Inertial navigation and telescope mutual alignment and inertial navigation precision detection method

Abstract

The application provides a kind of inertial navigation and telescope mutual alignment and inertial navigation precision detection method, and relates to the field of attitude measurement and error detection. For the mutual alignment problem of inertial navigation and telescope, currently, the least square fitting rotation matrix between the coordinate systems of two instruments is usually based on the pointing vector, and the measurement error of inertial navigation is regarded as a random disturbance term, and the calculation is relatively complex. For the inertial navigation attitude measurement precision detection problem, traditionally, the Euler angle comparison method is used in the laboratory with the help of high-precision turntable, which is difficult to operate. The application provides an installation error estimation method between the coordinate systems of two instruments based on the equivalent rotation vector idea, and the preliminary mutual alignment of inertial navigation and telescope and the overall evaluation of inertial navigation attitude measurement precision are realized through data analysis after one rotation test, which has the advantages of simple operation, quickness and strong practicability.

Description

Technical Field

[0001] This invention relates to the technical field of attitude measurement and processing, specifically to a method for mutual alignment of inertial navigation and telescope and for detecting the accuracy of inertial navigation. Background Technology

[0002] In telescope orientation systems based on inertial / astronomical combined attitude determination schemes, the strapdown inertial measurement unit (SMU) of the telescope's pointing axis acts as an attitude sensor. The attitude measurement error of the inertial navigation system and its alignment error with the equipment directly affect the telescope's line-of-sight pointing accuracy. Therefore, in engineering applications, corresponding alignment and accuracy testing steps are essential before the system operates.

[0003] Although hardware methods can be used during assembly to align the inertial navigation system's body coordinate system (composed of the sensitive axes) with the telescope's reference coordinate system as closely as possible, the remaining error often reaches the angle minute level, causing significant deviations in their attitude movements. Under field testing conditions, available reference information is limited and constrained by observability factors. In such cases, encoders on both axes of the telescope typically need to provide accurate attitude rotation reference information. Based on error analysis and modeling, this alignment deviation is then compensated for via software.

[0004] For mutual alignment strategies between inertial navigation systems (INS) and telescopes, the rotation matrix between the two instrument coordinate systems is often obtained based on the pointing vector. First, it is assumed that the two instruments are approximately co-aligned and that no calibration of measurement errors is needed. Then, a series of measurements recorded simultaneously by both instruments under inertial attitudes are obtained. The telescope's pointing vector *t* is obtained from the encoder measurements on the telescope's azimuth and pitch axes; the rotation matrix *A* is obtained from the INS attitude measurements. Since only the aiming direction is needed, this matrix simplifies to the pointing vector *a*. Because the angular difference between the pointing directions of the two instruments can be interpreted as rotation, the two pointing vectors can be related by the following equation: *a* = *M* *t*, where *M* is the fixed matrix between the instrument coordinate systems. Using redundant data obtained from measurements in more than three attitudes, *M* is obtained through least-squares fitting. To obtain a more accurate fit, it is also assumed that the different attitudes selected for mutual calibration do not constitute a linear combination of the data. From the above process, it can be seen that the fixed matrix *M* is obtained by fitting its nine elements, where the measurement error is treated as a random term. In reality, the matrix has 3 degrees of freedom, and the elements are strongly correlated. This can lead to multicollinearity in the linear regression model, which in turn reduces the accuracy of parameter estimation.

[0005] As can be seen from the alignment strategies described above, alignment errors between the inertial navigation system (INS) and the telescope inevitably introduce attitude measurement errors into the INS itself; the two are mutually coupled. To address the issue of INS attitude measurement accuracy testing, in the laboratory, the INS under test is typically fixed on a high-precision three-axis turntable. The relative relationship between the INS and the turntable is calibrated, and the output data of the turntable's three-axis encoder and the INS are recorded under different attitudes. Then, based on the previously calibrated relationship, the two attitude data are unified into the same coordinate system, and the measurement accuracy of heading, pitch, and roll angles is evaluated by comparing Euler angles. To obtain relatively accurate error comparison data, the calibration accuracy of the INS installation position must be much higher than the measurement accuracy of Euler angles. However, under field testing conditions, high-precision installation error calibration is quite difficult. Therefore, while using Euler angle comparison to evaluate the attitude measurement accuracy of the INS is intuitive, it is technically challenging and costly. Moreover, the heading angle measurement error of inertial navigation is often larger than that of roll and pitch angle measurement errors, and in some cases, they are even on different orders of magnitude. Therefore, a holistic evaluation concept is needed to intuitively determine the accuracy level or error range of the inertial navigation attitude measurement being measured. Summary of the Invention

