Real-time health monitoring method for inertial device of modulation type inertial measurement unit

Abstract

The invention belongs to the technical field of inertial navigation, discloses a real-time monitoring method for the health state of an inertial device of a modulation type inertial measurement unit, and is suitable for application scenes such as aviation navigation and marine navigation. The relative output information of the two inertial navigation systems is cooperatively used to construct constraint observation, a joint error state adaptive filter is established as a state monitoring filter, a real-time state monitoring criterion is established based on the estimated output of the filter, a diagnosis threshold is determined, health state monitoring is performed, and the method has a wide application prospect. Meanwhile, an azimuth gyroscope drift variation fitting method is provided to monitor the abnormal state of the azimuth gyroscope. The inertial device health state monitoring method provided by the invention does not need the assistance of accurate reference information, and provides reliable guarantee for the safety and reliability of long-endurance navigation in a GNSS denial environment.

Description

Technical Field

[0001] The present invention belongs to the technical field of inertial navigation, and relates to a method for real-time monitoring of the health state of inertial devices of a modulation type inertial measurement unit, which is applicable to application scenarios such as aviation navigation and marine navigation. Background Art

[0002] As the core of autonomous navigation, an inertial navigation system determines the position, velocity, and attitude of a carrier without relying on external information. However, due to the inherent limitations of the accuracy of inertial devices, with the extension of navigation time, navigation errors gradually accumulate, affecting navigation accuracy. To solve this problem, the rotation modulation technology that periodically rotates the inertial measurement unit has emerged, which can effectively modulate the drift of inertial devices, thereby significantly improving navigation accuracy. At the same time, in application scenarios with extremely high safety requirements, such as airplanes and ships, in order to ensure the high reliability and fault tolerance of the navigation system, redundant configuration has become an essential part. By increasing the system-level redundant configuration of the inertial navigation system, not only the robustness of the system is enhanced, but also a hardware foundation is provided for the health state monitoring of the inertial navigation system or inertial devices. To enhance the reliability, safety, and maintenance efficiency of the entire navigation system, it is particularly important and necessary to deeply study the method for monitoring the health of inertial devices in a rotation inertial navigation architecture with system-level redundant configuration.

[0003] Currently, due to the relatively simple system-level redundant design and easy maintenance, large carriers usually have redundant configurations of two or more inertial navigation systems, and the health state of the inertial navigation system is monitored by comparing the consistency of navigation information between systems. However, in the situation where only two inertial navigation systems are equipped, when there is no auxiliary information such as satellite navigation, given the similar error characteristics and fault features between the two systems, it is difficult to monitor the health state of a single inertial navigation system.

[0004] Aiming at the existing problems and for application in a satellite navigation denial environment, the present invention proposes a method for real-time health monitoring of inertial devices of a modulation type inertial measurement unit. Using the relative velocity and relative position of two single-axis rotation modulation inertial navigation systems as constraint observations, a joint error state adaptive filter is established as the monitoring filter, and the health state of inertial devices is monitored in real time based on the estimated output of the filter. At the same time, to solve the problem that the azimuth gyro drift cannot be separately estimated when two single-axis rotation modulation inertial navigation systems are redundantly configured, a fitting estimation method for the change amount of azimuth gyro drift is designed to achieve the separate estimation of azimuth gyro drift, and further to realize the health state monitoring of all inertial devices including azimuth gyroscopes, providing a strong guarantee for the safety and reliability of long-duration navigation in a satellite navigation denial environment. Summary of the Invention

[0005] The present invention proposes a real-time health monitoring method for inertial devices of a modulation type inertial measurement unit, which can realize real-time monitoring of potential abnormal states of inertial devices without accurate external reference information.

