CN107357758B - Polynomial least square regression memorability speed calculation method for positioning information - Google Patents

Polynomial least square regression memorability speed calculation method for positioning information Download PDF

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CN107357758B
CN107357758B CN201710516014.2A CN201710516014A CN107357758B CN 107357758 B CN107357758 B CN 107357758B CN 201710516014 A CN201710516014 A CN 201710516014A CN 107357758 B CN107357758 B CN 107357758B
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CN107357758A (en
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车著明
刘涛
谢作敏
车云力
邹海彬
高东群
付玲
杨相林
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63796 FORCES PLA
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Abstract

The invention discloses a polynomial least square regression memorability speed calculation method for positioning information, and aims to provide a method for dynamically and accurately determining a speed information sequence through a position measurement information sequence under the condition of lacking speed measurement information. The measured data is not required to lack frames, the time is subjected to integral transformation, a mathematical model of polynomial regression memory compensation speed calculation of error convergence positioning information is established, and inversion ill-conditioned divergence of a polynomial regression matrix is avoided; and carrying out memory accumulation of the polynomial regression coefficient through real-time calculation. And finally, determining the speed near the latest time in real time by combining the memory coefficient and the hysteresis compensation value of the acceleration. The polynomial regression memory compensation method is obtained by actual measurement data simulation experiment, so that the speed calculation error is rapidly converged, and the precision and smoothness of the calculated speed are obviously improved compared with those of the conventional method.

Description

Polynomial least square regression memorability speed calculation method for positioning information
Technical Field
The invention relates to a differential smooth speed-calculating technology of positioning information, in particular to a polynomial least square regression memorial speed-calculating method of spacecraft positioning information, which is suitable for occasions that a speed information sequence is dynamically determined by a position information sequence containing random errors when speed-measuring elements of moving objects are lacked.
Background
In the tracking measurement of a satellite launching rocket, speed information is the most important ballistic information for completing ground safety control of rocket flight, the speed measurement information contribution rate of the ground safety control is more than 95%, and the contribution rate of position information is less than 5%. However, most reliable ground optical and radio radars are lack of speed measurement function, so in the practice of spacecraft ballistic data processing, when speed measurement information is lacked, the speed information must be obtained through differential smoothing by using position information, and the Unscented Kalman Filter (UKF) method is not only complex in algorithm, but also needs initial position speed and acceleration information, and needs relatively complete speed information to prevent ballistic filtering from diverging. In a longer time, we continue to use the simple and convenient equal time interval alpha beta gamma differential smooth speed-calculating method, when the data frame loss, the frame repetition or the time sequence reversal occurs, the error of the differential smooth speed-calculating is easy to occur after more interpolation, even the divergence phenomenon, and the polynomial least square regression smooth speed-calculating method is time-carrying and can not be influenced by the data frame loss, the frame repetition or the time sequence reversal. At present, the speed of a computer is accelerated, and the method is used for discussing a more complex algorithm with higher precision. Compared with the alpha beta gamma differential smooth speed-solving method, the 2-order polynomial regression smooth speed-solving method remarkably improves the speed precision determined by the position information (figure 1).
Disclosure of Invention
The invention aims to provide a method for dynamically and accurately determining a speed information sequence through a position measurement information sequence under the condition of lacking speed measurement information, which comprises the following steps:
s1: establishing a mathematical model for solving the speed by polynomial least square regression of the positioning information;
s2: sorting the time series;
s3: comparing and selecting polynomial order p values by a mathematical model of polynomial least square regression speed calculation of the positioning information in S1, calculating a regression coefficient, and calculating the speed and the acceleration of post processing near the midpoint of the time sequence;
s4: the formula of the regression coefficient, the speed and the acceleration obtained by S3 is utilized to carry out polynomial regression coefficient memory accumulation through real-time calculation;
s5: and determining the speed around the latest time in real time by combining the memory accumulation coefficient and the hysteresis compensation value of the acceleration.
