Dual-rotation inertial navigation polar region state monitoring method

Abstract

The invention belongs to the technical field of inertia, discloses a dual-rotation inertial navigation polar region state monitoring method, and is suitable for a plurality of inertial navigation systems with indexing mechanisms. In order to solve the problems that the polar environment is difficult to obtain external reference information, the precision is low, and inertial navigation is difficult to realize state monitoring in the absence of external observation conditions, a transverse geographic coordinate system under an earth ellipsoid model is used as a navigation coordinate system; the relative attitude, the relative speed and the relative position of the two inertial navigation systems under the coordinate system are used as constraint observation, and a joint error state Kalman filter suitable for the polar region is established. On-line estimation and monitoring of system gyroscopic drift and accelerometer zero offset are realized through a strong tracking filtering technology. And carrying out online monitoring on the running state of the inertial device based on the estimated error parameter. The method is completely autonomous, does not need external reference information, only needs navigation data of two sets of inertial navigation systems, adopts open-loop filtering, and ensures that normal operation of the systems is not influenced.

Description

Technical Field

[0001] The present invention belongs to the technical field of navigation, and relates to a method for monitoring the state of a redundant two-axis rotating inertial navigation system, in particular to a method for monitoring the state of a dual-rotating inertial navigation system in the polar region, which is applicable to the collaborative state monitoring among two or more inertial navigation systems with two-axis or three-axis indexing mechanisms. Background Art

[0002] The polar region has important values in aspects such as economy, scientific research, resources, waterways, etc. For various ships to safely reach the polar region and carry out activities such as scientific research operations in the polar region, it is inseparable from high-precision and high-reliability navigation equipment to provide navigation and positioning information.

[0003] Due to the special geographical location and harsh natural environment of the polar region, as well as the characteristics of long-term navigation of ships in the polar region, the core measuring components of the inertial navigation system, namely gyroscopes and accelerometers, are prone to output incorrect information due to complex reasons such as component aging, improper operation, and harsh external interference. The reliability of the carrier during navigation in the polar region cannot be guaranteed. Therefore, online monitoring of the state information of the ship's inertial navigation system is a key technology to ensure its long-term stability in the polar region.

[0004] Conventional state monitoring of inertial navigation systems usually uses external reference information as a basis. By combining external reference benchmarks such as speed and position information with the output information of the inertial navigation, the reliability of the current inertial navigation system is judged. However, for some situations where there is a lack of external reference information or the reference information is inaccurate, such as underwater environments, satellite navigation denial environments, and polar region environments, the use of inertial navigation system state monitoring technology will be severely restricted. In addition, the complex external environment in the polar region significantly affects the operating state of the inertial navigation system and will introduce additional environmental noise. The dynamic change of this environmental noise makes it difficult for traditional state monitoring methods based on fixed thresholds to adapt, and it is extremely easy to cause missed diagnosis or misdiagnosis.

[0005] Aiming at the problem of inertial navigation state monitoring under the current lack of external reference information, the present invention proposes a method for monitoring the state of a dual-rotating inertial navigation system in the polar region, which is applicable to the online state monitoring of carriers equipped with multiple inertial navigation systems with indexing mechanisms in the polar environment. Taking the transverse geographical coordinate system under the earth ellipsoid model as the navigation coordinate system, the relative attitude, relative velocity, and relative position of the two inertial navigation systems in the transverse geographical coordinate system are used as constraint observations, and a dual-inertial navigation joint state space model under the transverse coordinate system of the earth ellipsoid model is established. At the same time, strong tracking filtering based on residual normalization is used to perform online tracking estimation of the gyro drift and accelerometer zero bias of the two systems. Further, based on the estimated error parameter values, the inertial devices of the two inertial navigation systems are monitored online. This method is completely autonomous, does not require any external reference information, only requires the navigation information of the 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 method for monitoring the state of a dual-rotating inertial navigation system in the polar region. By using the transverse geographical coordinate system under the earth ellipsoid model as the navigation coordinate system, a joint state space model of the dual-inertial navigation system under the earth ellipsoid model is established. The strong tracking filter based on residual normalization is used to online track and estimate the gyro drift and accelerometer zero bias of the two systems. At the same time, based on the modified Bayes classification algorithm, the state of the inertial devices is detected and diagnosed according to the online estimated error parameters. This method is completely autonomous and does not require any external reference information, having important engineering practical value.

