CN117724141A - Beidou orthogonal baseline direction finding angle optimization method for aircraft - Google Patents
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Abstract
The invention relates to an angle optimization method for Beidou orthogonal baseline direction finding for an aircraft, which comprises the following steps: constructing an angle optimization problem aiming at an angle optimization model of the side direction of an orthogonal base line; constructing a popular space by using constraint conditions in the model, and defining inner products and directional derivatives in the popular space; establishing a relationship between the Riemann gradient and the European gradient according to the inner product, and further obtaining an expression of the Riemann gradient; calculating Riemann Heisen according to the Riemann gradient, then establishing a relation between the Riemann gradient and the Riemann Heisen, and solving an equation to obtain the fastest gradient descent direction; according to the fastest gradient descent direction, a retraction function is obtained; and when the value obtained at the previous moment of the retraction function is equal to the value at the next moment, iteration is completed, so that the optimal point is found, and the optimal attitude angle is obtained. The method has the advantages of small calculated amount, low complexity and good reliability.
Description
Technical Field
The invention belongs to the technical field of satellite navigation and positioning, and particularly relates to an angle optimization method for Beidou orthogonal baseline direction finding for an aircraft.
Background
Compared with the traditional inertial navigation, the method for calculating the carrier attitude by utilizing the Global Navigation Satellite System (GNSS) signal has the remarkable advantages of high precision, low cost, no drift and the like, and is widely applied. The classical GNSS attitude calculation method facing to the aircraft generally adopts three antennas, wherein two antennas respectively arranged at the positions of a fuselage, a nose and a wing form a base line, two antennas at the positions of the fuselage and the nose form another base line, then a whole-cycle ambiguity calculation technology is adopted to respectively obtain base line coordinates of the two base lines, and then an attitude angle is obtained according to the conversion relation between a carrier coordinate system and a geographic coordinate system.
However, in solving the baseline coordinates of the two baselines, there are two problems with the above method: (1) Because the original carrier phase observation value has rough differences and wild values, the base line component errors which are solved independently have rough differences, and then small angle jumps exist in the estimated attitude angle front and rear epochs, the attitude angle is not smooth enough, and the processing of an aircraft control system is not facilitated; (2) The two baselines are in an orthogonal geometric relationship, the constraint condition is not fully involved in estimation, and the algorithm is not optimal estimation.
Therefore, it is necessary to design an angle optimization method for Beidou orthogonal baseline direction finding for an aircraft, which integrates orthogonal constraint conditions into a baseline estimation process, aims at solving the problem of small angle jump caused by non-ideal original observation values, and optimizes the precision of baseline estimation values and final attitude angles.
Disclosure of Invention
In view of this, the present invention aims to overcome the shortcomings of the prior art, and provides an angle optimization method for Beidou orthogonal baseline direction finding for an aircraft, which uses the geometry and the baseline length of an antenna to reform the three-dimensional GNSS attitude determination problem into optimization for a non-convex set, and provides a highly accurate three-dimensional GNSS attitude determination method.
In order to achieve the above purpose, the technical scheme of the invention is realized as follows:
an angle optimization method for Beidou orthogonal baseline direction finding facing an aircraft comprises the following steps:
step 1: according to the positions of an aircraft body, wings and a nose, integrating three antennas by using orthogonal geometric configuration, selecting the direction from the aircraft body to the nose as a baseline vector x direction, the direction from the aircraft body to the wings as a baseline vector y direction, forming an orthogonal relation between x and y, and establishing an orthogonal baseline direction finding angle optimization model by using the attitude angle of the aircraft as an optimization target, wherein the objective function of the orthogonal baseline direction finding angle optimization model is as follows:
；
a is a matrix of m-dimensional vectors formed by observing m satellite carrier wave phase differences in the x direction; b is a matrix of m-dimensional vectors formed by observing m satellite carrier wave phase differences in the y direction; a is the product of the line of sight observed by m satellites of n receivers in the x direction and the shortest baseline distance in the x direction, and an m multiplied by n matrix is formed; b is the product of the sight distance observed by m satellites of n receivers in the y direction and the shortest baseline distance in the y direction to form an m multiplied by n matrix;
the constraint conditions are as follows:
x is orthogonal with y, and the cosine value of the included angle is 0;
step 2: determining a popular space M according to constraint conditions of the orthogonal baseline direction finding angle optimization model;
step 3: determining a tangent space with the point (x, y) of the popular space M according to the tangent vector of the point (x, y) of the popular space M, and an inner product derivative and a direction derivative in the tangent space;
step 4: determining the relationship between the Euclidean gradient and the directional derivative and the relationship between the Riemann gradient and the directional derivative according to the inner product derivative in the tangent space, further determining the relationship between the Riemann gradient and the Euclidean gradient, and obtaining the expression of the Riemann gradient;
step 5: determining the relationship between the Riemann gradient and the Riemann Heisen according to the Riemann gradient, and determining the direction of the fastest gradient descent;
step 6: and determining a retraction function according to the fastest gradient descent direction, judging whether a value obtained at the last moment of the retraction function is equal to a value at the next moment, and determining the optimal solution moment of the orthogonal baseline direction finding angle optimization model so as to determine the final attitude angle of the aircraft.
