RU2624408C2 - Method of autonomous estimation of orbit changes of sighted spacecraft - Google Patents

Abstract

FIELD: aviation.

SUBSTANCE: essence of the invention consists in autonomous determination, aboard a sighting spacecraft (SC) (Sc-1), of the changes in the orbit of a sighted SC (SC-2) on the basis of the autonomous generation of high-accuracy estimates of the parameters of the SC-2 orbit. These estimates are determined by solving a navigational problem according to the developed sighting method based on measurements of star coordinates and their stellar magnitudes in an optoelectron device (OED) placed in a cardan suspension and the sighting SC-2. The orientation of the "SC-1-SC-2" line of sight relative to the coordinate system, associated with the SC-1 body, is calculated as a result of measurements of the characteristics of stellar field observed in the OED rigidly fixed to the SC-1 body. The facts of changes in the orbit of SC-2 are established by analysing the sums of corrections to the orbit of SC-2 and the sums of the measurement discrepancies formed in the process of solving a navigational task by the tracking method. At the same time, it provides: autonomous high-accuracy estimation of the orbit of the observed SC, autonomous determination of the change in the orbit of the observed SC on the basis of passive measurements using only natural field radiation and excluding active measurements of range and radial velocity. Thus, the on-board control complex acquires a new function - tracking space objects of control and detecting the facts of changes in their orbits.

EFFECT: enhanced functional capacity.

2 dwg, 8 tbl

Description

The invention relates to spaceborne control systems (SCU) for spacecraft (SC) and provides, on board the sighting apparatus (KA-1), an autonomous high-precision estimate of the orbit of the sighting apparatus (KA-2), the orientation of the KA-1 hull and the line of sight in a geocentric equatorial inertial system coordinates (GEISK). Based on the KA-1 listed in BKU, the facts of a change in the KA-2 orbit are quickly determined.

The orientation of the KA-1 is estimated based on information from an optoelectronic device (OEP-1) that is rigidly fixed to its body. The determination of the KA-2 orbit is carried out on the basis of information from the OEP-2, placed in the gimbal and sighting the KA-2.

It is known that a theory has been developed for a relatively long time and modeling of the so-called mutual method of autonomous navigation of spacecraft has been carried out repeatedly [1, 2, 3], which provides for the simultaneous assessment of the state vectors of both vehicles participating in the "sighting spacecraft - sighting spacecraft" based on measurements of the spacecraft’s angle -2 - observed star ", their relative ranges and speeds (Fig. 1). Moreover, it was traditionally believed that the observed star is known. In [1, 2, 3], the option of measuring angles to two stars was considered, connecting a second star against the background of measuring range and radial velocity did not significantly increase the accuracy of navigation definitions.

However, a further increase in the number of measured angles (up to five) made it possible to exclude the measurement of range and relative speed.

If the sensitivity of the sighting EIA is not lower than the sixth magnitude, and the field of view is about 10 °, then the number of simultaneously observed stars is usually from 8 to 12 (at 15 ° - from 25 to 55, respectively), which allows their reliable recognition and provide simultaneous measurement of up to five angles. Theoretically, the number of measured angles can reach the number of recognized stars.

Advances in the development of star recognition algorithms make it possible at each measurement session to solve the problem of determining the orientation of the sighting spacecraft body in various orthogonal coordinate systems [4]. In addition, based on the idea of a mutual navigation method, it became possible not only to determine the orbit of the sighted spacecraft, but also to establish the fact of its change.

The mutual method involves determining the orbits of not only both vehicles, but also one (any) with the known orbit of the other. In the first case, the accuracy of the estimates of the orbits depend on each other nonlinearly, in the second case, with an increase in the accuracy of the known orbit, the accuracy of the determined one also increases. In practice, these accuracy are aligned, which contributes to the rapid detection of changes in the estimated orbit.

A navigation method using only the measurement of angles “KA - star” (with the known orbit of the sighting KA), called by the authors the tracking method.

Table 1 shows the comparative accuracy of the mutual method and the tracking method. An analysis of this table suggests that, with a mean square error (SQF) of measurements in the EEC of the order of 0.1 '' - 1 '', measuring five angles in the tracking method shows the accuracy of the estimates of the spacecraft orbit somewhat better (sometimes significantly) than with an additional measurement of the range with UPC in 10-15 m and measuring one or two angles of the "spacecraft - star" according to the mutual method algorithm. At least, this is true for the indicated pairs of orbits, both for single solutions and in statistics.