[0006] To solve the above technical problems, the solution proposed by the present invention is:

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

[0008] (1) Two single-axis rotation modulation inertial navigation systems operating in the navigation state rotate and modulate around their respective azimuth axes according to a set modulation strategy, and output navigation information; the two single-axis rotation modulation inertial navigation systems are defined as inertial navigation 1 and inertial navigation 2 respectively, and the body coordinate systems of the two inertial navigations are defined, 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";

[0009] (2) Establish a dynamic model based on geometric constraint observation by using the navigation output information of the two single-axis rotation modulation inertial navigation systems. The specific steps are as follows:

[0010] (2.1) Determine the combined error equation. By subtracting the error equations of the two inertial navigations, the combined error equation of the system is obtained:

[0011]

[0012] Wherein,

[0013]

[0014] δL 12 = δL1 - δL2, δλ 12 = δλ1 - δλ2

[0015]

[0016] In the formula, (·) 12 represents the difference between the corresponding error states of inertial navigation 1 and inertial navigation 2, represents the attitude error φ1 of inertial navigation 1 n and the attitude error φ2 of inertial navigation 2 n The subscripts E, N, and U respectively represent the components of the corresponding error quantities along the east, north, and up directions of the geographic coordinate system, and respectively represent the direction cosine matrices from the body coordinate system b1 of inertial navigation 1 and the body coordinate system b2 of inertial navigation 2 to the navigation coordinate system n, represents the velocity error of inertial navigation 1 and the velocity error of inertial navigation 2 The difference, where the subscripts E, N, and U represent the components of the corresponding error along the east, north, and up directions of the geographical coordinate system, and δL 12 represents the difference between the latitude error δL1 of inertial navigation 1 and the latitude error δL2 of inertial navigation 2, and δλ 12 represents the difference between the longitude error δλ1 of inertial navigation 1 and the longitude error δλ2 of inertial navigation 2, and v n =[v E v N v U T represents the true velocity of the vehicle, where the subscripts E, N, and U represent the components of the corresponding error along the east, north, and up directions of the geographical coordinate system, L and h represent the true latitude and altitude of the vehicle respectively, and R E and R N are the radius of the prime vertical and the radius of the meridian at the location of the vehicle respectively; is the angular velocity vector of the Earth's rotation, is the angular velocity of rotation of the navigation coordinate system relative to the Earth coordinate system, is the angular velocity of rotation of the navigation coordinate system relative to the inertial coordinate system, represents the difference in the angular velocity error of the Earth's rotation related to the latitude errors of the two sets of inertial navigations respectively, represents the difference in the transfer angular velocity error related to the latitude errors and velocity errors of the two sets of inertial navigations respectively, represents the gyro component error of inertial navigation m, where m is the number of inertial navigation 1 or inertial navigation 2, is modeled as a constant drift and gyro noise The sum of, where, represents the x-axis gyro drift of inertial navigation m, represents the y-axis gyro drift of inertial navigation m, represents the z-axis gyro drift of inertial navigation m, represent the x-axis, y-axis, and z-axis gyro noises of inertial navigation m respectively, represents the accelerometer component error of inertial navigation m, which is modeled as a constant zero bias and accelerometer noise The sum of, where, represents the x-axis accelerometer zero bias of inertial navigation m, represents the y-axis accelerometer zero bias of inertial navigation m, represents the z-axis accelerometer zero bias of inertial navigation m, represent the x-axis, y-axis, and z-axis accelerometer noises of inertial navigation m respectively;

[0017] (2.2) Determine the combined state equation:

[0018] ​

[0019] Among them,

[0020]

[0021] In the formula, X represents the combined error state vector, w represents the process noise vector, and the system state matrix F and the process noise matrix G are determined by the combined error equation;

[0022] (2.3) Determine the geometric constraint observation equation;

[0023] The navigation information output by the two sets of single-axis rotation modulation inertial navigation systems with redundant configuration actually reflects the motion of the same carrier. However, due to the existence of inertial sensor errors, the outputs of the two systems are different; considering the lever arm effect, determine the constraint conditions for the speed and position outputs of inertial navigation 1 and inertial navigation 2:

[0024]

[0025] Among them,

[0026]

[0027] In the formula, p = [L λ h] T represents the true position of the carrier, λ represents the true longitude of the carrier, and are respectively the speed output and position output of inertial navigation 1, and δp1 = [δL1 δλ1 δh1] T , δh1 represents the altitude error of inertial navigation 1, and are respectively the speed output and position output of inertial navigation 2, and δp2 = [δL2 δλ2 δh2] T , δh2 represents the altitude error of inertial navigation 2, represents the direction cosine matrix from the body coordinate system b to the navigation coordinate system n, represents the angular rate of the body coordinate system b relative to the earth coordinate system e, and are respectively the lever arms between the centers of inertial navigation 1 and inertial navigation 2 and the center of the carrier;

