A real-time health monitoring method for inertial devices of a modulated inertial measurement unit

Abstract

The present application belongs to the technical field of inertial navigation, and discloses a kind of modulation type inertial measurement unit's inertial device health state real-time monitoring method, suitable for aviation navigation, marine navigation and other application scenarios.The present application cooperates with the relative output information of two sets of inertial navigation system to construct constraint observation, establishes a joint error state adaptive filter as a state monitoring filter, establishes a real-time state monitoring criterion based on the estimated output of the filter, clearly defines the diagnostic threshold and performs health state monitoring, and proposes a bearing gyro drift change quantity fitting method to realize abnormal state monitoring of the bearing gyro.The inertial device health state monitoring method proposed by the present application does not require accurate reference information assistance, providing a reliable guarantee for the safety and reliability of long-time navigation in GNSS denial environment.

Description

Technical Field

[0001] This invention belongs to the field of inertial navigation technology and relates to a method for real-time monitoring of the health status of inertial devices in a modulated inertial measurement unit, which is applicable to application scenarios such as aviation navigation and maritime navigation. Background Technology

[0002] Inertial navigation systems (INS) are the core of autonomous navigation, determining the position, velocity, and attitude of a vehicle without relying on external information. However, due to the inherent limitations in the accuracy of inertial devices, navigation errors accumulate over time, affecting navigation accuracy. To address this issue, rotation modulation technology, which involves periodically rotating the inertial measurement unit (IMU), has emerged. This technology effectively modulates IMU drift, significantly improving navigation accuracy. Furthermore, in applications with extremely high safety requirements, such as aircraft and ships, redundancy is indispensable to ensure high reliability and fault tolerance of the navigation system. Increasing system-level redundancy in INS not only enhances system robustness but also provides the hardware foundation for monitoring the health status of the INS or IMUs. Therefore, to enhance the reliability, safety, and maintenance efficiency of the entire navigation system, in-depth research into IMU health monitoring methods under a system-level redundant rotating INS architecture is particularly important and necessary.

[0003] Currently, due to the relative simplicity and ease of maintenance of system-level redundancy design, large vehicles typically employ two or more redundant inertial navigation systems (INS) and monitor their health by comparing the consistency of navigation information across these systems. However, in scenarios with only two INS systems and lacking additional reference information such as satellite navigation, health monitoring of a single INS system becomes difficult due to the similar error characteristics and fault features between the two systems.

[0004] This invention addresses existing problems and is geared towards applications in satellite-denied environments. It proposes a real-time health monitoring method for inertial devices in a modulated inertial measurement unit (INS). Using the relative velocity and position of two single-axis rotating modulated inertial navigation systems as constrained observations, a joint error state adaptive filter is established as the monitoring filter. Based on the filter's estimated output, state monitoring parameters are designed to monitor the health status of the inertial devices in real time. Furthermore, to address the issue of inseparable estimation of azimuth gyroscope drift in redundant configurations of two single-axis rotating modulated inertial navigation systems, an azimuth gyroscope drift change fitting estimation method is designed to achieve separate estimation of azimuth gyroscope drift. This enables health status monitoring of all inertial devices, including the azimuth gyroscope, providing strong assurance for the safety and reliability of long-endurance navigation in satellite-denied environments. Summary of the Invention

[0005] This invention proposes a real-time health monitoring method for inertial devices in a modulated inertial measurement unit, which can realize real-time monitoring of potential abnormal states of inertial devices when there is no accurate external reference information.

