RU2279105C2 - Combined method for determination of coordinates and parameters of trajectory motion of aerospace objects observed by group of tracking stations - Google Patents

Abstract

FIELD: optoelectronic, radar and other tracking systems of aerospace objects.

SUBSTANCE: interstation duplex channels of information communication connect all the stations of the group irrespective of the type of their uniformity for exchange by all the measured, computed on them data on the parameters of trajectory motion of observed objects, with their individual numbers and the numbers of the stations that have transmitted the information, whose location coordinated are preset in the single earth-based basis system of co-ordinates, the excess quantity of algorithms of local integration is realized at each station of the group, with the aid of them the excess information on the parameters of trajectory motion of the observed objects is obtained, this information is statistically processed in the station computers of each integrated station of the group, and optimal in precision estimations of the information on the parameters of trajectory motion of the observed objects are obtained, then on the basis of these estimations according to the known algorithms of the kinematic equations of communication and matrix transformation the control signals of the station channels are formed at an interruption for a certain time because of some reason of the normal process of their functioning, as well as the estimations of information on the parameters of trajectory motion of the observed objects are transmitted via the interstation duplex channels of communication to the points of control of the aerospace, where they are presented in a single earth-based co-ordinate system, and as excess ones for a great number of stations, are statistically processed against, and refined estimations of information on the parameters of trajectory motion of the observed objects are obtained.

EFFECT: enhanced accuracy and antijamming capability due to system use of a group of tracking stations.

3 dwg, Appendix 1

Description

The invention relates to the field of optoelectronic, radar and other tracking systems for aerospace objects and can be used to increase their accuracy and noise immunity due to the systematic use of a group of these stations.

The patent search in the VTB is carried out according to the classifications G 01 S 13/00 “Radar tracking systems”, G 01 S 13/66 - 13/72, “for space purposes” B 64 G 1/24, G 01 S 17/06 - “To determine the location of the target”, 17/08 - “only range”, 17/42 - “simultaneous measurement of range and other coordinates”, 17/46 - “indirect determination of location data”, 17/58 - “to determine speed or trajectory movements ”, 17/66 -“ tracking systems using electromagnetic waves other than radar ”, 17/88 -“ lidar systems ”.

As a prototype, the method “determining coordinates of targets and their derivatives by calculation” closest in terms of technical and technological essence was taken, the essence of which is described in the book [1] by Grigorin-Ryabov and others. “Radar devices (theory and construction principles)”, M. , “Soviet Radio”, 1970, pp. 5–7, 34–39.

According to the prototype, currently for tracking aerospace objects (targets) and obtaining parameters of their motion, various three-dimensional, two-dimensional and one-dimensional stations are mainly used.

Three-dimensional stations independently measure all three components of the range vector D (t) to the target [1, p. 5 ÷ 7]:

where D (t) is the range modulus determined by the rangefinder channel of the station;

ε (t), β (t) are elevation and azimuth angles determined by goniometric channels.

In this case, the velocity vectors W (t) and acceleration J (t) of the target are calculated by differentiating the vector D (t):

According to the prototype, three-dimensional stations are sensors of full-sized (range vector D (t), speed W (t), acceleration J (t)) trajectory information about the observed target.

Note in advance that from each i-th three-dimensional station through inter-station duplex channels of information communication, it is possible to carry out full-size target designation of another k-th station of any dimension by vectors:

- range:

- speeds:

- acceleration:

where d _ki is the base vector between the k-th and i-th stations.

Two-dimensional direction finding stations measure only the angular coordinates of the range vector:

According to the prototype, to obtain full-sized trajectory information about the observed target, two two-dimensional stations [1, p. 34, 35] are locally complexed using inter-station duplex communication channels, through which measured values of these angles are transferred from one to another, and, using the sine theorem for "Triangle O ₁ CO ₂ " (figure 1), with a known base d between two stations determine the range modules D ₁ (t) and D ₂ (t):

