Gravitational acceleration measuring method based on strapdown inertial navigation system

Abstract

The invention provides a gravitational acceleration measuring method based on a strapdown inertial navigation system, which comprises the following steps of: compensating a parameter error of an accelerometer by a two-position acquisition method; a 16-order FIR low-pass filter and a multi-channel three-parameter notch filter are combined to carry out noise reduction processing on data of the gyroscope and the accelerometer, so that the influence of environmental interference is reduced; and reversely resolving the gravitational acceleration by adopting an inertial navigation error equation to finally obtain the high-precision gravitational acceleration. The method is simple, convenient and easy to implement, low in cost and easy to popularize, the use environment is basically not limited, and the method can be applied to both the laboratory environment and the field severe environment; the gravitational acceleration measuring method disclosed by the invention has relatively strong anti-interference capability, and high-precision gravitational acceleration measurement under a complex working state is ensured.

Description

Technical Field

[0001] The invention belongs to the technical field of gravity acceleration measurement, and in particular relates to a gravity acceleration measurement method based on a strapdown inertial navigation system. Background Art

[0002] Gravity acceleration is one of the important parameters in the field of inertial navigation, and is widely used in many fields such as marine resource development, geological exploration, geodesy and underwater matching navigation. The existing gravity reference map is not accurate, which makes it difficult to use, unusable and inapplicable in various surface applications, and its role is very limited; static gravimeters have defects in measurement efficiency and applicability. For other environments such as mountains and the wild, static gravimeters are expensive to use and susceptible to interference. In recent years, the inertial navigation system has been assisted by various external platform frames and other device methods to effectively measure gravity acceleration. Therefore, in an environment where gravity acceleration is unknown (especially in a non-laboratory environment in the wild), obtaining local gravity acceleration in a short time through a strapdown inertial navigation system is of great significance to various engineering application fields, especially the field of weapons and equipment.

[0003] As an inertial measurement device, the strapdown inertial navigation system includes gyroscopes and accelerometers, internal and external frame rotation mechanisms, etc. The strapdown inertial navigation system is equipped with three accelerometers, namely the X-axis accelerometer, the Y-axis accelerometer, and the Z-axis accelerometer. The three accelerometers are sensitive to the information of gravity acceleration. By correcting the parameters of the output of the accelerometers, the value of gravity acceleration can be obtained. In complex field environments, high-frequency disturbances such as carrier engines and low-frequency disturbances such as wind disturbances can easily interfere with the output data of the accelerometer, and the measurement accuracy of gravity acceleration is low. Summary of the invention

[0004] The purpose of the present invention is to provide a method for measuring gravity acceleration based on a strapdown inertial navigation system in view of the shortcomings of the prior art, and the gravity acceleration measurement has high accuracy.

[0005] In order to achieve the above object, the technical solution adopted by the present invention is:

[0006] A method for measuring gravity acceleration based on a strapdown inertial navigation system, wherein the strapdown inertial navigation system is provided with a platform assembly, the platform assembly comprising an X-axis accelerometer, a Y-axis accelerometer, a Z-axis accelerometer, an X-axis gyroscope, a Y-axis gyroscope and a Z-axis gyroscope, and the platform assembly is located on a transfer mechanism;

[0007] The following steps are involved:

[0008] S1: The Z-axis accelerometer faces the first position, and the X-axis accelerometer, the Y-axis accelerometer, the Z-axis accelerometer, the X-axis gyroscope, the Y-axis gyroscope, and the Z-axis gyroscope collect and obtain the incremental data of the first position. The collection start time is t1 and the end time is t2;

[0009] S2: the indexing mechanism rotates 180°, the Z-axis accelerometer faces the second position, the X-axis accelerometer, the Y-axis accelerometer, the Z-axis accelerometer, the X-axis gyroscope, the Y-axis gyroscope, and the Z-axis gyroscope collect and obtain the incremental data of the second position, and the collection start time is t3 and the end time is t4;

[0010] S3: performing noise reduction processing on the incremental data of the first position and the incremental data of the second position;

[0011] S4: Calculate the gravitational acceleration using the inertial navigation error equation using the data processed by S3. The expression of the gravitational acceleration g is as follows:

[0012]

[0013]

[0014]

[0015] Among them, f u is the data of the Z-axis accelerometer after noise reduction in the navigation coordinate system, v e 、v n are the velocity components of the strapdown inertial system in the navigation coordinate system in the X and Y directions, is the latitude of the strapdown inertial system, a is the radius of the earth, a = 6378.245km, e1 is the curvature calculation coefficient, e1 = 0.006092, ω ie is the angular velocity of the earth’s rotation, h is the height of the strapdown inertial system, and δ is the error.

