CN114326813B - Method and system for predicting residual flight time of unpowered aircraft - Google Patents
Method and system for predicting residual flight time of unpowered aircraft Download PDFInfo
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Abstract
The method comprises the steps of obtaining a target distance, a sight inclination angle, a sight deflection angle and a speed vector of the vehicle at the current moment, calculating a total lead angle, and judging turning flight or straight flight of the current flight behavior according to the total lead angle; if the turning flight is performed, segmenting according to the total lead angle, wherein the last segment is a straight line segment, the rest segments are turning segments, and predicting the rest flight time of the turning segments by adopting segmented iteration; calculating the remaining linear segment range, segmenting the linear segment according to the remaining linear segment range, and predicting the remaining flight time of the linear segment by adopting segmented iteration; the sum of the turning section residual flight time and the straight line section residual flight time is the predicted total residual flight time; if the straight line flight is adopted, calculating a remaining straight line flight path, segmenting the straight line according to the remaining straight line flight path, and predicting the remaining flight time of the straight line by adopting segmented iteration, wherein the remaining flight time of the straight line is the predicted total remaining flight time.
Description
Technical Field
The invention relates to the technical field of flight time control of unpowered aircrafts, in particular to a method and a system for predicting the remaining flight time of an unpowered aircraft.
Background
The aircraft attacks the target at a specified time, which is the basis for implementing a multi-aircraft collaborative saturation attack. To achieve accurate guidance with time constraints, more accurate time of flight remaining information is needed to form the control feedback. Since the remaining time of flight is often difficult to estimate accurately and the speed of an unpowered aircraft varies significantly and uncontrollably in actual flight, in this case, the uncertain change in speed presents certain difficulties in predicting the remaining time of flight. The existing methods predict the remaining flight time based on the assumption that the aircraft speed is constant and the lead angle is small, however, the limitation of the constant speed is too severe and ideal, the flying speed of the unpowered aircraft in the tail section is obviously reduced, and the change process is not controlled. If the method is adopted, the problem of inaccurate estimation of the residual flight time is caused, and the attack time control of the aircraft is failed.
Disclosure of Invention
In view of the above analysis, the embodiments of the present invention aim to provide a method and a system for predicting the remaining time of flight of an unpowered aircraft, which are used for solving the problem of inaccurate estimation of the existing remaining time of flight.
In one aspect, an embodiment of the present invention provides a method for predicting a remaining time of flight of an unpowered aircraft, including the steps of:
acquiring a target distance, a sight inclination angle, a sight deflection angle and a speed vector of an aircraft at the current moment, calculating a total lead angle based on the sight inclination angle, the sight deflection angle and the speed vector, and judging turning flight or straight flight of the current flight behavior according to the total lead angle;
if the turning flight is the turning flight, segmenting the turning section according to the total lead angle, and predicting the residual flight time of the turning section by adopting segmented iteration; calculating the remaining linear segment voyage according to the total lead angle of the starting point of the linear segment and the target distance, segmenting the linear segment according to the remaining linear segment voyage, and predicting the remaining flight time of the linear segment by adopting segmented iteration; the sum of the residual flight time of the turning section and the residual flight time of the straight line section is the predicted total residual flight time;
if the straight line flight is performed, calculating a remaining straight line segment course according to the total lead angle and the target distance, segmenting the straight line segment according to the remaining straight line segment course, and predicting the remaining flight time of the straight line segment by adopting segmented iteration, wherein the remaining flight time of the straight line segment is the predicted total remaining flight time.
Based on the further improvement of the technical scheme, the method for predicting the residual flight time of the turning section by adopting the piecewise iteration or predicting the residual flight time of the straight line section by adopting the piecewise iteration comprises the following steps:
for each segment, a state variable of the starting point of the current segment is obtained, wherein the state variable comprises a velocity module value v i Inclination angle theta of sight line L,i Sight line deflection angle psi L,i Front tilt angle eta z,i Front deflection angle eta y,i Ground level y i ；
If the current segment is in the turning segment, the state variable further comprises a total lead angle eta i And target distance D tc,i The method comprises the steps of carrying out a first treatment on the surface of the If the current segment is in a straight line segment, the state variables further comprise the remaining straight line segment voyage L i ；
If the current segment is in the turning segment, according to
Calculating the initial flight time predicted value of the current segment +.>
If the current segment is in the straight line segment, then according to +.>
Calculating the initial flight time predicted value of the current segment +.>
Wherein Δη i Representing the variation of the total lead angle of the current segment, delta L representing the range variation of the remaining straight line segment of the current segment, K N Representing a navigation ratio;
calculating the initial speed change rate of the current segment according to the dynamics equation of the mass center motion of the aircraft based on the state variable of the starting point of the current segment
Based on the initial rate of speed change
An initial time-of-flight prediction value for said current segment >
Correcting to obtain a current segment flight time correction value +.>
State variable based on current segment start point and said current segment time-of-flight correction value
Predicting a state variable of a current segment end point, wherein the state variable of the current segment end point is a state variable of a next segment start point;
all segmented time of flight correction values
And the remaining time of flight as a predicted turn or straight line segment.