[0028] Therefore, determine the difference between the speed error and position error of the two sets of inertial navigation systems as:

[0029]

[0030] After the system is installed, calibrate the lever arm accurately; and take the difference between the speed output and position output of the two single-axis rotation modulation inertial navigations as the observation output of the dynamic model based on geometric constraints, and represent the observation equation as:

[0031] Z = HX + ν

[0032] Among them,

[0033]

[0034] In the formula, \(Z\) represents the observation vector, \(H\) represents the observation matrix, \(\nu\) represents the observation noise vector, and \(I_2\) represents the \(2\times2\) identity matrix;

[0035] (3) Establish an adaptive state monitoring filter;

[0036] Introduce a time-varying fading factor \(\lambda\) k / k-1 into the one-step prediction error covariance \(P\) k to construct a strong tracking filter, expressed as:

[0037]

[0038] Among them,

[0039]

[0040] In the formula, \(\varPhi\) k / k-1 represents the one-step transition matrix after discretization, \(P\) k-1 represents the mean square error matrix of state estimation, \(\varGamma\) k-1 represents the noise distribution matrix, \(H\) k represents the observation matrix after discretization, \(Q\) k-1 represents the covariance matrix of the process noise \(w\) k-1 , \(\text{Tr}(\cdot)\) represents the rank of the matrix, \(R\) k represents the covariance matrix of the observation noise, \(l\) k represents the weakening factor, which is selected according to experience or obtained through computer simulation; in order to make full use of historical data and new observation information, determine the innovation variance of the actual filter as follows:

[0041]

[0042] In the formula, represents the innovation variance at time \(k\), represents the innovation variance at time \(k - 1\), represents the innovation at time \(0\), represents the innovation at time \(k\), and \(\rho\) represents the forgetting factor, taking \(0.95\leqslant\rho\leqslant0.995\);

[0043] (4) Real-time health status monitoring, the specific steps are as follows:

[0044] (4.1) Calculate the real-time state monitoring threshold:

[0045] When the inertial device state of the inertial measurement unit is abnormal, the corresponding gyroscope drift or accelerometer zero bias changes. Real-time health state monitoring of the inertial device is achieved by analyzing the output of the monitoring filter;

[0046] Step 1: Set a preselected data window that slides with time, with a length of N. The filter output information contained in this sliding window at time k is Calculate the data statistical characteristics as follows:

[0047]

[0048] In the formula, μ k and respectively represent the mean and variance of the real-time estimated parameters of the filter within the sliding window at time k. The dimensions of both are the same as those of ;

[0049] Step 2: Set a weighting coefficient α and perform iterative calculation on the mean of the historical sliding window:

[0050] Σ k = α·μ k +(1 - α)Σ k-1

[0051] In the formula, Σ k represents the mean of the sliding window after iteration at time k. Further determine the upper and lower thresholds as follows:

[0052] T - = Σ k + k1σ k

[0053] T + = k2Σ k

[0054] In the formula, k1 and k2 are parameters to be adjusted, and k1 ≥ 1, k2 > 1, taking integers; T + is the upper threshold, and T - is the lower threshold;

[0055] Step 3: Establish the health state monitoring criterion as:

[0056]

[0057] In the formula, represents the i-th component of the filter estimated output at time k + 1, and T + (i) and T - (i) respectively represent the i-th components of the calculated real-time upper threshold and lower threshold;

[0058] At this time, the health status monitoring of the horizontal inertial device and the abnormal state detection of the azimuth gyroscope can be realized. If an abnormal state of the azimuth gyroscope is detected, enter (4.2);

[0059] (4.2) Abnormal state monitoring of the azimuth gyroscope:

[0060] Within several hours of the abnormal state of the azimuth gyroscope, the influences of the Foucault oscillation and the 24-hour oscillation can be ignored, and the error propagation characteristics in the north channel, east channel, and vertical channel can be considered independently; Analyze the influence of the abnormal state of the azimuth gyroscope in the north channel:

[0061]

[0062] In the formula, τ * represents the time when the abnormality is detected, t represents the time after the abnormality is detected, and △v N (t) = δv N (t) - δv N (τ * ) represents the northward velocity increment, represents the change in the azimuth gyroscope drift, ω s represents the Schuler frequency. The change in the azimuth gyroscope drift of each is respectively fitted by using the damped northward velocity increment of the two inertial navigation systems, and the abnormal state diagnosis of the azimuth gyroscope is realized through comparison.