[0006] The technical problem this invention aims to solve is that, under field testing conditions, the available reference information is limited. The coupling between the installation deviation between the inertial navigation system (INS) and the telescope, and the measurement error of the INS itself, makes the alignment of the two instruments and the assessment of the INS attitude measurement accuracy quite difficult. To address the problems of preliminary mutual alignment between the INS and the telescope and the detection of the INS attitude accuracy in field environments, this invention provides a method for estimating the installation error between the coordinate systems of the two instruments based on the concept of equivalent rotating vectors, and comprehensively assesses the INS attitude measurement accuracy through direct calculation.

[0007] The technical solution adopted in this invention is as follows:

[0008] A method for mutual alignment of inertial navigation system and telescope, and for detecting inertial navigation system accuracy, the method comprising the following steps:

[0009] Step (1): Fix the inertial navigation system to be measured on the pointing axis of the telescope, and drive the telescope to keep the pitch angle of the pointing axis at zero;

[0010] Step (2): Rotate the telescope and record the attitude data output by the encoder and inertial navigation system of the telescope at the same time.

[0011] Step (3): Convert the attitude data into two sets of standard quaternion data;

[0012] Step (4): Calculate the rotation change between the two corresponding quaternions in the two sets of standard quaternion data, and represent the rotation change using an equivalent rotation vector to obtain the rotation angle sequence and the rotation axis vector sequence; take the mean of the rotation angle sequence and the center of the rotation axis vector sequence to form a new equivalent rotation vector, and then solve the rotation matrix as the installation error between the inertial navigation system and the telescope.

[0013] Step (5): For the two sets of standard quaternion data, first calculate the rotation change in each set using two adjacent quaternions to obtain two new quaternion sequences. Represent the two new quaternion sequences with equivalent rotation vectors to obtain two rotation angle sequences. Subtract the two rotation angle sequences to obtain the error angle, which represents the measurement error sequence of the inertial navigation system. Calculate the mean square error of the measurement error sequence as the measurement accuracy index of the inertial navigation system.

[0014] Furthermore, in step (2), the telescope rotates around the azimuth axis while the pitch axis remains at zero.

[0015] Furthermore, in step (3), when converting the encoder output data into a quaternion, the roll angle is set to 0.

[0016] Furthermore, in step (4), let Q be the quaternion obtained from the attitude data output by the encoder. b The quaternion obtained from the attitude data output by the inertial navigation system is Q. m ,use Calculate the rotational change; when converting the quaternion ΔQ into an equivalent rotation vector, according to... The rotation angle can be calculated as θ = 2·arccos(u), and the unit vector of the rotation axis is... The mean of the rotation angle sequence and the center vector of the rotation axis vector sequence are used to construct a new equivalent rotation vector. This new equivalent rotation vector represents the fixed matrix of the two instruments, the inertial navigation system and the telescope. The rotation order of Euler angles is kept consistent when solving the rotation matrix from this new equivalent rotation vector and when converting the attitude data into normalized quaternion data.

[0017] The principle of this invention is as follows:

[0018] This invention utilizes the principle that, during the rotation of the telescope, the relationship between the inertial navigation system (INS) and the telescope remains constant. Without considering other errors, the rotation matrix between the two instruments does not change with the device's attitude. From the perspective of the equivalent rotation vector, the rotation angle is constant, and the rotation axis vector is a constant vector. The fluctuations generated by the sample sequence in actual testing are considered as error interference terms, and the fixed matrix between the two instrument coordinate systems can be solved based on the sample mean. Furthermore, the changes in the rotation angles of the telescope and the INS are theoretically the same; the resulting deviation can be considered as the measurement error of the INS, and a single numerical value can intuitively reflect the accuracy of the INS.