The mathematical model for solving the speed by polynomial least squares regression for positioning information established in the step S1 is as follows:
Y=DB+E,V=DU,B=(DTD)-1DTY
in the formula:
wherein, bjJ is 0,1,2, … p is the polynomial regression coefficient to be solved, yjJ is 1,2, … n is the j th sampling point measured value of the ballistic parameters x, y and z or the time sequence t of the parameters of the measuring element R, A, E, p is the polynomial order, and the random variable sequence epsiloni~N(0,σ),i=1,2,…n,εi,εj(i ≠ j) are independent of each other, and obey a normal distribution with 0 mean variance σ; t is tiN (0, σ), i ═ 1,2, … N is a time series of measurement parameters, N is the number of polynomial regression fit drops, V is a velocity series of position measurement data series, U is a coefficient vector of velocity, Y is a time series measurement value vector of ballistic parameters, D is a time series matrix, B is a polynomial regression coefficient vector, and E is a random vector that follows a normal distribution.
The polynomial order p may be 2, 3, 4 … …, or y may be obtained if p is 0jAverage value of (d); if p is 1, y can be obtainedjThe polynomial regression of (a) and the average of the velocity during the period, but no acceleration information is obtained; the number n of the polynomial regression fitting paragraph points is calculated in real time at a sampling rate of 20Hz, and n is 21; for the post calculation, n is 81, and the smoothed position, velocity and acceleration results near the middle of the time are taken, and are not affected by the absence of 40 frames of data. (where real-time computation requires high timeliness, which is generally true to realityThe time lag of data processing of the inter-flight is less than 0.5 second, namely the real-time calculation of real-time situation evaluation is needed; the post calculation is evaluation analysis or identification typing analysis calculation after the aerospace flight is finished, does not require timeliness, and requires high precision and high reliability. )
To ensure that the matrix inversion does not cause ill-conditioned divergence, S2 is normalized by the following formula:
t=F(T-T0)
wherein T is the time sequence variable of the original measured data (equal intervals are not required, namely 20 frames can be lost at most in 1 calculation period during real-time calculation, and 40 frames can be lost at most in 1 calculation period during post calculation); f is the sampling frequency of the ballistic parameters; t is0Time of the first parameter (time minimum) participating in polynomial regression smoothing; and t is the time sequence of the measurement data after the normalization transformation.
In S3, in order to ensure the positioning speed-finding smooth accuracy as much as possible by simulation error analysis, p 2 is selected for comparison to obtain the best experimental effect, and the regression coefficient b is found from the mathematical model of polynomial least squares regression speed-finding of the positioning information in S11、b2And the polynomial regression (smoothing) for obtaining the post-processing speed and acceleration near the midpoint of the time series is:
y(T)=b0+b1t+b2t2
where y (T) represents a time series fitting polynomial of the ballistic parameter,indicating the speed relative to the time before warping,indicating acceleration.
In real-time calculation, when 21 points are accumulated for the first time, all 21 point parameters can be estimated (smoothed) and calculated at one time, or interpolation calculation is carried out nearby, when 22 points are accumulated, the first point is removed, the matrix is solved again, and polynomial regression coefficient memory accumulation is carried out, wherein:
b0'=b0
b'1=0.05b1+0.95b10
b'2=0.05b2+0.95b20
in the formula: b0′、b1′、b2′;b0、b1、b2;b00(b00≡0)、b10、b20Time series polynomial 0,1,2 degree term coefficients representing the most recently determined, the most recently calculated, and the last regression cycle determined trajectory parameters, respectively.
During calculation, y (T) is always calculated by the current unweighted regression coefficient, and the velocity and acceleration polynomial regression coefficients are accumulated by memory when the memory times reach more than 20 times and when the memory times reach more than 20 timesWhen the temperature of the water is higher than the set temperature,wherein a ismaxAs ballistic parameter yjMaximum theoretical acceleration of the time series in the measuring arc, F2(2b2) The above process is then repeated for the acceleration-lag compensation value on the ballistic parameter velocity.
Advantageous effects
The invention does not require no frame lack of measured data, and establishes a mathematical model of error convergence positioning information polynomial regression memory compensation speed calculation by utilizing the time to carry out integral transformation, thereby avoiding inversion ill-condition divergence of a polynomial regression matrix; and carrying out memory accumulation of the polynomial regression coefficient through real-time calculation. And finally, determining the speed near the latest time in real time by combining the memory coefficient and the hysteresis compensation value of the acceleration.
The method is characterized in that the problem of pathological divergence caused by matrix inversion is solved by finding a method for rounding the time sequence; the polynomial regression memory compensation method is obtained by actual measurement data simulation experiment, so that the speed calculation error is rapidly converged, and the precision and smoothness of the calculated speed are obviously improved compared with those of the conventional method.