The navigation problem in the tracking method is solved using the method of least squares (OLS), based on the calculation of the residuals of measurements and partial derivatives of the measured parameters according to the estimated. Approximate estimates of the KA-2 orbit at a certain point in time, taken as the beginning of the measured interval t = 0, are assumed to be a priori known — the reference orbit (q _{0 a n} ). Calculation of amendments to it is the essence of solving the problem.

Based on the known orbit and the calculated orientation of the KA-1, as well as in the presence of initial approximations q _{0 a n} of the KA-2 orbit, the line of sight "KA-1-KA-2" is calculated. When sighting at each navigation session, the instrumental coordinates of the observed stars are measured, their magnitude is estimated.

After taking measurements during the measuring interval, statistical processing of the measurement results is carried out, the parameters of the KA-2 orbit are iteratively corrected:

moreover, at zero iteration (c = 0) q ₀₀ = 4 _{0 a n} . Corrections are calculated according to the following algorithm [1, 2]:

where c is the iteration number;

j is the number of the navigation session;

n is the number of navigation sessions on the measured interval;

- градиентная матрица, т.е. матрица производных от текущей (на момент навигационного сеанса) измеряемой функции по начальным параметрам опорной орбиты q_0c, i=1, …, m, i - номер навигационного параметра, m - размерность вектора измеряемых параметров;

is the gradient matrix, i.e. a matrix of derivatives of the current (at the time of the navigation session) measured function with respect to the initial parameters of the reference orbit q _0c , i = 1, ..., m, i is the number of the navigation parameter, m is the dimension of the vector of the measured parameters;

G _j - matrix of derivatives from Lij to the current parameters of the reference orbit;

- матрица баллистических (изохронных) производных;

- matrix of ballistic (isochronous) derivatives;

- весовая матрица измерений, K_Lj - матрица вторых моментов погрешностей измерений на j-м навигационном сеансе;

- weighted matrix of measurements, K _Lj - matrix of second moments of measurement errors at the j-th navigation session;

ΔL _j = L _jism -L _jcalc - vector of measurement residuals, the difference between the vector functions of the navigation parameters measured and calculated from the reference orbit;

q = {r, v}, Δq 0c = {Δr _with, Δv _c}, where r - the radius vector of the spacecraft position, v - velocity vector, Δr _s and Δv _c - amendments thereto.

The iteration ends when the condition | Δq _0c | <ε.

In the simulation model of the tracking method that implements the solution of the navigation problem according to the algorithm (1) - (2), the dimension of the vector of the measured parameters varies in the general case from one to five. With an increase in the number of angles from two to five, the accuracy of estimates of the radius vector increases, depending on the considered pairs of orbits, by an average of three times, and an increase in the accuracy of estimates of the modulus of the velocity vector reaches an order of magnitude.

In this case, to clarify the KA-1 orbit, a method of autonomous navigation through virtual measurements of stellar zenith distances is also used, which also uses measurements only in the EIA. The accuracy of the latter for any orbits with measurement errors of the order of 0.1 '' is in the range from 1 to 10 m in position and from 1 to 10 mm / s modulo the velocity vector [5, 6]. Solutions to navigation problems were carried out with 500 measurements on a measured interval at the start date of decisions (randomly selected). The measured interval is set as a multiple of the time of one revolution of KA-2.

Note that all calculations were carried out in an environment developed by the authors of an automated system of scientific research of methods and algorithms for autonomous navigation and orientation of spacecraft, which provides ample opportunity to build research processes and their analysis, including various calculation tactics. There are either one-time (single) solutions to the problem, while the accuracy indicator is the maximum error in the parameters of the orbits over the entire dimensional interval, or a set of statistics of solutions when the navigation problem is solved at 35 consecutive dimensional intervals. Statistical results are presented taking into account the aforementioned maximum errors of single solutions, such as maximum maximum, mathematical expectation and standard deviation of the errors in the parameters of the orbits for the entire set of solutions. Each set of statistics is made out in the form of an entry in the decision database with the corresponding comments [1, 2].