[0063] Further, in step (1), both inertial navigation 1 and inertial navigation 2 perform four-position rotation and stop modulation around their respective azimuth axes, and the rotation order is reverse.

[0064] Further, in step (1), inertial navigation 1 and inertial navigation 2 rotate at different times according to the same rotation order, that is, the two inertial navigations rotate in an asynchronous manner according to the same rotation scheme.

[0065] Further, in step (3), the covariance matrix R k of the observation noise is selected according to the filtering innovation value without faults.

[0066] Further, in step (4), the length N of the preselected data window is determined according to the rotation period of the redundant inertial navigation system.

[0067] Further, the method of the present invention is not only applicable to the case where both inertial navigation 1 and inertial navigation 2 are single-axis rotation modulation inertial navigations, but also applicable to the cases where inertial navigation 1 and inertial navigation 2 are two-axis rotation modulation inertial navigations or three-axis rotation modulation inertial navigations.

[0068] Compared with the prior art, the present invention has the following advantages:

[0069] Without specific configuration of the inertial navigation system, the health status monitoring of inertial devices is achieved by jointly using the output information of two inertial navigation systems. Meanwhile, the azimuth gyro drift increment estimation method solves the problem of abnormal state monitoring of azimuth gyros and realizes device-level health monitoring. The present invention does not require accurate reference information assistance, providing a reliable guarantee for the safety and reliability of long-endurance navigation in GNSS-denied environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 is a flowchart of the method provided by an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0071] In order to make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below with reference to the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0072] As Figure 1 shown, a method for real-time health monitoring of inertial devices of a modulation-type inertial measurement unit is as follows in specific embodiments:

[0073] (1) Two single-axis rotation modulation inertial navigation systems operating in the navigation state rotate and modulate around their respective azimuth axes according to the 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 respectively, and define the body coordinate systems of the two inertial navigations. Among them, 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";

[0074] (2) Establish a dynamic model based on geometric constraint observation by using the navigation output information of the two single-axis rotation modulation inertial navigation systems. The specific steps are as follows:

[0075] (2.1) Determine the combined error equation. By subtracting the error equations of the two inertial navigations, the combined error equation of the system is obtained:

[0076]

[0077] Among them,

[0078]

[0079] δL 12 = δL1 - δL2, δλ 12 = δλ1 - δλ2

[0080]

[0081] In the formula, (·) 12 represents the difference between the corresponding error states of inertial navigation 1 and inertial navigation 2, Denote the attitude error φ1 of INS1 n and the attitude error φ2 of INS2 n The difference between them. The subscripts E, N, U respectively represent the components of the corresponding error quantities along the east, north, and up directions of the geographic coordinate system. and respectively represent the direction cosine matrices from the body coordinate system b1 of INS1 and the body coordinate system b2 of INS2 to the navigation coordinate system n. Denote the velocity error of INS1 and the velocity error of INS2 The difference between them. The subscripts E, N, U respectively represent the components of the corresponding error quantities along the east, north, and up directions of the geographic coordinate system. δL 12 Denote the difference between the latitude error δL1 of INS1 and the latitude error δL2 of INS2. δλ 12 Denote the difference between the longitude error δλ1 of INS1 and the longitude error δλ2 of INS2. v n =[v E v N v U T Denote the true velocity of the carrier. The subscripts E, N, U respectively represent the components of the corresponding error quantities along the east, north, and up directions of the geographic coordinate system. L and h respectively represent the true latitude and height of the carrier. R E and R N respectively represent the radius of the prime vertical and the radius of the meridian at the location of the carrier. is the angular velocity vector of the Earth's rotation. is the angular velocity of the rotation of the navigation coordinate system relative to the Earth coordinate system. is the angular velocity of the rotation of the navigation coordinate system relative to the inertial coordinate system. Denote the difference between the angular velocity errors of the Earth's rotation related to the latitude errors of the two sets of INSs respectively. Denote the difference between the transfer angular velocity errors related to the latitude errors and velocity errors of the two sets of INSs respectively. Denote the gyro component error of INS m, where m is the number of INS1 and INS2. is modeled as a constant drift and gyro noise The sum of them, where Denote the gyro drift of the x-axis of INS m. Denote the gyro drift of the y-axis of INS m. Denote the gyro drift of the z-axis of INS m respectively denote the gyro noises of the x-axis, y-axis, and z-axis of INS m. Denote the accelerometer component error of INS m, which is modeled as a constant zero bias and accelerometer noise The sum of them, where​ denotes the zero bias of the x-axis accelerometer of inertial navigation m denotes the zero bias of the y-axis accelerometer of inertial navigation m denotes the zero bias of the z-axis accelerometer of inertial navigation m respectively denote the noises of the x-axis, y-axis, and z-axis accelerometers of inertial navigation m;

