A method for monitoring the external state of a redundant dual-axis rotating inertial navigation system

Abstract

This invention addresses the limitation of online monitoring of inertial navigation systems (INS) when there is no external reference information. It discloses a method for monitoring the external state of a redundant dual-axis rotating INS, applicable to platforms with multiple INS systems equipped with rotation mechanisms. This invention establishes a joint error state Kalman filter through joint rotation of the two INS systems, utilizing the geometric constraints between the two INS systems—relative attitude, velocity, and position—as observations. A strong tracking filter based on residual normalization is used to estimate and monitor the gyroscope drift and accelerometer bias of the two systems. Thresholds are updated in real-time based on the error parameters monitored online to evaluate the device state. This method is completely autonomous, requiring no external reference information, only information from the two INS systems as input. The state monitoring process uses open-loop filtering, and the algorithm does not affect the normal operation of the system.

Description

Technical Field

[0001] This invention belongs to the field of navigation technology and relates to a method for monitoring the state of inertial navigation systems. In particular, it relates to a method for monitoring the state of a redundant dual-axis rotating inertial navigation system in the field, which is applicable to the state monitoring of two or more inertial navigation systems with dual-axis or tri-axis indexing mechanisms. Background Technology

[0002] With the development of the shipping industry, ship navigation technology is evolving towards longer endurance and higher reliability. Inertial navigation systems, due to their independence and autonomy, have become an indispensable part of modern ship navigation technology. If an inertial navigation system provides erroneous information, it will seriously affect the navigation safety of the vessel; therefore, inertial navigation condition monitoring technology has become an indispensable part of navigation research.

[0003] Field condition monitoring technology generally relies on externally provided basic reference information. Determining the reliability of the current inertial navigation system by combining external reference data such as velocity and position with the inertial navigation system's output information has been a key research focus in recent years. However, field condition monitoring has requirements regarding the vehicle's motion state and external reference information. In situations lacking external reference information, such as underwater environments or GNSS-denied environments, the use of field condition monitoring technology is severely limited.

[0004] Existing long-endurance vehicles typically carry multiple inertial navigation systems (INS) with shifting mechanisms, such as shipboard redundant dual-axis rotary modulation INS. Recent research has shown that fusing redundant information from multiple INS systems can effectively improve the observability of certain error states. By building an information fusion model of multiple INS systems and designing a reasonable state monitoring filter algorithm, it is possible to identify abnormal INS information. Furthermore, traditional state monitoring methods often rely on expert experience or historical data analysis to set fixed thresholds, which are easily affected by equipment dynamics, environmental noise, and changes in operating conditions. When the operating environment of the INS changes significantly, fixed thresholds may lead to a significant increase in the risk of false alarms or missed detections.

[0005] This invention addresses the problem of inertial navigation system (INS) state monitoring in the absence of external reference information by proposing a method for monitoring the external state of redundant dual-axis rotating INS systems. This method is applicable to platforms equipped with multiple INS systems featuring rotation mechanisms. Based on the navigation information of two INS systems operating in dual-axis rotation modulation mode, a joint state Kalman filter for the two INS systems is constructed, utilizing the geometric constraints between the two INS systems—relative attitude, relative velocity, and relative position—as observations. A strong tracking filter based on residual normalization is employed to perform online tracking estimation of gyroscope drift and accelerometer bias in both systems. Furthermore, a state monitoring threshold is adaptively constructed based on the online estimated error parameters to achieve online state monitoring of the redundant INS system. This method is completely autonomous, requiring no external reference information; it only needs the navigation information from the two INS systems as input. 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] This invention proposes an external field state monitoring method for redundant dual-axis rotating inertial navigation systems. It is not affected by the absolute error of the reference inertial navigation system and can realize autonomous state monitoring at the device level of the redundant dual-axis rotating inertial navigation system, which has important engineering practical value.

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

[0008] A method for monitoring the external state of a redundant dual-axis rotating inertial navigation system, the method comprising the following steps:

[0009] (1) Set the rotation order of two sets of dual-axis rotating inertial navigation systems. Define the two redundant inertial navigation systems as Inertial Navigation 1 and Inertial Navigation 2. The rotation order of both is dual-axis 16 sequence, and different rotation methods are used.

[0010] (2) Define two sets of inertial navigation system volume coordinate systems. The volume coordinate system b1 of inertial navigation system 1 and the volume coordinate system b2 of inertial navigation system 2 are both defined as "right-front-up". The navigation coordinate system n is the local geographic coordinate system, defined as "east-north-sky". Using the attitude, velocity, and position information output by the two dual-axis rotating inertial navigation systems, establish a state-space model. The specific steps are as follows:

[0011] (2.1) Determine the joint error equation of the system:

[0012]

[0013] in,

[0014]