For the simplicity of presentation, the prototype apparently does not provide three-dimensional, but plane illustrations and, accordingly, formalization (7) of the problems of local integration of two direction finding type stations when φ ₁ (t) = {β ₁ (t), ε ₁ (t) }, φ ₂ (t) = {β ₂ (t), ε ₂ (t)}. The author obtained a working algorithm for determining the distance modulus of the observed object Ob (t) from a prototype (Fig. 2) in three-dimensional space by two locally integrated direction finding stations D ² ₁ (X _N1 Y _G1 Z ₁ ), D ² ₂ (X _N2 Y _G2 Z ₂ ), where X _N , Y _G , Z are the geographical coordinates of the stations. We present the obtained basic algorithm for local integration of two direction finding type stations, firstly, to confirm the capabilities of the prototype, and secondly, to justify its use in conjunction with additional ones in order to have an excessive number of algorithms inherent in the present invention. The stations are removed from each other on the vector base d = L ₂₁ :

In station coordinate systems, D ₁ (X _N1 Y _G1 Z ₁ ) X _N Y _G Z and D ₂ (X _N2 Y _G2 Z ₂ ) X _N Y _G Z, whose corresponding axes have the same directions, simultaneously measure the angles β ₁ (t ), ε ₁ (t), β ₂ (t), ε ₂ (t), the values of which are transferred from one station to another via duplex channels of information communication.

The range modulus D ₁ (t) of the observed object Ob (t) relative to the first station is determined by the formulas:

Similarly, using similar formulas, the range of the observed object D ₂ (t) is calculated relative to the second station:

As can be seen from the presented local integration algorithms (6), (8) ÷ (10), (2), the informational and mathematical programming unity of the two direction finding type stations provides the obtaining of the only current values with a full-sized trajectory of information about the observed target.

So, according to the prototype method, when two two-dimensional direction finding stations are locally integrated, firstly, the angles φ ₁ (t) = {β ₁ (t), ε ₁ (t)}, φ ₂ (t) = {β ₂ ( t), ε ₂ (t)} is measured in station coordinate systems, the corresponding axes of which have the same directions, secondly, the angles are measured synchronously, thirdly, the measured values of the angles are sent from one station to another via inter-station duplex communication channels, fourthly, the calculation of range modules by algorithms of type (8) ÷ (10) is performed in station computers, fifth, two-dimensional Stations for organizing a local complex mode each need target designation (3) from other stations to accompany the same target, sixth, two-dimensional stations can not independently target either other stations or to each other, and only work stably in the complex mode, they are able to give the only current values of the full-sized parameters of the trajectory movement of the observed target and the full-sized target designation (3) ÷ (5) to other stations.

One-dimensional stations [1, p. 35], "measuring only the range" D (t), which according to the prototype in pair, using the cosine theorem, allow for the purpose to determine "angular coordinates in the plane of the triangle O ₁ ЦО ₂ :

Note that (11) in the prototype is valid only for planar setting, since the three-dimensional vector D (t) cannot be uniquely determined in three-dimensional space by only two scalar quantities D ₁ (t) and D ₂ (t). The author obtained a system of working algorithms for local integration of one-dimensionally-ranging stations and confirmed the possibility of determining by them the full-sized trajectory of information about the observed target in three-dimensional space (Fig. 3), although according to the data of not two, but three of these stations:

- нелинейные, неявно выраженные системы уравнений с указанными в скобках аргументами.Where

- nonlinear, implicitly expressed systems of equations with the arguments indicated in brackets.

Algorithm (12) and (2) confirms that the information and software-mathematical unity of the three stations of the one-dimensionally-range-measuring type ensures that the only current values are obtained by the full-sized trajectory of information about the observed target.

Apparently there is no need to give this cumbersome algorithm in the expanded form in the description, especially since the calculation procedure for it is multi-step, iterative. This algorithm is presented as a reference in Appendix No. 1 to the description.

Again, we note that according to the prototype method and for three one-dimensionally-ranging stations, the range modules D ₁ (t), D ₂ (t), D ₃ (t) are measured in station coordinate systems, the corresponding axes of which have certain directions, the indicated ranges are measured synchronously, the measured range values are sent from one station to another via inter-station duplex information communication channels, the calculation of the angles ε ₁ (t), β ₁ (t), ε ₂ (t), β ₂ (t), ε ₃ (t), β ₃ (t) type of algorithms (12) (see para. Annex №1) operate at the station calculators, one- dimensionally hundred rangefinder In order to organize the initial phase of the complex mode, each one needs target designation (3) from other stations in order to accompany the same goal, one-dimensionally-ranging stations cannot autonomously target either other stations or to each other, and only work stably in a complex mode, capable of giving not only full-sized trajectory information (12), (2), but also full-sized (3) ÷ (5) target designation to other stations.

