# Method for autonomous navigation and orientation of spacecrafts

FIELD: onboard system for controlling spacecrafts for autonomous estimation of orbit and orientation of spacecraft body.

SUBSTANCE: method for autonomous navigation and orientation of spacecrafts includes computer calculation of position in three-dimensional space of ort of radius-vector of support (calculated, a priori assumed) orbit, rigid attachment of optical-electronic device on the body of spacecraft and measurement of coordinates and brightness of stars, which are in the field of view during navigational sessions, in it.

EFFECT: increased number of performed tasks, expanded capabilities of method application environment for any orbits, reduced number of measuring devices and mass and size characteristics of onboard system for controlling a spacecraft.

2 dwg

The invention relates to the electrical control system of spacecraft for Autonomous (independent from the ground control center - LVDS) evaluation of the orbit and orientation of the body of the SPACECRAFT.

Known methods of Autonomous navigation, as applicable to manned and unmanned SPACECRAFT. The first method was implemented on manned stations "Salyut". It included the measurement of the moments of sunrise (sunset) stars beyond the horizon of the planet when the orbital motion of the station. To increase the accuracy of navigation was additionally measured moving speed relative to the ground radio beacons and flight altitude. Theoretical foundations of this system are set forth in article Unibin "the method for Autonomous navigation of satellites" (magazine "Space research", .VII, v.2, 1969). The second method was used on the devices 11 F and consisted in measuring Zenith distances of two stars with two Astrovirus devices (AVA) and radio Builder local vertical. Additionally, to measure the altitude Builder local vertical was supplied with another receiving-transmitting device. This method is described in the book "Mathematical and software systems Autonomous navigation KA 11 F", edited by Uguntina and Shimakawa, the USSR Ministry of defense, 1986

The closest the technical nature of the claimed invention should be considered as the second method, which is taken as a prototype. A common feature of the prototype and the proposed method is the presence on Board of two opto-electronic devices. In addition to these devices in the known method is used for radio Builder vertical, which is limited to a flight altitude of about 500 km, This Builder is necessary because to solve navigation tasks in addition to directions on the infinitely remote star you want to have the second direction, it is associated with the orbital motion of the SPACECRAFT.

The algorithm AVA is built on the combination of the optical axis of the viewfinder with the image of the given GCC stars. For this AVA is placed in the gimbal.

The disadvantage of this method is the forced separation of the body KA locations Kardanov suspension and mounting Builder vertically, which reduces the measurement accuracy of the Zenith distances of the stars due to temperature deformations of the body of the SPACECRAFT. To maintain navigation accuracy is measured additionally altitude flight over the oceans. However, the number of measurements because of the shift track of the orbit on the Earth's surface changes over time. In addition, the number of measurements depends on the inclination. The operability of the radio altimeter, as noted, is limited by the altitude of the SPACECRAFT. As a result, the maintenance required is echnosti determine the orbit of a periodic correction from NKU information of the Autonomous system, that is, this system is actually only partially Autonomous, that is admitted by the developers. In addition, the Builder of the local vertical roughly (to within a few tens of minutes of arc) determine only two orientation angle of the hull (pitch and roll) and do not determine the yaw angle. As a result the orientation of the SPACECRAFT cannot be determined completely and with high precision.

The purpose of this invention is to improve the accuracy of navigation estimates and receive full assessments guidance for the reduction in weight and size characteristics of on-Board SPACECRAFT control systems, as well as the extensibility of the application of this method, an Autonomous navigation and attitude control for a SPACECRAFT to any orbits (up to heights of geostationary and more and any inclinations).

The proposed method is that instead of AVA use opto-electronic device (EIA), allowing not only to step up the star, but also to measure the instrument coordinates of the stars, fell into the field of vision of the device, and radio Builder vertically replace the computer calculation of Orta radius-vector of the reference (a priori believe) orbit. This ORT acts as a line associated with the orbital motion of the SPACECRAFT, and allows us to calculate the angular distance of the star.

When the hard mount EIA on the body of the SPACECRAFT and the tracking system SPACECRAFT stabilization, hot which would be roughly (within ± 5°), directions to the center of the planet, it is possible to solve together the problems of navigation and orientation.

In this case, the coordinates of the working of stars (i.e. the most bright of the stars, fell into the field of view of the instrument) contains information about the location of the SPACECRAFT in inertial space (for the coordinates change as you move along the orbit), and the information about the actual orientation of the body of the SPACECRAFT (the axis of the associated coordinate system) with respect to the axes of the current orbital coordinate system (task), taken as the base. The problem is how to use this information together with data about the reference orbit, and to solve both tasks: navigation and orientation.