Drawings
FIG. 1 is a system integration schematic;
FIG. 2 is a diagram of the steps of polynomial least squares regression speedup of positioning information;
fig. 3 is a comparison of the speed of the 2 nd order polynomial regression smoothing and the fast results of the α β γ filtering.
Detailed Description
The invention aims to provide a method for dynamically and accurately determining a speed information sequence through a position measurement information sequence under the condition of lacking speed measurement information, which comprises the following steps:
s1: establishing a mathematical model for solving the speed by polynomial least square regression of the positioning information;
s2: sorting the time series;
s3: when the polynomial least square regression of the positioning information in S1 is used to calculate the velocity of the mathematical model, and the selected polynomial order p is compared with 2, the regression coefficient b is calculated1、b2And obtaining the speed and acceleration of post-processing near the midpoint of the time sequence;
s4: the formula of the regression coefficient, the speed and the acceleration obtained by S3 is utilized to carry out polynomial regression coefficient memory accumulation through real-time calculation;
s5: and determining the speed around the latest time in real time by combining the memory coefficient and the hysteresis compensation value of the acceleration.
FIGS. 1 and 2 are diagrams illustrating the determination of velocity from spacecraft flight position measurement information without spacecraft flight velocity measurement information by the system integration shown in FIG. 1 and the determination process shown in FIG. 2; the method accurately determines the flight speed of the spacecraft, and greatly improves the smoothness of determining the flight speed of the spacecraft by the position information of the spacecraft in real time when no measurement information of the speed of the spacecraft exists.
Fig. 2 shows the procedure of the polynomial least squares regression speedup of the positioning information.
The mathematical model for solving the speed by polynomial least squares regression for positioning information established in the step S1 is as follows:
Y=DB+E,V=DU,B=(DTD)-1DTY
in the formula:
wherein, bjJ is 0,1,2, … p is the polynomial regression coefficient to be solved, yjJ is 1,2, … n is the j th sampling point measured value of the ballistic parameters x, y and z or the time sequence t of the parameters of the measuring element R, A, E, p is the polynomial order, and the random variable sequence epsiloni~N(0,σ),i=1,2,…n,εi,εj(i ≠ j) are independent of each other, and obey a normal distribution with 0 mean variance σ; t is tiN (0, σ), i ═ 1,2, … N is a time series of measurement parameters, N is the number of polynomial regression fit drops, V is a velocity series of position measurement data series, U is a coefficient vector of velocity, Y is a time series measurement value vector of ballistic parameters, D is a time series matrix, B is a polynomial regression coefficient vector, and E is a random vector that follows a normal distribution.
The polynomial order p may be 2, 3, 4 … …, or y may be determined if p is 0jAverage value of (d); if p is 1, y can be obtainedjThe polynomial regression of (a) and the average of the velocity during the period, but no acceleration information is obtained; if p is 0, then y is obtainedjAverage value of (d); if p is 1, y can be obtainedjPolynomial regression of (c) and average of the period velocity, but no acceleration information is obtained); n is the number of polynomial regression fitting paragraph points, for the frame frequency of 20HZ measurement elements, the real-time calculation n is 21, in order to ensure the smooth speed-calculating precision and not to influence the real-time performance, only the end point smooth speed-calculating can be used, the value of n for the end point smooth speed-calculating cannot be too large, the too large number of data needs to be accumulated, and the influence on the large number of data needs to be accumulatedReal-time performance, and the 1 st data has a lagging influence on the last data; the real-time calculation of n values cannot be too small, and the smoothing effect cannot be displayed. And performing real-time calculation, weighting the obtained polynomial coefficient and performing acceleration lag compensation, wherein the weighting and compensation method needs actual measurement data simulation calculation and exploration. For the post calculation, the number n of regression segment points is 81, and the smooth position, speed and acceleration results near the middle point of time are obtained, so that the accurate smooth result can be obtained and the influence of 40 frames of data left and right missing can be avoided.
To ensure that the matrix inversion does not cause ill-conditioned divergence, S2 is normalized by the following formula:
t=F(T-T0)
wherein T is the time sequence variable of the original measured data (equal intervals are not required, namely 20 frames can be lost at most in 1 calculation period during real-time calculation, and 40 frames can be lost at most in 1 calculation period during post calculation); f is the sampling frequency of the ballistic parameters; t is0Time of the first parameter (time minimum) participating in polynomial regression smoothing; and t is the time sequence of the measurement data after the normalization transformation.
