CN116481535A - Calculation method for correcting flight trajectory data by using inertial navigation data - Google Patents
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Abstract
The invention discloses a calculation method for correcting flight trajectory data by using inertial navigation data, which comprises the following steps: selecting a time t to be corrected 0 And at t 0 N times { t } selected for auxiliary calculation near the time i I=1, 2 … N, N being adjustable according to the actual situation; solving t by inertial navigation data 0 Time of day and N auxiliary times { t } i Ground acceleration (a) of i=1, 2 … N } x2 ,a y2 ,a z2 ) The method comprises the steps of carrying out a first treatment on the surface of the By a means ofThe inertial navigation data refers to triaxial overload of an engine system measured by an inertial navigation system and quaternion for describing the attitude of an aircraft; the inertial navigation system comprises an accelerometer and a gyroscope; the triaxial overload is (a) x ,a y ,a z ) The method comprises the steps of carrying out a first treatment on the surface of the The quaternion is q= (Q 0 ,q 1 ,q 2 ,q 3 ) The method comprises the steps of carrying out a first treatment on the surface of the N auxiliary moments { t } solved by using step two i Acceleration (a of i=1, 2 … N } x2 ,a y2 ,a z2 ) Further solve t 0 Velocity v (t) 0 ) And the coordinates x (t) 0 ) The method comprises the steps of carrying out a first treatment on the surface of the According to the method, any nonlinear trajectory is converted into a linear relation, then data are calculated and corrected through a linear fitting method, and the influence of random noise of flight data x (t) and a (t) on a calculation result is obviously weakened through linear fitting.
Description
Technical Field
The invention relates to the technical field of flight trajectory data calculation, in particular to a calculation method for correcting flight trajectory data by using inertial navigation data.
Background
Trajectory data of the aircraft, such as coordinates x, velocity v, acceleration a, etc., are important fundamental data for analyzing the flight experimental process. The coordinates of the aircraft can be obtained through an onboard GPS, and then the primary difference and the secondary difference are carried out on the coordinates, so that the speed and the acceleration can be obtained, and the central difference is taken as an example, and the formula is as follows:
however, the raw coordinate data actually measured inevitably has various noises, resulting in a large error in the data obtained by direct difference. At an initial velocity of 0m/s and an acceleration of 1m/s 2 For example, the one-dimensional motion of (2) is given by the equation of motion x (t) =0.5 t 2 Let equation of motion x (t) =0.5 t 2 Substituting formula (a) to obtain a velocity v:
if a random noise of + -5 m is added to the measured coordinate data x (t), the equation of motion becomes x (t) =0.5 t 2 +rd (t), where rd (t) is a random number uniformly distributed between the ranges (-5, 5). Accordingly, the velocity v becomes
Although the coordinate data and the theoretical solution are not very different (as shown in fig. 1), there is a significant oscillation in the velocity v (Δt=1s) calculated by the formula (d) (as shown in fig. 2).
In order to reduce the influence of noise on the calculation result, Δt may be increased at the time of calculation. Fig. 3 shows the calculated speed of equation (d) at Δt=10s, which can be seen to agree well with the theoretical result.
However, the increase Δt of fig. 3 can only be achieved when the speed is linearly variable over time, which can lead to an increase in the error of the differential calculation if the speed is non-linear over time (i.e., the acceleration is variable over time). Let the equation of motion be x (t) =t 3 For example (without taking random noise into account), substituting the equation of motion into equation (1) yields:
it can be seen that since the change in speed over time is non-linear, when Δt >0, there is a systematic error in the speed calculated by equation (e) and the error increases as Δt increases.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a calculation method for correcting flight trajectory data by using inertial navigation data; the purpose is to solve the problem that when the change of speed over time is nonlinear, there is systematic error in the speed v calculated by equation (a) and the error increases as Δt increases.
The invention adopts the following technical scheme for solving the technical problems.
