CN113790737A - On-site rapid calibration method of array sensor - Google Patents
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Abstract
The invention discloses a field quick calibration method of an array sensor, belonging to the field of intelligent system navigation measurement. The method can realize the real-time quick calibration of the array sensor on a task site, estimates the optimal calibration parameter by a least square fitting method and corrects the zero offset and the scale factor of the IMU by using the correlation of the array sensor and the method of combining the static test and the dynamic test, can obviously improve the navigation precision, greatly reduces the on-site use difficulty of the array sensor, and can ensure the reliability of the calibration by checking the calibration result.
Description
Technical Field
The invention relates to the field of intelligent system navigation measurement, in particular to a field rapid calibration method of an array sensor.
Background
With the rapid development of science and technology, no matter intelligent vehicles, unmanned aerial vehicles or high-precision accurate striking weapons, the research and development of the intelligent vehicle and unmanned aerial vehicles are far from an inertial navigation system. The inertial navigation system provides accurate attitude and position information for navigation and positioning of intelligent and automatic machinery, wherein the MEMS inertial device plays a key role in various industries due to the characteristics of low cost, small volume, light weight and easy batch production.
The inertial navigation system can be used without prior calibration. The traditional calibration method is characterized in that a mounting reference surface is used as a reference, calibration is carried out based on a speed position turntable, and zero position and scale factor calibration is mainly completed, wherein the mounting error is only related to the initial relative position relation, the parameter stability of the general mounting error is good after calibration is completed, but the parameter stability of the zero position and the scale factor is poor. As the time of leaving factory is prolonged, the parameter retention capability of the zero position and the scale factor of the MEMS inertial device is poor, which may cause the performance degradation of the MEMS inertial device, and therefore, a simple field calibration method is required to calibrate the parameters quickly.
The field rapid calibration technology of the array sensor is beneficial to correcting various parameters of the IMU sensor, improves the navigation precision and can greatly reduce the field use difficulty. The research on the field calibration technology of the array sensor is not only beneficial to the field of automatic driving, but also beneficial to the relevant field of navigation measurement of the array sensor. Therefore, research on the field rapid calibration technology of the array sensor is very important.
Disclosure of Invention
In view of this, the invention provides a field rapid calibration method for an array sensor, which is used for rapidly calibrating the array sensor on the product use field, correcting the residual error of the sensor and reducing the field use difficulty.
The invention provides a field rapid calibration method of an array sensor, which comprises the following steps:
s1: turning over the array sensor at least at 6 different positions, and simultaneously performing static sampling on each position for a first preset time length by using the array sensor to obtain static sampling data; the overturning position ensures that acceleration projection components exist on the x axis, the y axis and the z axis of all sensors in the array sensor;
s2: freely rotating the array sensor, and dynamically sampling for a second preset time by using the array sensor to obtain dynamic sampling data; the free rotation ensures angular velocity projection components on the x axis, the y axis and the z axis of all sensors in the array sensor;
s3: respectively selecting data with the maximum acceleration of the sensor to be calibrated in the x axis, the y axis and the z axis from the static sampling data, and calculating the zero offset and the scale factor of the accelerometer of the sensor to be calibrated by using the selected data and the acceleration data of other sensors except the sensor to be calibrated in the static sampling data; calculating the zero offset and the scale factor of the gyroscope of the sensor to be calibrated by utilizing the angular velocity data of other sensors except the sensor to be calibrated in the dynamic sampling data; repeating the step S3 until all sensors in the array sensor are traversed;
s4: the zero offset of the accelerometers and gyros of all sensors in the array sensor is verified, and the scale factors of the accelerometers and gyros of all sensors in the array sensor are verified.
In a possible implementation manner, in the method for quickly calibrating an array sensor on site provided by the present invention, in step S1, the turning the array sensor over at least 6 different positions specifically includes:
the array sensors are turned to be vertically upward along the x axes of all the sensors, the array sensors are turned to be vertically downward along the x axes of all the sensors, the array sensors are turned to be vertically upward along the y axes of all the sensors, the array sensors are turned to be vertically downward along the y axes of all the sensors, the array sensors are turned to be vertically upward along the z axes of all the sensors, and the array sensors are turned to be vertically downward along the z axes of all the sensors.