The time matrix of the polynomial regression smoothing must be rounded. Because to ask for (D)TD)-1The value of (2) is regressed by a polynomial of order 2, the number of primary regression data points is 21, more than 8000 times of time parameter 6 power arithmetic operation occurs, floating point number items of single time parameter 6 power arithmetic operation at least generate data of 30 bits of effective bits for hundreds of seconds accurate to millisecond, 18 bits are behind the decimal point, and matrix operation is carried out after multiplication and addition and subtraction of diagonal elements.
If the time parameter T is not normalized, the appearance is easy to appear (D)TD)-1The matrix inversion of (a) is ill-conditioned such that a is (a)ij)3×3=(DTD)(DTD)-1Not an identity matrix, see table 1.
T(s) A11 A12 A13 A21 A22 A33 A31 A32 A33
210.042 1.000 -0.00 0.00 -0.01 1.000 0.00 -1.76 -0.01 1.000
210.092 1.000 0.00 0.00 -0.01 1.000 0.00 -1.55 0.00 1.000
210.142 1.000 0.00 0.00 -0.02 1.000 0.00 -3.36 0.01 1.000
210.192 1.000 0.00 -0.00 0.00 1.000 -0.00 0.37 0.01 1.000
210.242 1.000 -0.00 0.00 -0.01 1.000 0.00 -2.87 -0.01 1.000
210.292 1.000 0.00 0.00 -0.01 1.000 0.00 -2.96 0.00 1.000
210.342 1.000 -0.00 -0.00 -0.02 1.000 -0.00 -3.19 -0.03 1.000
210.492 1.000 0.00 -0.00 -0.01 1.000 -0.00 -1.72 0.00 1.000
TABLE 1 time series A ═ without regularization of 2 nd order polynomial (A ═ Aij)3×3=(DTD)(DTD)-1Not an identity matrix
The time parameter is normalized, i.e. T is taken as F (T-T)0) Where F is the sampling frequency of the ballistic parameter. T is0For the time of the first (time-minimum) parameter participating in the polynomial regression smoothing, a ═ aij)3×3=(DTD)(DTD)-1Precision becomes the identity matrix, see table 2.
T(s) A11 A12 A13 A21 A22 A33 A31 A32 A33
210.042 1.000 -0.00 -0.00 -0.00 1.000 -0.00 -0.00 -0.00 1.000
210.092 1.000 0.00 0.00 0.00 1.000 0.00 0.00 0.00 1.000
210.142 1.000 -0.00 0.00 -0.00 1.000 0.00 -0.00 -0.00 1.000
210.192 1.000 -0.00 0.00 -0.00 1.000 0.00 -0.00 -0.00 1.000
210.242 1.000 0.00 0.00 0.00 1.000 0.00 0.00 0.00 1.000
210.292 1.000 -0.00 -0.00 -0.00 1.000 -0.00 -0.00 -0.00 1.000
210.342 1.000 -0.00 0.00 -0.00 1.000 0.00 -0.00 -0.00 1.000
210.392 1.000 -0.00 0.00 -0.00 1.000 0.00 -0.00 0.00 1.000
TABLE 2 time-series normalized 2-degree polynomial A ═ A (A)ij)3×3=(DTD)(DTD)-1Is an identity matrix
In S3, a mathematical model for solving the speed of error convergence positioning information by polynomial regression memory compensation is created. Through simulation error analysis, in order to ensure the positioning speed-calculating smooth precision as much as possible, when p is selected to be 2, the experimental effect is best, and the regression coefficient b is calculated according to a mathematical model of polynomial least square regression speed-calculating of the positioning information in S11、b2And calculating the speed and the sum of post-processing near the midpoint of the time seriesThe polynomial regression (smoothing) of the velocities is:
y(T)=b0+b1t+b2t2
wherein y (T),A time series fitting polynomial representing ballistic parameters, and velocity and acceleration expressions relative to time before regularization, respectively.