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

[0008] A method for monitoring the state of a dual-rotating inertial navigation system in the polar region, the method comprising the following steps:

[0009] (1) Set the rotation order of two sets of two-axis rotating inertial navigation systems, define the two redundant 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;

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

[0011] Taking the intersection of the equator and the 90° east longitude meridian as the north pole in the e' system of the transverse earth coordinate system, defined as the transverse north pole, and the intersection of the equator and the 90° west longitude meridian as the south pole in the transverse earth coordinate system, defined as the transverse south pole. The meridian circle formed by the 0° meridian and the 180° meridian is defined as the transverse equator. 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. The conversion relationship is expressed as:

[0012]

[0013] 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. The conversion relationship between the longitude λ and latitude L defined in the earth coordinate system and the transverse longitude λ t and transverse latitude L t is expressed as:

[0014]

[0015] Based on the transverse latitude and longitude grid, define the transverse geographical coordinate system. The transverse north direction points to the transverse north pole, the normal of the location points upward to the sky direction, and the transverse east direction is defined according to the right-hand coordinate system. The conversion relationship is expressed as:

[0016]

[0017] In the formula, β represents the rotation angle between the geographic coordinate system and the transverse geographic coordinate system;

[0018] Determine the conversion relationship between β, longitude and latitude, and transverse longitude and latitude:

[0019]

[0020] (3) Use the navigation information output by two sets of two-axis rotation inertial navigation systems to establish a state space model in the transverse geographic coordinate system. The specific steps are as follows:

[0021] (3.1) Determine the system combined error equation in the transverse geographic coordinate system:

[0022]

[0023]

[0024] Among them,

[0025]

[0026] In the formula, represents the attitude error angle of inertial navigation 1 in the transverse geographic coordinates, represents the eastward attitude error angle of inertial navigation 1 in the transverse geographic coordinate system, represents the northward attitude error angle of inertial navigation 1 in the transverse geographic coordinate system, represents the upward attitude error angle of inertial navigation 1 in the transverse geographic coordinate system, represents the velocity error vector of inertial navigation 1 in the transverse geographic coordinate system, which are the transverse eastward velocity error transverse northward velocity error transverse upward velocity error represents the transverse latitude error of inertial navigation 1, represents the transverse longitude error of inertial navigation 1, and δh1 represents the height error of inertial navigation 1, represents the angular velocity error of the transverse geographic coordinate system relative to the inertial coordinate system related to the transverse latitude error of inertial navigation 1 and the velocity error in the transverse geographic coordinate system, represents the angular velocity error of the earth's rotation related to the transverse latitude error of inertial navigation 1, represents the transfer angular velocity error related to the transverse latitude error of inertial navigation 1 and the velocity error in the transverse geographic coordinate system, represents the direction cosine matrix from the body coordinate system of inertial navigation 1 to the transverse geographic coordinate system, represents the attitude error angle of inertial navigation 2 in the transverse geographic coordinates, Denote the velocity error vector of INS 2 in the transverse geographic coordinate system, which are the transverse eastward velocity error, the transverse northward velocity error, and the transverse upward velocity error, Denote the transverse latitude error of INS 2, denote the transverse longitude error of INS 2, and δh2 denote the altitude error of INS 2, Denote the angular velocity error of the transverse geographic coordinate system relative to the inertial coordinate system related to the transverse latitude error of INS 2 and the velocity error in the transverse geographic coordinate system, Denote the angular velocity error of the Earth's rotation related to the transverse latitude error of INS 2, Denote the transfer angular velocity error related to the transverse latitude error of INS 2 and the velocity error in the transverse geographic coordinate system, Denote the direction cosine matrix from the body coordinate system of INS 2 to the transverse geographic coordinate system, v t Denote the velocity vector of the carrier in the transverse geographic coordinate system, is the rotation angular velocity of the transverse geographic coordinate system relative to the inertial coordinate system, is the angular velocity vector of the Earth's rotation, is the rotation angular velocity of the transverse geographic coordinate system relative to the Earth coordinate system, g t Denote the gravity vector at the location of the carrier, Denote the velocities of the carrier in the transverse eastward, transverse northward, and upward directions respectively, L t and h are the transverse latitude and altitude at the location of the carrier, R x is the radius of curvature in the transverse eastward direction at the location of the carrier, R y is the radius of curvature in the transverse northward direction at the location of the carrier, is the distortion rate at the location of the carrier, R E and R N are the radius of the prime vertical and the radius of the meridian at the location of the carrier respectively, Denote the gyro component error of INS 1, modeled as a constant drift and gyro noise The sum of them, where, Denote the gyro drift of the x-axis of INS 1, Denote the gyro drift of the y-axis of INS 1, Denote the gyro drift of the z-axis of INS 1, Denote the accelerometer component error of INS 1, modeled as a constant zero bias and accelerometer noise The sum of them, where, Denote the zero bias of the x-axis accelerometer of INS 1, Denote the zero bias of the y-axis accelerometer of INS 1, Denote the zero bias of the z-axis accelerometer of INS 1, Indicates the gyro component error of INS2, modeled as a constant drift and gyro noise The sum of, where Indicates the x-axis gyro drift of INS2, Indicates the y-axis gyro drift of INS2, Indicates the z-axis gyro drift of INS2, Indicates the accelerometer component error of INS2, modeled as a constant bias and accelerometer noise The sum of, where Indicates the x-axis accelerometer bias of INS2, Indicates the y-axis accelerometer bias of INS2, Indicates the z-axis accelerometer bias of INS2;

[0027] (3.2) Determine the joint state equation:

[0028]

[0029] Among them, the state vector x(t) is expressed as:

[0030]

[0031] The noise distribution matrix G(t) and the noise matrix w(t) are expressed as:

[0032]

[0033] The state transition matrix F(t) is expressed as:

[0034]

[0035]

[0036]

[0037] In the formula, 0 i×j Represents the zero matrix of the i-th row and j-th column, λ t Represents the longitude of the carrier's location, ω ie Represents the magnitude of the earth's angular velocity of rotation, Respectively represent the specific force projections in the transverse east, transverse north, and vertical directions;

[0038] (3.3) Determine the state constraint observation equation:

[0039] Define the coordinate systems b 10 system and b 20 system when the transposition mechanisms of INS1 and INS2 are in the zero position. The attitude matrices output by the two sets of two-axis rotating INSs and is expressed as:

[0040]

[0041] wherein, is the direction cosine matrix from the body coordinate system b of Inertial Navigation 1 when the indexing mechanism is at the zero position 10 to the transverse geographic coordinate system, and respectively represent the attitude matrices of the indexing mechanisms of Inertial Navigation 1 and Inertial Navigation 2 relative to their zero positions at time t, represents b 20 system and b 10 system between the attitude matrix;

[0042] The difference expression for determining the attitude errors of two sets of two-axis rotating inertial navigations is:

[0043]

[0044] wherein, is the direction cosine matrix from the body coordinate system of Inertial Navigation 1 to the body coordinate system at time t when the indexing mechanism is at the zero position, represents the direction cosine matrix from the transverse geographic coordinate system to the body coordinate system of Inertial Navigation 2 at time t for Inertial Navigation 2. Considering the lever arm, the velocity and position outputs of Inertial Navigation 1 and Inertial Navigation 2 in the transverse geographic coordinate system are expressed as:

[0045]

[0046] wherein, and respectively represent the velocity information in the transverse geographic coordinate system output by Inertial Navigation 1 and Inertial Navigation 2, represents the position information in the transverse geographic coordinate system output by Inertial Navigation 1, represents the position information in the transverse geographic coordinate system output by Inertial Navigation 2, r t represents the true position of the carrier in the transverse geographic coordinate system, represents the position error output by Inertial Navigation 1 in the transverse geographic coordinate system, represents the position error output by Inertial Navigation 2 in the transverse geographic coordinate system, represents the velocity difference of Inertial Navigation 2 relative to Inertial Navigation 1 in the transverse geographic coordinate system caused by the external lever arm between the two sets of inertial navigations, l r12 represents the position difference of Inertial Navigation 2 relative to Inertial Navigation 1 caused by the external lever arm between the two sets of inertial navigations;

[0047] Therefore, the differences of the velocity and position vectors of the two sets of inertial navigation systems are expressed as:

[0048]

[0049] The observation equation is expressed as:

[0050] z(t) = H(t)x(t) + υ(t),

[0051] where z(t) represents the observation vector, H(t) represents the observation transition matrix, which are respectively expressed as:

[0052]

[0053] In the formula, I 3×3 represents the 3×3 identity matrix, I 2×2 represents the 2×2 identity matrix, and υ(t) is the noise vector corresponding to the observed quantity;

[0054] (4) Establish an adaptive error parameter estimation filter;

[0055] Use a strong tracking filter based on residual normalization to track and estimate the error state, and express the one-step prediction of the filter covariance matrix as:

[0056]

[0057] In the formula,

[0058]

[0059] And there is

[0060]

[0061] 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 process noise allocation 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 residual covariance matrix at time k, represents the residual covariance matrix at time k - 1, 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 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;

[0062] (5) Perform real-time status monitoring based on the error parameters output by the filter;

[0063] When the status of the inertial device is abnormal, the corresponding gyro drift or accelerometer zero bias changes, and the real-time health status monitoring of the inertial device is realized by analyzing the output of the monitoring filter;

[0064] Set a sliding data window 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:

[0065]

[0066] In the formula, 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 ;

[0067] Set a weighting coefficient α and perform iterative calculation on the mean of the historical sliding window:

[0068] Σ k = α·μ k +(1 - α)Σ k-1

[0069] In the formula, Σ k represents the mean of the sliding window after iteration at time k. Determine the upper and lower thresholds as follows:

[0070] T - = Σ k + k1σ k

[0071] T + = k2Σ k

[0072] In the formula, k1 and k2 are parameters to be adjusted, and k1 ≥ 1, k2 > 1. T + is the upper threshold, and T - is the lower threshold;

[0073] Establish the health status monitoring criterion as:

[0074]

[0075] In the formula, represents the i-th component of the estimated output of the filter at time k + 1, T + (i) and T -(i) The \(i\) -th component representing the real - time high threshold and low threshold to be obtained respectively. 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.

[0076] Based on the joint rotation mode given in step (1), make inertial navigation 1 and inertial navigation 2 in the normal navigation state, and construct a dual - inertial - navigation 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 inertial navigation system can be realized through step (5).

[0077] Further, in step (1), inertial navigation 1 and inertial navigation 2 rotate at different times according to the same rotation sequence, that is, the two inertial navigations rotate in an asynchronous manner according to the same rotation scheme.