[0015] In the formula, This represents the attitude error vector of inertial navigation system 1. This indicates the eastward attitude error of inertial navigation system 1. This indicates the northward attitude error of inertial navigation system 1. Indicates the azimuth attitude error of the inertial navigation system, v n This represents the actual speed of the vehicle in the navigation coordinate system. Let δL1 represent the velocity error vector of inertial navigation system 1, δλ1 represent the latitude error of inertial navigation system 1, and δh1 represent the altitude error of inertial navigation system 1. This indicates the eastward velocity error of inertial navigation system 1. This indicates the northbound velocity error of inertial navigation system 1. This indicates the azimuth velocity error of the inertial navigation system. This represents the angular velocity error of the navigation coordinate system relative to the inertial coordinate system, which is related to the latitude and velocity errors of the inertial navigation system. This represents the Earth's rotational angular velocity error related to the latitude error of the inertial navigation system. This indicates the transfer angular velocity error related to the latitude and velocity errors of the inertial navigation system. This represents the direction cosine matrix from the inertial navigation system's body coordinate system to the navigation coordinate system. This represents the attitude error vector of inertial navigation system 2. This represents the eastward attitude error of inertial navigation system 2. This represents the northward attitude error of inertial navigation system 2. This represents the upward attitude error of inertial navigation system 2. Let δL represent the velocity error vector of inertial navigation system 2, δL2 represent the latitude error of inertial navigation system 2, δλ2 represent the longitude error of inertial navigation system 2, and δh2 represent the altitude error of inertial navigation system 2. This indicates the eastward velocity error of inertial navigation system 2. This indicates the northbound velocity error of the inertial navigation system 2. This indicates the 2-axis velocity error of the inertial navigation system. This represents the angular velocity error of the navigation coordinate system relative to the inertial coordinate system, which is related to the inertial navigation 2-dimensional error and velocity error. This represents the Earth's rotational angular velocity error related to the latitude error of the inertial navigation system. This indicates the transfer angular velocity error related to the inertial navigation system's 2-dimensional error and velocity error. This represents the direction cosine matrix from the inertial navigation system's two-body coordinate system to the navigation coordinate system. Let be the angular velocity of the navigation coordinate system relative to the inertial coordinate system. Let be the Earth's rotational angular velocity vector. f is the angular velocity of the navigation coordinate system relative to the Earth coordinate system. n To compare the projection of the force in the navigation coordinate system, v E R represents the eastward velocity of the carrier, L and h represent the latitude and altitude of the carrier's location, and R represents the eastward velocity of the carrier. E and R NThese are the radii of the east-west circle and the meridian circle, respectively, representing the location of the carrier. The error of the gyroscope component in inertial navigation system 1 is modeled as a constant drift. and gyroscope noise The sum of, among which, This indicates the x-axis gyroscope drift of inertial navigation system 1. This indicates the y-axis gyroscope drift of inertial navigation system 1. This indicates the z-axis gyroscope drift of inertial navigation system 1. The error of the accelerometer component of inertial navigation system 1 is modeled as a constant zero bias. and accelerometer noise The sum of, among which, This indicates that the x-axis accelerometer of inertial navigation system 1 has zero bias. This indicates that the y-axis accelerometer of inertial navigation system 1 has zero bias. This indicates that the z-axis accelerometer of inertial navigation system 1 has zero bias. The error of the gyroscope component in Inertial Navigation System 2 is modeled as a constant drift. and gyroscope noise The sum of, among which, This indicates the x-axis gyroscope drift of inertial navigation system 2. This indicates the y-axis gyroscope drift of inertial navigation system 2. This indicates the z-axis gyroscope drift of inertial navigation system 2. The error of the accelerometer component in inertial navigation system 2 is modeled as a constant zero bias. and accelerometer noise The sum of, among which, This indicates that the x-axis accelerometer of inertial navigation system 2 has zero bias. This indicates that the y-axis accelerometer of inertial navigation system 2 has zero bias. This indicates that the z-axis accelerometer of inertial navigation system 2 has zero bias;

[0016] (2.2) Determine the joint state equations:

[0017]

[0018] in,

[0019]

[0020]

[0021]

[0022] In the formula, F(t) represents the system state matrix, 0 i×j V represents the zero matrix in row i and column j. N v U λ represents the northward and celestial velocities of the carrier, λ represents the longitude of the carrier's location, and ω represents the velocities of the carrier. ief represents the Earth's angular velocity of rotation. E f N f U These represent the projections of the force in the east, north, and sky directions, respectively.

[0023] The state vector x(t) is represented as:

[0024]

[0025] The noise distribution matrix G(t) and the noise matrix w(t) are expressed as follows:

[0026]

[0027] (2.3) Determine the state constraint observation equations:

[0028] Define the coordinate system of inertial navigation system 1 and inertial navigation system 2 when the indexing mechanism is in the zero position as s. 10 System and s 20 The coordinate system is b, and the attitude matrices output by the two sets of dual-axis rotating inertial navigation systems are shown. and Represented as:

[0029]

[0030] In the formula, When the indexing mechanism is in the zero position, the inertial navigation coordinate system s 10 The direction cosine matrix to the navigation coordinate system, and Let represent the attitude matrices of the rotation mechanisms of inertial navigation system 1 and inertial navigation system 2 at time t relative to their zero position. s 20 System and s 10 Attitude matrix between systems;

[0031] The expression for the difference in attitude error between the two sets of dual-axis rotating inertial navigation systems is determined as follows:

[0032]

[0033] Considering the lever arm, the velocity and position outputs of inertial navigation systems 1 and 2 are expressed as follows:

[0034]

[0035] In the formula, and These represent the velocity information in the navigation coordinate system output by inertial navigation system 1 and inertial navigation system 2, respectively. n This represents the actual speed of the vehicle in the navigation coordinate system. This represents the difference between the velocity output by inertial navigation system 1 in the navigation coordinate system and the actual velocity of the vehicle. This represents the difference between the velocity output by inertial navigation system 2 in the navigation coordinate system and the actual velocity of the vehicle. This indicates the position information output by inertial navigation system 1. This represents the position information output by inertial navigation system 2, r n This represents the actual position of the carrier in the navigation coordinate system. This represents the difference between the position output by inertial navigation system 1 in the navigation coordinate system and the actual position of the vehicle. This represents the difference between the position output by inertial navigation system 2 in the navigation coordinate system and the actual position of the vehicle. The value of l represents the velocity difference between inertial navigation system 2 and inertial navigation system 1 caused by the outer arm between the two inertial navigation systems. r12 This represents the position difference of inertial navigation system 2 relative to inertial navigation system 1 caused by the outer arm between the two inertial navigation systems.

