CN113804185A - Novel inertial navigation system based on MEMS array - Google Patents
Novel inertial navigation system based on MEMS array Download PDFInfo
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Abstract
The invention discloses a novel inertial navigation system based on an MEMS array, which comprises an MEMS array and a fiber-optic gyroscope, wherein the MEMS array is axially installed in parallel, the fiber-optic gyroscope is installed in an inclined mode in space, the MEMS array is orthogonally configured along the X, Y, Z axial direction, each axial direction comprises a plurality of MEMS accelerometers and a plurality of MEMS uniaxial gyroscopes, and the fiber-optic gyroscope realizes the online calibration of the measurement errors of the MEMS uniaxial gyroscopes; meanwhile, an information fusion and calibration method of the inertial navigation system is disclosed, wherein the information fusion method comprises an MEMS array device fusion technology and an MEMS gyroscope and optical fiber gyroscope fusion method. The system can exert the performance of each sub-sensor in the MEMS array to the maximum extent, get rid of the process bottleneck of the traditional MEMS inertial device, realize the application of the system in accurate guided weapon equipment, promote the microminiaturization, low cost and intelligent development of batch equipment, and meet the requirement of future combat.
Description
Technical Field
The invention belongs to the technical field of inertia, and particularly relates to a novel inertial navigation system based on an MEMS array.
Background
The inertial technology is a bottleneck for restricting the rapid response of missile weapons, is also a highly sensitive core technology of various military and strong countries, and has become the core of the navigation control of intelligent military equipment by taking an inertial navigation system INS as a main part for autonomous navigation. The traditional inertial navigation system is divided into a platform type inertial navigation system and a strapdown type inertial navigation system, has the characteristics of high power consumption, large volume, heavy weight, complex structure, high cost and the like, cannot meet the development requirement of miniaturization of future intelligent military equipment, and is a necessary trend of intelligent development of the military equipment.
MEMS inertial devices are being applied to the field of intelligent military equipment gradually by virtue of their advantages of small size, low cost, etc. However, the MEMS inertial device, particularly the MEMS gyroscope, has the problems of poor precision and poor environmental adaptability, and cannot independently depend on the MEMS inertial navigation system to complete a long-time high-precision autonomous navigation task, so that the application of the MEMS inertial device in the field of rocket military missile equipment is restricted.
Disclosure of Invention
The invention provides a novel inertial navigation system based on an MEMS array, which adopts a plurality of groups of low-precision inertial devices and a single-shaft inclined fiber-optic gyroscope array configuration, and constructs a configuration mode of parallel installation of the array MEMS devices and inclined arrangement of the single-shaft fiber-optic gyroscope by taking optimal navigation performance and reliability as a criterion; after the spatial configuration is determined, an information processing system of the MEMS array type navigation system is set up, and multi-sensor device level information fusion and system level navigation error correction are completed; an inclined fiber-optic gyroscope is introduced to provide an additional angular velocity reference for an MEMS gyroscope in an array navigation system, and errors and correlation coefficients of various sensors are corrected in real time through an online calibration technology, so that the problem of poor successive repeatability of an MEMS device is solved; the working state of the sub-sensors in the MEMS array can be monitored in real time, and fault isolation and processing can be performed in time when a fault occurs, so that the reliability and stability of the inertial navigation system are improved; the system exerts the performance of each sub-sensor in the MEMS array to the maximum extent, improves the use precision and the environmental adaptability of the MEMS, and greatly reduces the cost, the volume and the weight of the inertial navigation system.
The invention adopts the following technical scheme:
a novel inertial navigation system based on a MEMS array comprises a MEMS array and a fiber-optic gyroscope, wherein the MEMS array is arranged in parallel along the axial direction, the MEMS array is arranged orthogonally along X, Y, Z axial directions, each axial direction comprises a plurality of MEMS accelerometers and a plurality of MEMS single-axis gyroscopes, the MEMS accelerometers are used for measuring acceleration, and the MEMS single-axis gyroscopes are used for measuring angular velocity; the fiber optic gyroscope is arranged obliquely in space, and online calibration of X, Y, Z axial angular velocity measurement errors is achieved.