[0016] The present invention compensates for the parameter error of the accelerometer itself through a two-position acquisition method; combines noise reduction processing on the accelerometer data to reduce the influence of environmental interference; the present invention adopts an inertial navigation error equation to reversely solve the gravity acceleration. Since the speed error equation calculation can be considered as the accelerometer output error integral, the high-frequency signal of the data can be smoothed to improve the measurement accuracy of gravity acceleration.

[0017] Furthermore, the first position is a celestial position or a terrestrial position of a strapdown inertial navigation system.

[0018] Furthermore, the specific implementation process of S3 includes:

[0019] Preprocessing the incremental data of the first position and the incremental data of the second position by using a 16-order FIR low-pass filter to filter out high-frequency noise;

[0020] Fast Fourier transform is used to perform spectrum analysis on the preprocessed data;

[0021] A multi-channel three-parameter notch filter is used to filter the data processed by the 16th-order FIR low-pass filter to remove low-frequency interference noise.

[0022] Compared with the prior art, the present invention has the following beneficial effects:

[0023] The present invention can effectively offset the equivalent zero bias error and scale factor error of the accelerometer through a two-position testing method, thereby improving measurement accuracy.

[0024] The present invention combines a 16-order FIR low-pass filter and a multi-channel notch filter to perform noise reduction processing on the accelerometer data, thereby reducing the impact of environmental interference, so that the accelerometer data output is not affected by high-frequency disturbances such as carrier engines and low-frequency disturbances such as wind disturbances in complex field environments; the data measurement accuracy can be improved, thereby improving the measurement accuracy of gravity acceleration.

[0025] The present invention adopts the inertial navigation error equation to reversely solve the gravity acceleration. Since the speed error equation calculation can be regarded as the accelerometer output error integral, the high-frequency signal of the data can be smoothed to improve the measurement accuracy of gravity acceleration.

[0026] The method of the present invention is simple and easy to implement, has low cost, is easy to promote, and has no restrictions on the use environment, and can be applied in both laboratory environments and harsh outdoor environments.

[0027] The gravity acceleration measurement method of the present invention has strong anti-interference ability and ensures high-precision gravity acceleration measurement under complex working conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 It is a flow chart of a method for measuring gravity acceleration based on a strapdown inertial navigation system of the present invention;

[0029] Figure 2 It is a schematic diagram of the process of data noise reduction processing of the present invention. DETAILED DESCRIPTION

[0030] The present invention will be described in detail below in conjunction with the embodiments. It should be noted that the embodiments and features of the embodiments of the present invention can be combined with each other without conflict. For the convenience of description, if the words "upper", "lower", "left" and "right" appear in the following, they only indicate that the upper, lower, left and right directions are consistent with the drawings themselves, and do not limit the structure.

[0031] Example

[0032] This embodiment aims at the problem of how to quickly obtain effective gravity acceleration that can be used for inertial navigation system in a short time under an environment with unknown gravity acceleration (especially in a field non-laboratory environment), and proposes a gravity acceleration measurement method based on strapdown inertial navigation system. First, the strapdown inertial navigation system is turned on and preheated for 30 minutes or other functional tests are performed for more than 30 minutes, and then the Z-direction accelerometer of the strapdown inertial navigation system is located at the first position facing the sky to collect data, and then the Z-direction accelerometer of the strapdown inertial navigation system is rotated at a speed of 20° / s to be located at the second position facing the ground, and data is also collected, and then the data is subjected to noise reduction processing, and fast Fourier transform is used for spectrum analysis, and filters are set for each interference to extract effective information of accelerometer and gyroscope, and the processed data is used to calculate the gravity acceleration.

[0033] The strapdown inertial navigation system is a kind of reference carrier, and its general structure is composed of a platform assembly (including gyroscopes and accelerometers), an inner and outer frame rotation mechanism (transposition mechanism), a circuit board (power supply and signal acquisition machine data processing) and a base. The strapdown inertial navigation system is equipped with an X-axis accelerometer, a Y-axis accelerometer, a Z-axis accelerometer, an X-axis gyroscope, a Y-axis gyroscope, and a Z-axis gyroscope, and the X-axis accelerometer, the Y-axis accelerometer, the Z-axis accelerometer, the X-axis gyroscope, the Y-axis gyroscope, and the Z-axis gyroscope are arranged on the transposition mechanism.

[0034] The method can be used for a strapdown inertial navigation system with an external frame or an internal indexing mechanism rotating around a horizontal axis, so as to realize rotation between two positions.

[0035] Navigation coordinate system: a coordinate system selected as a navigation reference according to the needs of the navigation system during navigation. In this embodiment, the northeast celestial coordinate system is selected as the navigation coordinate system, that is, Ox points to the horizontal east direction (e, X direction), Oy axis points to the horizontal north direction (n, Y direction), and Oz points to the sky along the vertical direction (u, X direction).