[0036] Therefore, the difference between the velocity error and position error of the two inertial navigation systems can be expressed as:

[0037]

[0038] The observation equation is expressed as:

[0039] z(t)=H(t)x(t)+υ(t),

[0040] Where z(t) represents the observation vector and H(t) represents the observation transition matrix, they are expressed as follows:

[0041]

[0042] In the formula, I 3×3 I represents a 3x3 identity matrix. 2×2 Let υ(t) represent a 2x2 identity matrix, where υ(t) is the noise vector corresponding to the observation.

[0043] (3) Establish an adaptive error parameter estimation filter;

[0044] A strong tracking filter based on residual normalization is used to track and estimate the error state. The one-step prediction of the filter covariance matrix is ​​expressed as:

[0045]

[0046] In the formula,

[0047]

[0048] And there are

[0049]

[0050]

[0051] Where, λ k P is the fading factor. k / k-1 To predict the covariance matrix in one step, Φ k / k-1 P represents the state transition matrix in one step. k-1 Let G be the covariance matrix at time k-1. k-1 The process noise assignment matrix at time k-1, Q k-1 Let H be the system noise matrix at time k-1, tr(·) be the matrix trace operator, and H be the system noise matrix at time k-1. k Let R be the system observation matrix at time k. k Let l be the observation noise matrix at time k. k λ is a weakening factor. 0,k The fading factor is calculated at time k. Let k represent the residual covariance matrix at time k. Let represent the residual covariance matrix at time k-1, ρ be the forgetting factor (taken as 0.95 ≤ ρ ≤ 0.995), γ0 represent the innovation at time 0, and γ k Represents the information at time k, and η is the normalization parameter used to eliminate the problem of reduced response speed of error state estimation caused by information asymmetry due to differences in the residual values ​​themselves.

[0052] (4) Real-time status monitoring is performed based on the error parameters output by the filter;

[0053] When the inertial device is in an abnormal state, the corresponding gyroscope drift or accelerometer zero bias changes. Real-time health status monitoring of the inertial device is achieved by analyzing the output of the monitoring filter.

[0054] A data window is set to slide over time, with a length of N. At time k, the filter output information contained in the sliding window is... The statistical characteristics of the calculated data are as follows:

[0055]

[0056] In the formula, μ k and Let represent the mean and variance of the real-time estimated parameters of the filter within the sliding window at time k, respectively, and their dimensions are and . Same dimension;

[0057] Set a weighting coefficient α and iteratively calculate the mean of the historical sliding windows:

[0058] Σ k =α·μ k +(1-α)Σ k-1

[0059] In the formula, Σ k The sliding window mean after iterations at time k is used to determine the two thresholds as follows:

[0060] T - =Σ k +k1σ k

[0061] T + =k2Σ k

[0062] In the formula, k1 and k2 are the parameters to be adjusted, and k1≥1 and k2>1, T + For a high threshold, T - Low threshold;

[0063] The guidelines for establishing health status monitoring are as follows:

[0064]

[0065] In the formula, T represents the i-th component of the filter's estimated output at time k+1. + (i) and T - (i) represents the i-th component of the desired real-time high threshold and low threshold, respectively. The monitoring threshold of each inertial device is updated in real time according to the sliding window. When all error parameter values ​​estimated by the filter are less than the low threshold, the output system is fault-free. When the i-th error parameter value estimated by the filter is greater than the low threshold but less than the high threshold, a fault warning is issued. When the i-th error parameter value estimated by the filter is greater than the high threshold, the output device i is faulty.

[0066] Based on the joint rotation method given in step (1), inertial navigation system 1 and inertial navigation system 2 are in normal navigation state. A dual inertial navigation state space model is constructed through steps (2) and (3). Based on the error parameters output by the filter, the state monitoring of the inertial navigation system can be realized through step (4).

[0067] Furthermore, in step (1), inertial navigation system 1 and inertial navigation system 2 rotate at different times according to the same rotation sequence, that is, the two inertial navigation systems rotate asynchronously according to the same rotation scheme.

[0068] Furthermore, in step (1), inertial navigation system 1 and inertial navigation system 2 adopt different rotation sequences and rotate synchronously.

[0069] Furthermore, the relative attitude of inertial navigation system 1 and inertial navigation system 2 when they are at zero position in step (2) After the two inertial navigation systems are installed, the attitude can be determined by aligning the two systems separately or by using an external attitude reference.

[0070] Furthermore, in step (2), the lever arm between inertial navigation system 1 and inertial navigation system 2 is calibrated and determined after the two sets of inertial navigation systems are installed.

[0071] Furthermore, in step (2) and The angular position of the rotating frame is determined by the output of the indexing mechanism.