The information fusion method of the inertial navigation system is characterized by comprising the following steps of performing information fusion between the same axial MEMS array device and information fusion between three axial MEMS gyroscopes and a single-axis fiber-optic gyroscope:
1) information fusion between same-axis MEMS array devices
MEMS uniaxial gyroscope outputs y (t) all comprise trueAngular velocity ω (t), white noise n (t), and stochastic drift b (t), wherein the stochastic drift is modeled as a first order Markov process
The output model of the MEMS uniaxial gyroscope is as follows:
for the array type navigation system, n MEMS single-axis gyroscopes in the same axial direction are supposed to realize the measurement of the angular velocity, and according to the output model of the MEMS single-axis gyroscope, the angular velocity measurement value not only comprises the real angular velocity, but also has related random drift and measurement white noise; the modeling estimation of random drift and real angular velocity is realized through the fusion of a plurality of measured values; if the true angular velocity ω (t) and the random drift b (t) are selected as the state variables, the state variables x (t) can be expressed as:
X(t)＝[b ω]T,b＝[b1 ... bn]T
wherein, the upper right corner T of the matrix represents the matrix transposition, and n refers to the number of the MEMS uniaxial gyroscopes;
using a linear kalman filter model, the covariance matrix differential equation is as follows:
K(t)＝P(t)HTR-1
wherein,
the differential of the covariance matrix is represented,
expressing the estimated value of the matrix X (t), solving a Riccati differential equation of the covariance matrix to obtain a steady state value of the covariance matrix; considering that the system is random, observable and stable, convergence is realized through fixed gain and covariance, and optimal fusion of measurement data is realized; where Z (t) is measurement information, H is a measurement matrix, K (t) is gain, R is measurement noise-1Is the inverse of the matrix R, p (t) is the state-filtered covariance,
for its differential, qωIs the filtering error;
2) information fusion between three axial MEMS single-axis gyroscope and optical fiber gyroscope
Firstly, a measurement model of a novel inertial navigation system based on a MEMS array is given, and the theoretical angular rates of an x axis, a y axis and a z axis under a b system are assumed as follows: omega ═ omegax ωy ωz]TThe measurement values of the MEMS uniaxial gyroscope and the inclined-axis fiber optic gyroscope which are arranged in the x axis, the y axis and the z axis are as follows: m ═ Mx i My i Mz i Mf i]T1,2,3, the following relationships are satisfied between the measured values and the theoretical values of the x-axis, the y-axis, and the z-axis
M＝Hω+ξ
Wherein H is a measurement matrix; xi is residual noise, generally, it is assumed that xi is white gaussian noise, and the statistical properties satisfy: e [ xi ]]＝0， E[ξξT]＝σ2I; where I is the identity matrix, σ is the mean square error, E [ xi ]]A desire of ξ;
the difference Δ M between a true angular velocity synthesis vector h ω and an actual measurement value M,
ΔM＝ωM-M
considering the performance difference between the MEMS uniaxial gyroscope and the fiber optic gyroscope in the array navigation system, when the angular velocity fusion is carried out, the weighting fusion is needed to be carried out, an objective function Q introducing a weight matrix S is given, as shown in the following,
the fusion relief angle velocity output can be obtained for the above objective function as follows,
wherein the upper right corner T represents the transpose of the matrix, -1 represents the inverse of the matrix;
the statistical variance of each measurement axis is used to construct a weight matrix S, which, as shown below,
wherein σxi、σyi、σzi、σfiThe variance of the MEMS gyroscope and FOG on each measurement axis in the ith statistical step is shown.