[0036] Carrier coordinate system: The origin O is located at the center of gravity of the strapdown inertial navigation system, and the longitudinal axis Oy b Along its fore-aft line and pointing forward, the horizontal axis Ox b Pointing to the right, Oz b Perpendicular to Ox b y b , pointing upward along the vertical axis of the strapdown inertial navigation system.

[0037] like Figure 1 , a method for measuring gravity acceleration based on a strapdown inertial navigation system, comprising the following processes:

[0038] Step 1: Install the strapdown inertial navigation system on a stable platform, with the Z-axis accelerometer facing upward in the first position, and input the local position information, longitude λ, latitude

[0039] Step 2: After the strapdown inertial navigation system is turned on and preheated for 30 minutes or other functional tests are performed for more than 30 minutes, perform initial alignment to obtain the attitude conversion matrix and the initial attitude angle φ e ,φ n ,φ u (The error angles of the carrier coordinate system relative to the navigation coordinate system, namely the east angle error, north angle error and celestial angle error)

[0040] Step 3: Gyroscope and accelerometer incremental data are collected at the first position (sampling frequency 1k), with the collection starting time being t1 and ending time being t2;

[0041] The indexing mechanism is controlled to rotate at a speed of 20° / s so that the Z-direction accelerometer is located at a second position facing the ground. Incremental data of the gyroscope and accelerometer are collected at the second position, with the collection starting time being t3 and the end time being t4.

[0042] The incremental data is the data after the original output pulses of the gyroscope and accelerometer are compensated by the calibration parameters (scale factor, zero position and installation error).

[0043] Step 4: Figure 2 , the data collected at the first position and the second position are subjected to noise reduction processing, as follows:

[0044] (1) A low-pass FIR digital filter is designed using the equiripple design method. Considering that the bandwidth of the gyroscope and accelerometer data output signal is generally less than about 100 Hz, in order to minimize the attenuation of the effective data signal, the passband frequency is set to 200 Hz, the stopband frequency is set to 350 Hz, and the sampling frequency is 1000 Hz. Considering the phase delay and data calculation amount, the filter order is set to 16 based on engineering experience to ensure that high-frequency noise signals are filtered out.

[0045] The general principle of FIR low-pass filter is as follows:

[0046]

[0047] Where n is the sample index; x(n) is the input data, y(n) is the output data, b(k) is the kth coefficient of the filter, k ranges from 0 to N-1, and N is the length of the filter (i.e. the number of coefficients);

[0048] (2) Perform fast Fourier transform on the data processed by the 16th-order FIR low-pass filter for spectrum analysis, find low-frequency disturbance signals within 100 Hz and aliasing signal noise of high-frequency signals at low frequencies, design multi-channel three-parameter notch filters for different interference frequencies, and finally extract clean gyroscope and accelerometer output data. Multi-channel notch filters use multiple notch filters in series, find the number of disturbance frequencies based on Fourier transform, and determine the number of notch filters based on this number. Three important indicators of notch filters: ω n (notch center frequency), notch depth depth (attenuation multiple at the center frequency), notch bandwidth ωb (frequency difference when attenuated to -3db). According to spectrum analysis, the initial value of notch depth is set to 100, and the initial value of notch bandwidth is designed to be 5Hz.

[0049] The discrete form of the three-parameter filter is as follows:

[0050]

[0051] Among them, x1(n) is the input and y1(n) is the output; a1, a2, a3, and b1, b2, b3 are notch filter parameters, which are calculated by the notch frequency, notch depth and notch bandwidth through the MATLAB filter toolbox or filter function design.

[0052] Step 5: Calculate the gravitational acceleration using the inertial navigation error equation using the denoised data. The specific calculation formula is as follows:

[0053] The strapdown inertial system velocity equation is as follows:

[0054]

[0055] in: is the latitude, ω ie is the angular velocity of the earth's rotation; R1=(a+h) / (1-e1 2 sin 2 φ) 0.5 , R 2＝ (a+h) / (1-e1 2 ) / (1-e1 2 sin 2 φ) 1.5 , a = 6378.245 km is the radius of the earth, e1 = 0.006092 is the curvature calculation coefficient, h is the height of the strapdown inertial system, v i (i=e,n,u) is the velocity component (X, Y, Z direction) of the strapdown inertial system in the navigation coordinate system, is to differentiate the velocity component in the navigation coordinate system (X, Y, and Z directions), f i(i=e,n,u) is the output component of the accelerometer after noise reduction in the navigation coordinate system (X-axis, Y-axis, and Z-axis accelerometers), f b is the output component of the accelerometer along the three axes in the carrier coordinate system, It is the attitude transformation matrix from the carrier coordinate system to the navigation coordinate system, obtained by initial alignment or calibration, and g is the gravitational acceleration.

