. Considering the lever arm, determine that the velocity and position outputs of Inertial Navigation 1 and Inertial Navigation 2 are respectively expressed as: where, v t represents the vehicle velocity vector in the transverse geographic coordinate system, r t represents the position radius vector in the transverse geographic coordinate system, and respectively represent the position information output by inertial navigation 1 and inertial navigation 2, represents the difference in the velocities of the two inertial navigation systems caused by the external lever arm, l r12 represents the relative position between inertial navigation 2 and inertial navigation 1; Since the two sets of systems reflect the velocity information and position information of the same carrier, the observed quantities essentially constitute the constraints of the velocity errors and position errors of Inertial Navigation 1 and Inertial Navigation 2 respectively. Express the observed quantities as: Express the observation equation as: z(t) = H(t)x(t) + υ(t) where where \(z(t)\) represents the observation vector of the system, \(H(t)\) represents the observation matrix of the system, \(\upsilon(t)\) is the noise vector corresponding to the observed quantity, \(H_1\) represents the first two rows of the skew-symmetric matrix of the first two rows of the skew-symmetric matrix of 2×2 and \(I\) represents the \(2\times2\) identity matrix; (4) Establish an adaptive error parameter estimation filter. Adopt a strong tracking filter based on residual normalization to track and estimate the error state. The one-step prediction of the filter covariance matrix is expressed as: In the formula, and there is Among them, λ k is the fading factor, P k / k-1 is the one-step prediction covariance matrix, Φ k / k-1 represents the state one-step transition matrix, P k-1 is the covariance matrix at time k - 1, G k-1 is the noise distribution matrix at time k - 1,, Q k-1 is the system noise matrix at time k - 1, tr(·) is the matrix trace operator, H k is the system observation matrix at time k, R k is the observation noise matrix at time k, l k is the weakening factor, λ 0,k is the fading factor calculated at time k, represents the innovation covariance matrix of the actual filtering, ρ is the forgetting factor, taking 0.95 ≤ ρ ≤ 0.995, γ0 represents the innovation at time 0, γ k represents the innovation at time k, η is the normalization parameter, which is used to eliminate the problem that the information asymmetry caused by the difference in the values of the residuals themselves leads to a decrease in the response speed of the error state estimation; (5) Based on the error parameters output by the filter, perform real-time state monitoring. When the state of the inertial device is abnormal, the corresponding gyro drift or accelerometer zero bias changes. Real-time health state monitoring of the inertial device is realized by analyzing the output of the monitoring filter. Set a data window that slides over time, with a length of N. The filter output information included in the sliding window at time k is Calculate the data statistical characteristics as follows: where, μ k and represent the mean and variance of the real-time estimated parameters of the filter within the sliding window at time k, respectively. The dimensions of both are the same as those of and are of the same dimension; Set a weighting coefficient α and perform iterative calculation on the mean value of the historical sliding window. Σ k = α·μ k +(1 - α)Σ k-1 where, Σ k represents the sliding window mean value after iteration at time k, and the upper and lower thresholds are determined as follows: T - = Σ k + k1σ k T + = k2Σ k where k1 and k2 are parameters to be adjusted, and k1≥1, k2>1, T + is the high threshold, and T - is the low threshold; Establish a health state monitoring criterion as: In the formula, represents the i-th component of the filter estimated output at the (k + 1)-th moment, T + (i) and T - (i) respectively represent the i-th components of the required real-time high threshold and low threshold. The monitoring thresholds of each inertial device are updated in real time according to the sliding window. When all the error parameter values estimated by the filter are less than the low threshold, it is output that the system has no fault; when the i-th error parameter value estimated by the filter is greater than the low threshold and less than the high threshold, a fault warning is given; when the i-th error parameter value estimated by the filter is greater than the high threshold, it is output that device i has a fault.

2. The dual-inertial navigation state monitoring method based on a correction model in a polar environment according to claim 1, wherein In step (1), Inertial Navigation 1 and Inertial Navigation 2 rotate at different times according to the same indexing order, that is, the two inertial navigations rotate in an asynchronous manner according to the same rotation scheme.

3. The dual-inertial navigation state monitoring method based on a correction model in a polar environment according to claim 1, characterized in that, In step (1), Inertial Navigation 1 and Inertial Navigation 2 adopt different indexing orders and rotate synchronously.

4. The dual-inertial navigation state monitoring method based on a correction model in a polar environment according to claim 1, characterized in that The coordinate system adopted in step (2) is the grid coordinate system.

5. The dual-inertial navigation state monitoring method based on a correction model in a polar environment according to claim 1, characterized in that The relative attitude of the inertial navigation 1 and the inertial navigation 2 when the indexing mechanism is in the zero position in the step (3). It is determined after the alignment of the two sets of inertial navigation systems respectively after the installation of the two sets of inertial navigation systems, or determined with the help of an external attitude reference.

6. The dual inertial navigation state monitoring method based on a correction model in a polar environment according to claim 1, characterized in that The lever arm between Inertial Navigation 1 and Inertial Navigation 2 in step (3) is calibrated and determined after the two sets of inertial navigations are installed.

7. The dual inertial navigation state monitoring method based on a correction model in a polar environment according to claim 1, characterized in that The method of the present invention is applicable not only to the case where both inertial navigation 1 and inertial navigation 2 are two-axis rotationally modulated inertial navigations, but also to the cases where both inertial navigation 1 and inertial navigation 2 are three-axis rotationally modulated inertial navigations, inertial navigation 1 is a two-axis rotationally modulated inertial navigation or a three-axis rotationally modulated inertial navigation and inertial navigation 2 is a single-axis rotationally modulated inertial navigation, inertial navigation 1 is a single-axis rotationally modulated inertial navigation and inertial navigation 2 is a two-axis rotationally modulated inertial navigation or a three-axis rotationally modulated inertial navigation, and the redundant configurations of multiple sets of two-axis rotational inertial navigations and multiple sets of three-axis rotational inertial navigations.

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