One-dimensional stations that determine the “radial velocity” V _P (t) by the Doppler method V _P (t) = F _D (t) · λ / 2 open up additional possibilities for determining primarily the parameters of the target’s movement. According to the prototype [1, p. 35] "The target’s speed W _C (t) is conveniently determined through its orthogonal components: radial W _P (t), directed along the radar line - the target, and tangential W _T (t)":

where ω _φ (t) is the angular velocity of the target.

“The angular velocity of the target ω _φ (t) can also be determined using two radars measuring Doppler frequency shifts” [1, p. 37] F _D1 (t) and F _D2 (t):

In (13) and (14), W _Ц (t) and ω _φ (t) are scalar quantities (again, a planar formulation and formalization of the problem), and practice requires the determination of three-dimensional vectors of linear W _Ц (t) and angular ω _φ (t ) speeds of the observed target. In addition, the angular velocity of the line “station - target" ω _φ (t) according to the prototype method is calculated under the assumptions that d≤D (t) / 1000, the angle of sight on the target φ (t), measured relative to the normal to d, in three-dimensional space is practically undefined, and the stations themselves must not only operate at the same wavelength λ, but also be coherent. These assumptions are so difficult that in practice this method for determining the angular velocity ω _φ (t) (15) for calculating (13) the tangential component of the velocity W _T (t) was not found and we exclude it from consideration in the above statement.

The prototype method of determining the parameters of the trajectory movement of objects has the following disadvantages:

1. Low noise immunity and accuracy of determining the coordinates and parameters of the trajectory movement of the observed objects. In the presence of interference or due to a partial equipment failure, the tracking stations are not always able to perform their functions in full. So, for example, “range-leading” interference can turn a three-dimensional station into two-dimensional, and one-dimensional ranging can be suppressed altogether, “leading away by angular coordinates” can turn a three-dimensional station into one-dimensional D (t), a two-dimensional direction finding type can be suppressed altogether, etc. . Usually, under these conditions, auto-tracking is interrupted and information about the coordinates and parameters of the target’s movement is lost.

2. A limited number of stations are integrated into the system: two-dimensional - two, and one-dimensional - three.

3. Complexes of uniform dimensionality are integrated into the system: two-dimensional with two-dimensional, one-dimensional with one-dimensional.

4. A three-dimensional station is not integrated into a system with either a three-dimensional, two-dimensional, or one-dimensional.

5. To integrate stable stations, all integrated stations need target designation (3) from other stations to ensure tracking of the same goal.

6. Existing redundant information on the observed object, for example, on the distance vectors D ₁ (t), D ₂ (t) at two locally complex two-dimensional stations, D ₁ (t), D ₂ (t), D ₃ (t) at a locally complexed three one-dimensionally-ranging stations are not used to improve the accuracy of their assessment.

7. At the stations, predictive models of the movement of targets are not used to increase noise immunity and accuracy.

The purpose of the invention is to improve the accuracy and noise immunity of the grouping of tracking stations for aerospace objects.

The above disadvantages of the existing method are proposed to be eliminated by introducing additional, partial use and modification of existing technological methods, in accordance with which:

I. As in the prototype method:

1. Use a common coordinate system for complex stations.

2. The coordinates of the targets at the complex stations are measured synchronously, that is, in a single time system (SEV).

3. Produce information exchange between the integrated stations using inter-station duplex channels of information communication.

4. When determining the desired coordinates and motion parameters of the observed objects, they are used as a component and the existing computational algorithms for the local integration of stations: two-dimensional - (8) ÷ (10), (2) and one-dimensionally-ranging - (12) - Appendix No. 1, ( 2).

5. The desired full-sized coordinates and motion parameters of the observed objects are calculated in the computers of the integrated stations.

II. Additional, new:

1. All stations of the group, regardless of the type of their dimension, are connected by inter-station duplex channels of information communication.

2. In order to ensure information compatibility, a common basic coordinate system Ob (t ₀ ) X _N Y _G Z for the grouping stations is introduced, the ordinate of which Ob (t ₀ ) Y _G is the local vertical, Ob (t ₀ ) X _N is the abscissa, oriented to the north, and the applicate Ob (t ₀ ) Z - completes the construction of the right rectangular coordinate system.