In a possible implementation manner, in the method for rapidly calibrating the array sensor on site provided by the present invention, in step S1, the first preset time period is at least 3 min.
In a possible implementation manner, in the method for quickly calibrating the array sensor on the spot provided by the invention, in step S2, the second preset time period is at least 3 min.
In a possible implementation manner, in the field rapid calibration method of the array sensor provided by the present invention, step S3 is to select the data with the maximum acceleration of the sensor to be calibrated in the x-axis, the y-axis and the z-axis from the static sampling data, and calculate the zero offset and the scaling factor of the accelerometer of the sensor to be calibrated by using the selected data and the acceleration data of the other sensors except the sensor to be calibrated in the static sampling data; the method comprises the following steps of calculating the zero offset and the scale factor of a gyroscope of a sensor to be calibrated by utilizing the angular velocity data of other sensors except the sensor to be calibrated in dynamic sampling data, and specifically comprises the following steps:
assuming that the array sensor comprises N +1 sensors, the measurement equation of the gyroscope or accelerometer aiming at the x axis, the y axis and the z axis of the p-th sensor to be calibrated is as follows:
wherein ireal-x、ireal-yAnd ireal-zRespectively representing the dimension-based theoretical values of the x axis, the y axis and the z axis of the sensor to be calibrated, and fusing and determining the other N sensors except the sensor to be calibrated through a Kalman filter; measured value sensorpx、sensorpyAnd sensorpzRespectively representing output digital quantities without dimension of an x axis, a y axis and a z axis of the sensor to be calibrated; SFpx、SFpy and SFpz represents the scaling factors of the x-axis, y-axis and z-axis of the p-th sensor to be calibrated, respectively, bpRepresents the zero offset, v, of the p-th sensor to be calibratedpRepresenting the residual error of the p-th sensor to be calibrated;
for the MEMS array composed of other N sensors except the sensor to be calibrated, the measurement equation and the observation equation are as follows:
Z(t)＝H·ω+v(t) (3)
wherein, X (t) represents a state variable of the Kalman filter, the state variable is a real acceleration or a real angular velocity, and the state variable is 1-dimensional; z (t) represents the output values of other N sensors except the sensor to be calibrated; h is a measurement matrix which represents the conversion relation between each sensor and the carrier system; ω represents the true acceleration or true angular velocity,
nωrepresents a mean of 0 and a variance of qωWhite noise of (2); f is a zero matrix, ω (t) is process noise, v (t) is observation noise;
the kalman filter equation is:
K(t)＝P(t)HTR-1 (5)
wherein K (t) represents the gain variation of the Kalman filter along with time, and P (t) represents the estimation error variation of the Kalman filter along with time; r is the covariance matrix of the measurement noise, expressed as:
wherein q isnRepresenting the variance of ARW noise of the sensor to be calibrated, and rho representing the cross-correlation coefficient of the array sensor;
k (t) iteratively converges to a fixed value, which is given by:
c＝HTR-1H (8)
wherein, K∞Representing the iterative convergence of the gain of the Kalman filter, P∞Representing the iterative convergence value of the estimation error of the Kalman filter;
using k (t) to derive a continuous-time kalman filter state variable estimate as:
discretizing the Kalman filtering state variable of continuous time, using zero-order holding, assuming that the acceleration or the angular speed is a constant value in the whole sampling period, obtaining:
wherein, t0Which represents the interval of sampling,
output of a gyro or accelerometer representing a virtual sensor consisting of N sensors other than the sensor to be calibrated, Zk+1Representing the original output of other N sensors except the sensor to be calibrated; performing linear least square fitting by utilizing the relationship between the output of the sensor to be calibrated and the virtual sensor to obtain the zero offset and the scale factor of the sensor to be calibrated:
wherein the content of the first and second substances,
represents the scaling factor of the sensor to be calibrated,
indicating the zero offset of the sensor to be calibrated.