[0082] (2.2) Determine the combined state equation:

[0083]

[0084] wherein,

[0085]

[0086] In the formula, X represents the combined error state vector, w represents the process noise vector, and the system state matrix F and the process noise matrix G are determined by the combined error equation;

[0087] (2.3) Determine the geometric constraint observation equation;

[0088] The navigation information output by two sets of single-axis rotation modulation inertial navigation systems with redundant configuration actually reflects the motion of the same carrier. However, due to the existence of inertial sensor errors, the outputs of the two systems are different; considering the influence of the lever arm, determine the constraint conditions for the speed and position outputs of inertial navigation 1 and inertial navigation 2:

[0089]

[0090] wherein,

[0091]

[0092] In the formula, p = [L λ h] T represents the true position of the carrier, λ represents the true longitude of the carrier, and are respectively the speed output and position output of inertial navigation 1, and δp1 = [δL1 δλ1 δh1] T , δh1 represents the height error of inertial navigation 1, and are respectively the speed output and position output of inertial navigation 2, and δp2 = [δL2 δλ2 δh2] T , δh2 represents the height error of inertial navigation 2, represents the direction cosine matrix from the carrier coordinate system b to the navigation coordinate system n, represents the angular rate of the carrier coordinate system b relative to the earth coordinate system e, and are respectively the lever arms between the centers of inertial navigation 1 and inertial navigation 2 and the center of the carrier;

[0093] Therefore, the differences between the speed errors and position errors of the two inertial navigation systems are determined as:

[0094]

[0095] After the system is installed, the lever arm is accurately calibrated; and the differences between the speed outputs and position outputs of the two single-axis rotation modulation inertial navigations are used as the observation outputs of the dynamic model based on geometric constraints. The observation equation is expressed as:

[0096] Z = HX + ν

[0097] where

[0098]

[0099] In the formula, Z represents the observation vector, H represents the observation matrix, ν represents the observation noise vector, and I2 represents the 2×2 identity matrix;

[0100] (3) Establish an adaptive state monitoring filter;

[0101] A time-varying fading factor λ is introduced into the one-step prediction error covariance P k / k-1 to construct a strong tracking filter, which is expressed as: k

[0102]

[0103] where

[0104]

[0105] In the formula, Φ k / k-1 represents the one-step transition matrix after discretization, P k-1 represents the mean square error matrix of state estimation, Γ k-1 represents the noise distribution matrix, H k represents the observation matrix after discretization, Q k-1 represents the covariance matrix of the process noise w k-1 Tr(·) represents the rank of the matrix, R k represents the covariance matrix of the observation noise, l k represents the weakening factor, which is selected according to experience or obtained through computer simulation; in order to make full use of historical data and new observation information, the innovation variance of the actual filter is determined as follows:

[0106]

[0107] In the formula, represents the innovation variance at time k, denotes the innovation variance at time k-1, denotes the innovation at time 0, denotes the innovation at time k, and ρ denotes the forgetting factor, usually taking 0.95 ≤ ρ ≤ 0.995;

[0108] (4) Real-time health status monitoring, and the specific steps are as follows:

[0109] (4.1) Calculate the real-time status monitoring threshold:

[0110] When the status of the inertial devices in the inertial measurement unit is abnormal, the corresponding gyroscope drift or accelerometer zero bias changes. The real-time health status monitoring of the inertial devices is realized by analyzing the output of the monitoring filter;

[0111] Step 1: Set a preselected data window that slides with time, with a length of N. The filter output information included in this sliding window at time k is Calculate the data statistical characteristics as follows:

[0112]

[0113] In the formula, μ k and respectively denote the mean and variance of the real-time estimated parameters of the filter within the sliding window at time k, and the dimensions of both are the same as those of ;