Further, based on the initial rate of speed change
An initial time-of-flight prediction value for said current segment>
Correcting to obtain a current segment flight time correction value +.>
Comprising the following steps:
based on the initial rate of speed change
And said initial time of flight prediction value +.>
According to the formula
Obtaining a first speed predictive value v of the segment end point p, i；
A first speed predictor v based on the segment end point p, i and said initial time of flight prediction value
Calculating a first rate of change of velocity from the kinetic equation of the movement of the aircraft centroid>
According to the formula
Calculating to obtain a first average correction speed +.>
If the current segment is in the turning segment, according to
Calculating the current segment time of flight correction +.>
If the current segment is in the straight line segment, then according to +.>
Calculating the current segment time of flight correction +. >
Further, a first speed predictor v based on the segment end point p,i And the initial time-of-flight prediction value
Calculating a first rate of change of velocity from the kinetic equation of the movement of the aircraft centroid>
Comprising the following steps:
according to the first speed predictive value v p, i and said initial time of flight prediction value
Correcting the sight inclination angle and the sight deflection angle of the current segment to respectively obtain a first corrected sight inclination angle theta Lp,i And a first corrected line-of-sight offset angle ψ Lp,i ；
If the current segment is in the turning segment, then according to formula y p,i ＝-D tc,i+1 sin(θ Lp,i ) Calculating a first corrected ground height y p,i The method comprises the steps of carrying out a first treatment on the surface of the If the current segment is in a straight line segment, then according to formula y p,i ＝-L i+1 sin(θ Lp,i ) Calculating a first corrected ground height y p,i The method comprises the steps of carrying out a first treatment on the surface of the Wherein D is tc,i+1 Representing the target distance of the starting point of the i+1 segment, L i+1 Representing the rest straight-line segment course of the starting point of the i+1 segment;
based on the first corrected line of sight inclination angle theta Lp,i First corrected line-of-sight offset angle ψ Lp,i And a first speed predictive value v p,i Calculating a first velocity vector in the base reference coordinate systemComponents of each coordinate axis; calculating a first corrected ballistic inclination angle theta based on the components of each coordinate axis of the first velocity vector in the base reference coordinate system p,i ；
Based on the first speed predictive value v p,i First corrected ground height y p,i First corrected ballistic tilt angle theta p,i Calculating a first corrected speed change rate according to a kinetic equation of the mass center motion of the aircraft
Further, according to the first speed predictive value v p,i And the initial time-of-flight prediction value
Correcting the sight inclination angle and the sight deflection angle of the current segment to respectively obtain a first corrected sight inclination angle theta Lp,i And a first corrected line-of-sight offset angle ψ Lp,i Comprising:
correcting the sight inclination angle of the current segment according to the following formula to obtain a first corrected sight inclination angle theta Lp,i ：
If the current segment is in the turning segment, according to
Calculating the initial gaze tilt rate +.>
And a first corrected gaze inclination rate of change +>
If the current segment is in the straight line segment, then according to
Calculating the initial gaze tilt rate +.>
And a first corrected gaze inclination rate of change +>
According to the formula
Obtaining a first corrected sight inclination angle theta Lp,i ；
Correcting the sight line deflection angle of the current segment according to the following formula to obtain a first corrected sight line deflection angle phi Lp,i ：
If the current segment is in the turning segment, according to
Calculating the initial line of sight deflection change rate +.>
And a first corrected line-of-sight angle change rate
If the current segment is in the straight line segment, then according to
Calculating the initial line of sight deflection change rate +.>
And a first corrected line-of-sight angle change rate 
According to the formula
Obtaining a first corrected sight offset angle psi Lp,i 。
Further, a state variable based on a current segment start point and the current segment time of flight correction value
Predicting a state variable for a current segment end point, comprising:
initial rate of speed change according to current segment