[0006] To solve the above-mentioned technical problems, the solution proposed by this invention is as follows:

[0007] A method for real-time health monitoring of inertial devices in a modulated inertial measurement unit, the method comprising the following steps:

[0008] (1) Two single-axis rotation modulation inertial navigation systems operating in navigation mode rotate and modulate around their respective azimuth axes according to a set modulation strategy, and output navigation information; define the two single-axis rotation modulation inertial navigation systems as Inertial Navigation 1 and Inertial Navigation 2, and define the volume coordinate systems of the two inertial navigation systems, wherein the volume coordinate system of Inertial Navigation 1 is... with the body coordinate system of inertial navigation system 2 All are defined as "right-front-up";

[0009] (2) A dynamic model based on geometrically constrained observations is established using the navigation output information of two sets of single-axis rotation modulation inertial navigation systems. The specific steps are as follows:

[0010] (2.1) Determine the joint error equation. By subtracting the error equations of the two sets of inertial navigation systems, the joint error equation of the system is obtained:

[0011] ,

[0012] ,

[0013] ,

[0014] ,

[0015] in,

[0016] ,

[0017] ,

[0018] ,

[0019] In the formula, This represents the difference between the corresponding error states of inertial navigation system 1 and inertial navigation system 2. Indicates the attitude error of inertial navigation system 1 Attitude error compared to inertial navigation system 2 The difference between them, with subscripts E, N, and U representing the components of the corresponding error along the geographic system in the east, north, and celestial directions, respectively. and Representing the inertial navigation system 1 volume coordinate system and inertial navigation two-body coordinate system The direction cosine matrix to the navigation coordinate system n, Indicates the velocity error of inertial navigation system 1 velocity error with inertial navigation system 2 The difference, with subscripts E, N, and U representing the components of the corresponding error along the geographic system in the east, north, and celestial directions, respectively. Indicates the latitude error of inertial navigation system 1 Latitude error with inertial navigation system 2 The difference, Indicates the longitude error of inertial navigation system 1 Longitude error with inertial navigation system 2 The difference, This represents the true velocity of the carrier. The subscripts E, N, and U represent the components of the corresponding error along the geographic system in the east, north, and celestial directions, respectively. L and h represent the true latitude and altitude of the carrier, respectively. R E and R N These are the radii of the east-west circle and the meridian circle, respectively, representing the location of the carrier. Let be the Earth's rotational angular velocity vector. Let be the angular velocity of the navigation coordinate system relative to the Earth coordinate system. Let be the angular velocity of the navigation coordinate system relative to the inertial coordinate system. This represents the difference in Earth's rotation angular velocity errors related to the latitude errors of the two inertial navigation systems, respectively. This represents the difference in transfer angular velocity errors related to the latitude and velocity errors of the two inertial navigation systems, respectively. Inertial navigation The error of the gyroscope component, where, These are the inertial navigation systems 1 and 2. Modeled as constant drift and gyroscope noise The sum of, among which, This represents the x-axis gyroscope drift of the inertial navigation system m. This represents the y-axis gyroscope drift of the inertial navigation system m. This represents the z-axis gyroscope drift of the inertial navigation system m. , , These represent the x-axis, y-axis, and z-axis gyroscope noise of the inertial navigation system m, respectively. The accelerometer component error, representing the inertial navigation system (INS) m, is modeled as a constant zero bias. and accelerometer noise The sum of, among which, This indicates that the x-axis accelerometer of the inertial navigation system (m) has zero bias. This indicates that the y-axis accelerometer of the inertial navigation system m has zero bias. This indicates that the z-axis accelerometer of the inertial navigation system m has zero bias. , , These represent the x-axis, y-axis, and z-axis accelerometer noise of the inertial navigation system m, respectively.

[0020] (2.2) Determine the joint state equations:

[0021] ,

[0022] in,

[0023]

[0024] ,

[0025] In the formula, Represents the joint error state vector. Represents the process noise vector and the system state matrix. and process noise matrix Determined by the joint error equation;

[0026] (2.3) Determine the geometrically constrained observation equations;

[0027] The navigation information output by the two redundantly configured single-axis rotation modulation inertial navigation systems actually reflects the motion of the same vehicle. However, due to inertial sensor errors, the outputs of the two systems are different. Considering the influence of the lever arm, determine the constraints on the velocity and position outputs of inertial navigation systems 1 and 2:

[0028] ,

[0029] ,

[0030] in,

[0031] ,

[0032] In the formula, Indicates the actual location of the carrier. Indicates the true longitude of the carrier. and These are the velocity and position outputs of inertial navigation system 1, respectively. , This indicates the altitude error of inertial navigation system 1. and These are the velocity and position outputs of inertial navigation system 2, respectively. , This indicates the altitude error of inertial navigation system 2. This represents the direction cosine matrix from the vehicle coordinate system b to the navigation coordinate system n. This represents the angular velocity of the carrier coordinate system b relative to the Earth coordinate system e. and These are the levers between the centers of inertial navigation system 1 and inertial navigation system 2 and the center of the carrier, respectively.