A calculation method for correcting flight trajectory data by using inertial navigation data is characterized in that: comprises the steps of,
step one, selecting a time t to be corrected 0 And at t 0 N times { t } selected for auxiliary calculation near the time i I=1, 2 … N, N being adjustable according to the actual situation;
step two, solving t by using inertial navigation data 0 Time of day and N auxiliary times { t } i Ground acceleration (a) of i=1, 2 … N } x2 ,a y2 ,a z2 ) The method comprises the steps of carrying out a first treatment on the surface of the The inertial navigation data refer to triaxial overload of an engine system measured by an inertial navigation system and quaternion for describing the attitude of an aircraft; the inertial navigation system comprises an accelerometer and a gyroscope; the triaxial overload is (a) x ,a y ,a z ) The method comprises the steps of carrying out a first treatment on the surface of the The quaternion is q= (Q 0 ,q 1 ,q 2 ,q 3 )；
Step three, solving N auxiliary moments { t } by utilizing the step two i Acceleration (a of i=1, 2 … N } x2 ,a y2 ,a z2 ) Further solve t 0 Velocity v (t) 0 ) And the coordinates x (t) 0 )。
Further, the specific steps of the second process are as follows:
1) Establishing an attitude quaternion q= (Q) 0 ,q 1 ,q 2 ,q 3 ) Triaxial overload (a) x ,a y ,a z ) Relationship with ground fixation:
wherein M is 1 To describe the transformation matrix of the attitude of an aircraft, M 2 The conversion matrix is used for describing the initial corresponding relation between the machine system and the ground system.
2) Calculate M 1 ：M 1 Can be calculated from quaternions
3) Calculate M 2 ：M 2 A conversion matrix for describing the initial corresponding relation of the machine system and the ground system; taking the common definition in the aviation field as an example, the three axes of the machine system are the front, right and lower directions of the aircraft, the aircraft is initially placed horizontally and the aircraft nose faces north, and the east, north and sky of the ground system correspond to the right, front and upper directions of the machine system respectively, so that the aircraft can be obtained
4) Adding the gravity acceleration g into the result of the last step to obtain the east, north and sky acceleration (a) x2 ,a y2 ,a z2 )；
Further, the specific steps of the process three, process 1) are as follows:
(1) establishing an integral relation between the speed v and the acceleration a;
(2) establishing an integral relation between a coordinate x and a speed v;
(3) the formula is carried over into the formula flatly, the formula x is available;
(4) the terms related to the variables x (t) and a (t) in the formula I and II are moved to the left, and the rest terms are moved to the right, so that a formula I and II are obtained; looking at the formula, it can be seen that the left side can be calculated directly from the flight data, while the right side is a linear equation for t.
(5) Let f (t) be the left side of the equation, i.e.:
wherein x (t) is obtained by airborne GPS measurement, and a (t) is obtained by inertial navigation data conversion;
(6) let the slope of the right linear equation of formula k and the intercept b, namely:
k＝v(t 0 ) (11)
b＝x(t 0 )-v(t 0 )t 0 (12)
(7) then there is
f(t)＝kt+b (13)
(8) Taking t 0 N times { t around the time i I=1, 2 … N } calculates the corresponding f (t i )；
(9) For N data points (t i ，f(t i ) Linear fitting to obtain slope k and intercept b;
v (t) is obtained by formulas (11) and (12) 0 ) And x (t) 0 )。
Advantageous effects of the invention
The invention gives up the conventional differential thinking of coordinates, arrival speed and arrival acceleration, obtains the acceleration through coordinate transformation by utilizing inertial navigation data through reverse thinking, and then calculates the speed and the coordinates through a new algorithm based on a linear fitting principle. By linear fitting, the influence of random noise of flight data x (t), a (t) on the calculation result is remarkably reduced, so that more accurate and reliable speed and coordinates can be obtained.
Drawings
FIG. 1 is original coordinate data, 1 is a result after random noise is added, and 2 is a theoretical result;
fig. 2 shows the velocity (Δt=1s) obtained by differentiating the coordinates once, 1 is the result after adding random noise, and 2 is the theoretical result;
fig. 3 shows the velocity (Δt=10s) obtained by differentiating the coordinates once. 1 is a result after random noise is added, and 2 is a theoretical result;
FIG. 4 is a flow chart of the calculation method of the present invention. The method comprises the steps of carrying out a first treatment on the surface of the
FIG. 5 is an on-board GPS given world coordinates;
FIG. 6 is a triaxial overload given by the inertial navigation system;
FIG. 7 is a pose quaternion given by the inertial navigation system;
FIG. 8 is a graph of the differential of the radial coordinates once to obtain the radial velocity;
FIG. 9 is a graph of the differential of the secondary differential of the world coordinates;
FIG. 10 illustrates the corrected lateral acceleration by the present invention;
FIG. 11 illustrates corrected world coordinates by the present invention;
fig. 12 illustrates the corrected tangential velocity according to the present invention.