3. For each station, through inter-station duplex information communication channels, all current coordinates and parameters of the movement of targets located in the coverage area of this station, individual numbers of these goals q, individual numbers S of stations D _S (X _NS Y _GS Z _S ), transmitting information, the coordinates of the location X _NS , Y _GS , Z _{S of} which in the Earth's basic coordinate system are pre-stored in the databases of computers of the grouping stations.

Due to the continuous exchange of extended information about the targets between the grouping stations via duplex communication channels, the presence of an excessive number of complexing algorithms on each of them, they obtain redundant full-sized trajectory information about the observed targets and implement full-sized target designation to other stations:

A) For one-dimensionally ranging stations D ¹ _S (X _NS Y _GS Z _S ) - upon receipt of additional current angles (3) ε _kCU (t), βε _kCU (t)

and application of three-dimensional stations as additional algorithms (2).

цели по составляющим в общей земной базисной системе ДХ_NY_GZ координат, соответствующие оси которой имеют одинаковые направления со станционными системами координат Д^lД _k(X_NkY_GkZ_k)X_NY_GZ:B) For one-dimensional Doppler stations D ^1D _Sk (X _NS Y _GS Z _S ) - upon receipt of additional current values (3) of the range D _kCU (t) and angles ε _{k CU} (t), β _{k CU} (t), k≥3 and application of (17), (20) and the new algorithm (18), (19) obtained by the author of the direct determination of the velocity vector

goals according to the components in the common earth base system of the HX _N Y _G Z coordinates, the corresponding axes of which have the same directions with the station coordinate systems Д ^lД _k (X _Nk Y _Gk Z _k ) X _N Y _G Z:

The current range modules for each of the Doppler stations after target designation are calculated by the integration method:

The components of the angular velocity vector of the line “station - target” in the coordinate system associated with the kinematics of the station are calculated by the formulas:

where W _CYD (t), W _CZD (t) are the components of the target linear velocity vector W _C (t) in the coordinate system associated with the kinematics of the station, obtained using the well-known transition matrix M _{D ← 1} (β _kCU (t), ε _kCU (t)) from the earth station coordinate system to the coordinate system associated with the kinematics of the station:

Algorithm (17) ÷ (22) is assigned to the existing method and then we will use it when implementing the principle of algorithmic redundancy of the proposed method.

C) For two-dimensional stations D ² _S (X _NS Y _GS Z _S ) of direction finding type - upon receipt of additional current values (3) of the range D _kCC (t)

and the simultaneous application of redundant algorithms (23), (8) ÷ (10), (2).

D) For three-dimensional stations D ³ _S (X _NS Y _GS Z _S ) - upon receipt of additionally continuous current values of target designation parameters (3) ÷ (5) from other grouping stations and the simultaneous use of one-dimensional ranging algorithms: (12) - Appendix No. 1 and (2), two-dimensional direction finding stations: (6), (8) ÷ (10), (2).

4. Excessive full-sized trajectory information about each of the goals q is received at each grouping station S of the group:

- through inter-station duplex channels of information communication;

- methods of direct measurements;

- calculation methods according to the set out redundant algorithms.

5. At each complexable station S, groupings perform statistical processing of redundant information about each of the goals q to obtain optimal estimates of accuracy, for example, using the algorithm of the current moving average:

where n is the number of values (transmitted, measured, calculated) of specific parameters processed at the station at the current time t.

6. The obtained "station" estimates of parameters that are optimal in accuracy (24) are used using well-known algorithms of kinematic communication equations and matrix transformations (22) to generate station channel control signals during interruption for a time τ for any reason of the normal station measurement process:

- rangefinder:

- angular azimuthal:

- angular:

- speed approach (Doppler):

Thus, the predicted target designation at each grouping station is realized. Current continuous target designation from other stations and their own predicted target designation (25) ÷ (28) at each station significantly increase their noise immunity.

7. “Stationary” parameter estimates (24) in the interest of further improving the accuracy of coordinates and motion parameters estimates for each target q are transmitted via inter-station duplex communication channels to aerospace control points - to information consumers, where they are presented in the earth's basic coordinate system and as redundant for many stations again statistically processed, for example, by the method of the current average:

where S is the number of stations that transmitted their current estimates of the coordinates and motion parameters q of the target.