In a possible implementation manner, in the method for rapidly calibrating the array sensor in the field provided by the present invention, in step S4, the zero-offset of the accelerometers and the gyros of all sensors in the array sensor is checked, and the calibration factors of the accelerometers and the gyros of all sensors in the array sensor are checked, which specifically includes:
s41: standing the array sensor, collecting an accelerometer output value and a gyro output value of each sensor in the array sensor, checking the zero-offset calibration effect of the accelerometer by using the fact that the sum of squares of the accelerometer output values of the sensors is equal to the acceleration of gravity, and checking the zero-offset calibration effect of the gyro by using the fact that the gyro output value of each sensor is zero;
s42: and the array sensor is placed back to the original position after freely rotating, and the calibration effect of the scale factors of the accelerometer and the gyroscope is checked by performing navigation calculation on the accelerometer and the gyroscope.
The invention provides a field rapid calibration method of an array sensor, which belongs to the field of intelligent system navigation measurement. The method can realize the real-time quick calibration of the array sensor on a task site, estimates the optimal calibration parameter by a least square fitting method and corrects the zero offset and the scale factor of the IMU by using the correlation of the array sensor and the method of combining the static test and the dynamic test, can obviously improve the navigation precision, greatly reduces the on-site use difficulty of the array sensor, and can ensure the reliability of the calibration by checking the calibration result.
Drawings
Fig. 1 is a schematic flow chart of a method for on-site rapid calibration of an array sensor according to embodiment 1 of the present invention;
FIG. 2 is a graph of the raw output of a sensor including zero offset and scale factor error;
FIG. 3 is a schematic diagram of the generation of raw data as shown in FIG. 2 using a sensor trajectory generator;
FIG. 4 is a graph of compensated sensor output;
FIG. 5 is a diagram of a noise model for a single axis sensor;
FIG. 6 is a flow chart of Kalman filtering of an array sensor.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only illustrative and are not intended to limit the present invention.
The invention provides a field rapid calibration method of an array sensor, which comprises the following steps:
s1: turning over the array sensor at least at 6 different positions, and simultaneously performing static sampling on each position for a first preset time length by using the array sensor to obtain static sampling data; the overturning position ensures that acceleration projection components exist on the x axis, the y axis and the z axis of all sensors in the array sensor;
s2: freely rotating the array sensor, and dynamically sampling for a second preset time by using the array sensor to obtain dynamic sampling data; the free rotation ensures angular velocity projection components on the x axis, the y axis and the z axis of all sensors in the array sensor;
s3: respectively selecting data with the maximum acceleration of the sensor to be calibrated in the x axis, the y axis and the z axis from the static sampling data, and calculating the zero offset and the scale factor of the accelerometer of the sensor to be calibrated by using the selected data and the acceleration data of other sensors except the sensor to be calibrated in the static sampling data; calculating the zero offset and the scale factor of the gyroscope of the sensor to be calibrated by utilizing the angular velocity data of other sensors except the sensor to be calibrated in the dynamic sampling data; repeating the step S3 until all sensors in the array sensor are traversed;
s4: the zero offset of the accelerometers and gyros of all sensors in the array sensor is verified, and the scale factors of the accelerometers and gyros of all sensors in the array sensor are verified.
The following is a detailed description of an implementation of the method for rapidly calibrating the array sensor on site according to an embodiment of the present invention.
Example 1:
taking a Micro-Electro-Mechanical System (MEMS) array as an example, a single-axis sensor in a sub-IMU in the MEMS array is first modeled, and for an accelerometer or a gyroscope of a q-th axis sensor of a p-th sub-IMU, a model formula of the sensor is as follows:
wherein x ism、ym、zmRespectively representing the real acceleration or angular velocity of the x axis, the y axis and the z axis of the selected carrier coordinate system; the h matrix is a transformation matrix which is converted from a carrier coordinate system to a sub-IMU coordinate system, and is determined to be known when the MEMS array configuration is determined and is installed on the carrier; sensorpRepresenting a digital quantity of the p-th sub-sensor measurement without dimension;
representing the zero offset of the q-th axis sensor of the p-th sub-IMU,
representing the random noise of the q-axis sensor of the p-th sub-IMU.