[0078] Further, in step (1), inertial navigation 1 and inertial navigation 2 adopt different rotation sequences and rotate synchronously.

[0079] Further, the coordinate system adopted in step (2) includes but is not limited to the transverse geographical 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.

[0080] Further, the lever arm between inertial navigation 1 and inertial navigation 2 in step (2) is calibrated after the installation of the two sets of inertial navigations.

[0081] Further, the relative attitude of inertial navigation 1 and inertial navigation 2 when in the zero position in step (3) is determined after the alignment of the two sets of systems respectively after the installation of the two sets of inertial navigations, or is determined with the help of an external attitude reference.

[0082] Further, in step (3) and is determined by the angular position of the rotating frame output by the rotation mechanism.

[0083] Further, the method of the present invention is not only applicable to the case where both inertial navigation 1 and inertial navigation 2 are two - axis rotation - modulated inertial navigations, but also applicable to the cases where both inertial navigation 1 and inertial navigation 2 are three - axis rotation - modulated inertial navigations, inertial navigation 1 is a two - axis rotation - modulated inertial navigation or a three - axis rotation - modulated inertial navigation, inertial navigation 2 is a single - axis rotation - modulated inertial navigation, inertial navigation 1 is a single - axis rotation - modulated inertial navigation, inertial navigation 2 is a two - axis rotation - modulated inertial navigation or a three - axis rotation - modulated inertial navigation, and the redundant configuration cases of multiple sets of two - axis rotation - modulated inertial navigations and multiple sets of three - axis rotation - modulated inertial navigations.

[0084] In summary, the advantages and positive effects of the present invention are as follows: The present invention establishes a combined state Kalman filter under the transverse geographical coordinate system based on the earth ellipsoid model, solving the problem of the failure of the traditional inertial navigation system with the local horizontal coordinate system as the navigation coordinate system in the polar region; through the asynchronous rotation of two sets of two-axis rotating inertial navigation systems, the redundant information of the two inertial navigation systems is used 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, and is not restricted by the use environment, having important engineering significance. BRIEF DESCRIPTION OF THE DRAWINGS

[0085] Figure 1 is a flowchart provided by an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0086] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the 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.

[0087] In the high-latitude polar region, due to the rapid convergence of the meridians, there are large errors in the navigation scheme with the traditional geographical coordinate system as the navigation coordinate system. In the harsh natural geographical environment of the polar region, the inertial navigation system lacks reliable external reference information when applied in the polar region, and the method of monitoring the state of the inertial navigation system only relying on external auxiliary conditions is not applicable to the harsh environment of the polar region. To solve the above technical problems, the present invention proposes a method for monitoring the state of a dual-rotating inertial navigation system in the polar region, and the state monitoring method is as Figure 1 shown. The specific implementation manners are as follows:

[0088] A method for monitoring the state of a dual-rotating inertial navigation system in the polar region, the method comprising the following steps:

[0089] (1) Set the indexing 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 indexing orders are both the two-axis 16 order, and different indexing methods are adopted;

[0090] (2) Construct a transverse earth coordinate system based on the earth ellipsoid model;

[0091] Taking the intersection of the equator and the 90° east longitude meridian as the north pole under the e' system of the transverse earth coordinate system, defined as the transverse north pole, and the intersection of the equator and the 90° west longitude meridian as the south pole under the transverse earth coordinate system, defined as the transverse south pole, the meridian circle formed by the 0° meridian and the 180° meridian is defined as the transverse equator, taking the half great 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, and the conversion relationship e between the earth coordinate system is expressed as:

[0092]

[0093] 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. The longitude λ, latitude L defined in the Earth coordinate system and the transverse longitude λ t , transverse latitude L t The conversion relationship between them is expressed as:

[0094]

[0095] Based on the transverse latitude and longitude grid, the transverse geographic coordinate system is defined. The transverse north direction points to the transverse north pole, the normal of the location points upward to the celestial 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:

[0096]

[0097] In the formula, β represents the rotation angle between the geographic coordinate system and the transverse geographic coordinate system;

[0098] Determine the conversion relationship between β and longitude and latitude, transverse longitude and latitude:

[0099]

[0100] (3) Use the navigation information output by two sets of two-axis inertial navigation systems to establish a state space model in the transverse geographic coordinate system. The specific steps are as follows:

[0101] (3.1) Determine the system combined error equation in the transverse geographic coordinate system:

[0102]

[0103] Among them,

[0104]