In real-time calculation, when 21 points are accumulated for the first time, all 21 point parameters can be estimated (smoothed) and calculated at one time, or interpolation calculation is carried out nearby, when 22 points are accumulated, the first point is removed, the matrix is solved again, and polynomial regression coefficient memory accumulation is carried out, wherein:
b0'=b0
b'1=0.05b1+0.95b10
b'2=0.05b2+0.95b20
in the formula: b0′、b1′、b2′;b0、b1、b2;b00(b00≡0)、b10、b20Time series polynomial 0,1,2 degree term coefficients representing the most recently determined, the most recently calculated, and the last regression cycle determined trajectory parameters, respectively
In the formula b10,b20B for last smoothing estimation process1,b2The corresponding coefficients, y (T), are always calculated using the currently unweighted regression coefficients, while the velocity and acceleration polynomial regression coefficients are accumulated using memory when the number of memory times reaches more than 20, and when the number of memory times reaches more than 20When the temperature of the water is higher than the set temperature,wherein a ismaxAs ballistic parameter yjMaximum theoretical acceleration of the time series in the measuring arc, F2(2b2) The above process is then repeated for the acceleration-lag compensation value on the ballistic parameter velocity.
Fig. 3 shows the comparison between the speed of smoothing by 2-order polynomial regression and the quick result of filtering by α β γ, which shows that the speed error distribution of 2-order polynomial regression is enveloped in the α β γ differential speed error distribution, and the difference between the two is large.
The O-type point line is an error distribution curve of alpha beta gamma filtering speed calculation and accurate ballistic velocity, and the type point line is an error distribution curve of 2-order polynomial regression speed calculation and accurate ballistic velocity (accurate ballistic refers to a ballistic calculated by short-baseline interferometer speed measurement information).
The following table shows statistical data of a stable segment of fast-acting results obtained by polynomial regression smoothing speed calculation and alpha beta gamma filtering, wherein the total speed errors of 3 methods including 2-order polynomial regression smoothing speed calculation, 3-order polynomial regression smoothing speed calculation and alpha beta gamma filtering speed calculation are respectively about 2.67, 3.67 and 14.57m/s, which indicates that the fast-acting results obtained by 2-order polynomial regression smoothing are the best, the fast-acting results obtained by 3-order polynomial regression smoothing are the second best, and the fast-acting results obtained by alpha beta gamma filtering are the worst.
Table 3: polynomial regression smoothing speed calculation and alpha beta gamma filtering quick-result stable segment statistical data calculation
The following is a method of alpha-beta-gamma real-time filtering in fig. 3 compared to polynomial regression smoothing speed finding.
1 selection of initial value
The first and second points are not evaluated by filtering, and the third point is evaluated as follows:
a^3=-a1/6+a2/3+5a3/6
u^3=-a1/2+a3/2
s^3=(a1-2a2+a3)/2
starting from the fourth point to be the initial value a ^ a3、u^3、s^3Entering an alpha-beta-gamma filter to newly input information anEstimating to obtain a filtered estimate a ^n,da^n,dda^n
Calculation formula of 2 alpha-beta-gamma filter
And (3) prediction:
x^n/n-1=x^n-1+u^n-1+s^n-1
u^n/n-1=u^n-1+2s^n-1
s^n/n-1=s^n-1
and (3) correction:
x^n=x^n/n-1+α(xn-x^n/n-1)
u^n=u^n/n-1+β(xn-x^n/n-1)
s^n=s^n/n-1+γ(xn-x^n/n-1)
the input of the filter is xn(information after selection, N is 1,2 … N), and the output is x ^ dn,dx^n,ddx^n(dx^n=u^n/h,ddx^n=2s^n/h2H is the measurement information sampling interval time), and is given by x ^ cn,u^n,s^nAs the initial filtering value of the next sampling information.
3 selection of filter parameters alpha, beta, gamma
For the information of the last 10 sampling points of the measurement information with the tracking stability of the equipment for 2 seconds, the parameter alpha of the growing memory filter is usedn、βn、γnAre filtered separately, alphan、βn、γnThe value of (d) is calculated by:
αn=3(3N2-3N+2)/(N(N+1)(N+2))
βn=18(2N-1)/(N(N+1)(N+2))
γn=30/(N(N+1)(N+2))N=1…10;
obtaining:
after that, the filter parameters are changed to α -0.2, β -0.014862535, and γ -0.00018416391, and the filter enters an α - β - γ filter.