[0072] Furthermore, the method of the present invention is not only applicable to the case where both inertial navigation system 1 and inertial navigation system 2 are dual-axis rotation modulation inertial navigation systems, but also applicable to the case where both inertial navigation system 1 and inertial navigation system 2 are triaxial rotation modulation inertial navigation systems, inertial navigation system 1 is a dual-axis rotation modulation inertial navigation system or a triaxial rotation modulation inertial navigation system, inertial navigation system 2 is a single-axis rotation modulation inertial navigation system, and multiple sets of dual-axis rotation inertial navigation systems or multiple sets of triaxial rotation inertial navigation systems are redundantly configured.

[0073] In summary, the advantages and positive effects of this invention are as follows: This invention achieves online monitoring of the inertial navigation system at the device level by asynchronously rotating two sets of dual-axis rotating inertial navigation systems and utilizing the redundant information of the two inertial navigation systems. The method proposed in this invention is completely autonomous, does not rely on any external reference information, is not limited by the usage environment, and can improve the accuracy of inertial device status monitoring on mobile platforms, which has important engineering practical significance. Attached Figure Description

[0074] Figure 1 This is a flowchart of the method provided in the example of the present invention;

[0075] In the picture and These represent the attitude matrices output by inertial navigation system 1 and inertial navigation system 2, respectively. and These represent the velocities output by inertial navigation systems 1 and 2, respectively, in the navigation system. and These represent the positions output by inertial navigation system 1 and inertial navigation system 2, respectively. Detailed Implementation

[0076] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0077] Existing inertial navigation system (INS) field state monitoring schemes require both the carrier's motion state and external reference information. However, for environments without external reference information, such as underwater environments, current general-purpose schemes cannot meet these requirements. To address this issue, this invention, based on the current practice of carriers typically carrying multiple INS systems, proposes a redundant dual-axis rotating INS field state monitoring method. The method is as follows: Figure 1 As shown. The specific implementation method is as follows:

[0078] To solve the above-mentioned technical problems, the solution proposed by this invention is as follows:

[0079] A method for monitoring the external state of a redundant dual-axis rotating inertial navigation system, the method comprising the following steps:

[0080] (1) Set the rotation order of two sets of dual-axis rotating inertial navigation systems. Define the two redundant inertial navigation systems as Inertial Navigation 1 and Inertial Navigation 2. The rotation order of both is dual-axis 16 sequence, and different rotation methods are used.

[0081] (2) Define two sets of inertial navigation system volume coordinate systems. The volume coordinate system b1 of inertial navigation system 1 and the volume coordinate system b2 of inertial navigation system 2 are both defined as "right-front-up". The navigation coordinate system n is the local geographic coordinate system, defined as "east-north-sky". Using the attitude, velocity, and position information output by the two dual-axis rotating inertial navigation systems, establish a state-space model. The specific steps are as follows:

[0082] (2.1) Determine the joint error equation of the system:

[0083]

[0084] in,

[0085]

[0086] In the formula, This represents the attitude error vector of inertial navigation system 1. This indicates the eastward attitude error of inertial navigation system 1. This indicates the northward attitude error of inertial navigation system 1. Indicates the azimuth attitude error of the inertial navigation system, v n This represents the actual speed of the vehicle in the navigation coordinate system. Let δL1 represent the velocity error vector of inertial navigation system 1, δλ1 represent the latitude error of inertial navigation system 1, and δh1 represent the altitude error of inertial navigation system 1. This indicates the eastward velocity error of inertial navigation system 1. This indicates the northbound velocity error of inertial navigation system 1. This indicates the azimuth velocity error of the inertial navigation system. This represents the angular velocity error of the navigation coordinate system relative to the inertial coordinate system, which is related to the latitude and velocity errors of the inertial navigation system. This represents the Earth's rotational angular velocity error related to the latitude error of the inertial navigation system. This indicates the transfer angular velocity error related to the latitude and velocity errors of the inertial navigation system. This represents the direction cosine matrix from the inertial navigation system's body coordinate system to the navigation coordinate system. This represents the attitude error vector of inertial navigation system 2. This represents the eastward attitude error of inertial navigation system 2. This represents the northward attitude error of inertial navigation system 2. This represents the upward attitude error of inertial navigation system 2. Let δL represent the velocity error vector of inertial navigation system 2, δL2 represent the latitude error of inertial navigation system 2, δλ2 represent the longitude error of inertial navigation system 2, and δh2 represent the altitude error of inertial navigation system 2. This indicates the eastward velocity error of inertial navigation system 2. This indicates the northbound velocity error of the inertial navigation system 2. This indicates the 2-axis velocity error of the inertial navigation system. This represents the angular velocity error of the navigation coordinate system relative to the inertial coordinate system, which is related to the inertial navigation 2-dimensional error and velocity error. This represents the Earth's rotational angular velocity error related to the latitude error of the inertial navigation system. This indicates the transfer angular velocity error related to the inertial navigation system's 2-dimensional error and velocity error. This represents the direction cosine matrix from the inertial navigation system's two-body coordinate system to the navigation coordinate system. Let be the angular velocity of the navigation coordinate system relative to the inertial coordinate system. Let be the Earth's rotational angular velocity vector. f is the angular velocity of the navigation coordinate system relative to the Earth coordinate system. n To compare the projection of the force in the navigation coordinate system, v E R represents the eastward velocity of the carrier, L and h represent the latitude and altitude of the carrier's location, and R represents the eastward velocity of the carrier. E and R N These are the radii of the east-west circle and the meridian circle, respectively, representing the location of the carrier. The error of the gyroscope component in inertial navigation system 1 is modeled as a constant drift. and gyroscope noise The sum of, among which, This indicates the x-axis gyroscope drift of inertial navigation system 1. This indicates the y-axis gyroscope drift of inertial navigation system 1. This indicates the z-axis gyroscope drift of inertial navigation system 1. The error of the accelerometer component of inertial navigation system 1 is modeled as a constant zero bias. and accelerometer noise The sum of, among which, This indicates that the x-axis accelerometer of inertial navigation system 1 has zero bias. This indicates that the y-axis accelerometer of inertial navigation system 1 has zero bias. This indicates that the z-axis accelerometer of inertial navigation system 1 has zero bias. The error of the gyroscope component in Inertial Navigation System 2 is modeled as a constant drift. and gyroscope noise The sum of, among which, This indicates the x-axis gyroscope drift of inertial navigation system 2. This indicates the y-axis gyroscope drift of inertial navigation system 2. This indicates the z-axis gyroscope drift of inertial navigation system 2. The error of the accelerometer component in inertial navigation system 2 is modeled as a constant zero bias. and accelerometer noise The sum of, among which, This indicates that the x-axis accelerometer of inertial navigation system 2 has zero bias. This indicates that the y-axis accelerometer of inertial navigation system 2 has zero bias. This indicates that the z-axis accelerometer of inertial navigation system 2 has zero bias;