[0114] Step 2: Set the weighting coefficient α and perform iterative calculation on the mean of the historical sliding window:

[0115] Σ k = α·μ k +(1 - α)Σ k-1

[0116] In the formula, Σ k denotes the mean of the sliding window after iteration at time k, and further determine the following high and low thresholds:

[0117] T - = Σ k + k1σ k

[0118] T + = k2Σ k

[0119] In the formula, k1 and k2 are parameters to be adjusted, and k1 ≥ 1, k2 > 1, taking integers; T + is the high threshold, and T - is the low threshold;

[0120] Step 3: Establish the health status monitoring criterion as:

[0121]

[0122] In the formula, represents the i-th component of the estimated output of the filter at the (k + 1)-th moment, T + (i) and T - (i) respectively represent the i-th components of the required real-time high threshold and low threshold;

[0123] At this time, the health state monitoring of the horizontal inertial device and the abnormal state detection of the azimuth gyro can be realized. If an abnormal state of the azimuth gyro is found, it enters (4.2);

[0124] (4.2) Diagnose the abnormality of the azimuth gyro:

[0125] Within several hours of the azimuth gyro failure, the effects of the Foucault oscillation and the 24-hour oscillation can be ignored, and the error propagation characteristics in the north channel, east channel, and vertical channel can be considered independently; Analyze the influence of the abnormal state of the azimuth gyro in the north channel:

[0126]

[0127] In the formula, τ * represents the time when the abnormality is detected, t represents the time after the abnormality is detected, △v N (t) = δv N (t) - δv N (τ * ) represents the northward velocity increment, represents the change in the azimuth gyro drift, ω s represents the Schuler frequency. The change in the azimuth gyro drift is respectively fitted by using the northward velocity increment after damping of the two inertial navigation systems, and the abnormal state diagnosis of the azimuth gyro is realized through comparison.

[0128] Furthermore, in step (1), both inertial navigation 1 and inertial navigation 2 perform four-position rotation and stop modulation around their respective azimuth axes, and the rotation order is reversed.

[0129] Furthermore, in step (1), inertial navigation 1 and inertial navigation 2 rotate at different times according to the same rotation order, that is, the two inertial navigations rotate in an asynchronous manner according to the same rotation scheme.

[0130] Furthermore, in step (3), the covariance matrix R of the observation noise k is selected according to the filter innovation value when there is no fault.

[0131] Furthermore, in step (4), the length N of the preselected data window is determined according to the rotation period of the redundant inertial navigation system.

[0132] Furthermore, the method of the present invention is applicable not only to the case where both inertial navigation 1 and inertial navigation 2 are single-axis rotation modulation inertial navigations, but also to the cases where inertial navigation 1 and inertial navigation 2 are dual-axis rotation modulation inertial navigations or tri-axis rotation modulation inertial navigations.

[0133] The present invention will be further described below in conjunction with experiments:

[0134] Experiments were carried out using two sets of laser gyro inertial navigation systems. Among them, the gyro drift stability was better than 0.003° / h, and the accelerometer zero stability was better than 20 μg. After initial alignment, both sets of inertial navigations worked in the autonomous navigation state, and the original data was collected and processed offline. To verify the effectiveness of the present invention, abnormal states were artificially designed to occur in the gyroscopes or accelerometers of inertial navigation 1 or inertial navigation 2, and then the method proposed in this paper was used to perform real-time health monitoring on them. Repeated experiments showed that the diagnostic results were consistent with the design results, verifying that the method proposed in the present invention can achieve reliable real-time health monitoring.

[0135] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. All technical solutions falling within the scope of the inventive concept of the present invention belong to the protection scope of the present invention. Several improvements and refinements made without departing from the principle of the present invention shall also be regarded as within the protection scope of the present invention.