[0033] Therefore, the difference between the velocity error and position error of the two inertial navigation systems is determined to be:

[0034]

[0035] After system installation, adjust the lever arm. Perform precise calibration; and use the difference between the velocity and position outputs of the two single-axis rotationally modulated inertial navigation systems as the observation output of the dynamic model based on geometric constraints, expressing the observation equation as:

[0036] ,

[0037] in,

[0038]

[0039] In the formula, Represents the observation vector. Represents the observation matrix. Represents the observation noise vector. Represents a 2x2 identity matrix;

[0040] (3) Establish an adaptive state monitoring filter;

[0041] In one step, the prediction error covariance Introducing a time-varying fading factor Construct a strong tracking filter, represented as:

[0042] ,

[0043] in,

[0044] ,

[0045] ,

[0046] ,

[0047] In the formula, This represents the one-step transition matrix after discretization. Let represent the mean square error matrix of the state estimation. Represents the noise distribution matrix. This represents the discretized observation matrix. Indicates process noise The covariance matrix, This indicates finding the rank of a matrix. The covariance matrix representing the observation noise. The weakening factor is selected empirically or obtained through computer simulation; to fully utilize historical data and new observation information, the innovation variance of the actual filter is determined. as follows:

[0048] ,

[0049] In the formula, The variance of the information at time k is represented. express The new information variance at any given moment This indicates the information at time 0. Let ρ represent the information at time k, and let ρ represent the forgetting factor, which is taken as 1. ;

[0050] (4) Real-time health status monitoring, the specific steps are as follows:

[0051] (4.1) Calculate the real-time status monitoring threshold:

[0052] When the inertial devices of the inertial measurement unit are in an abnormal state, the corresponding gyroscope drift or accelerometer zero bias changes. Real-time health status monitoring of the inertial devices is achieved by analyzing the output of the monitoring filter.

[0053] Step 1: Set a pre-selected data window that slides over time, with a length of N. At time k, the filter output information contained in this sliding window is... The statistical characteristics of the calculated data are as follows:

[0054] ,

[0055] ,

[0056] In the formula, 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] Step 2: Set weighting coefficients The mean of the historical sliding windows is calculated iteratively:

[0058] ,

[0059] In the formula, Let represent the sliding window mean after iteration at time k. Further, the two thresholds, high and low, are determined as follows:

[0060] ,

[0061] ,

[0062] In the formula, , The parameter to be adjusted is usually an integer. For a high threshold, Low threshold;

[0063] Step 3: Establish health status monitoring criteria as follows:

[0064] ,

[0065] In the formula, express The filter estimates the i-th component of the output at time step. and Let i and ii represent the i-th components of the desired real-time high threshold and low threshold, respectively.

[0066] This step enables the monitoring of the health status of horizontal inertial devices and the detection of abnormal states of azimuth gyroscopes. If an abnormal state of the azimuth gyroscope is detected, proceed to (4.2).

[0067] (4.2) Monitoring of abnormal states of azimuth gyroscope:

[0068] Within several hours of an azimuth gyroscope state anomaly, the effects of Foucault oscillations and 24-hour oscillations can be neglected, and the error propagation characteristics in the north, east, and vertical channels can be considered independently; the impact of azimuth gyroscope state anomalies is analyzed in the north channel:

[0069] ,

[0070] In the formula, This indicates the time when the anomaly was detected, and t represents the time after the anomaly was detected. Indicates the northbound speed increment. This indicates the change in the azimuth gyroscope's drift. The Schuler frequency is used to fit the northward velocity increment after damping by two inertial navigation systems, and the drift change of the azimuth gyroscope is fitted to each system. By comparison, the abnormal state of the azimuth gyroscope can be diagnosed.