A calibration method of an inertial navigation system aims at the novel MEMS array-based inertial navigation system to carry out calibration, and comprises the steps of calibration before delivery and dynamic online calibration in the navigation process after delivery:
1) factory calibration
The error comprises a zero offset related error, a scale factor error and a mounting error, and the calibration of the zero offset related error and the scale factor error is carried out by adopting a multi-position method and a rate method;
the mounting error comprises an MEMS device mounting error and an inclined optical fiber gyro mounting error, the MEMS device mounting error is calibrated by adopting a projection relation and performance, and the inclined optical fiber gyro mounting error is calibrated by adopting the following method:
assuming the direction vector h of the sensitive axis of the inclined optical fiber gyroscopei' and ideal axis hiWith small angle error delta alphaiAnd δ βiDirection vector h of sensitive axis of optical fiber gyroscopei' at Xb-YbProjection vector and X on planebThe angle of the axes being alphai'，And Xb-YbAngle of plane is betai', so that:
hi'＝[cos(αi')cos(βi')]·i+[sin(αi')cos(βi')]·j+[sin(βi')]·k
wherein, δ αiFor azimuthal error, δ βiFor altitude angle error, i, j, k represent three orthogonal vector directions, let αi'＝αi-δαiAnd betai'＝βi+δβiSubstituting into the above equation, neglecting the second order small quantity (delta alpha)i·δβi) And sin (delta alpha)i)、sin(δβi) Linearized as δ αi、δβi，cos(δαi)、cos(δβi) Approximately 1, one can obtain:
hi'＝hi+δαi·pi+δβi·qi
wherein p isiAnd q isiIs the vector shown below:
2) post-factory dynamic online calibration method
The dynamic online calibration comprises MEMS uniaxial gyroscope zero error calibration and scale error calibration;
aiming at zero error calibration of the MEMS uniaxial gyroscope, the inclined high-precision fiber optic gyroscope is introduced, the static working condition is utilized to carry out real-time calibration of the correlation coefficient on the random drift term of the first-order Markov modeling, the one-time power-on stability of the correlation coefficient is fully utilized, and the subsequent fusion performance is guaranteed;
and aiming at calibration of the scale error of the MEMS uniaxial gyroscope, in the dynamic process, the scale error of the gyroscope is calibrated in real time by fusing with reference data of the fiber-optic gyroscope.
Compared with the prior art, the invention has the beneficial effects that:
firstly, a novel inertial navigation system concept and framework based on MEMS array type are provided for the first time, the structural mode of the existing traditional inertial navigation is broken through, the problems of poor precision and poor environmental adaptability of MEMS inertial devices are solved, the high-precision application of low-precision MEMS is realized, and the requirements of low cost, low power consumption and miniaturization of rocket military and missile weapons are met;
secondly, an information fusion system for the MEMS array is provided, and the fusion precision of the system is improved through the fusion between MEMS devices, between a high-precision fiber-optic gyroscope and the MEMS and the space-time fusion;
thirdly, a calibration method of the MEMS array type inertial navigation system is provided, and calibration of the scale error and the zero error is completed before delivery and in the on-line use process;
drawings
FIG. 1 is a diagram of a MEMS array configuration.
FIG. 2 is a schematic diagram of an array inertial navigation system configured in an inclined manner in MEMS + fiber-optic gyroscope space; wherein, FIG. 2(a) is a schematic diagram of an array configuration; fig. 2(b) is a diagram of a test verification object of the MEMS array navigation system.
FIG. 3 is a structural diagram of an MEMS array inertial navigation system.
FIG. 4 shows the installation relationship of the actual sensor axial direction and the system body coordinate system.
Detailed Description
The invention will be described in further detail below with reference to the drawings and examples.
Example one
A novel inertial navigation system based on MEMS array type is characterized in that a scheme of MEMS array axial parallel installation configuration and optical fiber gyro oblique installation configuration is adopted, an output reference plane of the array type inertial navigation system is set as a coordinate system b, a configuration scheme of each inertial navigation system under the coordinate system b is shown in figure 1, the MEMS devices are installed in parallel to form an array (X, Y, Z three directions), the middle of the optical fiber gyro is obliquely arranged to realize on-line calibration of all MEMS gyros on a quadrature axis, and a brand-new low-cost high-precision inertial navigation system is formed by combining.
As shown in fig. 2(a), under an orthogonal axis system, each axis direction comprises a plurality of MEMS accelerometers for measuring the acceleration and a plurality of MEMS uniaxial gyroscopes for measuring the angular velocity, thereby realizing redundant measurement of the acceleration and the angular velocity. The optical fiber gyroscope is obliquely arranged, so that the online calibration of the angular velocity error measured by the MEMS gyroscope is realized; the inclined installation mode of the fiber-optic gyroscope adopts a spatial inclined mode, and the spatial inclined mode of an O-xyz spatial coordinate system can realize the online calibration of X, Y, Z axial angular velocity measurement errors; the physical test verification is shown in fig. 2 (b).