And said current segment time of flight correction value +.>
According to the formula->
Obtaining a second speed predicted value v of the current segment end point q,i ；
A second velocity predictor v based on the segment end point q,i And the current segment time of flight correction value
Calculating a second rate of change of velocity from the kinetic equation of the movement of the aircraft centroid>
For initial rate of speed change
And a second corrected speed change rate->
Averaging to obtain a second average correction speed
Based on the second average corrected speed
Calculating a third speed predicted value of the end point of the current segment
The third speed predicted value is the predicted speed v of the ending point of the current segment i+1 ；
Line of sight inclination angle theta according to current segment start point L,i Speed v of end point of current segment i+1 And said current segment time of flight correction value
Calculating the sight inclination angle theta of the end point of the current segment L,i+1 The method comprises the steps of carrying out a first treatment on the surface of the Line-of-sight offset angle psi according to the current segment start point L,i Speed v of end point of current segment i+1 And said current segment time of flight correction value +.>
Calculating to obtain the sight offset angle psi of the end point of the current segment L,i +1；
If the current segment is in the turning segment, then according to formula y i+1 ＝-D tc,i+1 sinθ L,i+1 Calculating the ground height of the ending point of the current segment; if the current segment is in a straight line segment, then according to y i+1 ＝-L i+1 sinθ L,i+1 The ground height of the end point of the current segment is calculated.
Further, based on the state variable of the starting point of the current segment, calculating the initial speed change rate of the current segment according to the dynamics equation of the movement of the mass center of the aircraft
Comprising the following steps:
based on the inclination angle theta of the sight line L,i Sight line deflection angle psi L,i Front tilt angle eta z,i Front deflection angle eta y,i And velocity module v i Calculating components of the speed vector in each coordinate axis in the base reference coordinate system; calculating the component of each coordinate axis in the basic reference coordinate system based on the velocity vector to obtain the initial ballistic inclination angle theta of the current segment i ；
If the current segment is in the turning segment, the method is based on the formula
Calculating components of acceleration in a ballistic coordinate system; if the current segment is in the straight line segment, then according to the formula +.>
Calculating components of acceleration in a ballistic coordinate system;
according to the ground height y i Interpolation to obtain the atmospheric density ρ and the sound speed aT, and Mach number is calculated according to the atmospheric density ρ and the sound speed aT 
And dynamic pressure->
Calculating the lift coefficient C according to the following formula Ld,i ：
F y ＝MT·g tc cosθ i +MT·a y,i ，F z ＝MT·a z,i ，
Based on Mach and lift coefficient C Ld,i Calculating the attack angle command alpha by Newton iteration method c,i ；
Based on the Mach number Mach and the angle of attack command alpha c,i Calculating a resistance coefficient C according to the fitting formula D,i ；
According to the formula
The rate of change of the initial velocity is calculated,
wherein MT represents the mass of the aircraft, ST represents the reference area of the aircraft, g tc Representing the gravitational constant.
Further, after the state variable of the current segment start point is obtained for each segment, the initial speed change rate is based on
An initial time-of-flight prediction value for said current segment>
Before the correction, the method further comprises the following steps:
if the current segment is in the turning segment, calculating the prepositioning angle eta of the ending point of the current segment according to the following formula z,i+1 Front deflection angle eta y,i+1 And a total lead angle eta i+1 ：
η y,i+1 ＝η y,i +Δη y,i ，η z,i+1 ＝η z,i +Δη z,i ，η i+1 ＝arccos(cosη y,i+1 cosη z,i+1 )；
According to the formula
Calculating a target distance D of the end point of the current segment tc,i+1 ；
If the current segment is in the straight line segment, calculating the remaining straight line segment range L of the ending point of the current segment according to the following formula i+1 Front tilt angle eta z,i+1 And a prepositive deflection angle eta y,i+1 ：
L i+1 ＝L i -ΔL，
Wherein K is N Represents the navigation ratio, delta η Indicating the pre-angle segment quantity constant and NumP indicates the number of segments of the turn segment.