[0019] The advantages of this invention compared to the prior art are:

[0020] (1) This invention has few dependent conditions. After the inertial navigation system and the telescope are roughly aligned by hardware, high-precision calibration is not required.

[0021] (2) This invention is highly practical. After a rotation test, data analysis can not only obtain the fixed matrix between the inertial navigation and telescope coordinate systems, but also evaluate the attitude measurement accuracy of the inertial navigation.

[0022] (3) The attitude evaluation results of the present invention are more holistic, using only one value to reflect the error status and error magnitude range of the inertial navigation system. Attached Figure Description

[0023] Figure 1 This is a flowchart of a method for mutual alignment of inertial navigation systems and telescopes and for detecting inertial navigation accuracy based on equivalent rotation vectors. Detailed Implementation

[0024] The technical solutions provided by the present invention will be described in detail below with reference to specific embodiments. It should be understood that the following specific embodiments are only for illustrating the present invention and are not intended to limit the scope of the present invention. The specific embodiments of the mutual alignment method between inertial navigation and telescope and the inertial navigation accuracy detection method provided by the present invention will be described in detail below with reference to the accompanying drawings.

[0025] In the following specific embodiment, after the coordinate systems of the inertial navigation system and the telescope are roughly aligned by hardware, the pitch angle of the telescope's pointing axis is kept at 0. The two instruments rotate around the azimuth axis of the telescope. Using the encoder readings and attitude data obtained by the inertial navigation system, the mutual alignment of the inertial navigation system and the telescope is achieved by calculating a fixed matrix between the coordinate systems of the two instruments, and the accuracy of the inertial navigation system is further calculated.

[0026] Assuming the device begins to rotate around the azimuth axis, let the Euler angle data recorded by the encoder be: heading angle ψ bi Pitch angle θ biAnd roll angle 0. Where subscript b represents the telescope, and subscript i represents the number of data points. Let the Euler angle data recorded by the inertial navigation system be: heading angle ψ mi Pitch angle θ mi and roll angle γ mi Where m represents inertial navigation, and the same subscript i indicates data acquired at the same time. Euler angle attitude data are converted into canonical quaternion data using the following formula:

[0027] q0=cos(ψ / 2)cos(θ / 2)cos(γ / 2)-sin(ψ / 2)sin(θ / 2)sin(γ / 2) (1)

[0028] q1=cos(ψ / 2)sin(θ / 2)cos(γ / 2)-sin(ψ / 2)cos(θ / 2)sin(γ / 2) (2)

[0029] q2=sin(ψ / 2)sin(θ / 2)cos(γ / 2)+cos(ψ / 2)cos(θ / 2)sin(γ / 2) (3)

[0030] q3=sin(ψ / 2)cos(θ / 2)cos(γ / 2)+cos(ψ / 2)sin(θ / 2)sin(γ / 2) (4)

[0031] The two sets of quaternion sequences are as follows:

[0032] Telescope quaternion sequence: Q bi =[q bi0 q bi1 q bi2 q bi3 ] = , i = 1, 2, ..., n, where n is the number of samples.

[0033] Inertial navigation quaternion sequence: Q mi =[q mi0 q mi1 q mi2 q mi3 ], where i is the data sequence number, and i corresponding to the telescope quaternion sequence represents the same sampling time.

[0034] The rotational changes corresponding to these two sets of quaternions are calculated using the following formula and then converted into equivalent rotation vectors:

[0035]

[0036]

[0037] Where (Δq0, Δq1, Δq2, Δq3) are the four elements of ΔQ. Let be the real and imaginary parts of ΔQ, respectively, and θ be the rotation angle. The unit vector is the axis of rotation.