Assembling the novel inertial navigation system based on the MEMS array type to form the inertial navigation device, as shown in fig. 3, arranging a frame structure and a structural member, wherein the frame structure is provided with a middle through hole and a surface groove, the positioning of the fiber-optic gyroscope and the MEMS array is respectively realized, and the structural member coats the frame structure to form the inertial navigation device.
The MEMS single axis gyro output can be described by the following mathematical model:
w＝wm+b+ε (1)
wherein w is the actual output of the MEMS gyroscope, wmFor the outer actual angular rate, b is zero offset and ε is noise. In general, ε follows a normal distribution of N to (0, σ). When n gyros are placed on the same axis, the output of the n gyros on the axis can be expressed by the following formula:
in the actual use process, the n gyro outputs are output after being fused, and can be simplified into output after average processing of each output, and then:
order to
Then there is wo＝wm+ b + δ, where ε follows a normal distribution of N to (0, σ).
When epsilon1,ε2...εnIndependent of each other, then delta is obeyed
The noise level can be reduced
In order of magnitude.
When epsilon1,ε2...εnWhen the correlation coefficients among the array gyroscopes are all fixed values rho, and when the number of the single axial array gyroscopes is n, the variance of the noise level can be expressed as:
namely, through setting up a plurality of MEMS unipolar gyro arrays, effectively reduced the noise level, improved measurement accuracy.
In the novel inertial navigation system based on the MEMS array, the output of a gyroscope and an accelerometer array is converted from a sensor coordinate system to a carrier coordinate system, multi-sensing information fusion and online calibration are carried out after conversion, fault detection and isolation are completed based on observation information in the fusion process, and finally a high-precision navigation result is output.
Example two
An information fusion method for an MEMS array type navigation system comprises the fusion between MEMS array devices and the fusion between an MEMS gyroscope and a fiber-optic gyroscope.
1) MEMS array device fusion method
The key of the MEMS array information fusion technology is that a plurality of common low-precision MEMS sensors form an array, an optimal filter is designed by carrying out redundancy detection on the same signal, the error of each sensor in the MEMS array is estimated in real time, and the measurement output information is compensated and corrected to obtain a high-precision measurement value. The fusion technology is based on an inertial device error model, and completes noise smoothing and model parameter estimation while estimating the true angular velocity. In general, gyro output y (t) includes true angular velocity ω(t), white noise n (t), and stochastic drift b (t), wherein the stochastic drift can be modeled as a first order Markov process
The gyro output can be written as:
for the array type navigation system, a plurality of angular velocity measurements exist in the same channel, but each angular velocity measurement not only has a real angular velocity, but also has related random drift and measurement white noise. Therefore, in the fusion process, modeling estimation needs to be performed on the random drift and the true angular velocity, and the true angular velocity ω (t) and the random drift b (t) are selected as state quantities, so that the state variable x (t) can be represented as:
X(t)＝[b ω]T,b＝[b1 ... bn]T (6)
in the formula, the upper right corner T of the matrix represents the matrix transposition.
Taking the linear kalman filter model as an example, the covariance matrix differential equation is as follows:
in the formula,
the differential of the covariance matrix is represented,
the estimated value of the matrix X (t) is expressed, and the steady state value of the variance matrix can be obtained by solving the Riccati differential equation of the covariance matrix. Convergence is achieved by fixing the gain and covariance, considering that the system is randomly observable and stable. Where Z (t) is measurement information, H is a measurement matrix, K (t) is gain, R is measurement noise-1Is the inverse of the matrix RP (t) is the state-filtered covariance,
for its differential, qωIs the filtering error.
2) MEMS gyroscope and optical fiber gyroscope fusion method
A self-adaptive weighted data fusion algorithm is provided, the weight of each inertia device is measured by utilizing the variance of a statistical interval, the fusion error is reduced, and a better estimation result is obtained.