Information sources

1. Systems for tracking and determining the coordinates of artificial earth satellites, the Civil Code of the USSR CM on radio electronics, review, issue 28, 1961, pp. 12 ÷ 29.

2. Grigorin-Ryabov VV, Dudnik P.I. and other radar devices

(Theory and principles of construction), ed. “Soviet Radio”, Moscow, 1970, pp. 5–7, 34–39.

List of graphic materials

1. "Determination of the target range by stations located at two points O ₁ and O ₂ ".

2. Vector scheme for observing an object by two direction finding type stations in three-dimensional space.

3. Vector scheme for observing an object with three stations of the one-dimensionally-ranging type in three-dimensional space.

Appendix No. 1

A working algorithm for determining station angles of a distance vector when combining three one-dimensionally-ranging stations

For each rangefinder point (Figure 3), an intermediate right rectangular coordinate system is introduced. The abscissa axis of the first rangefinder point is directed along the vector L ₂₁ , that is, to the second rangefinder point, the unit vector of this axis has an analytical expression:

where "T" is the symbol for transposition.

The abscissa axis of the second rangefinder point is oriented along the vector L ₃₂ to the third rangefinder point and its unit vector is:

The abscissa axis of the third point is directed along the vector L ₁₃ to the first point and its unit vector has the expression:

Analytical expressions for the ordinate axes are obtained using vector products:

Where

Similarly, analytical expressions for applicate are obtained:

Transition matrices when turning from SC, associated with rangefinding points, to Earth SC formally have the form:

where i is the number of the rangefinder item.

Based on the foregoing, analytical expressions are obtained for all the directing cosines of the transition matrices (11p):

After geodesic binding of rangefinding points to the terrestrial spacecraft one-time calculations are performed according to the algorithms (1p) ÷ (14p) in the interest of determining all of these constants, including the direction cosines of the transformation matrix during rotations (11p) ÷ (14p) and the constants of the algorithm (15p) of the complete transformation of position coordinates when moving from s.c. associated with rangefinding points to the terrestrial SC taking into account both rotation and displacement s.k .:

Next, an algorithm for iteratively searching the values of the angles (see Fig. 3) β ₁ (t) and ε ₁ (t), β ₂ (t) and ε ₂ (t), β ₃ (t) and ε ₃ (t) is used. For each synchronous measurement of the range modules D ₁ (t), D ₂ (t), D ₃ (t), their values are substituted into the system of equations:

The algorithm of the iterative process for solving the obtained equations:

1. Enter the necessary constants L ₂₁ , L ₃₂ , L ₁₃ , γ ₁ , γ ₂ , γ ₃ , S _Δ and the initial t ₀ conditions D ₁ (t ₀ ), D ₂ (t ₀ ), D ₃ (t ₀ ) .

2. Organize a “zero” cycle to determine β ₁ (t ₀ ) and ε ₁ (t ₀ ), β ₂ (t ₀ ) and ε ₂ (t ₀ ), β ₃ (t ₀ ) and ε ₃ (t ₀ ) :

2.1. Using equation (19p), sin (β ₁ (t)) is calculated explicitly, then β ₁ (t), cos (β ₁ (t)) and cos (β ₁ (t) -γ ₁ ).

2.2. Substitute cos (β ₁ (t)) and cos (β ₁ (t) -γ ₁ ) in equations (16p) and (17p), sin (β ₁ (t))

- in equation (19p), β ₁ (t) - is used to assess the convergence of the iterative solution process.

2.3. Again, using equation (19p), they are calculated explicitly, but now sin (β ₂ (t)), then β ₂ (t), cos (β ₂ (t)) and cos (γ ₂ -β ₂ (t)) .

2.4. Substitute cos (β ₂ (t)) and cos (γ ₂ -β ₂ (t)) in equations (17p) and (18p), sin (β ₂ (t))

- in equation (19p), β ₂ (t) - is used to assess the convergence of the iterative solution process.