Because the array sensor can sense gravity as a known stimulus when standing, the zero offset and scale factor of the accelerometer of the array sensor can be calibrated by using gravity as a reference. Since the rotational angular velocity of the earth is an imperceptible small quantity for the MEMS gyroscope, an external excitation needs to be additionally provided to calibrate the gyroscope of the MEMS array, and particularly, the angular velocity excitation can be applied to the MEMS array by a method of rotating the handheld MEMS array.
When the accelerometer in the MEMS array is calibrated by utilizing gravity excitation, the gravity excitation is required to be applied to the three axes x, y and z, and because the equation (1) comprises 6 unknowns, namely zero offset and scale of the accelerometer of the three-axis x, y and z sensors, the MEMS array needs to be overturned for 6 different positions to perform IMU sampling, and then each calibration parameter of the accelerometer of the MEMS array is obtained by solving an equation set (consisting of equations of each axis of each sensor). For a gyroscope, a handheld MEMS array needs to rotate freely, and the rotation only needs to ensure that the x, y, and z axes of all sensors in the MEMS array can sense the angular velocity.
As shown in fig. 1, the specific steps are as follows:
the first step is as follows: turning over the array sensor at least at 6 different positions, and simultaneously performing static sampling on each position for a first preset time length by using the array sensor to obtain static sampling data; the turning position is required to ensure that acceleration projection components exist on the x-axis, the y-axis and the z-axis of all sensors in the array sensor.
Specifically, flipping the array sensor over at least 6 different positions can be achieved by: the array sensors are turned to be vertically upward along the x axes of all the sensors, the array sensors are turned to be vertically downward along the x axes of all the sensors, the array sensors are turned to be vertically upward along the y axes of all the sensors, the array sensors are turned to be vertically downward along the y axes of all the sensors, the array sensors are turned to be vertically upward along the z axes of all the sensors, and the array sensors are turned to be vertically downward along the z axes of all the sensors. The first preset time is at least 3 min.
The second step is that: freely rotating the array sensor, and dynamically sampling for a second preset time by using the array sensor to obtain dynamic sampling data; wherein the free rotation ensures angular velocity projection components on the x-axis, y-axis and z-axis of all sensors in the array sensor.
Specifically, the array sensor can be freely rotated by being held by a hand, and the second preset time is at least 3 min.
The third step: respectively selecting data with the maximum acceleration of the sensor to be calibrated in the x axis, the y axis and the z axis from the static sampling data, and calculating the zero offset and the scale factor of the accelerometer of the sensor to be calibrated by using the selected data and the acceleration data of other sensors except the sensor to be calibrated in the static sampling data; and calculating the zero offset and the scale factor of the gyroscope of the sensor to be calibrated by utilizing the angular velocity data of other sensors except the sensor to be calibrated in the dynamic sampling data.
Specifically, assuming that the array sensor includes N +1 sensors, the measurement equation of the gyroscope or accelerometer for the x-axis, y-axis and z-axis of the p-th sensor to be calibrated may be:
wherein ireal-x、ireal-yAnd ireal-zRespectively representing the dimension-based theoretical values of the x axis, the y axis and the z axis of the sensor to be calibrated, and fusing and determining the other N sensors except the sensor to be calibrated through a Kalman filter; measured value sensorpx、sensorpyAnd sensorpzRespectively representing output digital quantities without dimension of an x axis, a y axis and a z axis of the sensor to be calibrated; SFpx、SFpy and SFpz represents the scaling factors of the x-axis, y-axis and z-axis of the p-th sensor to be calibrated, respectively, bpRepresents the zero offset, v, of the p-th sensor to be calibratedpRepresenting the residual error of the p-th sensor to be calibrated.