Detailed Description
The invention is further explained below with reference to the drawings:
principle of design of the invention
1. The method converts any nonlinear trajectory into a linear relation, and then calculates and corrects data through a linear fitting method, which is an innovation point of the invention.
The nonlinear trajectory refers to the nonlinear relationship between the speed and time (namely, the acceleration is changed along with the time). The linear relationship is derived from the present invention, see equation (13).
The left side f (t) of the formula (13) is calculated, and coordinates x (t) and acceleration a (t) are needed, wherein the coordinates x (t) are directly given by an onboard GPS, and the acceleration a (t) is obtained by converting inertial navigation data. Although there may be signal noise in the coordinates x (t) and acceleration a (t), the linear relation to equation (13) is passedFitting can eliminate signal noise to obtain accurate slope k and intercept b, and then obtaining accurate velocity v (t) through formulas (11) and (12) 0 ) And the coordinates x (t) 0 )。
2. The invention has the design difficulty that: the difficulty is how to find a new algorithm based on the principle of linear fitting and how to calculate the velocity v (t) 0 ) And the coordinates x (t) 0 ). Equations (6) through (13) show how to find such a new algorithm based on the linear fitting principle. Equations (2) through (5) illustrate how acceleration is obtained via coordinate transformation using inertial navigation data. The conventional method is a conventional differential thought of coordinates, arrival speed and arrival acceleration, the invention adopts reverse thinking, firstly, acceleration (formula (2) to formula (5)) is obtained by utilizing inertial navigation data through coordinate transformation, and then the speed and the coordinates are calculated through a new algorithm based on a linear fitting principle.
3. And establishing a relation between the known data and the data to be corrected. The relation is established from formula (6) to formula (9): put "known data" containing x (t) and a (t) to the left of the equation; to the right of the equation is the data to be corrected, e.g. time t 0 Corresponding velocity v (t 0 ) And the coordinates x (t) 0 ). The "known data" refers to data that can be calculated from on-board GPS data and inertial navigation data.
4. V (t) on the right of the correction equation 0 ) And x (t) 0 ) Four types of data need to be calculated: x (t), a (t) on the left of the equation are calculated, and the slope k, truncated moment b on the right of the equation are calculated. The x (t) on the left side of the equation is obtained by on-board GPS measurement, the a (t) on the left side of the equation is obtained by inertial navigation data conversion, and the detailed formula is shown in the formula (2) to the formula (5). The slope k to the right of the equation is calculated, and the intercept b is detailed in equations (6) to (13). Calculating the slope k, the intercept b is calculated by calculating a series of f (t i ) And the obtained product. Take t specifically 0 N times { t around the time i I=1, 2 … N } calculates the corresponding f (t i ) Then for N data points (t i ，f(t i ) Linear fitting to obtain slope k and intercept b, where f (t) i ) Obtained from equation (10). A (t) in formula (10) 2 ) Obtained from equation (5).
Based on the principle, the invention designs a calculation method for correcting flight trajectory data by using inertial navigation data, which is characterized in that: comprises the steps of,
step one, selecting a time t to be corrected 0 And at t 0 N times { t } selected for auxiliary calculation near the time i I=1, 2 … N, N being adjustable according to the actual situation;
step two, solving t by using inertial navigation data 0 Time of day and N auxiliary times { t } i Ground acceleration (a) of i=1, 2 … N } x2 ,a y2 ,a z2 ) The method comprises the steps of carrying out a first treatment on the surface of the The inertial navigation data refer to triaxial overload of an engine system measured by an inertial navigation system and quaternion for describing the attitude of an aircraft; the inertial navigation system comprises an accelerometer and a gyroscope; the triaxial overload is (a) x ,a y ,a z ) The method comprises the steps of carrying out a first treatment on the surface of the The quaternion is q= (Q 0 ,q 1 ,q 2 ,q 3 )；
Step three, solving N auxiliary moments { t } by utilizing the step two i Acceleration (a of i=1, 2 … N } x2 ,a y2 ,a z2 ) Further solve t 0 Velocity v (t) 0 ) And the coordinates x (t) 0 )。
Further, the specific steps of the second process are as follows:
1) Establishing an attitude quaternion q= (Q) 0 ,q 1 ,q 2 ,q 3 ) Triaxial overload (a) x ,a y ,a z ) Relationship with ground fixation:
wherein M is 1 To describe the transformation matrix of the attitude of an aircraft, M 2 The conversion matrix is used for describing the initial corresponding relation between the machine system and the ground system.