[0105] In the formula, represents the attitude error angle of inertial navigation 1 in the transverse geographic coordinates, represents the eastward attitude error angle of inertial navigation 1 in the transverse geographic coordinate system, represents the northward attitude error angle of inertial navigation 1 in the transverse geographic coordinate system, represents the celestial attitude error angle of inertial navigation 1 in the transverse geographic coordinate system, represents the velocity error vector of inertial navigation 1 in the transverse geographic coordinate system, which are the eastward velocity error northward velocity error celestial velocity error represents the transverse latitude error of inertial navigation 1, represents the longitudinal and latitudinal errors of INS 1, and δh1 represents the altitude error of INS 1. represents the angular velocity error of the transverse geographic coordinate system relative to the inertial coordinate system, which is related to the transverse latitude error and velocity error of INS 1 in the transverse geographic coordinate system. represents the angular velocity error of the Earth's rotation related to the transverse latitude error of INS 1. represents the transfer angular velocity error related to the transverse latitude error and velocity error of INS 1 in the transverse geographic coordinate system. represents the direction cosine matrix from the body coordinate system of INS 1 to the transverse geographic coordinate system. represents the attitude error angle of INS 2 in the transverse geographic coordinates. represents the velocity error vector of INS 2 in the transverse geographic coordinate system, which are respectively the transverse eastward velocity error transverse northward velocity error transverse upward velocity error represents the transverse latitude error of INS 2. represents the longitudinal and latitudinal errors of INS 2, and δh2 represents the altitude error of INS 2. represents the angular velocity error of the transverse geographic coordinate system relative to the inertial coordinate system, which is related to the transverse latitude error and velocity error of INS 2 in the transverse geographic coordinate system. represents the angular velocity error of the Earth's rotation related to the transverse latitude error of INS 2. represents the transfer angular velocity error related to the transverse latitude error and velocity error of INS 2 in the transverse geographic coordinate system. represents the direction cosine matrix from the body coordinate system of INS 2 to the transverse geographic coordinate system, v t represents the velocity vector of the vehicle in the transverse geographic coordinate system. is the rotation angular velocity of the transverse geographic coordinate system relative to the inertial coordinate system. is the angular velocity vector of the Earth's rotation. is the rotation angular velocity of the transverse geographic coordinate system relative to the Earth coordinate system, g t represents the gravity vector at the location of the vehicle. respectively represent the velocities of the vehicle in the transverse eastward, transverse northward, and upward directions, L t and h are the transverse latitude and altitude at the location of the vehicle, R x is the radius of curvature in the transverse eastward direction at the location of the vehicle, R y is the radius of curvature in the transverse northward direction at the location of the vehicle. is the distortion rate at the location of the vehicle, R E and R N are respectively the radius of the prime vertical and the radius of the meridian at the location of the vehicle. represents the gyro component error of INS 1, modeled as a constant drift and gyro noise The sum, where 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 accelerometer assembly error of inertial navigation 1, modeled as a constant bias and accelerometer noise The sum, where represents the x-axis accelerometer bias of inertial navigation 1, represents the y-axis accelerometer bias of inertial navigation 1, represents the z-axis accelerometer bias of inertial navigation 1, represents the gyro assembly error of inertial navigation 2, modeled as a constant drift and gyro noise The sum, where 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 accelerometer assembly error of inertial navigation 2, modeled as a constant bias and accelerometer noise The sum, where represents the x-axis accelerometer bias of inertial navigation 2, represents the y-axis accelerometer bias of inertial navigation 2, represents the z-axis accelerometer bias of inertial navigation 2;

[0106] (3.2) Determine the joint state equation:

[0107]

[0108] where the state vector x(t) is expressed as:

[0109]

[0110] The noise distribution matrix G(t) and the noise matrix w(t) are expressed as:

[0111]

[0112] The state transition matrix F(t) is expressed as:

[0113]

[0114]

[0115]

[0116] In the formula, 0i×j Denote the zero matrix of the \(i\)-th row and \(j\)-th column, \(\lambda\) t Denote the longitude of the carrier's location, \(\omega\) ie Denote the magnitude of the earth's angular velocity of rotation, Respectively denote the specific force projections in the transverse eastward, transverse northward, and upward directions;

[0117] (3.3) Determine the state constraint observation equation:

[0118] Define the coordinate systems \(b\) and \(b\) when the indexing mechanisms of INS1 and INS2 are in the zero position 10 systems, and the attitude matrices output by the two sets of two-axis rotating INSs 20 are expressed as: and are expressed as:

[0119]

[0120] In the formula, is the direction cosine matrix from the body coordinate system \(b\) of INS1 to the horizontal geodetic coordinate system when the indexing mechanism is in the zero position, 10 to the horizontal geodetic coordinate system, and respectively represent the attitude matrices of the indexing mechanisms of INS1 and INS2 relative to their zero positions at time \(t\), represents the attitude matrix between the \(b\) 20 system and the \(b\) 10 system;

[0121] Determine the difference expression of the attitude errors of the two sets of two-axis rotating INSs as:

[0122]

[0123] In the formula, is the direction cosine matrix from the body coordinate system of INS1 to the body coordinate system at time \(t\) when the indexing mechanism is in the zero position, represents the direction cosine matrix from the horizontal geodetic coordinate system to the body coordinate system of INS2 at time \(t\). Considering the lever arm, determine the velocity and position outputs of INS1 and INS2 in the horizontal geodetic coordinate system as:

[0124]