Due to the real-time requirement of the system and the limitation of factors such as the limited storage data space of a navigation computer, the measurement error data needs to be preprocessed before variance statistics is carried out on the measurement error. Filtering outliers by median filtering based on limited memory. The estimation value of the measurement result in the self-adaptive limited memory median filtering method depends on the information provided by the latest data with limited length, is not influenced by the old data except the data length of the section, the influence on the estimation value of the measurement result is always the latest data with limited length, and the statistical variance of the measurement result can be adjusted through the difference of the set length, thereby ensuring the real-time performance and the accuracy of the system.
Taking a gyroscope as an example, analyzing data of the array type inertial navigation system. Assuming that the theoretical angular rates of the x-axis, the y-axis and the z-axis under the b system are as follows: omega ═ omegax ωy ωz]TThe measurement values of the MEMS gyroscope and the inclined-axis fiber optic gyroscope which are configured in the x-axis, the y-axis and the z-axis are as follows: m ═ Mx i My i Mz i Mf i]T1,2,3, the following relationships are satisfied between the measured values and the theoretical values of the x-axis, the y-axis, and the z-axis
M＝Hω+ξ (8)
In the formula, H is a measurement matrix; xi is residual noise, generally, it is assumed that xi is white gaussian noise, and the statistical properties satisfy: e [ xi ]]＝0， E[ξξT]＝σ2I. Where I is the identity matrix, σ is the mean square error, E [ xi ]]Is the expectation of ξ.
The difference Δ M between a true angular velocity synthesis vector h ω and an actual measurement value M,
ΔM＝ωM-M (9)
considering the performance difference between the MEMS gyroscope and the fiber optic gyroscope in the array navigation system, when the angular velocity fusion is performed, the weighting fusion is required to be performed, an objective function Q introducing a weight matrix S is given as follows,
the fusion relief angle velocity output can be obtained for the above objective function as follows,
the upper right corner T represents the transpose of the matrix, -1 represents the inverse of the matrix.
The statistical variance of each measuring axis is used for forming a weight matrix S to obtain
In the formula, σxi、σyi、σzi、σfiThe variance of the MEMS gyroscope and the fiber-optic gyroscope on each measuring axis in the ith statistical step length respectively. The variance is a statistical result obtained from real-time measurement errors of each measurement axis, so that the weight matrix S can be adaptively adjusted according to the output value of each measurement axis.
EXAMPLE III
Errors of the MEMS array type navigation system mainly comprise zero errors, scale errors and installation errors, and the errors need to be initially calibrated before delivery. The installation error can be guaranteed to be a constant value after leaving the factory through structural machining, the zero position error and the calibration error can change along with storage time, and online calibration needs to be carried out by means of external excitation during the storage period or the use process of the weapon system.
The calibration method of the novel inertial navigation system based on the MEMS array comprises the following steps:
1) factory calibration method
The error of the MEMS array type navigation system must be modeled before the calibration work of the MEMS array type navigation system is completed. Generally, the error model mainly comprises the zero offset correlation error, the scale factor and the mounting misalignment angle of each device. The zero-offset-related error and scale factor error calibration is not different from the conventional inertial measurement unit calibration, so that the calibration can be completed by adopting the conventional multi-position method and the conventional velocity method.
Because the array type navigation system internally comprises the MEMS devices which are orthogonally and parallelly installed and the optical fiber gyro which is obliquely installed, the installation error comprises a conversion matrix from all the MEMS devices which are parallelly installed to the system and a conversion matrix from the oblique optical fiber gyro to the system. The installation error conversion matrix of the MEMS device obeys small angle assumption, and can adopt projection relation direct and performance calibration. However, the mounting error of the obliquely-arranged fiber optic gyroscope does not satisfy the assumption of a small angular velocity, and the following processing is required.
In the MEMS array type navigation system, the tilted MEMS-INS coordinate system is not parallel to the coordinate system of the reference plane, and the tilted axis is described by the usable azimuth angle and the altitude angle. In the actual installation process, the direction vector h of the sensitive axis of the optical fiber gyroscope cannot be ensuredi' and ideal axis hiExact coincidence, assuming both have a small angle error δ αiAnd δ βiAs shown in fig. 4.