2) Calculate M 1 ：M 1 Can be calculated from quaternions
3) Calculate M 2 ：M 2 A conversion matrix for describing the initial corresponding relation of the machine system and the ground system; taking the common definition in the aviation field as an example, the three axes of the machine system are the front, right and lower directions of the aircraft, the aircraft is initially placed horizontally and the aircraft nose faces north, and the east, north and sky of the ground system correspond to the right, front and upper directions of the machine system respectively, so that the aircraft can be obtained
4) Adding the gravity acceleration g into the result of the last step to obtain the east, north and sky acceleration (a) x2 ,a y2 ,a z2 )；
Further, the specific steps of the process three, process 1) are as follows:
supplementary explanation 1
The following formulas (18) to (19) are given as examples in the x-direction to obtain v (t) 0 ) And x (t) 0 ) Similarly, v (t) in the y and z directions can be obtained from the formulas (20) to (21) 0 ) And x (t) 0 )。
(1) Establishing an integral relation between the speed v and the acceleration a;
(2) establishing an integral relation between a coordinate x and a speed v;
(3) the formula is carried over into the formula flatly, the formula x is available;
(4) the terms related to the variables x (t) and a (t) in the formula I and II are moved to the left, and the rest terms are moved to the right, so that a formula I and II are obtained; looking at the formula, it can be seen that the left side can be calculated directly from the flight data, while the right side is a linear equation for t.
(5) Let f (t) be the left side of the equation, i.e.:
wherein x (t) is obtained by airborne GPS measurement, and a (t) is obtained by inertial navigation data conversion;
supplementary explanation 2
A (t) in formula (10) 2 ) Obtained from equation (5): the reason for the absence of a in equation (4) is that for a single instant, the time integral required for equation (10) has t in brackets.
(6) Let the slope of the right linear equation of formula k and the intercept b, namely:
k＝v(t 0 ) (27)
b＝x(t 0 )-v(t 0 )t 0 (28)
(7) then there is
f(t)＝kt+b (29)
(8) Taking t 0 N times { t around the time i I=1, 2 … N } calculates the corresponding f (t i )；
(9) For N data points (t i ，f(t i ) Linear fitting to obtain slope k and intercept b;
v (t) is obtained by formulas (11) and (12) 0 ) Andx(t 0 )。
example 1
Taking a real flight data as an example, the description will be given. The aircraft starts at altitude 30km and after 80s of gliding, the altitude is reduced to altitude 15km. The change of the space coordinate z (t) (i.e. altitude) given by the onboard GPS along with time is shown in fig. 5, and the triaxial overload (a) given by the inertial navigation system x ,a y ,a z ) Gesture quaternion q= (Q) 0 ,q 1 ,q 2 ,q 3 ) The time course is shown in fig. 6 and 7.
The first difference and the second difference are directly carried out on the space coordinate z (t) to obtain the space velocity v z (t) and the acceleration in the sky direction a z (t), see fig. 8 and 9. It can be seen that the differential velocity and acceleration have significant fluctuations due to the signal noise present in the world coordinate data, wherein the acceleration is almost unrecognizable.
The corrected tangential acceleration a can be obtained by using the triaxial overload and attitude quaternion given by the inertial navigation system and the formulas (2) to (5) of the invention z,m (t) (see fig. 10).
The coordinates and the speeds at each moment in the flying process are corrected one by utilizing the formulas (6) to (13), and the corrected tangential coordinates z can be obtained m (t) and heavyweight velocity v z,m (t), see fig. 11 and 12.