[0125] In the formula, and respectively represent the velocity information in the horizontal geodetic coordinate system output by INS1 and INS2, represents the position information in the horizontal geodetic coordinate system output by INS1, represents the position information in the horizontal geodetic coordinate system output by INS2, \(r\) t represents the true position of the carrier in the horizontal geodetic coordinate system, Denotes the position error output by INS 1 in the transverse geographic coordinate system, Denotes the position error output by INS 2 in the transverse geographic coordinate system, Denotes the velocity difference of INS 2 relative to INS 1 caused by the external lever arm between the two INSs in the transverse geographic coordinate system, l r12 Denotes the position difference of INS 2 relative to INS 1 caused by the external lever arm between the two INSs;

[0126] Therefore, the differences in velocity and position vectors between the two INS systems are expressed as:

[0127]

[0128] The observation equation is expressed as:

[0129] z(t) = H(t)x(t) + υ(t),

[0130] where z(t) represents the observation vector, H(t) represents the observation transfer matrix, and they are respectively expressed as:

[0131]

[0132] In the formula, I 3×3 represents a 3×3 identity matrix, I 2×2 represents a 2×2 identity matrix, and υ(t) is the noise vector corresponding to the observed quantity;

[0133] (4) Establish an adaptive error parameter estimation filter;

[0134] Adopt a strong tracking filter based on residual normalization to track and estimate the error state, and express the one-step prediction of the filter covariance matrix as:

[0135]

[0136] In the formula,

[0137]

[0138] And there is

[0139]

[0140] 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 transfer matrix, P k-1 is the covariance matrix at time k - 1, G k-1 is the process noise allocation matrix at time k - 1, Q k-1 is the system noise matrix at time k - 1, and tr(·) is the matrix trace operator, Hk 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 residual covariance matrix at time k, represents the residual covariance matrix at time k-1, 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, used to eliminate the problem that the information asymmetry caused by the difference in the numerical value of the residual itself leads to a decrease in the response speed of the error state estimation;

[0141] (5) Based on the error parameters output by the filter, perform real-time state monitoring;

[0142] 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;

[0143] 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:

[0144]

[0145]

[0146] 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 the dimension;

[0147] Set a weighting coefficient α to perform iterative calculation on the mean of the historical sliding window:

[0148] Σ k = α·μ k +(1-α)Σ k-1

[0149] In the formula, Σ k represents the mean of the sliding window after iteration at time k, and determine the upper and lower thresholds as follows:

[0150] T - = Σ k + k1σ k

[0151] T + = k2Σ k

[0152] 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;

[0153] The health status monitoring criterion is established as follows:

[0154]

[0155] wherein, represents the i-th component of the estimated output of the filter at the (k + 1)-th moment, 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.

[0156] Based on the joint rotation mode given in step (1), make Inertial Navigation 1 and Inertial Navigation 2 in the normal navigation state, and construct a dual-inertial navigation 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 inertial navigation system can be realized through step (5).

[0157] The method of the present invention has no requirements on the motion state of the carrier, and online state monitoring can be realized whether the carrier is in a moored state or a moving state; there are no requirements on the environment where the carrier is located, and it is applicable in underwater environments and GNSS-denied environments.

[0158] As an improvement, the joint rotation sequence in step (1) is applicable to the online state monitoring between two sets of inertial navigation systems with a two-axis rotation mechanism. For the case where both Inertial Navigation 1 and Inertial Navigation 2 are three-axis rotation modulation inertial navigation systems, Inertial Navigation 1 is a two-axis rotation modulation inertial navigation system or a three-axis rotation modulation inertial navigation system, Inertial Navigation 2 is a single-axis rotation modulation inertial navigation system, Inertial Navigation 1 is a single-axis rotation modulation inertial navigation system, Inertial Navigation 2 is a two-axis rotation modulation inertial navigation system or a three-axis rotation modulation inertial navigation system, and the redundant configuration of multiple sets of two-axis rotation inertial navigation systems and multiple sets of three-axis rotation inertial navigation systems are all applicable.

[0159] As an improvement, in step (1), Inertial Navigation 1 and Inertial Navigation 2 rotate at different times according to the same rotation sequence, that is, the two inertial navigations rotate in an asynchronous manner according to the same rotation scheme.

[0160] As an improvement, in step (1), Inertial Navigation 1 and Inertial Navigation 2 adopt different rotation sequences and rotate synchronously.

[0161] As an improvement, the coordinate system adopted in the step (2) includes but is not limited to the transverse geographic coordinate system. The use of a grid coordinate system and other coordinate systems applicable to the polar region all fall within the scope of the present invention.

[0162] As an improvement, the lever arm between the inertial navigation 1 and the inertial navigation 2 in the step (2) is determined after the installation of the two sets of inertial navigation systems is completed.

[0163] As an improvement, the relative attitude of the inertial navigation 1 and the inertial navigation 2 when they are in the zero position in the step (3) is determined after the alignment of the two sets of systems respectively after the installation of the two sets of inertial navigation systems is completed, or is determined with the aid of an external attitude reference.

[0164] As an improvement, in the step (3) and is determined by the angular position of the rotating frame output by the indexing mechanism.