[0087] (2.2) Determine the joint state equations:

[0088]

[0089] in,

[0090]

[0091]

[0092]

[0093] In the formula, F(t) represents the system state matrix, 0 i×j V represents the zero matrix in row i and column j. N v U λ represents the northward and celestial velocities of the carrier, λ represents the longitude of the carrier's location, and ω represents the velocities of the carrier. ie f represents the Earth's angular velocity of rotation. E f N f U These represent the projections of the force in the east, north, and sky directions, respectively.

[0094] The state vector x(t) is represented as:

[0095]

[0096] The noise distribution matrix G(t) and the noise matrix w(t) are expressed as follows:

[0097]

[0098] (2.3) Determine the state constraint observation equations:

[0099] Define the coordinate system of inertial navigation system 1 and inertial navigation system 2 when the indexing mechanism is in the zero position as s. 10 System and s 20 The coordinate system is b, and the attitude matrices output by the two sets of dual-axis rotating inertial navigation systems are shown. and Represented as:

[0100]

[0101] In the formula, When the indexing mechanism is in the zero position, the inertial navigation coordinate system s10 The direction cosine matrix to the navigation coordinate system, and Let represent the attitude matrices of the rotation mechanisms of inertial navigation system 1 and inertial navigation system 2 at time t relative to their zero position. s 20 System and s 10 Attitude matrix between systems;

[0102] The expression for the difference in attitude error between the two sets of dual-axis rotating inertial navigation systems is determined as follows:

[0103]

[0104] Considering the lever arm, the velocity and position outputs of inertial navigation systems 1 and 2 are expressed as follows:

[0105]

[0106] In the formula, and These represent the velocity information in the navigation coordinate system output by inertial navigation system 1 and inertial navigation system 2, respectively. n This represents the actual speed of the vehicle in the navigation coordinate system. This represents the difference between the velocity output by inertial navigation system 1 in the navigation coordinate system and the actual velocity of the vehicle. This represents the difference between the velocity output by inertial navigation system 2 in the navigation coordinate system and the actual velocity of the vehicle. This indicates the position information output by inertial navigation system 1. This represents the position information output by inertial navigation system 2, r n This represents the actual position of the carrier in the navigation coordinate system. This represents the difference between the position output by inertial navigation system 1 in the navigation coordinate system and the actual position of the vehicle. This represents the difference between the position output by inertial navigation system 2 in the navigation coordinate system and the actual position of the vehicle. The value of l represents the velocity difference between inertial navigation system 2 and inertial navigation system 1 caused by the outer arm between the two inertial navigation systems. r12 This represents the position difference of inertial navigation system 2 relative to inertial navigation system 1 caused by the outer arm between the two inertial navigation systems.

[0107] Therefore, the difference between the velocity error and position error of the two inertial navigation systems can be expressed as:

[0108]

[0109] The observation equation is expressed as:

[0110] z(t)=H(t)x(t)+υ(t),

[0111] Where z(t) represents the observation vector and H(t) represents the observation transition matrix, they are expressed as follows:

[0112]

[0113] In the formula, I 3×3 I represents a 3x3 identity matrix. 2×2 Let υ(t) represent a 2x2 identity matrix, where υ(t) is the noise vector corresponding to the observation.

[0114] (3) Establish an adaptive error parameter estimation filter;

[0115] A strong tracking filter based on residual normalization is used to track and estimate the error state. The one-step prediction of the filter covariance matrix is ​​expressed as:

[0116]

[0117] In the formula,

[0118]

[0119] And there are

[0120]

[0121]

[0122] Where, λ k P is the fading factor. k / k-1 To predict the covariance matrix in one step, Φ k / k-1 P represents the state transition matrix in one step. k-1 Let G be the covariance matrix at time k-1. k-1 The process noise assignment matrix at time k-1, Q k-1 Let H be the system noise matrix at time k-1, tr(·) be the matrix trace operator, and H be the system noise matrix at time k-1. k Let R be the system observation matrix at time k. k Let l be the observation noise matrix at time k. k λ is a weakening factor. 0,k The fading factor is calculated at time k. Let k represent the residual covariance matrix at time k. Let represent the residual covariance matrix at time k-1, ρ be the forgetting factor (taken as 0.95 ≤ ρ ≤ 0.995), γ0 represent the innovation at time 0, and γ k Represents the information at time k, and η is the normalization parameter used to eliminate the problem of reduced response speed of error state estimation caused by information asymmetry due to differences in the residual values ​​themselves.