Claims

1. A real-time health monitoring method for inertial devices of a modulation type inertial measurement unit, characterized in that, The method includes the following steps: (1) Two single-axis rotation modulation inertial navigation systems operating in the navigation state rotate and modulate around their respective azimuth axes according to the 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 respectively, and define the body coordinate systems of the two inertial navigations. Among them, 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) Establish a dynamic model based on geometric constraint observation by using the navigation output information of the two single-axis rotation modulation inertial navigation systems. The specific steps are as follows: (2.1) Determine the combined error equation. By subtracting the error equations of the two inertial navigations, obtain the combined error equation of the system: Where, δL 12 = δL1 - δL2, δλ 12 = δλ1 - δλ2 where (·) 12 represents the difference between the corresponding error states of INS 1 and INS 2, represents the attitude error of INS 1 and the attitude error of INS 2 The subscripts E, N, and U respectively represent the components of the corresponding error quantities along the east, north, and up directions of the geographical coordinate system, and respectively represent the direction cosine matrices from the body coordinate system b1 of INS 1 and the body coordinate system b2 of INS 2 to the navigation coordinate system n, represents the velocity error of INS 1 and the velocity error of INS 2 The subscripts E, N, and U respectively represent the components of the corresponding error quantities along the east, north, and up directions of the geographical coordinate system, δL 12 represents the difference between the latitude error δL1 of INS 1 and the latitude error δL2 of INS 2, δλ 12 represents the difference between the longitude error δλ1 of INS 1 and the longitude error δλ2 of INS 2, v n =[v E v N v U T represents the true velocity of the vehicle, and the subscripts E, N, and U respectively represent the components of the corresponding error quantities along the east, north, and up directions of the geographical coordinate system. L and h respectively represent the true latitude and height of the vehicle, R E and R N are respectively the radius of the prime vertical and the radius of the meridian at the location of the vehicle; is the angular velocity vector of the earth's rotation, is the angular velocity of the rotation of the navigation coordinate system relative to the earth coordinate system, is the angular velocity of the rotation of the navigation coordinate system relative to the inertial coordinate system, represents the difference between the angular velocity errors of the earth's rotation respectively related to the latitude errors of the two sets of INSs, represents the difference between the transfer angular velocity errors respectively related to the latitude errors and velocity errors of the two sets of INSs, represents the gyro component error of INS m, where m is the number of INS 1 and INS 2, is modeled as the sum of a constant drift and gyro noise where, represents the gyro drift of the x-axis of INS m, represents the gyro drift of the y-axis of INS m, represents the gyro drift of the z-axis of INS m, respectively represent the gyro noises of the x-axis, y-axis, and z-axis of INS m, ​Denote the accelerometer component error of inertial navigation m, which is modeled as a constant bias and the accelerometer noise The sum of, where Denote the zero bias of the x-axis accelerometer of inertial navigation m, Denote the zero bias of the y-axis accelerometer of inertial navigation m, Denote the zero bias of the z-axis accelerometer of inertial navigation m, Respectively denote the x-axis, y-axis, and z-axis accelerometer noises of inertial navigation m; (2.2) Determine the combined state equation: Where, In the formula, X represents the combined error state vector, w represents the process noise vector, and the system state matrix F and the process noise matrix G are determined by the combined error equation; (2.3) Determine the geometric constraint observation equation; Considering the influence of the lever arm, determine the constraint conditions for the speed and position outputs of inertial navigation 1 and inertial navigation 2: Where, where p = [Lλh] T represents the true position of the vehicle, λ represents the true longitude of the vehicle, and are the velocity output and position output of INS 1 respectively, and δp1 = [δL1δλ1δh1] T , δh1 represents the height error of INS 1, and are the velocity output and position output of INS 2 respectively, and δp2 = [δL2δλ2δh2] T , δh2 represents the height error of INS 2, represents the direction cosine matrix from the vehicle coordinate system b to the navigation coordinate system n, represents the angular rate of the vehicle coordinate system b relative to the earth coordinate system e, and are the lever arms between the centers of INS 1 and INS 2 and the vehicle center respectively; Therefore, determine the difference between the speed error and the position error of the two inertial navigation systems as: Precisely calibrate the lever arm after system installation and use the difference between the speed outputs and position outputs of the two single-axis rotation modulation inertial navigations as the observation output of the dynamic model based on geometric constraints. The observation equation is expressed as: Z = HX + ν Where, In the formula, Z represents the observation vector, H represents the observation matrix, ν represents the observation noise vector, and I2 represents the 2×2 identity matrix; (3) Establish an adaptive state monitoring filter; Introduce a time-varying fading factor λ k / k-1 into the one-step prediction error covariance P k to construct a strong tracking filter, expressed as: Where, where, Φ k / k-1 represents the one-step transition matrix after discretization, P k-1 represents the mean square error matrix of state estimation, Γ k-1 represents the noise distribution matrix, H k represents the observation matrix after discretization, Q k-1 represents the covariance matrix of the process noise w k-1 , Tr(·) represents taking the rank of a matrix, R k represents the covariance matrix of the observation noise, l k represents the weakening factor, which is selected according to experience or obtained through computer simulation; in order to make full use of historical data and new observation information, the innovation variance of the actual filtering is determined as follows: wherein, represents the innovation variance at time k, represents the innovation variance at time k-1, represents the innovation at time 0, represents the innovation at time k, ρ represents the forgetting factor, and is taken as 0.95 ≤ ρ ≤ 0.995; (4) Real-time health state monitoring. The specific steps are as follows: (4.1) Calculate the real-time state monitoring threshold: When the state of the inertial device in the inertial measurement unit is abnormal, the corresponding gyro drift or accelerometer zero bias changes. The real-time health state monitoring of the inertial device is realized by analyzing the output of the monitoring filter; Step 1: Set a preselected data window that slides over time, with a length of N. The filter output information contained in this sliding window at time k is Calculate the data statistical characteristics as follows: where μ k and represent the mean and variance of the real-time estimated parameters of the filter within the sliding window at time k, respectively, and the dimensions of both are the same as those of ; Step 2: Set the weighting coefficient α and perform iterative calculation on the mean value of the historical sliding window: Σ k = α·μ k + (1 - α)Σ k-1 where, Σ k represents the sliding window mean value after iteration at time k, and the upper and lower thresholds are further determined as follows: T - = Σ k + k1σ k T + = k2Σ k wherein, k1 and k2 are parameters to be adjusted, and k1≥1, k2>1, taking integers; T + is the high threshold, and T - is the low threshold; Step 3: Establish the health state monitoring criterion as: In the formula, represents the i-th component of the filter estimated output at the (k + 1)-th moment, T + (i) and T - (i) respectively represent the i-th components of the sought real-time high threshold and low threshold; At this time, the health state monitoring of the horizontal inertial device and the abnormal state detection of the azimuth gyro can be realized. If the abnormal state of the azimuth gyro is found, enter (4.2); (4.2) Azimuth gyro abnormal state monitoring: Within several hours when the azimuth gyro state is abnormal, the influence of the Foucault oscillation and the 24-hour oscillation can be ignored, and the error propagation characteristics in the north channel, east channel, and vertical channel can be considered independently. Analyze the influence of the abnormal state of the azimuth gyro in the north channel: where τ * represents the time when an anomaly is detected, t represents the time after the anomaly is detected, and Δv N (t) = δv N (t) - δv N (τ * ) represents the northward velocity increment, represents the change in the azimuth gyro drift, ω s represents the Schuler frequency. The change in the azimuth gyro drift is respectively fitted by using the northward velocity increment after damping of the two inertial navigation systems, and the anomaly diagnosis of the azimuth gyro is realized through comparison.