Further, in the step 6, determining the retraction function includes:
the cut space is projected to the popular space, and the next predicted point is found.
The invention also provides an angle optimization system for Beidou orthogonal baseline direction finding facing the aircraft, which comprises the following steps:
the model construction module is used for integrating three antennas according to the positions of an aircraft body, wings and a aircraft nose by using an orthogonal geometric configuration, selecting the direction from the aircraft body to the aircraft nose as a baseline vector x direction, selecting the direction from the aircraft body to the aircraft wing as a baseline vector y direction, forming an orthogonal relation by x and y, taking the attitude angle of the aircraft as an optimization target, and establishing an orthogonal baseline direction finding angle optimization model, wherein the objective function of the orthogonal baseline direction finding angle optimization model is as follows:
；
a is a matrix of m-dimensional vectors formed by observing m satellite carrier wave phase differences in the x direction; b is a matrix of m-dimensional vectors formed by observing m satellite carrier wave phase differences in the y direction; a is the product of the line of sight observed by m satellites of n receivers in the x direction and the shortest baseline distance in the x direction, and an m multiplied by n matrix is formed; b is the product of the sight distance observed by m satellites of n receivers in the y direction and the shortest baseline distance in the y direction to form an m multiplied by n matrix;
the constraint conditions are as follows:
x is orthogonal to y, and the cosine value of the included angle is0；
The popular space determining module is used for determining a popular space M according to constraint conditions of the orthogonal baseline direction finding angle optimization model;
a tangent space determining module for determining a tangent space with the point (x, y) of the popular space M, and inner product derivatives and direction derivatives in the tangent space according to the tangent vector of the point (x, y) of the popular space M;
the Riemann gradient determining module is used for determining the relationship between the Euclidean gradient and the direction derivative and the relationship between the Riemann gradient and the direction derivative according to the inner product derivative in the tangent space, further determining the relationship between the Riemann gradient and the Euclidean gradient, and obtaining an expression of the Riemann gradient;
the gradient descent fastest direction determining module is used for determining the relationship between the Riemann gradient and the Riemann Heisen according to the Riemann gradient and determining the gradient descent fastest direction;
and the result determining module is used for determining a retraction function according to the fastest gradient descent direction, judging whether the value obtained at the last moment of the retraction function is equal to the value at the next moment, and determining the optimal solution moment of the orthogonal baseline direction finding angle optimizing model so as to determine the final attitude angle of the aircraft.
Compared with the prior art, the Beidou orthogonal baseline direction finding angle optimization method for the aircraft has the following advantages:
firstly, by introducing a Riemann optimization method, the influence of factors such as signal propagation errors, atmospheric conditions, receiver errors and the like on baseline estimation can be reduced, the estimation precision and reliability are improved, the Riemann optimization method has universality, can adapt to different scenes and problems, and can be combined with other technologies to further improve the estimation performance;
secondly, the method combines the advantages of Riemann geometry and an optimization algorithm, utilizes Li Manji to describe the geometric features of satellite orbit and signal propagation, and utilizes the optimization algorithm to find the best estimated value of the baseline, so that the precision and reliability of baseline estimation can be improved;
third, the method of the invention has small calculated amount and low complexity, and is suitable for low-cost processors such as single chip computers and the like.
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The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the invention. In the drawings:
FIG. 1 is a schematic diagram of a modeling architecture in the method of the present invention.
Fig. 2 is a flowchart of an angle optimization method for orthogonal Beidou baseline direction finding for an aircraft.
Detailed Description
It should be noted that, without conflict, the embodiments of the present invention and features of the embodiments may be combined with each other.