After obtaining static sampling data for 6 positions, the accelerometer of the 1 st sensor in the MEMS array is calibrated first, and then the accelerometers of the next N sensors are calibrated in sequence. Taking the accelerometer of the x axis of the first sensor in the MEMS array as an example, 2 groups of data with the largest average output of the accelerometer of the x axis of the 1 st sensor are selected from the 6 groups of data to be used as the data group calibrated by the accelerometer of the x axis, and the virtual accelerometer composed of the accelerometers of the other N sensors performs zero offset and scale factor correction on the accelerometer to be calibrated. For the gyroscope, after acquiring the dynamically freely rotating gyroscope data, calibrating the gyroscope of the 1 st sensor, and then sequentially calibrating the gyroscopes of the following N sensors, taking the x-axis gyroscope of the first sensor in the MEMS array as an example, and performing zero offset and scale factor correction on the accelerometer to be calibrated through the virtual gyroscope formed by the gyroscopes of other N sensors.
For the MEMS array composed of other N sensors except the sensor to be calibrated, the measurement equation and the observation equation are as follows:
Z(t)＝H·ω+v(t) (4)
wherein, X (t) represents a state variable of the Kalman filter, the state variable is a real acceleration or a real angular velocity, and the state variable is 1-dimensional; z (t) represents the output values of other N sensors except the sensor to be calibrated; h is a measurement matrix which represents the conversion relation between each sensor and the carrier system; ω represents the true acceleration or true angular velocity,
nωrepresents a mean of 0 and a variance of qωWhite noise of (2); f is the zero matrix, ω (t) is the process noise, and v (t) is the observation noise.
The kalman filter equation can be expressed as:
K(t)＝P(t)HTR-1 (6)
wherein K (t) represents the gain variation of the Kalman filter along with time, and P (t) represents the estimation error variation of the Kalman filter along with time; r is a covariance matrix of the measurement noise, the R matrix is not a diagonal matrix because of the correlation between different MEMS sensors, and the R matrix is expressed as:
wherein q isnThe variance of ARW noise of the sensor to be calibrated is represented, and rho represents the cross-correlation coefficient of the array sensor.
Since the kalman filter system is entirely observable, the k (t) iteration converges to a fixed value, which can be obtained by:
c＝HTR-1H (9)
wherein, K∞Representing the iterative convergence of the gain of the Kalman filter, P∞And the estimated error of the Kalman filter is expressed by the iterative convergence value.
Using k (t) to derive a continuous-time kalman filter state variable estimate as:
discretizing the Kalman filtering state variable of continuous time, using zero-order hold, assuming that the acceleration or angular velocity is constant in the whole sampling period, obtaining:
wherein, t0Which represents the interval of sampling,
output of a gyro or accelerometer representing a virtual sensor consisting of N sensors other than the sensor to be calibrated, Zk+1Representing the original output of other N sensors except the sensor to be calibrated; performing linear least square fitting by utilizing the relationship between the output of the sensor to be calibrated and the virtual sensor to obtain the zero offset and the scale factor of the sensor to be calibrated:
wherein the content of the first and second substances,
represents the scaling factor of the sensor to be calibrated,
indicating the zero offset of the sensor to be calibrated.
And repeating the third step until all the sensors in the array sensor are traversed.
The fourth step: the zero offset of the accelerometers and gyros of all sensors in the array sensor is verified, and the scale factors of the accelerometers and gyros of all sensors in the array sensor are verified.
Specifically, the array sensor is placed still, the accelerometer output value and the gyroscope output value of each sensor in the array sensor are collected, the calibration effect of the zero offset of the accelerometer is tested by using the fact that the sum of squares of the accelerometer output values of each sensor is equal to the acceleration of gravity, and the calibration effect of the zero offset of the gyroscope is tested by using the fact that the gyroscope output value of each sensor is zero; then, the array sensor is placed back to the original position after freely rotating, and the calibration effect of the scale factors of the accelerometer and the gyroscope is checked by performing navigation calculation on the accelerometer and the gyroscope.