[0123] (4) Real-time status monitoring is performed based on the error parameters output by the filter;

[0124] When the inertial device is in an abnormal state, the corresponding gyroscope drift or accelerometer zero bias changes. Real-time health status monitoring of the inertial device is achieved by analyzing the output of the monitoring filter.

[0125] A data window is set to slide over time, with a length of N. At time k, the filter output information contained in the sliding window is... The statistical characteristics of the calculated data are as follows:

[0126]

[0127] In the formula, μ k and Let represent the mean and variance of the real-time estimated parameters of the filter within the sliding window at time k, respectively, and their dimensions are and . Same dimension;

[0128] Set a weighting coefficient α and iteratively calculate the mean of the historical sliding windows:

[0129] Σ k =α·μ k +(1-α)Σ k-1

[0130] In the formula, Σ k The sliding window mean after iterations at time k is used to determine the two thresholds as follows:

[0131] T - =Σ k +k1σ k

[0132] T + =k2Σ k

[0133] In the formula, k1 and k2 are the parameters to be adjusted, and k1≥1 and k2>1, T + For a high threshold, T - Low threshold;

[0134] The guidelines for establishing health status monitoring are as follows:

[0135]

[0136] In the formula, T represents the i-th component of the filter's estimated output at time k+1. + (i) and T -(i) represents the i-th component of the desired real-time high threshold and low threshold, respectively. The monitoring threshold of each inertial device is updated in real time according to the sliding window. When all error parameter values ​​estimated by the filter are less than the low threshold, the output system is fault-free. When the i-th error parameter value estimated by the filter is greater than the low threshold but less than the high threshold, a fault warning is issued. When the i-th error parameter value estimated by the filter is greater than the high threshold, the output device i is faulty.

[0137] Based on the joint rotation method given in step (1), inertial navigation system 1 and inertial navigation system 2 are in normal navigation state. A dual inertial navigation state space model is constructed through steps (2) and (3). Based on the error parameters output by the filter, the state monitoring of the inertial navigation system can be realized through step (4).

[0138] In step (1), inertial navigation system 1 and inertial navigation system 2 rotate at different times according to the same rotation sequence, that is, the two inertial navigation systems rotate asynchronously according to the same rotation scheme.

[0139] In step (1), inertial navigation system 1 and inertial navigation system 2 rotate in different rotation sequences and rotate synchronously.

[0140] The relative attitude of inertial navigation system 1 and inertial navigation system 2 when they are at zero position in step (2) After the two inertial navigation systems are installed, the attitude can be determined by aligning the two systems separately or by using an external attitude reference.

[0141] In step (2), the lever arm between inertial navigation system 1 and inertial navigation system 2 is calibrated and determined after the two sets of inertial navigation systems are installed.

[0142] In step (2) and The angular position of the rotating frame is determined by the output of the indexing mechanism.

[0143] The method of the present invention is applicable not only to the case where both inertial navigation system 1 and inertial navigation system 2 are dual-axis rotation modulation inertial navigation systems, but also to the case where both inertial navigation system 1 and inertial navigation system 2 are triaxial rotation modulation inertial navigation systems, inertial navigation system 1 is a dual-axis rotation modulation inertial navigation system or a triaxial rotation modulation inertial navigation system, inertial navigation system 2 is a single-axis rotation modulation inertial navigation system, and multiple sets of dual-axis rotation inertial navigation systems or multiple sets of triaxial rotation inertial navigation systems are redundantly configured.

[0144] The method of the present invention has no requirements on the motion state of the carrier, and can be realized whether the carrier is in a moored state or in motion; it has no requirements on the environment in which the carrier is located, and is applicable in underwater environment and GNSS denied environment.

[0145] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. All technical solutions falling within the scope of the present invention's concept are protected by the present invention. Any improvements and modifications made without departing from the principles of the present invention should also be considered within the scope of protection of the present invention.