[0165] 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 idea of the present invention are within the protection scope of the present invention. Several improvements and refinements, etc. 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-rotation inertial navigation polar region state monitoring method, characterized in that The method includes the following steps: (1) Set the indexing order of two sets of biaxial rotation 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 biaxial 16 order, and different indexing methods are adopted; (2) Construct a transverse earth coordinate system based on the earth ellipsoid model; Taking the intersection point of the equator and the 90° east longitude meridian as the north pole in the transverse Earth coordinate system e' system, which is defined as the transverse north pole, and the intersection point of the equator and the 90° west longitude meridian as the south pole in the transverse Earth coordinate system, which is defined as the transverse south pole. The meridian circle formed by the 0° meridian and the 180° meridian is defined as the transverse equator. Taking the half great 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, the conversion relationship between the Earth coordinate system e and the transverse Earth coordinate system e′ is expressed as: 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 meridian and latitude grid. The transverse north direction points to the transverse north pole, the normal direction at the location is upward as the celestial 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: 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, longitude and latitude, and transverse longitude and latitude: (3) Use the navigation information output by the two sets of biaxial rotation 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 in the transverse geographic coordinate system: Among them, In the formula, represents the attitude error angle of inertial navigation 1 in the transverse geographical coordinate system, represents the eastward attitude error angle of inertial navigation 1 in the transverse geographical coordinate system, represents the northward attitude error angle of inertial navigation 1 in the transverse geographical coordinate system, represents the upward attitude error angle of inertial navigation 1 in the transverse geographical coordinate system, represents the velocity error vector of inertial navigation 1 in the transverse geographical coordinate system, which are the transverse eastward velocity error transverse northward velocity error transverse upward velocity error represents the transverse latitude error of inertial navigation 1, represents the transverse longitude error of inertial navigation 1, and δh1 represents the altitude error of inertial navigation 1, represents the angular velocity error of the transverse geographical coordinate system relative to the inertial coordinate system related to the transverse latitude error of inertial navigation 1 and the velocity error in the transverse geographical coordinate system, represents the angular velocity error of the Earth's rotation related to the transverse latitude error of inertial navigation 1, represents the transfer angular velocity error related to the transverse latitude error of inertial navigation 1 and the velocity error in the transverse geographical coordinate system, represents the direction cosine matrix from the body coordinate system of inertial navigation 1 to the transverse geographical coordinate system, represents the attitude error angle of inertial navigation 2 in the transverse geographical coordinate system, represents the velocity error vector of inertial navigation 2 in the transverse geographical coordinate system, which are the transverse eastward velocity error transverse northward velocity error transverse upward velocity error represents the transverse latitude error of inertial navigation 2, represents the transverse longitude error of inertial navigation 2, and δh2 represents the altitude error of inertial navigation 2, represents the angular velocity error of the transverse geographical coordinate system relative to the inertial coordinate system related to the transverse latitude error of inertial navigation 2 and the velocity error in the transverse geographical coordinate system, represents the angular velocity error of the Earth's rotation related to the transverse latitude error of inertial navigation 2, represents the transfer angular velocity error related to the transverse latitude error of inertial navigation 2 and the velocity error in the transverse geographical coordinate system, represents the direction cosine matrix from the body coordinate system of inertial navigation 2 to the transverse geographical coordinate system, v t represents the velocity vector of the carrier in the transverse geographical coordinate system, is the rotational angular velocity of the transverse geographical coordinate system relative to the inertial coordinate system, is the Earth's rotation angular velocity vector, 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 location of the carrier, Represent the velocities of the vehicle in the transverse eastward, transverse northward, and upward directions respectively. L t , h are the transverse latitude and altitude of the vehicle's location, R x is the radius of curvature in the transverse eastward direction of the vehicle's location, R y is the radius of curvature in the transverse northward direction of the vehicle's location, is the twist rate of the vehicle's location, R E and R N are the radius of the prime vertical and the radius of the meridian of the vehicle's location respectively, Represents the gyro component error of Inertial Navigation 1, modeled as a constant drift and gyro noise The sum of them, where, 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, δf b1 Represents the accelerometer component error of Inertial Navigation 1, modeled as a constant zero bias and accelerometer noise The sum of them, where, Represents the x-axis accelerometer zero bias of Inertial Navigation 1, Represents the y-axis accelerometer zero bias of Inertial Navigation 1, Represents the z-axis accelerometer zero bias of Inertial Navigation 1, Represents the gyro component error of Inertial Navigation 2, modeled as a constant drift and gyro noise The sum of them, where, 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 accelerometer component error of Inertial Navigation 2, modeled as a constant zero bias and accelerometer noise The sum of them, where, Represents the x-axis accelerometer zero bias of Inertial Navigation 2, Represents the y-axis accelerometer zero bias of Inertial Navigation 2, Represents the z-axis accelerometer zero bias of Inertial Navigation 2; (3.2) Determine the combined state equation: Among them, the