Fig. 2 shows an example of a gyro output value in the x-axis direction, and 4-axis gyro data is generated by simulation. Then, by matlab software, the angular random walk ARW parameter of the gyros within the MEMS array is set to 0.0833 °/(h ^ (1/2)), the rate random walk RRW parameter is 600 °/(h ^ (3/2)), the input angular rate is zero, 18000s of sensor raw data is generated according to the trajectory generator as shown in FIG. 3, the sampling interval is set to 10ms, and zero offset and scale factor error are added. FIG. 4 is the calibrated gyro output value, and it can be seen from FIG. 4 that the residual zero offset and the scale factor of the sensor are obtained through the data of 4 gyros in the array generated through simulation and calibration, and the peak-to-peak value of the compensated angular velocity error is reduced from 1 °/s to 0.3 °/s, which indicates that the accuracy of the sensor is obviously improved.
Fig. 5 is a diagram of a single-axis sensor noise model, where T in fig. 5 is a sensor sampling period, and the output of each single-axis sensor can be modeled as a combination of a true angular velocity, an angular random walk ARW, and an angular rate random walk RRW, which are unified into the same unit (deg/s) from the conversion relationship in fig. 5.
Fig. 6 is a kalman filtering flowchart of the array sensor, and by the method shown in fig. 6, the output of the calibration reference virtual sensor at the current time can be obtained through iteration after each sampling.
The invention provides a field rapid calibration method of an array sensor, which belongs to the field of intelligent system navigation measurement. The method can realize the real-time quick calibration of the array sensor on a task site, estimates the optimal calibration parameter by a least square fitting method and corrects the zero offset and the scale factor of the IMU by using the correlation of the array sensor and the method of combining the static test and the dynamic test, can obviously improve the navigation precision, greatly reduces the on-site use difficulty of the array sensor, and can ensure the reliability of the calibration by checking the calibration result.
It will be apparent to those skilled in the art that various changes and modifications may be made in the present invention without departing from the spirit and scope of the invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.
Claims (6)
1. A field rapid calibration method of an array sensor is characterized by comprising the following steps:
s1: turning over the array sensor at least at 6 different positions, and simultaneously performing static sampling on each position for a first preset time length by using the array sensor to obtain static sampling data; the overturning position ensures that acceleration projection components exist on the x axis, the y axis and the z axis of all sensors in the array sensor;
s2: freely rotating the array sensor, and dynamically sampling for a second preset time by using the array sensor to obtain dynamic sampling data; the free rotation ensures angular velocity projection components on the x axis, the y axis and the z axis of all sensors in the array sensor;
s3: respectively selecting data with the maximum acceleration of the sensor to be calibrated in the x axis, the y axis and the z axis from the static sampling data, and calculating the zero offset and the scale factor of the accelerometer of the sensor to be calibrated by using the selected data and the acceleration data of other sensors except the sensor to be calibrated in the static sampling data; calculating the zero offset and the scale factor of the gyroscope of the sensor to be calibrated by utilizing the angular velocity data of other sensors except the sensor to be calibrated in the dynamic sampling data; repeating the step S3 until all sensors in the array sensor are traversed;
s4: the zero offset of the accelerometers and gyros of all sensors in the array sensor is verified, and the scale factors of the accelerometers and gyros of all sensors in the array sensor are verified.
2. The method for on-site rapid calibration of the array sensor according to claim 1, wherein the step S1 of turning the array sensor over at least 6 different positions specifically comprises:
the array sensors are turned to be vertically upward along the x axes of all the sensors, the array sensors are turned to be vertically downward along the x axes of all the sensors, the array sensors are turned to be vertically upward along the y axes of all the sensors, the array sensors are turned to be vertically downward along the y axes of all the sensors, the array sensors are turned to be vertically upward along the z axes of all the sensors, and the array sensors are turned to be vertically downward along the z axes of all the sensors.
3. The method for on-site rapid calibration of an array sensor according to claim 1, wherein in step S1, the first predetermined time period is at least 3 min.
4. The method for on-site rapid calibration of an array sensor according to claim 1, wherein in step S2, the second predetermined time period is at least 3 min.