Claims

1. A method for monitoring the external state of a redundant dual-axis rotating inertial navigation system, characterized in that, The method includes the following steps: (1) Set the rotation order of two sets of dual-axis rotating inertial navigation systems. Define the two redundant inertial navigation systems as Inertial Navigation 1 and Inertial Navigation 2. The rotation order of both is dual-axis 16 sequence, and different rotation methods are used. (2) Define two sets of inertial navigation system volume coordinate systems. The volume coordinate system b1 of inertial navigation system 1 and the volume coordinate system b2 of inertial navigation system 2 are both defined as "right-front-up". The navigation coordinate system n is the local geographic coordinate system, defined as "east-north-sky". Using the attitude, velocity, and position information output by the two dual-axis rotating inertial navigation systems, establish a state-space model. The specific steps are as follows: (2.1) Determine the joint error equation of the system: in, In the formula, This represents the attitude error vector of inertial navigation system 1. This indicates the eastward attitude error of inertial navigation system 1. This indicates the northward attitude error of inertial navigation system 1. Indicates the azimuth attitude error of the inertial navigation system, v n This represents the actual speed of the vehicle in the navigation coordinate system. Let δL1 represent the velocity error vector of inertial navigation system 1, δλ1 represent the latitude error of inertial navigation system 1, and δh1 represent the altitude error of inertial navigation system 1. This indicates the eastward velocity error of inertial navigation system 1. This indicates the northbound velocity error of inertial navigation system 1. This indicates the azimuth velocity error of the inertial navigation system. This represents the angular velocity error of the navigation coordinate system relative to the inertial coordinate system, which is related to the latitude and velocity errors of the inertial navigation system. This represents the Earth's rotational angular velocity error related to the latitude error of the inertial navigation system. This indicates the transfer angular velocity error related to the latitude and velocity errors of the inertial navigation system. This represents the direction cosine matrix from the inertial navigation system's body coordinate system to the navigation coordinate system. This represents the attitude error vector of inertial navigation system 2. This represents the eastward attitude error of inertial navigation system 2. This represents the northward attitude error of inertial navigation system 2. This represents the upward attitude error of inertial navigation system 2. Let δL represent the velocity error vector of inertial navigation system 2, δL2 represent the latitude error of inertial navigation system 2, δλ2 represent the longitude error of inertial navigation system 2, and δh2 represent the altitude error of inertial navigation system 2. This indicates the eastward velocity error of inertial navigation system 2. This indicates the northbound velocity error of the inertial navigation system 2. This indicates the 2-axis velocity error of the inertial navigation system. This represents the angular velocity error of the navigation coordinate system relative to the inertial coordinate system, which is related to the inertial navigation 2-dimensional error and velocity error. This represents the Earth's rotational angular velocity error related to the latitude error of the inertial navigation system. This indicates the transfer angular velocity error related to the inertial navigation system's 2-dimensional error and velocity error. This represents the direction cosine matrix from the inertial navigation system's two-body coordinate system to the navigation coordinate system. Let be the angular velocity of the navigation coordinate system relative to the inertial coordinate system. Let be the Earth's rotational angular velocity vector. f is the angular velocity of the navigation coordinate system relative to the Earth coordinate system. n To compare the projection of the force in the navigation coordinate system, v E R represents the eastward velocity of the carrier, L and h represent the latitude and altitude of the carrier's location, and R represents the eastward velocity of the carrier. E and R N These are the radii of the east-west circle and the meridian circle, respectively, representing the location of the carrier. The error of the gyroscope component in inertial navigation system 1 is modeled as a constant drift. and gyroscope noise The sum of, among which, This indicates the x-axis gyroscope drift of inertial navigation system 1. This indicates the y-axis gyroscope drift of inertial navigation system 1. This indicates the z-axis gyroscope drift of inertial navigation system 1. The error of the accelerometer component of inertial navigation system 1 is modeled as a constant zero bias. and accelerometer noise The sum of, among which, This indicates that the x-axis accelerometer of inertial navigation system 1 has zero bias. This indicates that the y-axis accelerometer of inertial navigation system 1 has zero bias. This indicates that the z-axis accelerometer of inertial navigation system 1 has zero bias. The error of the gyroscope component in Inertial Navigation System 2 is modeled as a constant drift. and gyroscope noise The sum of, among which, This indicates the x-axis gyroscope drift of inertial navigation system 2. This indicates the y-axis gyroscope drift of inertial navigation system 2. This indicates the z-axis gyroscope drift of inertial navigation system 2. The error of the accelerometer component in inertial navigation system 2 is modeled as a constant zero bias. and accelerometer noise The sum of, among which, This indicates that the x-axis accelerometer of inertial navigation system 2 has zero bias. This indicates that the y-axis accelerometer of inertial navigation system 2 has zero bias. This indicates that the z-axis accelerometer of inertial navigation system 2 has zero bias; (2.2) Determine the joint state equations: in, In the formula, F(t) represents the system state matrix, 0 i×j V represents the zero matrix in row i and column j. N v U λ represents the northward and celestial velocities of the carrier, λ represents the longitude of the carrier's location, and ω represents the velocities of the carrier. ie f represents the Earth's angular velocity of rotation. E f N f U These represent the projections of the force in the east, north, and sky directions, respectively. The state vector x(t) is represented as: The noise distribution matrix G(t) and the noise matrix w(t) are expressed as follows: (2.3) Determine the state constraint observation equations: Define the coordinate system of inertial navigation system 1 and inertial navigation system 2 when the indexing mechanism is in the zero position as s. 10 System and s 20 The coordinate system is b, and the attitude matrices output by the two sets of dual-axis rotating inertial navigation systems are shown. and Represented as: In the formula, When the indexing mechanism is in the zero position, the inertial navigation coordinate system s 10 The direction cosine matrix to the navigation coordinate system, and Let represent the attitude matrices of the rotation mechanisms of inertial navigation system 1 and inertial navigation system 2 at time t relative to their zero position. s 20 System and s 10 Attitude matrix between systems; The expression for the difference in attitude error between the two sets of dual-axis rotating inertial navigation systems is determined as follows: Considering the lever arm, the velocity and position outputs of inertial navigation systems 1 and 2 are expressed as follows: In the formula, and These represent the velocity information in the navigation coordinate system output by inertial navigation system 1 and inertial navigation system 2, respectively, v n This represents the actual speed of the vehicle in the navigation coordinate system. This represents the difference between the velocity output by inertial navigation system 1 in the navigation coordinate system and the actual velocity of the vehicle. This represents the difference between the velocity output by inertial navigation system 2 in the navigation coordinate system and the actual velocity of the vehicle. This indicates the position information output by inertial navigation system 1. This represents the position information output by inertial navigation system 2, r n δr1 represents the actual position of the carrier in the navigation coordinate system. n This represents the difference between the position output by inertial navigation system 1 in the navigation coordinate system and the actual position of the vehicle. This represents the difference between the position output by inertial navigation system 2 in the navigation coordinate system and the actual position of the vehicle. The value of l represents the velocity difference between inertial navigation system 2 and inertial navigation system 1 caused by the outer arm between the two inertial navigation systems. r12 This represents the position difference between inertial navigation system 2 and inertial navigation system 1 caused by the outer arm between the two inertial navigation systems. Therefore, the difference between the velocity error and position error of the two inertial navigation systems can be 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, they are expressed as follows: In the formula, I 3×3 I represents a 3x3 identity matrix. 2×2 Let υ(t) represent a 2x2 identity matrix, where υ(t) is the noise vector corresponding to the observation. (3) Establish an adaptive error parameter estimation filter; A strong tracking filter based on residual normalization is used to track and estimate the error state. The one-step prediction of the filter covariance matrix is ​​expressed as: In the formula, And there are Where, λ k P is the fading factor. k / k-1 To predict the covariance matrix in one step, Φ k / k-1 P represents the state transition matrix in one step. k-1 Let G be the covariance matrix at time k-1. k-1 The process noise assignment matrix at time k-1, Q k-1 Let H be the system noise matrix at time k-1, tr(·) be the matrix trace operator, and H be the system noise matrix at time k-1. k Let R be the system observation matrix at time k. k Let l be the observation noise matrix at time k. k λ is a weakening factor. 0,k The fading factor is calculated at time k. Let k represent the residual covariance matrix at time k. Let represent the residual covariance matrix at time k-1, ρ be the forgetting factor (taken as 0.95 ≤ ρ ≤ 0.995), γ0 represent the innovation at time 0, and γ k Represents the information at time k, and η is the normalization parameter used to eliminate the problem of reduced response speed of error state estimation caused by information asymmetry due to differences in the residual values ​​themselves. (4) Real-time status monitoring is performed based on the error parameters output by the filter; When the inertial device is in an abnormal state, the corresponding gyroscope drift or accelerometer zero bias changes. Real-time health status monitoring of the inertial device is achieved by analyzing the output of the monitoring filter. A data window is set to slide over time, with a length of N. At time k, the filter output information contained in the sliding window is... The statistical characteristics of the calculated data are as follows: In the formula, μ k and Let represent the mean and variance of the real-time estimated parameters of the filter within the sliding window at time k, respectively, and their dimensions are and . Same dimension; Set a weighting coefficient α and iteratively calculate the mean of the historical sliding windows: S k =a·m k +(1-a)S k-1 In the formula, Σ k The sliding window mean after iterations at time k is used to determine the two thresholds as follows: T - =S k +k1σ k T + =k2Σ k In the formula, k1 and k2 are the parameters to be adjusted, and k1≥1 and k2>1, T + For a high threshold, T - Low threshold; The guidelines for establishing health status monitoring are as follows: In the formula, T represents the i-th component of the filter's estimated output at time k+1. + (i) and T - (i) represents the i-th component of the desired real-time high threshold and low threshold, respectively. The monitoring threshold of each inertial device is updated in real time according to the sliding window. When all error parameter values ​​estimated by the filter are less than the low threshold, the output system is fault-free. When the i-th error parameter value estimated by the filter is greater than the low threshold but less than the high threshold, a fault warning is issued. When the i-th error parameter value estimated by the filter is greater than the high threshold, the output device i is faulty.