2. The real-time health monitoring method for the inertial device of a modulation type inertial measurement unit according to claim 1, wherein, In step (1), both inertial navigation 1 and inertial navigation 2 perform four-position rotation and stop modulation around their respective azimuth axes, and the rotation order is reversed.

3. The real-time health monitoring method for the inertial device of a modulation type inertial measurement unit according to claim 1, wherein, In step (1), inertial navigation 1 and inertial navigation 2 rotate at different times according to the same rotation order, that is, the two inertial navigations rotate in an asynchronous manner according to the same rotation scheme.

4. The real-time health monitoring method for inertial devices of a modulation type inertial measurement unit according to claim 1, characterized in that The covariance matrix R of the observation noise in the step (3) k Selected according to the filtering innovation value when there is no fault.

5. The real-time health monitoring method for the inertial device of a modulation type inertial measurement unit according to claim 1, characterized in that In step (4), the length N of the preselected data window is determined according to the rotation period of the redundant inertial navigation system.

6. The real-time health monitoring method for the inertial device of a modulation type inertial measurement unit according to claim 1, wherein The method of the present invention is not only applicable to the case where both inertial navigation 1 and inertial navigation 2 are single-axis rotation modulation inertial navigations, but also applicable to the cases where inertial navigation 1 and inertial navigation 2 are two-axis rotation modulation inertial navigations or three-axis rotation modulation inertial navigations.

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