[0071] Furthermore, in step (1), both inertial navigation system 1 and inertial navigation system 2 are subjected to four-position rotation and stop modulation around their respective azimuth axes, with the rotation order being reversed.

[0072] 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.

[0073] Furthermore, in step (3), the covariance matrix of the observed noise The filter information value is selected based on the fault-free condition.

[0074] Furthermore, the length N of the preselected data window in step (4) is determined based on the rotation period of the redundant inertial navigation system.

[0075] 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 single-axis rotation modulation inertial navigation systems, but also applicable to the case where both inertial navigation system 1 and inertial navigation system 2 are dual-axis rotation modulation inertial navigation systems or tri-axis rotation modulation inertial navigation systems.

[0076] Compared with the prior art, the present invention has the following advantages:

[0077] This invention eliminates the need for specific configuration of the inertial navigation system (INS), enabling health monitoring of inertial devices through the coordinated use of output information from two INS systems. Simultaneously, the azimuth gyroscope drift increment estimation method solves the challenge of monitoring abnormal azimuth gyroscope states, achieving device-level health monitoring. Furthermore, this invention does not require accurate reference information, providing a reliable guarantee for the safety and reliability of long-endurance navigation in GNSS-denied environments. Attached Figure Description

[0078] Figure 1 This is a flowchart of the method provided in an embodiment of the present invention. Detailed Implementation

[0079] 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.

[0080] like Figure 1 As shown, a method for real-time health monitoring of inertial devices in a modulated inertial measurement unit is described below:

[0081] (1) Two single-axis rotation modulation inertial navigation systems operating in navigation mode rotate and modulate around their respective azimuth axes according to a set modulation strategy, and output navigation information; define the two single-axis rotation modulation inertial navigation systems as Inertial Navigation 1 and Inertial Navigation 2, and define the volume coordinate systems of the two inertial navigation systems, wherein the volume coordinate system of Inertial Navigation 1 is... with the body coordinate system of inertial navigation system 2 All are defined as "right-front-up";

[0082] (2) A dynamic model based on geometrically constrained observations is established using the navigation output information of two sets of single-axis rotation modulation inertial navigation systems. The specific steps are as follows:

[0083] (2.1) Determine the joint error equation. By subtracting the error equations of the two sets of inertial navigation systems, the joint error equation of the system is obtained:

[0084] ,

[0085] ,

[0086] ,

[0087] ,

[0088] in,

[0089] ,

[0090] ,

[0091] ,

[0092] In the formula, This represents the difference between the corresponding error states of inertial navigation system 1 and inertial navigation system 2. Indicates the attitude error of inertial navigation system 1 Attitude error compared to inertial navigation system 2 The difference between them, with subscripts E, N, and U representing the components of the corresponding error along the geographic system in the east, north, and celestial directions, respectively. and Representing the inertial navigation system 1 volume coordinate system and inertial navigation two-body coordinate system The direction cosine matrix to the navigation coordinate system n, Indicates the velocity error of inertial navigation system 1 velocity error with inertial navigation system 2 The difference, with subscripts E, N, and U representing the components of the corresponding error along the geographic system in the east, north, and celestial directions, respectively. Indicates the latitude error of inertial navigation system 1 Latitude error with inertial navigation system 2 The difference, Indicates the longitude error of inertial navigation system 1 Longitude error with inertial navigation system 2 The difference, This represents the true velocity of the carrier. The subscripts E, N, and U represent the components of the corresponding error along the geographic system in the east, north, and celestial directions, respectively. L and h represent the true latitude and altitude of the carrier, respectively. R E and R N These are the radii of the east-west circle and the meridian circle, respectively, representing the location of the carrier. Let be the Earth's rotational angular velocity vector. Let be the angular velocity of the navigation coordinate system relative to the Earth coordinate system. Let be the angular velocity of the navigation coordinate system relative to the inertial coordinate system. This represents the difference in Earth's rotation angular velocity errors related to the latitude errors of the two inertial navigation systems, respectively. This represents the difference in transfer angular velocity errors related to the latitude and velocity errors of the two inertial navigation systems, respectively. Inertial navigation The error of the gyroscope component, where, These are the inertial navigation systems 1 and 2. Modeled as constant drift and gyroscope noise The sum of, among which, This represents the x-axis gyroscope drift of the inertial navigation system m. This represents the y-axis gyroscope drift of the inertial navigation system m. This represents the z-axis gyroscope drift of the inertial navigation system m. , , These represent the x-axis, y-axis, and z-axis gyroscope noise of the inertial navigation system m, respectively. The accelerometer component error, representing the inertial navigation system (INS) m, is modeled as a constant zero bias. and accelerometer noise The sum of, among which, This indicates that the x-axis accelerometer of the inertial navigation system (m) has zero bias. This indicates that the y-axis accelerometer of the inertial navigation system m has zero bias. This indicates that the z-axis accelerometer of the inertial navigation system m has zero bias. , , These represent the x-axis, y-axis, and z-axis accelerometer noise of the inertial navigation system m, respectively.