And filtering by using a set of filtering parameters of 0.6, 0.18046526 and 0.009115835 within two seconds after each shutdown point.

Claims (5)

1. The polynomial least square regression memorability speed calculation method of the positioning information is characterized in that the speed is determined by the flight position measurement information of the spacecraft, and the method comprises the following 5 steps:
s1: establishing a mathematical model for solving the speed by polynomial least square regression of the positioning information;
s2: the time series is normalized, and the formula is as follows:
t=F(T-T0)
wherein T is the time series variable of the original measurement data; f is the sampling frequency of the ballistic parameters; t is0Time of a first parameter participating in polynomial regression smoothing; t is the time sequence of the measurement data after the normalization transformation;
s3: comparing and selecting polynomial order p values by a mathematical model of polynomial least square regression speed calculation of the positioning information in S1, calculating a regression coefficient, and calculating the speed and the acceleration of post processing near the midpoint of the time sequence;
s4: and (3) carrying out polynomial regression coefficient memory accumulation by real-time calculation by using formulas of regression coefficient, speed and acceleration obtained by S3, wherein:
b'0=b0
b'1=0.05b1+0.95b10
b'2=0.05b2+0.95b20
in the formula: b0′、b1′、b2′;b0、b1、b2;b00、b10、b20Time-series polynomial 0,1,2 degree term coefficients, b, representing the most recently determined, the most recently calculated, and the last regression cycle determined trajectory parameters, respectively00≡0;
S5: determining the speed near the latest time in real time by combining the memory accumulation coefficient and the hysteresis compensation value of the acceleration; when the number of memorization times reaches more than 20, and whenWhen the temperature of the water is higher than the set temperature,wherein T ═ F (T-T)0) F is the sampling frequency of the ballistic parameter, amaxAs ballistic parameter yjMaximum theoretical acceleration of the time series in the measuring arc, F2(2b2) Is an acceleration hysteresis compensation value on the ballistic parameter velocity.
2. The method for solving the speed of the positioning information by the polynomial least squares regression memorial method according to claim 1, wherein the mathematical model for solving the speed of the positioning information by the polynomial least squares regression established in S1 is:
Y=DB+E,V=DU,B=(DTD)-1DTY
in the formula:
wherein, bjIs to be treatedObtaining polynomial regression coefficient, j equals 0,1,2, … p, yjJ is the j-th sampling point measurement value of the time sequence t of the trajectory parameters x, y and z, j is 1,2, … n, p is a polynomial order, and the random variable sequence epsiloni~N(0,σ),i=1,2,…n,εi,εj(i ≠ j) are independent of each other, and obey a normal distribution with 0 mean variance σ; t is tiN (0, σ) is a time series of measurement parameters, i is 1,2, … N, N is the number of polynomial regression fit drops, V is a velocity series of position measurement data series, U is a coefficient vector of velocity, Y is a time series measurement value vector of ballistic parameters, D is a time series matrix, B is a polynomial regression coefficient vector, and E is a random vector following a normal distribution.
3. The polynomial least squares regression memorial velocity method for localization information according to claim 2 wherein said polynomial order p can be 2, 3, 4 … …; the number n of the polynomial regression fitting paragraph points is taken as 21 in real-time calculation for the sampling rate with the frame frequency of 20 Hz; in the post calculation, n is 81, and the smoothed position, velocity and acceleration results around the middle point in time are obtained, and are not affected by the absence of 40 frames of data.
4. The polynomial least squares regression memorial velocity method for localization information according to claim 1, wherein the time series variable T of the original measurement data of S2 does not require equal intervals, that is, 20 frames at most can be lost in 1 calculation period in real time calculation and 40 frames at most can be lost in 1 calculation period in post calculation.
5. The method of solving the speed of the memory of the polynomial least squares regression of the positioning information as set forth in claim 1, wherein said S3 compares the order p of the selected polynomial with 2, and said regression coefficient b is obtained1、b2And the formulas for obtaining the post-processing speed and acceleration near the midpoint of the time series are respectively as follows:
y(T)=b0+b1t+b2t2
wherein T ═ F (T-T)0) Y (T) a time series fitting polynomial representing ballistic parameters,indicating the speed relative to the time before warping,indicating acceleration.
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CN104318119A (en) * 2014-11-03 2015-01-28 北京航空航天大学 Start point centroid error compensation method in high dynamic situation

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