The ability to solve the tracking problem is determined by the mutual arrangement of the orbits of the devices. Based on the data on the reference orbits, a plurality of segments of the measured interval are preliminarily formed, on which KA-2 is observed from the KA-1, i.e. not obscured by the Earth, not illuminated by the Sun or Moon, and on which, therefore, measurements are possible. Such segments are called navigation. The forecast for a successful solution of the navigation problem by the tracking method is considered positive if the total length of the navigation segments T _N is not less than 60% of the measuring interval T, negative if T _N <0.3 T. Otherwise, when 0.3 T <T _N <0.6 T, the possibility of solving the problem is determined by the location of the navigation segments on the measured interval; for a positive forecast, they should be located both on its first and second half.

Table 2 presents the simulation results of the tracking method for 33 turns of KA-2 for a pair of orbits No. 1, the parameters of which are contained in table 3. As can be seen, the preliminary analysis algorithm for the possibility of solving the navigation problem produced a negative result six times: turns 11-13 and 25 -27. At these turns, a ballistic calculation of the KA-2 orbit was carried out, without significantly lowering the accuracy of its estimates, which was made possible thanks to the high accuracy characteristics of the tracking method.

Table 4 presents the maximum errors in determining the KA-2 orbits in this way for single solutions for pairs of orbits, the initial parameters of which are described in Table 3. High and stable accuracy of navigation definitions favors a tracking method that seems promising for use in autonomous navigation systems and orientation.

When tracking KA-2 at each navigation session of the measured interval, the stars observed in the OEP are recognized [4, 7]. Recognition can be carried out both using the KA-2 reference orbit [7], and without it [4], but always based on the calculation of the matrix of angular distances between the stars.

After recognizing the stars in the OEP-1, the orientation of the KA-1 hull in the SEISK is determined. For this, initially, based on the calculated orts of the observed stars in the instrumental coordinate system (UCS) and known after recognition by the geocentric orts of these stars, the orientation of the OEDs in the GEISC is determined based on the well-known position that when moving from one orthogonal coordinate system to another, the angular distances between vectors are saved.

Therefore, based on the equality of the angular distances between the orts of the observed stars and the OES axes in the CSC, on the one hand, and between the guiding cosines of the recognized stars and the CES axes in the GEISC, on the other hand, it is possible to determine the orientation of the ξ, η, ζ UCS axes in the GEISC by solving three systems Q of linear equations with three unknowns:

where b _k = (b _k1 , b _k2 , b _k3 ) are the directing cosines of the stars in GEISK, k = 1, ... Q, Q is the number of recognized stars;

and _k = ( a _k1 , ak ₂ , and _k3 ) are the directing cosines of the stars in the UCS;

with _n = (with _n1 , with _n2 , with _n3 ) is the sought vector of the direction cosines of the OED axis in GEISK, n = 1 corresponds to the ξ axis, n = 2 to the η axis, and n = 3 to the ζ axis.

Each of the systems of conditional equations of the form (3) is solved using OLS, its solution is a vector with _n that minimizes the length of the residual vector (the difference between the right and left parts of the system), i.e.

составляется система нормальных уравненийAfter calculating the partial derivatives of function (4) taking into account

compiled a system of normal equations

; A=(A_j),

, i, j=1, 2, 3.moreover, B = (В _ij ),

; A = (A _j ),

, i, j = 1, 2, 3.

From the formula (5), after inversion of the matrix B, we find the desired vector

From vectors with _n obtained according to (3) - (6), the matrix is composed

M ₁ = {m _nj }, m _nj = c _nj , n, j = 1, 2, 3, which is the coordinate matrix of the unit vectors of the UCS axes in GEISC.

According to the known values of the fixing angles of the OEP-1 λ and ρ (Fig. 2), a transition matrix is formed from the associated coordinate system (SSC) to the UCS [1, 2]:

Matrix

is the transition matrix from GEISK to SSK. The required unit vectors of the KA-1 axes in GEISK are the first, second, and third rows of the matrix M ₃ , respectively.

Next, the orientation angles of the line of sight in the SSC KA-1 are calculated. The known coordinates of KA-1 (x ₁ , y ₁ , z ₁ ) and the reference coordinates of KA-2 (x ₂ , y ₂ , z ₂ ) determine the unit vector of the line of sight in GEISC a ( a _x , a _y , a ₂ ):

,

,

,

,

,

,

.Where

.

рассчитывается таким образом:Vector of the guides of the cosines of the line of sight in the CCK

calculated in this way:

,

. Значения λ₁, ρ₁ подаются на двигатели рамок карданова подвеса для физического ориентирования оптической оси ОЭП-2 в точку нахождения КА-2.The angles between the vector a 'and the axes X _s and Z _{c in} SSC are λ ₁ = arccos

,

. The values of λ ₁ , ρ ₁ are fed to the engines of the cardan suspension frames for the physical orientation of the optical axis OEP-2 at the location of KA-2.