[0093] (2.2) Determine the joint state equations:

[0094] ,

[0095] in,

[0096]

[0097] ,

[0098] In the formula, Represents the joint error state vector. Represents the process noise vector and the system state matrix. and process noise matrix Determined by the joint error equation;

[0099] (2.3) Determine the geometrically constrained observation equations;

[0100] The navigation information output by the two redundantly configured single-axis rotation modulation inertial navigation systems actually reflects the motion of the same vehicle. However, due to inertial sensor errors, the outputs of the two systems are different. Considering the influence of the lever arm, determine the constraints on the velocity and position outputs of inertial navigation systems 1 and 2:

[0101] ,

[0102] ,

[0103] in,

[0104] ,

[0105] In the formula, Indicates the actual location of the carrier. Indicates the true longitude of the carrier. and These are the velocity and position outputs of inertial navigation system 1, respectively. , This indicates the altitude error of inertial navigation system 1. and These are the velocity and position outputs of inertial navigation system 2, respectively. , This indicates the altitude error of inertial navigation system 2. This represents the direction cosine matrix from the vehicle coordinate system b to the navigation coordinate system n. This represents the angular velocity of the carrier coordinate system b relative to the Earth coordinate system e. and These are the levers between the centers of inertial navigation system 1 and inertial navigation system 2 and the center of the carrier, respectively.

[0106] Therefore, the difference between the velocity error and position error of the two inertial navigation systems is determined to be:

[0107]

[0108] After system installation, adjust the lever arm. Perform precise calibration; and use the difference between the velocity and position outputs of the two single-axis rotationally modulated inertial navigation systems as the observation output of the dynamic model based on geometric constraints, expressing the observation equation as:

[0109] ,

[0110] in,

[0111]

[0112] In the formula, Represents the observation vector. Represents the observation matrix. Represents the observation noise vector. Represents a 2x2 identity matrix;

[0113] (3) Establish an adaptive state monitoring filter;

[0114] In one step, the prediction error covariance Introducing a time-varying fading factor Construct a strong tracking filter, represented as:

[0115] ,

[0116] in,

[0117] ,

[0118] ,

[0119] ,

[0120] In the formula, This represents the one-step transition matrix after discretization. Let represent the mean square error matrix of the state estimation. Represents the noise distribution matrix. This represents the discretized observation matrix. Indicates process noise The covariance matrix, This indicates finding the rank of a matrix. The covariance matrix representing the observation noise. The weakening factor is selected empirically or obtained through computer simulation; to fully utilize historical data and new observation information, the innovation variance of the actual filter is determined. as follows:

[0121] ,

[0122] In the formula, The variance of the information at time k is represented. express The new information variance at any given moment This indicates the information at time 0. Let ρ represent the information at time k, and let ρ represent the forgetting factor, which is taken as 1. ;

[0123] (4) Real-time health status monitoring, the specific steps are as follows:

[0124] (4.1) Calculate the real-time status monitoring threshold:

[0125] When the inertial devices of the inertial measurement unit are in an abnormal state, the corresponding gyroscope drift or accelerometer zero bias changes. Real-time health status monitoring of the inertial devices is achieved by analyzing the output of the monitoring filter.