5. The on-site rapid calibration method for the array sensor according to claim 1, wherein in step S3, the data with the largest acceleration of the sensor to be calibrated in the x-axis, the y-axis and the z-axis are respectively selected from the static sampling data, and the zero offset and the scale factor of the accelerometer of the sensor to be calibrated are calculated by using the selected data and the acceleration data of the other sensors except the sensor to be calibrated in the static sampling data; the method comprises the following steps of calculating the zero offset and the scale factor of a gyroscope of a sensor to be calibrated by utilizing the angular velocity data of other sensors except the sensor to be calibrated in dynamic sampling data, and specifically comprises the following steps:
assuming that the array sensor comprises N +1 sensors, the measurement equation of the gyroscope or accelerometer aiming at the x axis, the y axis and the z axis of the p-th sensor to be calibrated is as follows:
wherein ireal-x、ireal-yAnd ireal-zRespectively representing the dimension-based theoretical values of the x axis, the y axis and the z axis of the sensor to be calibrated, and fusing and determining the other N sensors except the sensor to be calibrated through a Kalman filter; measured value sensorpx、sensorpyAnd sensorpzRespectively representing output digital quantities without dimension of an x axis, a y axis and a z axis of the sensor to be calibrated; SFpx、SFpy and SFpz represents the scaling factors of the x-axis, y-axis and z-axis of the p-th sensor to be calibrated, respectively, bpRepresents the zero offset, v, of the p-th sensor to be calibratedpRepresenting the residual error of the p-th sensor to be calibrated;
for the MEMS array composed of other N sensors except the sensor to be calibrated, the measurement equation and the observation equation are as follows:
Z(t)＝H·ω+v(t) (3)
wherein, X (t) represents a state variable of the Kalman filter, the state variable is a real acceleration or a real angular velocity, and the state variable is 1-dimensional; z (t) represents the output values of other N sensors except the sensor to be calibrated; h is a measurement matrix which represents the conversion relation between each sensor and the carrier system; ω represents the true acceleration or true angular velocity,
nωrepresents a mean of 0 and a variance of qωWhite noise of (2); f is a zero matrix, ω (t) is process noise, v (t) is observation noise;
the kalman filter equation is:
K(t)＝P(t)HTR-1 (5)
wherein K (t) represents the gain variation of the Kalman filter along with time, and P (t) represents the estimation error variation of the Kalman filter along with time; r is the covariance matrix of the measurement noise, expressed as:
wherein q isnRepresenting the variance of ARW noise of the sensor to be calibrated, and rho representing the cross-correlation coefficient of the array sensor;
k (t) iteratively converges to a fixed value, which is given by:
c＝HTR-1H (8)
wherein, K∞Representing the iterative convergence of the gain of the Kalman filter, P∞Representing the iterative convergence value of the estimation error of the Kalman filter;
using k (t) to derive a continuous-time kalman filter state variable estimate as:
discretizing the Kalman filtering state variable of continuous time, using zero-order holding, assuming that the acceleration or the angular speed is a constant value in the whole sampling period, obtaining:
wherein, t0Which represents the interval of sampling,
output of a gyro or accelerometer representing a virtual sensor consisting of N sensors other than the sensor to be calibrated, Zk+1Representing the original output of other N sensors except the sensor to be calibrated; performing linear least square fitting by utilizing the relationship between the output of the sensor to be calibrated and the virtual sensor to obtain the zero offset and the scale factor of the sensor to be calibrated:
wherein the content of the first and second substances,
represents the scaling factor of the sensor to be calibrated,
indicating the zero offset of the sensor to be calibrated.
6. The method for on-site rapid calibration of an array sensor according to claim 1, wherein step S4, the zero-offset test of the accelerometers and gyros of all sensors in the array sensor, and the calibration factor test of the accelerometers and gyros of all sensors in the array sensor, specifically include:
s41: standing the array sensor, collecting an accelerometer output value and a gyro output value of each sensor in the array sensor, checking the zero-offset calibration effect of the accelerometer by using the fact that the sum of squares of the accelerometer output values of the sensors is equal to the acceleration of gravity, and checking the zero-offset calibration effect of the gyro by using the fact that the gyro output value of each sensor is zero;
s42: and the array sensor is placed back to the original position after freely rotating, and the calibration effect of the scale factors of the accelerometer and the gyroscope is checked by performing navigation calculation on the accelerometer and the gyroscope.
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