[0038] A set of rotation angle sequences {θ} is obtained i} and a set of rotation axis vector sequences in

[0039] The mean rotation angle is obtained by calculating the mean of the two sequences separately. and the central axis vector A new canonical quaternion is constructed based on equation (5). The quaternion is then converted into a rotation matrix using the following formula, which serves as a fixed matrix between the two instrument coordinate systems, thereby achieving mutual alignment between the inertial navigation system and the telescope.

[0040]

[0041] To evaluate the attitude measurement accuracy of the inertial navigation system, the inertial navigation quaternion sequence {Q} is analyzed. mi} and the telescope quaternion sequence {Q bi The following processing is performed: Within each of the two sequences, the rotational changes of two adjacent quaternions are calculated successively, as shown below. This yields the inertial navigation difference quaternion sequences {ΔQ}. mi} and the telescope difference quaternion sequence {ΔQ bi}

[0042]

[0043] Converting the two sequences above into an equivalent rotation vector expression, focusing only on the rotation angle sequence, as shown below, we have the inertial guidance difference rotation angle sequence {Δθ}. mi} and the telescope difference rotation angle sequence {Δθ bi}

[0044]

[0045] The difference between the two sets of angle sequences is calculated as follows:

[0046] ε i =Δθ bi -Δθ mi (10)

[0047] The detection accuracy of the inertial navigation system is:

[0048]

[0049] The parts of this invention not described in detail are well-known in the art. The embodiments described above are merely preferred embodiments of the present invention, and do not exhaustively describe all details, nor do they limit the invention to the specific implementations described. Various modifications and improvements to the technical solutions of this invention made by those skilled in the art without departing from the spirit of the invention should fall within the protection scope defined by the claims of this invention.

Claims

1. A method for mutual alignment of inertial navigation system and telescope, and for detecting the accuracy of inertial navigation system, characterized in that, The method includes the following steps: Step (1): Fix the inertial navigation system to be measured on the pointing axis of the telescope, and drive the telescope to keep the pitch angle of the pointing axis at zero; Step (2): Rotate the telescope and record the attitude data output by the encoder and inertial navigation system of the telescope at the same time. Step (3): Convert the attitude data into two sets of standard quaternion data; Step (4): Calculate the rotational change between the two corresponding quaternions in the two sets of standard quaternion data, and represent the rotational change using an equivalent rotation vector to obtain the rotation angle sequence and the rotation axis vector sequence; take the mean of the rotation angle sequence and the center of the rotation axis vector sequence to form a new equivalent rotation vector, and then solve the rotation matrix as the installation error between the inertial navigation system and the telescope; including: let the quaternion obtained from the attitude data output by the encoder be... The quaternion obtained from the attitude data output by the inertial navigation system is The rotational changes of both are ;according to ,Will Converting to an equivalent rotation vector expression, the rotation angle is: The unit vector of the rotation axis is ;in for The four elements, They are respectively The real and imaginary parts; take the mean of the rotation angle sequence and the center vector of the rotation axis vector sequence to form a new equivalent rotation vector, which represents the fixed matrix of the inertial navigation and telescope instruments; when solving the rotation matrix from the new equivalent rotation vector, the rotation order of Euler angles is consistent with that in the process of converting attitude data into normalized quaternion data; Step (5): For the two sets of standard quaternion data, first calculate the rotation change amount within each set using two adjacent quaternions to obtain two new quaternion sequences. Represent the two new quaternion sequences with equivalent rotation vectors to obtain two sets of rotation angle sequences. Subtract the two sets of rotation angle sequences to obtain the error angle, which represents the measurement error sequence of the inertial navigation system. Calculate the mean square error of the measurement error sequence as the measurement accuracy index of the inertial navigation system.

2. The method for mutual alignment of inertial navigation and telescope and for detecting inertial navigation accuracy according to claim 1, characterized in that, In step (2), the telescope rotates around the azimuth axis while the pitch axis remains at zero.

3. The method for mutual alignment of inertial navigation and telescope and for detecting inertial navigation accuracy according to claim 1, characterized in that, In step (3), when the encoder output data is converted into a quaternion, the roll angle is set to 0.

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