[0126] Step 1: Set a pre-selected data window that slides over time, with a length of N. At time k, the filter output information contained in this sliding window is... The statistical characteristics of the calculated data are as follows:

[0127] ,

[0128] ,

[0129] In the formula, 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;

[0130] Step 2: Set weighting coefficients The mean of the historical sliding windows is calculated iteratively:

[0131] ,

[0132] In the formula, Let represent the sliding window mean after iteration at time k. Further, the two thresholds, high and low, are determined as follows:

[0133] ,

[0134] ,

[0135] In the formula, , The parameter to be adjusted is usually an integer. For a high threshold, Low threshold;

[0136] Step 3: Establish health status monitoring criteria as follows:

[0137] ,

[0138] In the formula, express The filter estimates the i-th component of the output at time step. and Let i and ii represent the i-th components of the desired real-time high threshold and low threshold, respectively.

[0139] This step enables the monitoring of the health status of horizontal inertial devices and the detection of abnormal states of azimuth gyroscopes. If an abnormal state of the azimuth gyroscope is detected, proceed to (4.2).

[0140] (4.2) Diagnosing azimuth gyroscope abnormalities:

[0141] Within a few hours of an azimuth gyroscope malfunction, the effects of Foucault oscillations and 24-hour oscillations can be neglected, and the error propagation characteristics in the north, east, and vertical channels can be considered independently; the impact of azimuth gyroscope anomalies is analyzed in the north channel:

[0142] ,

[0143] In the formula, This indicates the time when the anomaly was detected, and t represents the time after the anomaly was detected. Indicates the northbound speed increment. This indicates the change in the azimuth gyroscope's drift. The Schuler frequency is used to fit the northward velocity increment after damping by two inertial navigation systems, and the drift change of the azimuth gyroscope is fitted to each system. By comparison, the abnormal state of the azimuth gyroscope can be diagnosed.

[0144] Furthermore, in step (1), both inertial navigation system 1 and inertial navigation system 2 are subjected to four-position rotation and stop modulation around their respective azimuth axes, with the rotation order being reversed.

[0145] 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.

[0146] Furthermore, in step (3), the covariance matrix of the observed noise The filter information value is selected based on the fault-free condition.

[0147] Furthermore, the length N of the preselected data window in step (4) is determined based on the rotation period of the redundant inertial navigation system.

[0148] 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 single-axis rotation modulation inertial navigation systems, but also applicable to the case where both inertial navigation system 1 and inertial navigation system 2 are dual-axis rotation modulation inertial navigation systems or tri-axis rotation modulation inertial navigation systems.

[0149] The invention will be further illustrated below with reference to experiments:

[0150] Experiments were conducted using two laser gyroscope inertial navigation systems, with the gyroscope exhibiting a drift stability better than 0.003. The accelerometer's zero stability is better than 20. After initial alignment, both inertial navigation systems (INS) operated in autonomous navigation mode, collecting raw data and processing it offline. To verify the effectiveness of this invention, an abnormal state was artificially designed to occur in the gyroscope or accelerometer of INS1 or INS2, and the proposed method was used for real-time health monitoring. Repeated experiments showed that the diagnostic results were consistent with the design results, verifying that the method proposed in this invention can achieve reliable real-time health monitoring.