To correct both tasks measure the coordinates and brightness of the stars, fell into the field of vision of the device, and using data about the reference orbit and the stars, recognize the working of the star, i.e. determine its position in geocentric Equatorial inertial coordinate system (GEIS). Then calculate the angle of the axis of task-star" in the current coordinate system, taking the angle of the corner in the system GEIST and, when there are at least two such angles in the navigation session, addressing the challenge of navigating the aggregate navigation sessions.

1 shows a diagram of the measurements in the EIA. In the instrument coordinate system ξ, η, ζ from the similarity of the computers is epipedon,
built on the coordinates ORT stars (-ξ^{0}, -η^{0}that ζ^{0}) and the image coordinates of this star (ξ, η, ζ), determine, on the one hand, the value of the measured coordinates:

and, accordingly, the coordinate values of ORT stars:

where ξ^{0}that η^{0}that ζ^{0}coordinates ORT stars,

ξ, η, f - coordinates of the image of the stars,

, f is the focal length.

When rigid fixation EIA angles α and β for the building of the axes KA (X_{in}Y_{in}Z_{in}; X_{in}- along the longitudinal axis KA; Y_{St}- lateral axis) ORT stars in the coupled system define:

where M is the transition matrix from the instrument to the linked coordinate system:

At the beginning of the calculations, when an unknown error orientation, their guess of zero, so ORT starsdirectly transferred to the ORT stars in tasktaking into account the different directions of the axes of the associated current systems of coordinates (task: axis S on the radius-vector, the axis T - transversal, W axis - along the binormal orbit):

After expression ODI orientation angles form a matrix MP. Then:

where N matrix of transition from the bound to task reference orbit. One possible approximate form of this matrix, convenient for differentiation:

where ϑ is the pitch angle,

ψ - yaw,

γ - the roll angle.

From figure 2 it is clear that if desired angle ϕ to determine GEIST, different spatial position of the axes S' and S will lead to calculation errors of the measured value. If the same calculation ϕ to carry out in task, it is obvious: as in the system S W T', and in the system STW Horta respective axes S^{0}, T^{0}, W^{0}will consist of ones and zeros.

For example, ORTwritten. Therefore, the cosine of the angle between the corresponding axis task and direction of the star will be exactly equal to the corresponding coordinate ORTfor example:

At the same time, to any orbit - reference or true - to include the angle ϕ_{i}depends on vectorand since the latter is formed on the basis of actual measurements in the EIA (formula (2÷6)), it is clear that this is the value of the virtual measuring Zenith distances of the stars on the actual (true) orbit.

Since task, and GEIST - or agonalia system, the angle at the transition between them is maintained. This means that calculating thus the angle, we pass over the question of the actual misalignment of the axes of task reference orbit in comparison with task true orbit.

The latter circumstance is the basis for claims about the practical feasibility of the algorithm for solving the navigation task in a virtual dimension. In other words, despite the fact that all the solution of the navigation problem is GEIST (and provides the classical approach), the angle calculation is carried out in task.

In turn, the exclusion from the calculation of the angle ϕ_{i}the transition between task and GEIST leads to a significant increase in the accuracy of this calculation and, ultimately, to increase the accuracy of navigation.

Calculation of local gradients angle ϕ_{i}carried out in GEIS using the reference orbit. Because GEICKwhere- the radius vector of the orbit,the gradients are calculated as follows:

,

whereORT reference orbit in GEIS,

ORT directions to star in GEIS,

q - element array of parameters to the reference position KA GEIST, q={x,y,z}.

After calculation of the angle and its gradients in fact, navigatio the ing task traditionally, using the selected smoothing filter. For example, when applying the method of least squares amendments to the starting point of the reference orbit is determined by the formula:

,

where j is the number of navigation session

n is the number of navigation sessions on measuring interval

G_{0j}=G_{j}·f_{0j}- initial gradients, that is, derived from the current measurement function ϕ_{ij}initial reference orbit parameters q_{0},

the current (local) gradients

i=1, 2 is the number of measurements in the navigation session,

is the weight matrix of dimension j-m navigation session

To_{ϕj}matrix of second moments of the measurement error

- ballistic (isochronous) derivatives

q_{0}, q_{j}respectively the initial and the current settings of the reference orbit,

Δq_{0C}- amendment to the initial parameters of the reference orbit to the s-th iteration,

Δϕ_{ij}=ϕ_{ij ISM}-ϕ_{ij calc}- the discrepancy of measurements, Δϕ_{j}={Δϕ_{1j}that Δϕ_{2j}}.

The matrix K_{ϕj}and residual measurements calculated taking into account the influence of the inclination angles of the body of the SPACECRAFT relative to the axis of task:

where σ_{S}thatΔ
S - average RMS and bias calculation ORT the radius vector of the orbit,

σ_{EIA}that Δ_{EIA}a similar measurement errors in the EIA.

For independent axes:

,

,

where σ_{ϑ}that σ_{ψ}that σ_{γ}that Δϑ, Δψ, Δγ - the corresponding error system SPACECRAFT stabilization for the on-Board algorithm must be specified a priori.