The tracking method also contains an algorithm for solving the problem of the operational determination of the facts of changes in the KA-2 orbit, and these changes can be relatively minor.

These facts are established reliably under the condition of a high-precision solution of the navigation problem by the tracking method (the order of units, tens of meters in position and, accordingly, units, tens of mm / s modulo the velocity vector), which, in turn, assumes a similar accuracy in the development of orbit estimates KA-1.

Two methods have been developed for solving the problem of determining the facts of the KA-2 orbit change based on the analysis of the dynamics of the sums of corrections to the reference orbit by the radius vector (Δr), by the modulus of the velocity vector (Δv) and by the sum of the modules of the measurement residuals (μ) for the measured interval. The analyzed values are calculated in the process of solving the navigation problem according to the algorithm (1) - (2):

The first method is similar to the traditional set of statistics. Two options for its implementation have been developed. According to the first option, the Δr corrections are analyzed for the current measured interval in relation to this indicator at two previous intervals (the first criterion) and the current sum of residuals μ in comparison with the same amount in the previous interval (second criterion). According to the second option - Δr, Δv (first criterion) and μ (second criterion) in relations with similar amounts obtained in the previous measuring interval.

To assess the fact of the impulse, two calculation modes are provided - joint (mode A) and separate (mode B). In mode A, at the end of the current measuring interval, the impulse is recorded when both criteria exceed the set thresholds; in mode B, the excess of the corresponding threshold is taken into account only by one of the criteria.

Based on the modeling experience, value ranges were selected.

thresholds: for the first criterion - in the range from 2.0 to 3.0, for the second - from 1.25 to 2.5, depending on the pair of orbits. The results of fixing the facts of changes in the KA-2 orbit according to the first method are presented in table 5. In the column “Fixation”, the “+” sign marks the signal generated by the algorithm for successfully determining the fact of changing the orbit. After the decimal point, the number of false signals in all statistics of 35 decisions of the corresponding record of the decision base is indicated. In the "Visibility" column, an integrated characteristic of the ability to solve the navigation problem for all dimensional intervals of a given record is noted. “Different” means that part of the decisions was forced to be replaced by a ballistic forecast, in which case a possible change in the KA-2 orbit could not be established.

The second method is developed using two parallel programs. The first of them, called the flight one, calculates the updated reference orbit (UOO) KA-2 according to (1) - (2) based on the initial a priori data about this orbit and the on-board measurement model. It is believed that under real flight conditions, the measurement model in this program will be replaced by real measurements under the conditions of possible actual changes in the KA-2 orbit. The second program, the model one, implements an exclusively model algorithm, but in it the reference and true orbits are presented as worked out in the flight program UO, on the basis of which measurements are simulated; pulses supplied to change the KA-2 orbit are absent.

In the dynamics of statistics collection, the interaction of flight and model programs is as follows. During the first measuring interval, only the flight program that calculates the DOE is working. At the second and subsequent intervals, both programs operate in parallel. The model program in the process of solving the navigation problem produces the basic values of the criteria described in (7), with which the results of similar calculations of the flight program are compared. If they are exceeded by the first criterion three or more times, by the second criterion 1.25 or more times, the fact of a change in the KA-2 orbit is recorded.

The calculation results for this method are presented in tables 6, 7 and 8. Table 6 is made for the fourth pair, table 7 for the second and fourth pairs of orbits from table 5. Tables 5, 6 and 7 are made for the measured interval in one turn, table 8 - in half a turn.

Analysis of tables 5, 6, 7 and 8 shows that the first method, which is simpler for software implementation, allows you to confidently determine the change in the KA-2 orbit only with pulses of 20 m / s or more, but requires fine tuning of thresholds, depending on the pairs orbits to eliminate false signals. The second method is much more sensitive to the magnitude of the pulse (1-3 m / s) and is practically guaranteed against false signals, since it compares two solutions of the problem on each measuring interval using virtually the same algorithm with close source data. In the absence of impulses, the values of the criteria will be close, and their relations will be far from the threshold values. However, compared with the first, this method requires a significant complication of the program.

The pulse fixation time depends on the moment of its supply relative to the beginning of the measured interval. If this moment falls in the first half or middle of the interval, the impulse is fixed at its end, otherwise - during the next interval or, in extreme cases, at its completion (see lines 2 and 13, 7 and 14, 11 and 15 of the table 6).