[0151] 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 real-time health monitoring of inertial devices in a modulated inertial measurement unit, characterized in that, The method includes the following steps: (1) Two single-axis rotation modulation inertial navigation systems operating in navigation mode rotate and modulate around their respective azimuth axes according to a set modulation strategy and output navigation information; define the two single-axis rotation modulation inertial navigation systems as Inertial Navigation 1 and Inertial Navigation 2, and define the body coordinate systems of the two inertial navigation systems, wherein the body coordinate system b1 of Inertial Navigation 1 and the body coordinate system b2 of Inertial Navigation 2 are both defined as "right-front-up"; (2) A dynamic model based on geometrically constrained observations is established using the navigation output information of two sets of single-axis rotation modulation inertial navigation systems. The specific steps are as follows: (2.1) Determine the joint error equation. By subtracting the error equations of the two sets of inertial navigation systems, the joint error equation of the system is obtained: ， ， ， ， in, ， ， ， In the formula, (·) 12 This represents the difference between the corresponding error states of inertial navigation system 1 and inertial navigation system 2. Indicates the attitude error of inertial navigation system 1 Attitude error compared to inertial navigation system 2 The difference between them, with subscripts E, N, and U representing the components of the corresponding error along the geographic system in the east, north, and celestial directions, respectively. and Let b1 and b2 represent the direction cosine matrices from the inertial navigation system 1 (b1) and the inertial navigation system 2 (b2) to the navigation coordinate system n, respectively. Indicates the velocity error of inertial navigation system 1 velocity error with inertial navigation system 2 The difference, where subscripts E, N, and U represent the components of the corresponding error along the geographic system in the east, north, and celestial directions, respectively, δL 12 δλ represents the difference between the latitude error δL1 of inertial navigation system 1 and the latitude error δL2 of inertial navigation system 2. 12 This represents the difference between the longitude error δλ1 of inertial navigation system 1 and the longitude error δλ2 of inertial navigation system 2. This represents the true velocity of the carrier. The subscripts E, N, and U represent the components of the corresponding error along the geographic system in the east, north, and celestial directions, respectively. L and h represent the true latitude and altitude of the carrier, respectively. R E and R N These are the radii of the east-west circle and the meridian circle, respectively, representing the location of the carrier. Let be the Earth's rotational angular velocity vector. Let be the angular velocity of the navigation coordinate system relative to the Earth coordinate system. Let be the angular velocity of the navigation coordinate system relative to the inertial coordinate system. This represents the difference in Earth's rotation angular velocity errors related to the latitude errors of the two inertial navigation systems, respectively. This represents the difference in transfer angular velocity errors related to the latitude and velocity errors of the two inertial navigation systems, respectively. This represents the gyroscope component error of inertial navigation system m, where m is the number of inertial navigation system 1 or inertial navigation system 2. Modeled as constant drift and gyroscope noise The sum of, among which, This represents the x-axis gyroscope drift of the inertial navigation system m. This represents the y-axis gyroscope drift of the inertial navigation system m. This represents the z-axis gyroscope drift of the inertial navigation system m. , , These represent the x-axis, y-axis, and z-axis gyroscope noise of the inertial navigation system m, respectively. The accelerometer component error, representing the inertial navigation system (INS) m, is modeled as a constant zero bias. and accelerometer noise The sum of, among which, This indicates that the x-axis accelerometer of the inertial navigation system (m) has zero bias. This indicates that the y-axis accelerometer of the inertial navigation system m has zero bias. This indicates that the z-axis accelerometer of the inertial navigation system m has zero bias. , , These represent the x-axis, y-axis, and z-axis accelerometer noise of the inertial navigation system m, respectively. (2.2) Determine the joint state equations: ， in, ， ， In the formula, X represents the joint error state vector, w represents the process noise vector, and the system state matrix F and process noise matrix G are determined by the joint error equation; (2.3) Determine the geometrically constrained observation equations; Considering the influence of the lever arm, determine the constraints for the velocity and position outputs of inertial navigation systems 1 and 2: ， ， in, ， In the formula, λ represents the actual location of the carrier, and λ represents the actual longitude of the carrier. and These are the velocity and position outputs of inertial navigation system 1, respectively. δh1 represents the altitude error of inertial navigation system 1. and These are the velocity and position outputs of inertial navigation system 2, respectively. δh2 represents the altitude error of inertial navigation system 2. This represents the direction cosine matrix from the vehicle coordinate system b to the navigation coordinate system n. This