2. The method for monitoring the external state of a redundant dual-axis rotating inertial navigation system as described in claim 1, characterized in that, In step (1), inertial navigation system 1 and inertial navigation system 2 rotate at different times according to the same rotation sequence, that is, the two inertial navigation systems rotate asynchronously according to the same rotation scheme.

3. The method for monitoring the external state of a redundant dual-axis rotating inertial navigation system as described in claim 1, characterized in that, In step (1), inertial navigation system 1 and inertial navigation system 2 rotate in different rotation sequences and rotate synchronously.

4. The method for monitoring the external state of a redundant dual-axis rotating inertial navigation system as described in claim 1, characterized in that, The relative attitude of inertial navigation system 1 and inertial navigation system 2 when they are at zero position in step (2) After the two inertial navigation systems are installed, the attitude can be determined by aligning the two systems separately or by using an external attitude reference.

5. The method for monitoring the external state of a redundant dual-axis rotating inertial navigation system as described in claim 1, characterized in that, In step (2), the lever arm between inertial navigation system 1 and inertial navigation system 2 is calibrated and determined after the two sets of inertial navigation systems are installed.

6. The method for monitoring the external state of a redundant dual-axis rotating inertial navigation system as described in claim 1, characterized in that, In step (2) and The angular position of the rotating frame is determined by the output of the indexing mechanism.

7. The method for monitoring the external state of a redundant dual-axis rotating inertial navigation system as described in claim 1, characterized in that, The method of the present invention is applicable not only to the case where both inertial navigation system 1 and inertial navigation system 2 are dual-axis rotation modulation inertial navigation systems, but also to the case where both inertial navigation system 1 and inertial navigation system 2 are triaxial rotation modulation inertial navigation systems, inertial navigation system 1 is a dual-axis rotation modulation inertial navigation system or a triaxial rotation modulation inertial navigation system, inertial navigation system 2 is a single-axis rotation modulation inertial navigation system, and multiple sets of dual-axis rotation inertial navigation systems or multiple sets of triaxial rotation inertial navigation systems are redundantly configured.

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