state vector x(t) is expressed as: The noise distribution matrix G(t) and the noise matrix w(t) are expressed as: The state transition matrix F(t) is expressed as: In the formula, 0 i×j represents the zero matrix of the i-th row and j-th column, λ t represents the longitude of the carrier's location, ω ie represents the magnitude of the earth's angular velocity of rotation, respectively represent the specific force projections in the transverse eastward, transverse northward, and upward directions; (3.3) Determine the state constraint observation equation: Define the coordinate systems b 10 system and bsystem when the indexing mechanisms of INS1 and INS2 are at the zero position. The attitude matrices 20 and output by the two sets of two-axis rotating INSs are expressed as: Wherein, is the direction cosine matrix from the body coordinate system b of the inertial navigation 1 when the indexing mechanism is at the zero position 10 to the transverse geographic coordinate system, and respectively represent the attitude matrices of the indexing mechanisms of the inertial navigation 1 and the inertial navigation 2 relative to their zero positions at time t, represents 20 the attitude matrix between the b 10 system and the b system; Determine the difference expression of the attitude errors of the two sets of biaxial rotation inertial navigations: In the formula, is the direction cosine matrix from the inertial navigation 1 body coordinate system to the body coordinate system at time t when the indexing mechanism is at the zero position. represents the direction cosine matrix from the transverse geographical coordinate system to the inertial navigation 2 body coordinate system at time t. Considering the lever arm, the velocity and position outputs of inertial navigation 1 and inertial navigation 2 in the transverse geographical coordinate system are expressed as: Wherein, and respectively represent the velocity information in the transverse geographic coordinate system output by inertial navigation 1 and inertial navigation 2, represents the position information in the transverse geographic coordinate system output by inertial navigation 1, represents the position information in the transverse geographic coordinate system output by inertial navigation 2, r t represents the true position of the vehicle in the transverse geographic coordinate system, represents the position error output by inertial navigation 1 in the transverse geographic coordinate system, represents the position error output by inertial navigation 2 in the transverse geographic coordinate system, represents the velocity difference of inertial navigation 2 relative to inertial navigation 1 in the transverse geographic coordinate system caused by the external lever arm between the two sets of inertial navigations, l r12 represents the position difference of inertial navigation 2 relative to inertial navigation 1 caused by the external lever arm between the two sets of inertial navigations; Therefore, the differences in the velocities and position vectors of the two inertial navigation systems are expressed as: The observation equation is expressed as: z(t) = H(t)x(t) + υ(t), where z(t) represents the observation vector, and H(t) represents the observation transition matrix, which are respectively expressed as: where, I 3×3 represents a 3×3 identity matrix, I 2×2 represents a 2×2 identity matrix, and υ(t) is the noise vector corresponding to the observed quantity; (4) Establish an adaptive error parameter estimation filter; Adopt a strong tracking filter based on residual normalization to track and estimate the error state, and express the one-step prediction of the filter covariance matrix as: In the formula, And there is where λ k is the fading factor, P k / k-1 is the one-step prediction covariance matrix, Φ k / k-1 represents the one-step state transition matrix, P k-1 is the covariance matrix at time k-1, G k-1 is the process noise allocation 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 residual covariance matrix at time k, represents the residual covariance matrix at time k-1, 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, used to eliminate the problem that the information asymmetry caused by the difference in the numerical 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 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 the 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, the system is output as fault-free; 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-rotation inertial navigation polar region state monitoring method according to claim 1, wherein The combined indexing order in step (1) is a triaxial rotation modulation inertial navigation for both Inertial Navigation 1 and Inertial Navigation 2. Inertial Navigation 1 is a biaxial rotation modulation inertial navigation or a triaxial rotation modulation inertial navigation, Inertial Navigation 2 is a uniaxial rotation modulation inertial navigation, Inertial Navigation 1 is a uniaxial rotation modulation inertial navigation, Inertial Navigation 2 is a biaxial rotation modulation inertial navigation or a triaxial rotation modulation inertial navigation. The cases of redundant configuration of multiple sets of biaxial rotation inertial navigations and multiple sets of triaxial rotation inertial navigations are all applicable.

3. A dual-rotation inertial navigation polar region state monitoring method according to claim 1, characterized in that 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.

4. A dual-rotation inertial navigation polar region state monitoring method according to claim 1, characterized in that, In step (1), Inertial Navigation 1 and Inertial Navigation 2 adopt different indexing orders and rotate synchronously.

5. A dual-rotation inertial navigation polar region state monitoring method according to claim 1, characterized in that The polar coordinate system in step (2) adopts a grid coordinate system.

6. The dual-rotation inertial navigation polar region state monitoring method according to claim 1, characterized in that, The lever arm between Inertial Navigation 1 and Inertial Navigation 2 in step (2) is calibrated and determined after the installation of the two inertial navigations.

7. The dual-rotation inertial navigation polar region state monitoring method according to claim 1, characterized in that The relative attitude of Inertial Navigation 1 and Inertial Navigation 2 when they are at zero position in 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 with the help of an external attitude reference.

8. The dual-rotation inertial navigation polar region state monitoring method according to claim 1, wherein In the said step (3) and is determined by the angular position of the rotating frame output by the indexing mechanism.

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