Note that table 6 is compiled for one pair of orbits, but for different directions of a single pulse. Table 7 - for two pulses of the same direction, issued at different times at the same measured intervals, but for different pairs of orbits that are significantly different from each other. Tables 3 and 5 contain the entire range of pairs considered, containing orbits with altitudes from 250 to 20,000 km, eccentricities from 0.01 to 0.1, and inclinations from 56 ° to 104 °.

Thus, the data of tables 1-8 reflect the results of experimental verification of the implementation of the invention.

For the second evaluation method, from the considered criteria and calculation modes, the μ criterion is most preferable, containing the measurement discrepancies modules, delivering the largest number of impulse fact definitions without involving other criteria, i.e. mode B. For the first method, option 2 and mode A are preferred, i.e. joint use of all three criteria (7).

It follows from the foregoing that the proposed tracking method, based on passive inter-satellite astrometry, provides an operative determination of the fact of a change in the KA-2 orbit, the solution of problems of high-precision determination of the KA-2 orbit, the orientation of the KA-1 body and the line of sight in various coordinate systems.

The technical result of the invention is to exclude active measurements of range and radial velocity, while increasing the accuracy of the KA-2 orbit estimates, in calculating the physical orientation angles of the optical axis of the sighting OEP and in the possibility of implementing a new function of the autonomous navigation and orientation system — detecting KA-1 on board the fact of a change in orbit by the sighted KA-2.

The feasibility of the invention follows from the fact that it is based on the use of EIA and cardan suspension, long mastered by the industry.

The technical and economic efficiency of the invention consists in reducing the weight and size characteristics of the required meters, determining the impulse delivery to the sighted KA-2 without involving space monitoring equipment and the ground control complex.

Information sources

1. Kuznetsov V.I., Danilova T.V. An automated system for researching methods and algorithms for autonomous navigation and orientation of spacecraft. Textbook, St. Petersburg., VKA them. A.F. Mozhaysky, 2006, 322 p.

2. Kuznetsov V.I. Automated system for scientific research of methods and algorithms for autonomous navigation and orientation of spacecraft. Monograph, St. Petersburg. A.F. Mozhaysky, 2010, 453 p.

3. Kuznetsov V.I., Danilova T.V. Modeling the method of mutual navigation of spacecraft: new results, St. Petersburg, Izvestiya VUZov, Instrument Making, 2005, v. 48, No. 10, p. 20-27.

4. Danilova T.V., Arkhipova M.A. Determination of the orientation of the spacecraft’s hull in a geocentric equatorial inertial coordinate system based on astrometry in the absence of data on orbital parameters, St. Petersburg, Izvestiya VUZov, Instrument Engineering, 2013, v. 56, No. 7, p. 13-20.

5. Kuznetsov V.I., Danilova T.V. System of autonomous navigation and orientation of the satellite based on virtual measurements of the zenith distances of stars, M., Space Research, 2011, vol. 49, No. 6, p. 551-562.

6. Patent for invention No. 2454631 "Method for autonomous navigation and orientation of spacecraft based on virtual measurements of zenith distances of stars." Authors: Kuznetsov V.I., Danilova T.V., Kosulin D.M. Priority Invention October 28, 2010

7. Kuznetsov V.I., Danilova T.V. Recognition Algorithms for “Working” Stars by the Star Field, St. Petersburg, Izvestiya VUZov, Instrument Making, 2003, v. 46, No. 4, p. 16-23.

Claims (1)

A method for autonomously estimating changes in the orbit of a sighted spacecraft (KA-2) in the presence of high-precision navigation definitions of a sighting spacecraft (KA-1), characterized in that at each navigation session, the measured interval using an optical-electronic device rigidly fixed to the KA-1 body (OEP) measure the coordinates of stars and their stellar magnitudes, recognize stars, calculate the geocentric orientation of KA-1 and determine the direction of the line of sight "KA-1-KA-2", then using it placed in cardans on weight CES endorse the SC-2, measured magnitudes and the coordinates of the stars, the stars recognize, calculate angles "CA-2 - star" and their residuals; at the end of the measuring interval, the measurement results are processed using the algorithm for filtering measurement errors, form corrections to the KA-2 orbit; by analyzing the sums of corrections and the sums of residuals, the facts of changes in the KA-2 orbit are established.

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