represents the angular velocity of the carrier coordinate system b relative to the Earth coordinate system e. and These are the levers between the centers of inertial navigation system 1 and inertial navigation system 2 and the center of the carrier, respectively. Therefore, the difference between the velocity error and position error of the two inertial navigation systems is determined to be: ， After system installation, adjust the lever arm. Perform precise calibration; and use the difference between the velocity and position outputs of the two single-axis rotationally modulated inertial navigation systems as the observation output of the dynamic model based on geometric constraints, expressing the observation equation as: ， in, ， In the formula, Z represents the observation vector, H represents the observation matrix, υ represents the observation noise vector, and I2 represents the 2-row, 2-column identity matrix; (3) Establish an adaptive state monitoring filter; In the next step, the prediction error covariance P k / k-1 Introducing a time-varying fading factor λ k Construct a strong tracking filter, represented as: ， in, ， ， ， In the formula, Φ k / k-1 P represents the one-step transition matrix after discretization. k-1 Let Γ represent the mean square error matrix of the state estimation. k-1 H represents the noise distribution matrix. k Let Q represent the discretized observation matrix. k-1 Indicates process noise w k-1 The covariance matrix, Tr(·) denotes the rank of the matrix, R k The covariance matrix representing the observation noise, l k The weakening factor is selected empirically or obtained through computer simulation; to fully utilize historical data and new observation information, the innovation variance of the actual filter is determined. as follows: ， In the formula, The variance of the information at time k is represented. This represents the variance of the new information at time k-1. This indicates the information at time 0. Let ρ represent the information at time k, and let ρ represent the forgetting factor, which is taken as 1. ; (4) Real-time health status monitoring, the specific steps are as follows: (4.1) Calculate the real-time status monitoring threshold: When the inertial devices of the inertial measurement unit are in an abnormal state, the corresponding gyroscope drift or accelerometer zero bias changes. Real-time health status monitoring of the inertial devices is achieved by analyzing the output of the monitoring filter. Step 1: Set a pre-selected data window that slides over time, with a length of N. At time k, the filter output information contained in this sliding window is... The statistical characteristics of the calculated data are as follows: ， ， In the formula, 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; Step 2: Set the weighting coefficient α and iteratively calculate the mean of the historical sliding windows: ， In the formula, Let represent the sliding window mean after iteration at time k. Further, the two thresholds, high and low, are determined as follows: ， ， In the formula, , The parameter to be adjusted is usually an integer. For a high threshold, Low threshold; Step 3: Establish health status monitoring criteria as follows: ， In the formula, This represents the i-th component of the filter's estimated output at time k+1. and Let i and ii represent the i-th components of the desired real-time high threshold and low threshold, respectively. This step enables the monitoring of the health status of horizontal inertial devices and the detection of abnormal states of azimuth gyroscopes. If an abnormal state of the azimuth gyroscope is detected, proceed to (4.2). (4.2) Monitoring of abnormal states of azimuth gyroscope: Within several hours of an azimuth gyroscope state anomaly, the effects of Foucault oscillations and 24-hour oscillations can be neglected, and the error propagation characteristics in the north, east, and vertical channels can be considered independently; the impact of azimuth gyroscope state anomalies is analyzed in the north channel: ， In the formula, This indicates the time when the anomaly was detected, and t represents the time after the anomaly was detected. Indicates the northbound speed increment. ω represents the change in azimuth gyroscope drift. s The Schuler frequency is used to fit the northward velocity increment after damping by two inertial navigation systems, and the drift change of the azimuth gyroscope is fitted to each system. By comparison, the abnormal state of the azimuth gyroscope can be diagnosed.

2. The method for real-time health monitoring of inertial devices in a modulated inertial measurement unit as described in claim 1, characterized in that, In step (1), both inertial navigation system 1 and inertial navigation system 2 are subjected to four-position rotation and stop modulation around their respective azimuth axes, with the rotation order being reversed.

3. The method for real-time health monitoring of inertial devices in a modulated inertial measurement unit 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.

4. The method for real-time health monitoring of inertial devices in a modulated inertial measurement unit as described in claim 1, characterized in that, The covariance matrix R of the observed noise in step (3) k The filter information value is selected based on the fault-free condition.

5. The method for real-time health monitoring of inertial devices in a modulated inertial measurement unit as described in claim 1, characterized in that, The length N of the preselected data window in step (4) is determined based on the rotation period of the redundant inertial navigation system.

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