In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc. indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings, are merely for convenience in describing the present invention and simplifying the description, and do not indicate or imply that the devices or elements referred to must have a specific orientation, be configured and operated in a specific orientation, and thus should not be construed as limiting the present invention. Furthermore, the terms "first," "second," and the like, are used for descriptive purposes only and are not to be construed as indicating or implying a relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defining "a first", "a second", etc. may explicitly or implicitly include one or more such feature. In the description of the present invention, unless otherwise indicated, the meaning of "a plurality" is two or more.
In the description of the present invention, it should be noted that, unless explicitly specified and limited otherwise, the terms "mounted," "connected," and "connected" are to be construed broadly, and may be either fixedly connected, detachably connected, or integrally connected, for example; can be mechanically or electrically connected; can be directly connected or indirectly connected through an intermediate medium, and can be communication between two elements. The specific meaning of the above terms in the present invention can be understood by those of ordinary skill in the art in a specific case.
The invention will be described in detail below with reference to the drawings in connection with embodiments.
As shown in fig. 1-2, the invention provides an angle optimization method for Beidou orthogonal baseline direction finding for an aircraft, which comprises the following steps:
(1) According to the positions of an aircraft body, wings and a nose, integrating three antennas by using orthogonal geometric configuration, selecting the direction from the aircraft body to the nose as a baseline vector x direction, the direction from the aircraft body to the wings as a baseline vector y direction, forming an orthogonal relation between x and y, and establishing an orthogonal baseline direction finding angle optimization model by using the attitude angle of the aircraft as an optimization target, wherein the objective function of the orthogonal baseline direction finding angle optimization model is as follows:
（a）
a is a matrix of m-dimensional vectors formed by observing m satellite carrier wave phase differences in the x direction; b is a matrix of m-dimensional vectors formed by observing m satellite carrier wave phase differences in the y direction; a is the product of the line of sight observed by m satellites of n receivers in the x direction and the shortest baseline distance in the x direction, and an m multiplied by n matrix is formed; b is the product of the sight distance observed by m satellites of n receivers in the y direction and the shortest baseline distance in the y direction to form an m multiplied by n matrix;
the constraint conditions are as follows:
x is orthogonal with y, and the cosine value of the included angle is 0;
(2) Simplifying (a) into a general formula:. Since the above equation is non-convex, riemann optimization on manifold is utilizedThe method solves the problem. The manifold space M is established so as to meet constraint conditions, and the expression is as follows:
（b）
(3) Based on the tangent vectors of the step (2) at the points of the popular space (x, y), a tangent space is formed, and the inner product and the directional derivative are required to be defined on the tangent space, which comprises the following specific steps:
(3.1) the tangent vector at the (x, y) point of the popular space constitutes a tangent space：
（c）
Wherein the method comprises the steps ofIs the tangent vector at (x, y).
（3.2）The directional derivatives of these two directions +.>：
The tangent vector of the function f (x, y)The directional derivative of the direction is:
（d）
the tangent vector of the function f (x, y)The directional derivative of the direction is:
（e）
(4) According to the inner product, establishing a relation between the Euclidean gradient and the direction derivative and a relation between the Riemann gradient and the direction derivative, and solving the relation between the Riemann gradient and the Euclidean gradient to further obtain an expression of the Riemann gradient, wherein the specific steps are as follows:
(4.1) the relationship of the European gradient to the directional derivative is shown below:
at the first componentDenoted as->；
At a second componentRepresented as；
(4.2) European gradient solving as follows:
at the first componentDenoted as-> （f）
At a second componentRepresented as （g）
(4.3) relationship between Riemann gradient and directional derivative:
（h）
wherein the method comprises the steps ofIs the first component of the Riemann gradient;is the second component of the Riemann gradient;representing an inner product operation.
(4.4) relationship of European gradient and Riemann gradient and solving Riemann gradient:
（i）
wherein the method comprises the steps ofRepresenting orthogonal projections on a surrounding space except the tangential space, the expression is as follows:
（j）
（k）
wherein the method comprises the steps ofIs a scalar; u, v belong to the surrounding space。
(5) Based on the Riemann gradient in the step (4), establishing a relation between the Riemann gradient and Riemann Heisen, and solving an equation to obtain the direction of the fastest gradient descentThe method comprises the following specific steps of:
(5.1) first solving for Riemann Heisen from Riemann gradients:
（l）
(5.2) establishing a relationship between Riemann Heisen and Riemann gradient:
（m）
solving the direction in which the gradient drops most rapidly。
(6) Based on the fastest gradient descent direction in the step (5), a retraction function is obtained, namely, a cut space is projected to a popular space, and the next predicted point is found, wherein the specific steps are as follows:
(6.1) introducing differential isomorphism before computing the retract functionIs the concept of (1):
（n）
wherein the method comprises the steps ofRepresentation->Is a subset of the open subset of (a).