Further, calculating a total lead angle based on the gaze inclination angle, gaze deflection angle, and velocity vector, comprising:
Calculating a direction cosine matrix from the reference coordinate system to the sight line coordinate system according to the sight line inclination angle and the sight line deflection angle;
calculating a component of the velocity vector in the line-of-sight coordinate system based on the direction cosine matrix;
the total lead angle is calculated according to the following formula:
wherein v is xL 、v yL And v zL Respectively representing the components of the velocity vector in three coordinate axes of a sight line coordinate system, eta z Represents the prepositive dip angle eta y Represents the lead angle, and η represents the total lead angle.
Compared with the prior art, the method and the device have the advantages that the current flying behavior is judged to turn or fly straight according to the total lead angle according to the three-dimensional mass center equation of motion of the aircraft in a closed loop mode, the current flying behavior is segmented according to the total lead angle when the aircraft turns, the remaining flying time is segmented according to the remaining straight-line segment voyage when the aircraft turns, the remaining flying time is predicted by adopting segmented iteration, the future speed of the unpowered aircraft is predicted in a segmented mode through iteration solution, and the remaining flying time estimation formula is corrected in an iteration mode, so that the estimation of the remaining flying time is more accurate, and the remaining flying time can still be accurately predicted under the conditions that the total lead angle greatly changes and the flying speed of the unpowered aircraft is not controlled.
In another aspect, an embodiment of the present invention provides a system for predicting a remaining time of flight of an unpowered aircraft, including:
the data acquisition module is used for acquiring a target distance, a sight inclination angle, a sight deflection angle and a speed vector of the aircraft at the current moment, calculating a total lead angle based on the sight inclination angle, the sight deflection angle and the speed vector, and judging turning flight or straight line flight of the current flight behavior according to the total lead angle;
the turning flight prediction module is used for segmenting the turning section according to the total front angle if turning flight is performed, and predicting the remaining flight time of the turning section by adopting segmented iteration; calculating the remaining linear segment voyage according to the total lead angle of the starting point of the linear segment and the target distance, segmenting the linear segment according to the remaining linear segment voyage, and predicting the remaining flight time of the linear segment by adopting segmented iteration; the sum of the residual flight time of the turning section and the residual flight time of the straight line section is the predicted total residual flight time;
and the linear flight prediction module is used for calculating a remaining linear segment course according to the total lead angle and the target distance if the linear flight is linear flight, segmenting the linear segment according to the remaining linear segment course, and predicting the remaining flight time of the linear segment by adopting segmentation iteration, wherein the remaining flight time of the linear segment is the predicted total remaining flight time.
In the invention, the technical schemes can be mutually combined to realize more preferable combination schemes. Additional features and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. The objectives and other advantages of the invention may be realized and attained by the structure particularly pointed out in the written description and drawings.
Drawings
The drawings are only for purposes of illustrating particular embodiments and are not to be construed as limiting the invention, like reference numerals being used to refer to like parts throughout the several views.
FIG. 1 is a flow chart of a method of predicting remaining time of flight of an unpowered aircraft in accordance with an embodiment of the present invention;
FIG. 2 is a block diagram of a residual time of flight prediction system for an unpowered aircraft in accordance with an embodiment of the present invention;
FIG. 3 is a coordinate system diagram of an embodiment of the present invention;
fig. 4 is a graph showing comparison of results of different residual time estimation methods.
Detailed Description
Preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, which form a part hereof, and together with the description serve to explain the principles of the invention, and are not intended to limit the scope of the invention.
In order to solve the problem that the prediction of the residual time of the unpowered aircraft is inaccurate under the conditions that the speed changes along with the flight state and the leading angle is large, the current flying behavior turning flight or the straight line flight is judged according to the total leading angle according to a three-dimensional mass center equation of motion of the aircraft in a closed loop mode, the current flying behavior turning flight or the straight line flight is segmented according to the total leading angle when the current flying behavior turning flight is turning flight, the residual flight time is segmented according to the residual straight line section range when the current flying behavior turning flight is straight line flight, the segmentation iteration prediction is adopted, the segmentation prediction is carried out on the future speed of the unpowered aircraft through iteration solution, and the residual flight time estimation formula is iteratively corrected, so that the estimation of the residual flight time is more accurate, and the residual flight time can still be accurately predicted under the conditions that the total leading angle greatly changes and the flight speed of the unpowered aircraft is uncontrolled.
As shown in fig. 3, the coordinate system of the embodiment of the present invention includes a base reference coordinate system, a line-of-sight coordinate system, and a trajectory coordinate system.