It can be seen that the corrected velocity v z,m (t), acceleration a z,m The fluctuation of (t) is significantly reduced, and the coordinate z m The precision of (t) is also improved to a certain extent.
The present embodiment is only explained in terms of the day direction, and corresponding modifications can be made to the other two directions (east and north). Since the principle and the flow are the same, a detailed description thereof is omitted.
It should be emphasized that the above-described embodiments are merely illustrative of the invention, which is not limited thereto, and that modifications may be made by those skilled in the art, as desired, without creative contribution to the above-described embodiments, while remaining within the scope of the patent laws.
Claims (3)
1. A calculation method for correcting flight trajectory data by using inertial navigation data is characterized by comprising the following steps,
step one, selecting a time t to be corrected 0 And at t 0 N times { t } selected for auxiliary calculation near the time i I=1, 2 … N, N being adjustable according to the actual situation;
step two, solving t by using inertial navigation data 0 Time of day and N auxiliary times { t } i Ground acceleration (a) of i=1, 2 … N } x2 ,a y2 ,a z2 ) The method comprises the steps of carrying out a first treatment on the surface of the The inertial navigation data refer to triaxial overload of an engine system measured by an inertial navigation system and quaternion for describing the attitude of an aircraft; the inertial navigation system comprises an accelerometer and a gyroscope; the triaxial overload is (a) x ,a y ,a z ) The method comprises the steps of carrying out a first treatment on the surface of the The quaternion is q= (Q 0 ,q 1 ,q 2 ,q 3 )；
Step three, solving N auxiliary moments { t } by utilizing the step two i Acceleration (a of i=1, 2 … N } x2 ,a y2 ,a z2 ) Further solve t 0 Velocity v (t) 0 ) And the coordinates x (t) 0 )。
2. The method for calculating corrected flight trajectory data using inertial navigation data according to claim 1, wherein the second step is as follows:
1) Establishing an attitude quaternion q= (Q) 0 ,q 1 ,q 2 ,q 3 ) Triaxial overload (a) x ,a y ,a z ) Relationship with ground fixation:
wherein M is 1 To describe the transformation matrix of the attitude of an aircraft, M 2 A conversion matrix for describing the initial corresponding relation of the machine system and the ground system;
2) Meter with a meter bodyCalculate M 1 ：M 1 Can be calculated from quaternions
3) Calculate M 2 ：M 2 A conversion matrix for describing the initial corresponding relation of the machine system and the ground system; taking the common definition in the aviation field as an example, the three axes of the machine system are the front, right and lower directions of the aircraft, the aircraft is initially placed horizontally and the aircraft nose faces north, and the east, north and sky of the ground system correspond to the right, front and upper directions of the machine system respectively, so that the aircraft can be obtained
4) Adding the gravity acceleration g into the result of the last step to obtain the east, north and sky acceleration (a) x2 ,a y2 ,a z2 )；
3. The method for calculating corrected flight trajectory data using inertial navigation data according to claim 1, wherein the steps of process three, process 1) are as follows:
(1) establishing an integral relation between the speed v and the acceleration a;
(2) establishing an integral relation between a coordinate x and a speed v;
(3) the formula is carried over into the formula flatly, the formula x is available;
(4) the terms related to the variables x (t) and a (t) in the formula I and II are moved to the left, and the rest terms are moved to the right, so that a formula I and II are obtained; looking at the formula, it can be seen that the left side can be directly calculated from the flight data, while the right side is a linear equation for t;
(5) let f (t) be the left side of the equation, i.e.:
wherein x (t) is obtained by airborne GPS measurement, and a (t) is obtained by inertial navigation data conversion;
(6) let the slope of the right linear equation of formula k and the intercept b, namely:
k＝v(t 0 ) (10)
b＝x(t 0 )-v(t 0 )t 0 (11)
(7) then there is
f(t)＝kt+b (12)
(8) Taking t 0 N times { t around the time i I=1, 2 … N } calculates the corresponding f (t i )；
(9) For N data points (t i ，f(t i ) Linear fitting to obtain slope k and intercept b;
v (t) is obtained by formulas (10) and (11) 0 ) And x (t) 0 )。
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