The general calculation formula is derived from formula (n):
（o）
(6.2) introducing a retraction function concept:representing the mapping of tangent space to manifold space, the retract function expression（p）
(6.3) obtaining by using the Schmidt's orthonormal theoremIs represented by the expression:
（q）
wherein c 1 ，c 3 >0；；
(6.4) the baseline coordinates change during the flight of the aircraft, so there is a coordinate transformation, the formula of which is as follows: （r）
wherein the method comprises the steps ofRepresented as 。
(6.5) combining equation (o) and equation (p):
（s）
wherein each parameter is expressed as:
；
(6.6) combining equation (o), equation (p) and equation(s) to obtain a retraction function, the expression is as follows:
（t）
wherein the method comprises the steps ofIs a projection of the first component.
(7) When given an initial valueAnd calculating according to the formula (t) to obtain a value of the next moment, and repeating the steps (4.1) to (6.6).
When (when)The iteration is completed when the value obtained at the previous moment is equal to the value at the next moment, so that the optimal point is foundAnd obtaining three-dimensional attitude information of the aircraft, thereby determining the final attitude angle of the aircraft.
The invention also provides an angle optimization system for Beidou orthogonal baseline direction finding facing the aircraft, which comprises the following steps:
the model construction module is used for integrating three antennas according to the positions of an aircraft body, wings and a aircraft nose by using an orthogonal geometric configuration, selecting the direction from the aircraft body to the aircraft nose as a baseline vector x direction, selecting the direction from the aircraft body to the aircraft wing as a baseline vector y direction, forming an orthogonal relation by x and y, taking the attitude angle of the aircraft as an optimization target, and establishing an orthogonal baseline direction finding angle optimization model, wherein the objective function of the orthogonal baseline direction finding angle optimization model is as follows:
；
a is a matrix of m-dimensional vectors formed by observing m satellite carrier wave phase differences in the x direction; b is a matrix of m-dimensional vectors formed by observing m satellite carrier wave phase differences in the y direction; a is the product of the line of sight observed by m satellites of n receivers in the x direction and the shortest baseline distance in the x direction, and an m multiplied by n matrix is formed; b is the product of the sight distance observed by m satellites of n receivers in the y direction and the shortest baseline distance in the y direction to form an m multiplied by n matrix;
the constraint conditions are as follows:
x is orthogonal with y, and the cosine value of the included angle is 0;
the popular space determining module is used for determining a popular space M according to constraint conditions of the orthogonal baseline direction finding angle optimization model;
a tangent space determining module for determining a tangent space with the point (x, y) of the popular space M, and inner product derivatives and direction derivatives in the tangent space according to the tangent vector of the point (x, y) of the popular space M;
the Riemann gradient determining module is used for determining the relationship between the Euclidean gradient and the direction derivative and the relationship between the Riemann gradient and the direction derivative according to the inner product derivative in the tangent space, further determining the relationship between the Riemann gradient and the Euclidean gradient, and obtaining an expression of the Riemann gradient;
the gradient descent fastest direction determining module is used for determining the relationship between the Riemann gradient and the Riemann Heisen according to the Riemann gradient and determining the gradient descent fastest direction;
and the result determining module is used for determining a retraction function according to the fastest gradient descent direction, judging whether the value obtained at the last moment of the retraction function is equal to the value at the next moment, and determining the optimal solution moment of the orthogonal baseline direction finding angle optimizing model so as to determine the final attitude angle of the aircraft.
The foregoing description of the preferred embodiments of the invention is not intended to be limiting, but rather is intended to cover all modifications, equivalents, alternatives, and improvements that fall within the spirit and scope of the invention.