Suppose a sensor axis hi' at Xb-YbProjection vector and X on planebThe angle of the axes being alphai', and Xb-YbAngle of plane is betai', so that:
hi'＝[cos(αi')cos(βi')]·i+[sin(αi')cos(βi')]·j+[sin(βi')]·k (9)
wherein, δ αiFor azimuthal error, δ βiFor altitude angle error, i, j, k represent three orthogonal vector directions, let αi'＝αi-δαiAnd betai'＝βi+δβiSubstituting into the above equation, neglecting the second order small quantity (delta alpha)i·δβi) And sin (delta alpha)i)、sin(δβi) Linearized as δ αi、δβi，cos(δαi)、cos(δβi) Approximately 1, one can obtain:
hi'＝hi+δαi·pi+δβi·qi (10)
wherein p isiAnd q isiIs the vector shown below:
and calibrating the installation error of the inclined shaft according to the observation equation of the installation error.
2) Dynamic online calibration method
Considering that the scale repeatability and the correlation of the MEMS device change obviously along with time, the dynamic online calibration is mainly performed aiming at two errors, namely scale error and zero error.
Aiming at zero errors, due to the introduction of the inclined high-precision fiber-optic gyroscope, the real-time calibration of the correlation coefficient can be carried out on the random drift term of the first-order Markov modeling by using a static working condition, the one-time power-on stability of the correlation coefficient is fully utilized, and the subsequent fusion performance is guaranteed.
Aiming at the MEMS gyroscope scale factor, in the dynamic process, the scale error of the gyroscope is calibrated in real time by fusing with the reference data of the fiber-optic gyroscope.
The above description is only exemplary of the present invention and should not be taken as limiting the scope of the present invention, and any modifications, equivalents, improvements and the like that are within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (3)
1. A novel inertial navigation system based on a MEMS array is characterized by comprising MEMS arrays which are axially arranged in parallel and fiber-optic gyroscopes which are obliquely arranged, wherein the MEMS arrays are orthogonally arranged along X, Y, Z axial directions, each axial direction comprises a plurality of MEMS accelerometers and a plurality of MEMS single-axis gyroscopes, the MEMS accelerometers are used for measuring acceleration, and the MEMS single-axis gyroscopes are used for measuring angular velocity; the fiber optic gyroscope is arranged obliquely in space, and online calibration of X, Y, Z axial angular velocity measurement errors is achieved.
2. An information fusion method of an inertial navigation system, which adopts the novel MEMS array-based inertial navigation system of claim 1 to perform information fusion, and is characterized by comprising the information fusion between the same axial MEMS array device and the information fusion between three axial MEMS gyros and a single-axis fiber-optic gyroscope:
1) information fusion between same-axis MEMS array devices
The MEMS uniaxial gyro outputs y (t) all comprise true angular velocity omega (t), white noise n (t) and random drift b (t), wherein the random drift is modeled as a first order Markov process
The output model of the MEMS uniaxial gyroscope is as follows:
for the array type navigation system, n MEMS single-axis gyroscopes in the same axial direction are supposed to realize the measurement of the angular velocity, and according to the output model of the MEMS single-axis gyroscope, the angular velocity measurement value not only comprises the real angular velocity, but also has related random drift and measurement white noise; the modeling estimation of random drift and real angular velocity is realized through the fusion of a plurality of measured values; if the true angular velocity ω (t) and the random drift b (t) are selected as the state variables, the state variables x (t) can be expressed as:
X(t)＝[b ω]T，b＝[b1...bn]T
wherein, the upper right corner T of the matrix represents the matrix transposition, and n refers to the number of the MEMS uniaxial gyroscopes;
using a linear kalman filter model, the covariance matrix differential equation is as follows:
K(t)＝P(t)HTR-1
wherein,
the differential of the covariance matrix is represented,
expressing the estimated value of the matrix X (t), solving a Riccati differential equation of the covariance matrix to obtain a steady state value of the covariance matrix; considering that the system is random, observable and stable, convergence is realized through fixed gain and covariance, and optimal fusion of measurement data is realized; where Z (t) is measurement information, H is a measurement matrix, K (t) is gain, R is measurement noise-1Is the inverse of the matrix R, p (t) is the state-filtered covariance,