The final expression for the calculation of derivatives that are close to true, receive, using the expression for ORT axis EIA in the associated coordinate system, and the expressions for the coordinate axis S of the transition matrix (MP)^{T}.

For the same source of information: the measured coordinates of the detected working stars in two EIA and the reference orbit solve the task orientation.

To do this, determine the value of the matrix (N)^{T}by calculating the matrix of coordinate vectors of the same stars in the true and reference orbits.

According to (6):

where is the matrix of coordinates of the measured vectors of the three stars in the system X_{in}, Y_{c}, Z_{in}the true orbit

S - matrix coordinate of the calculated vectors of the same stars in the system task reference orbit. In the matrix coordinates of the feature vectors in the columns.

On the basis of the image coordinates is the position of the stars ξ that η according to (2) and (3) compute Century, the Calculated values of the columns of the matrix With the form:

,

where- Horta projections of the axes of task reference orbit in GEIST, which is determined on the basis of relations:

**,**

wherethe velocity vector.

Although for the solution of (10) requires Horta three stars, you actually need to measure the coordinates of the two stars working respectively in the two EIAs. ORT third star is obtained by calculations, assuming that the virtual star is perpendicular to the plane containing two of the measured stars, and the reference position of the SPACECRAFT.

The product of matrices In·^{-1}gives the numerical values of the matrix elements (N)^{T}but the element 1,3 of this matrix is equal to sinψ. For small values of orientation angles

.

Similarly, using the expression elements of 2.3 and 1.2, find the values γ and ϑ. Calculated according to (10) the matrix is checked for its orthogonality. In violation of the orthogonality of more than 10% of the measurement is rejected.

The algorithm gives the instantaneous value of the orientation angle, they are used in the algorithm for solving the navigation task, shaping (7).

Since the tasks of navigation and orientation solve in the same algo is itme almost simultaneously, correction of the orientation of the body of the SPACECRAFT depends on the clarification of the reference orbit and Vice versa. Therefore, use of a cyclic mode of solving these problems.

On the first cycle (and subsequent odd cycles) solve simultaneously both tasks: determine amendments to the reference orbit and the orientation angles. After the end of the iterations of the first cycle (and subsequent odd cycles) orientation angles smooth least-squares and remember. Thus the weight matrix of the measurement errors is defined as the sum of the errors of the orientation axis and the error of measurement of the coordinates of stars in the EIA (9). On the second cycle, adjust the starting point of the reference orbit by the amount of amendments and only solve the problem of navigation, taking into account developed in the first cycle of orientation angles. The weight matrix of the measurement errors only detect errors in the EIA. Typically, this leads to improved estimates of the reference orbit in the sense of approximation of its parameters to the true parameters. The third cycle begins with the revised starting point of the reference orbit, assessment, orientation zero and solve again both tasks. Taking into account the newly developed estimates of the orientation of the conduct of the fourth cycle, which only solve the problem of navigation. On even cycles summarize the residuals of measurements Δϕ_{k}all iterations of these loops. According to this algorithm h is readout and further even and odd cycles.
The end of the calculations are made on the achievement of conditions:

Δϕ_{k+2}>Δϕ_{k},

where k is the number of even-numbered cycle.

The number of cycles may not exceed ten. For the final solution results accept the results of the k-th (or 8th) cycle. In this case, the measurement model only on the zero iteration of the first loop. All calculations performed on the variable in each iteration of each cycle of the reference orbit.

Modeling decision problems of navigation and orientation using two EIA circular mode showed high accuracy and stability assessment for large (up to 3-5°) the error system SPACECRAFT stabilization considerable initial uncertainty in the knowledge of the orbit (up to several hundred kilometers), as for the near-circular orbits, and their significant ellipticity (the eccentricity of the order of 0.7).

The simulation results are shown in the attached instrument model tests Autonomous navigation and orientation of the SPACECRAFT.

How Autonomous navigation and orientation of the SPACECRAFT (SC), including the calculation of Zenith distances of two stars, characterized in that the measuring instrument coordinates and brightness of the stars, fell into the field of view is rigidly fixed to the body of the AC opto-electronic devices (EIA), stars recognize, and to determine the Zenith distance is I'm working, that is, the brightest stars, to solve the navigation task, determine the orientation of the body of the SPACECRAFT relative to the current orbital coordinate system, in addition to the information in the EIA uses the spatial position of the radius vector of the reference (a priori believe) orbit and other elements of this orbit, which define a computer calculation, as well as a priori believe (passport) data system functioning SPACECRAFT stabilization; tasks of navigation and orientation solve in parallel, and because the specification of the orientation of the body of the SPACECRAFT relative to the current orbital coordinate system increases the accuracy of the solution of the navigation problem and Vice versa, the solution to both problems is carried out in a cyclic mode.

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