2.5. Again, using equation (19p), they are calculated explicitly, but now sin (β ₃ (t)), then β ₃ (t), cos (β ₃ (t)) and cos (γ ₃ -β ₃ (t) )

2.6. Substitute cos (β ₃ (t)) and cos (γ ₃ -β ₃ (t)) into equations (18p) and (16p), sin (β ₃ (t))

- in equation (19p), β ₃ (t) - is used to assess the convergence of the iterative solution process.

2.7. The grouped equations (16p), (17p) are solved in the interests of obtaining cos (ε ₁ (t)), then ε ₁ (t):

2.8. Substitute cos (ε ₁ (t)) in equations (16п), (17п) and (19п), and ε ₁ (t) - used to assess the convergence of the iterative solution process.

2.9. The grouped equations (17p), (18p) are solved in the interests of obtaining cos (ε ₂ (t)), then ε ₂ (t):

2.10. Substitute cos (ε ₂ (t)) into equations (17п), (18п) and (19п), and ε ₂ (t) - they are used to assess the convergence of the iterative solution process.

2.11. The grouped equations (18p), (16p) are solved in the interests of obtaining cos (ε ₃ (t)), then ε ₃ (t):

2.12. Substitute cos (ε ₃ (t)) in equations (18п), (16п) and (19п), and ε ₂ (t) - used to assess the convergence of the iterative solution process.

2.13. Repeat steps 2.1. ÷ 2.12 a second time and find the differences δβ ₁ (t), δε ₁ (t):

δβ ₁ (t) = β ₁ (t) _HOB -β ₁ (t) _CT ; δβ ₂ (t) = β ₂ (t) _HOB -β ₂ (t) _CT ; δβ ₃ (t) = β ₃ (t) _HOB -β ₃ (t) _CT ;

δε ₁ (t) = ε ₁ (t) _NOV -ε ₁ (t) _ST ; δε ₂ (t) = ε ₂ (t) _HOB -ε ₂ (t) _ST ; δε ₃ (t) = ε ₃ (t) _HOB -ε ₃ (t) _ST .

If at least one of the differences turns out to be larger in magnitude than the allowable value of δ _DOP , then the iteration cycle (Sec. 2.1. ÷ 2.12) is repeated.

3. With the convergence of the iterative process of accuracy calculations, projections of distance vectors are now found first on the SC axis range-finding points, and then (15p) on the axis of the Earth’s SC ... Moreover, the components of the final range vector in the SC "G" is taken as the average of the three values obtained.

4. Proceed to the processing of the next synchronous measurements of the range modules D ₁ (t), D ₂ (t), D ₃ (t), and as the initial values for the iterative search of the angles β ₁ (t), β ₂ (t), β ₃ (t), ε ₁ (t), ε ₂ (t), ε ₃ (t) take their total values from the previous completed cycle of calculations.

Claims (1)

An integrated method for determining the coordinates and parameters of the trajectory motion of aerospace objects observed by a group of tracking stations, which consists in the fact that at the interacting stations in uniform coordinate systems whose corresponding axes have the same directions, the coordinates of the observed objects are synchronously measured, the values of which are transmitted to each other with using inter-station duplex information communication channels, they are calculated in station computers taking into account the known basic distances between by the stations of the measured and transmitted coordinates of the observed objects according to the calculation algorithms of local complexing, the only current values of the information on the parameters of the trajectory movement of the observed objects, characterized in that the inter-station duplex channels of information communication connect all the stations of the group, regardless of the type of dimension for the exchange of all measured, calculated on data on the parameters of the trajectory movement of the observed objects, with their individual numbers and station numbers, before which contain the above information, the location coordinates of which are set in a single earth basis coordinate system, at each station of the grouping, an excessive number of local integration algorithms are implemented, with the help of which redundant information is obtained about the parameters of the trajectory movement of the observed objects, which are statistically processed in the station computers of each complexable station and receive optimal accuracy estimates of this information about the parameters of the trajectory motion of the observed objects, then based on these estimates according to well-known algorithms of the kinematic equations of communication and matrix transformation, control signals of the rangefinder and goniometer channels of the stations are formed when the normal operation of the stations is interrupted for some reason for some reason, and information about the parameters of the trajectory motion of the observed objects is transmitted through inter-station duplex communication channels to control points in aerospace space, where they are represented in a single earth-based base system coordinates and the like of a plurality of stations redundant again statistically treated to obtain accurate estimates of information about the parameters of the trajectory of movement of the observed objects.

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