Claims (3)
1. An angle optimization method for Beidou orthogonal baseline direction finding facing an aircraft is characterized by comprising the following steps of: the method comprises the following steps:
step 1: according to the positions of an aircraft body, wings and a nose, integrating three antennas by using orthogonal geometric configuration, selecting the direction from the aircraft body to the nose as a baseline vector x direction, the direction from the aircraft body to the wings as a baseline vector y direction, forming an orthogonal relation between x and y, and establishing an orthogonal baseline direction finding angle optimization model by using the attitude angle of the aircraft as an optimization target, wherein the objective function of the orthogonal baseline direction finding angle optimization model is as follows:
；
a is a matrix of m-dimensional vectors formed by observing m satellite carrier wave phase differences in the x direction; b is a matrix of m-dimensional vectors formed by observing m satellite carrier wave phase differences in the y direction; a is the product of the line of sight observed by m satellites of n receivers in the x direction and the shortest baseline distance in the x direction, and an m multiplied by n matrix is formed; b is the product of the sight distance observed by m satellites of n receivers in the y direction and the shortest baseline distance in the y direction to form an m multiplied by n matrix;
the constraint conditions are as follows:
x is orthogonal with y, and the cosine value of the included angle is 0;
step 2: determining a popular space M according to constraint conditions of the orthogonal baseline direction finding angle optimization model;
step 3: determining a tangent space with the point (x, y) of the popular space M according to the tangent vector of the point (x, y) of the popular space M, and an inner product derivative and a direction derivative in the tangent space;
step 4: determining the relationship between the Euclidean gradient and the directional derivative and the relationship between the Riemann gradient and the directional derivative according to the inner product derivative in the tangent space, further determining the relationship between the Riemann gradient and the Euclidean gradient, and obtaining the expression of the Riemann gradient;
step 5: determining the relationship between the Riemann gradient and the Riemann Heisen according to the Riemann gradient, and determining the direction of the fastest gradient descent;
step 6: and determining a retraction function according to the fastest gradient descent direction, judging whether a value obtained at the last moment of the retraction function is equal to a value at the next moment, and determining the optimal solution moment of the orthogonal baseline direction finding angle optimization model so as to determine the final attitude angle of the aircraft.
2. The angle optimization method for Beidou orthogonal baseline direction finding for an aircraft of claim 1 is characterized by comprising the following steps: in the step 6, determining the retraction function includes:
the cut space is projected to the popular space, and the next predicted point is found.
3. An angle optimization system of big dipper quadrature baseline direction finding towards aircraft which characterized in that: comprising the following steps:
the model construction module is used for integrating three antennas according to the positions of an aircraft body, wings and a aircraft nose by using an orthogonal geometric configuration, selecting the direction from the aircraft body to the aircraft nose as a baseline vector x direction, selecting the direction from the aircraft body to the aircraft wing as a baseline vector y direction, forming an orthogonal relation by x and y, taking the attitude angle of the aircraft as an optimization target, and establishing an orthogonal baseline direction finding angle optimization model, wherein the objective function of the orthogonal baseline direction finding angle optimization model is as follows:
；
a is a matrix of m-dimensional vectors formed by observing m satellite carrier wave phase differences in the x direction; b is a matrix of m-dimensional vectors formed by observing m satellite carrier wave phase differences in the y direction; a is the product of the line of sight observed by m satellites of n receivers in the x direction and the shortest baseline distance in the x direction, and an m multiplied by n matrix is formed; b is the product of the sight distance observed by m satellites of n receivers in the y direction and the shortest baseline distance in the y direction to form an m multiplied by n matrix;
the constraint conditions are as follows:
x is orthogonal with y, and the cosine value of the included angle is 0;
the popular space determining module is used for determining a popular space M according to constraint conditions of the orthogonal baseline direction finding angle optimization model;
a tangent space determining module for determining a tangent space with the point (x, y) of the popular space M, and inner product derivatives and direction derivatives in the tangent space according to the tangent vector of the point (x, y) of the popular space M;
the Riemann gradient determining module is used for determining the relationship between the Euclidean gradient and the direction derivative and the relationship between the Riemann gradient and the direction derivative according to the inner product derivative in the tangent space, further determining the relationship between the Riemann gradient and the Euclidean gradient, and obtaining an expression of the Riemann gradient;
the gradient descent fastest direction determining module is used for determining the relationship between the Riemann gradient and the Riemann Heisen according to the Riemann gradient and determining the gradient descent fastest direction;
and the result determining module is used for determining a retraction function according to the fastest gradient descent direction, judging whether the value obtained at the last moment of the retraction function is equal to the value at the next moment, and determining the optimal solution moment of the orthogonal baseline direction finding angle optimizing model so as to determine the final attitude angle of the aircraft.
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