for its differential, qωIs the filtering error;
2) information fusion between three axial MEMS single-axis gyroscope and optical fiber gyroscope
Firstly, a measurement model of a novel inertial navigation system based on a MEMS array is given, and the theoretical angular rates of an x axis, a y axis and a z axis under a b system are assumed as follows: omega ═ omegax ωy ωz]TThe measurement values of the MEMS uniaxial gyroscope and the inclined-axis fiber optic gyroscope which are arranged in the x axis, the y axis and the z axis are as follows: m ═ Mx i My i Mz i Mf i]T1,2,3, the following relationships are satisfied between the measured values and the theoretical values of the x-axis, the y-axis, and the z-axis
M＝Hω+ξ
Wherein H is a measurement matrix; xi is residual noise, generally, it is assumed that xi is white gaussian noise, and the statistical properties satisfy: e [ xi ]]＝0，E[ξξT]＝σ2I; where I is the identity matrix, σ is the mean square error, E [ xi ]]A desire of ξ;
the difference Δ M between the true angular velocity resultant vector H ω and the actual measurement value M,
ΔM＝ωM-M
considering the performance difference between the MEMS uniaxial gyroscope and the fiber optic gyroscope in the array navigation system, when the angular velocity fusion is carried out, the weighting fusion is needed to be carried out, an objective function Q introducing a weight matrix S is given, as shown in the following,
the fusion relief angle velocity output can be obtained for the above objective function as follows,
wherein the upper right corner T represents the transpose of the matrix, -1 represents the inverse of the matrix;
the statistical variance of each measurement axis is used to construct a weight matrix S, which, as shown below,
wherein σxi、σyi、σzi、σfiThe variance of the MEMS gyroscope and FOG on each measurement axis in the ith statistical step is shown.
3. A calibration method of an inertial navigation system aims at the novel MEMS array-based inertial navigation system of claim 1, and is characterized by comprising the following steps of pre-factory calibration and dynamic online calibration in the post-factory navigation process:
1) factory calibration
The error comprises a zero offset related error, a scale factor error and a mounting error, and the calibration of the zero offset related error and the scale factor error is carried out by adopting a multi-position method and a rate method;
the mounting error comprises an MEMS device mounting error and an inclined optical fiber gyro mounting error, the MEMS device mounting error is calibrated by adopting a projection relation and performance, and the inclined optical fiber gyro mounting error is calibrated by adopting the following method:
assuming the direction vector h of the sensitive axis of the inclined optical fiber gyroscopei' and ideal axis hiWith small angle error delta alphaiAnd δ βiDirection vector h of sensitive axis of optical fiber gyroscopei' at Xb-YbProjection vector and X on planebThe angle of the axes being alphai', and Xb-YbAngle of plane is betai', so that:
hi′＝[cos(αi′)cos(βi′)]·i+[sin(αi′)cos(βi′)]·j+[sin(βi′)]·k
wherein, δ αiFor azimuthal error, δ βiFor altitude angle error, i, j, k represent three orthogonal vector directions, let αi′＝αi-δαiAnd betai′＝βi+δβiSubstituting into the above equation, neglecting the second order small quantity (delta alpha)i·δβi) And sin (delta alpha)i)、sin(δβi) Linearized as δ αi、δβi，cos(δαi)、cos(δβi) Approximately 1, one can obtain:
hi′＝hi+δαi·pi+δβi·qi
wherein p isiAnd q isiIs the vector shown below:
2) post-factory dynamic online calibration method
The dynamic online calibration comprises MEMS uniaxial gyroscope zero error calibration and scale error calibration;
aiming at zero error calibration of the MEMS uniaxial gyroscope, the inclined high-precision fiber optic gyroscope is introduced, the static working condition is utilized to carry out real-time calibration of the correlation coefficient on the random drift term of the first-order Markov modeling, the one-time power-on stability of the correlation coefficient is fully utilized, and the subsequent fusion performance is guaranteed;
and aiming at calibration of the scale error of the MEMS uniaxial gyroscope, in the dynamic process, the scale error of the gyroscope is calibrated in real time by fusing with reference data of the fiber-optic gyroscope.
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