[0056] The calculation of inertial navigation error is essentially an integration in the time domain. The starting acquisition time at the first position is t1 (the initial value is 1), the end time is t2 (t2-t1=10min), and the start and end time of the second position is t3 and t4 (t4-t3=10min). The celestial velocity increment V obtained at the first position 1u , the second position gets the velocity increment V 2u , the gravitational acceleration g is calculated as follows:

[0057]

[0058] v e 、v n 、v u By integrating formula (1), we can get: u The points are as follows:

[0059]

[0060] When the single-power-on stability accuracy of the gyroscope and accelerometer is relatively high, the attitude error caused by the gyroscope is very small. According to the following equation (4), the scale factor error of the accelerometer itself can be compensated by half, and the equivalent zero bias error can be completely compensated. Therefore, while the data noise is filtered out by the filter to improve the data measurement accuracy, the parameter error of the accelerometer itself is also basically eliminated, and the measurement accuracy of the gravity accelerometer can be significantly improved.

[0061] δf u =δK 1Z / 2+(Δ 1u -Δ 2u ) / twenty four)

[0062] Where: Δ 1u and Δ 2u is the equivalent zero bias error of the accelerometer at the first and second positions; δK 1z is the Z-axis accelerometer scale factor error; δf u is the accelerometer output error.

[0063] The method of this embodiment compensates for the parameter error of the accelerometer itself through a two-position acquisition method; combines a 16th-order FIR low-pass filter and a multi-channel three-parameter notch filter to perform noise reduction processing on the accelerometer data to reduce the impact of environmental interference; uses the inertial navigation error equation to reversely solve the gravity acceleration, and finally obtains high-precision gravity acceleration.

[0064] The method of this embodiment is simple and easy to implement, low in cost, easy to promote, and has basically no restrictions on the use environment. It can be applied in both laboratory environments and harsh outdoor environments.

[0065] The gravity acceleration measurement method of this embodiment has strong anti-interference ability, ensuring high-precision gravity acceleration measurement under complex working conditions.

[0066] The contents explained in the above embodiments should be understood as these embodiments are only used to more clearly illustrate the present invention, and are not used to limit the scope of the present invention. After reading the present invention, various equivalent forms of modifications to the present invention by those skilled in the art all fall within the scope defined by the claims attached to this application.

Claims

1. A method for measuring gravity acceleration based on a strapdown inertial navigation system, wherein the strapdown inertial navigation system is provided with a platform assembly, the platform assembly comprising an X-axis accelerometer, a Y-axis accelerometer, a Z-axis accelerometer, an X-axis gyroscope, a Y-axis gyroscope and a Z-axis gyroscope, and the platform assembly is located on a transfer mechanism; It is characterized in that The following steps are involved: S1: The Z-axis accelerometer faces the first position, and the X-axis accelerometer, the Y-axis accelerometer, the Z-axis accelerometer, the X-axis gyroscope, the Y-axis gyroscope, and the Z-axis gyroscope collect and obtain the incremental data of the first position. The collection start time is t1 and the end time is t2; S2: the indexing mechanism rotates 180°, the Z-axis accelerometer faces the second position, the X-axis accelerometer, the Y-axis accelerometer, the Z-axis accelerometer, the X-axis gyroscope, the Y-axis gyroscope, and the Z-axis gyroscope collect and obtain the incremental data of the second position, and the collection start time is t3 and the end time is t4; S3: performing noise reduction processing on the incremental data of the first position and the incremental data of the second position; S4: Calculate the gravitational acceleration using the inertial navigation error equation using the data processed by S3. The expression of the gravitational acceleration g is as follows: Among them, f u is the data of the Z-axis accelerometer after noise reduction in the navigation coordinate system, v e 、v n are the velocity components of the strapdown inertial system in the navigation coordinate system in the X and Y directions, is the latitude of the strapdown inertial system, a is the radius of the earth, a = 6378.245 km, e1 is the curvature calculation coefficient, e1 = 0.006092, ω ie is the angular velocity of the earth’s rotation, h is the height of the strapdown inertial system, and δ is the error.

2. The method for measuring gravity acceleration based on a strapdown inertial navigation system according to claim 1, wherein: The first position is the celestial position or the terrestrial position of the strapdown inertial navigation system.

3. The method for measuring gravity acceleration based on a strapdown inertial navigation system according to claim 1, characterized in that: The specific implementation process of S3 includes: Preprocessing the incremental data of the first position and the incremental data of the second position by using a 16-order FIR low-pass filter to filter out high-frequency noise; Fast Fourier transform is used to perform spectrum analysis on the preprocessed data; A multi-channel three-parameter notch filter is used to filter the data processed by the 16th-order FIR low-pass filter to remove low-frequency interference noise.

Images