The three-dimensional centroid of the aircraft is taken as an origin O in a base reference coordinate system, the X-axis direction is parallel to the horizontal plane and the pointing north is positive, and the base reference coordinate system is taken as X R The Y axis is vertically upward, in Y R The Z axis is parallel to the horizontal plane and is oriented according to the right hand rule, and Z is used for R And (3) representing.
The line-of-sight coordinate system takes the three-dimensional centroid of the aircraft as an origin O, the X-axis direction points to the target point from the aircraft, and the X L Indicating Z L The axial direction being parallel to the horizontal plane and pointing at X L Right is positive, the Y axis determines the direction according to the right hand rule, and Y is used for L And (3) representing.
The trajectory coordinate system takes the three-dimensional centroid of the aircraft as an origin O, and the X-axis direction is along the direction of a velocity vector, and takes X as the direction of the velocity vector V Representing Y V The axis contains the velocity vector and is vertical to the velocity vector and positive upwards in the vertical plane, the Z axis determines the direction according to the right hand rule, and Z is used for V And (3) representing.
Symbols used in the embodiments of the present application are collectively described as follows: d (D) tc Representing a linear distance between the aircraft and the target; f represents stress; f (F) L Representing the total lift; c (C) L Representing the lift coefficient; c (C) D Representing the resistance coefficient; η represents the total lead angle, i.e. the aircraft velocity vector and X L Is included in the plane of the first part; η (eta) y Representing the angular offset (velocity vector in line of sight coordinate system X L -O-Z L In-plane projection and X L An angle between the axes); η (eta) z Representing the pretilt angle (velocity vector and line-of-sight coordinate system X L -O-Z L Included angle of plane); Δη represents the total lead angle variation; Δη y Representing the front deflection angle variation; Δη z Representing the change amount of the pre-tilt angle; delta η A segment quantity constant for the lead angle; v represents a velocity module; 
Representing the rate of change of speed; />
Representing the average rate of change of speed; y represents the height from the ground; θ L Representing inclination of line of sight, i.e. line of sight vector X L And X is R -O-Z R An included angle of the planes; psi phi type L Representing the angle of gaze deviation, i.e. gaze vector X L At X R -O-Z R In-plane projection and X R An included angle of the shaft; />
And->
The change rate of the inclination angle of the line of sight and the change rate of the deflection angle of the line of sight are respectively represented; θ represents the ballistic dip, i.e., the angle of the velocity vector with the horizontal; a, a y And a z Respectively represent the acceleration Y in a ballistic coordinate system v Axis and Z v The component of the axis, L represents the remaining linear segment range, ΔL represents the linear segment segmentation constant; the index i indicates the current segment and index i+1 indicates the next segment.
In one embodiment of the present invention, a method for predicting the remaining time of flight of an unpowered aircraft is disclosed, as shown in fig. 1, comprising the steps of:
s1, acquiring a target distance, a sight inclination angle, a sight deflection angle and a speed vector of an aircraft at the current moment, calculating a total lead angle based on the sight inclination angle, the sight deflection angle and the speed vector, and judging turning flight or straight flight of the current flight behavior according to the total lead angle.
S2, if turning flight is performed, segmenting the turning section according to the total lead angle, and predicting the residual flight time of the turning section by adopting segmented iteration; calculating the remaining linear segment voyage according to the total lead angle of the starting point of the linear segment and the target distance, segmenting the linear segment according to the remaining linear segment voyage, and predicting the remaining flight time of the linear segment by adopting segmented iteration; the sum of the residual flight time of the turning section and the residual flight time of the straight line section is the predicted total residual flight time;
S3, if the straight line flight is performed, calculating a remaining straight line section course according to the total lead angle and the target distance, segmenting the straight line section according to the remaining straight line section course, and predicting the remaining flight time of the straight line section by adopting segmented iteration, wherein the remaining flight time of the straight line section is the predicted total remaining flight time.
The current flying behavior is judged to turn or fly straight according to the total lead angle, the current flying behavior is segmented according to the total lead angle when turning, the current flying behavior is segmented according to the residual straight line range when flying straight, the increment of the lead inclination angle of the aircraft in each segmented interval is guaranteed to be a small angle, and the residual flight time is predicted by adopting segmentation iteration, so that the residual flight time can still be accurately predicted under the conditions that the total lead angle is greatly changed and the flying speed of the unpowered aircraft is not controlled.
Wherein the acquired velocity vector is a velocity vector in a reference base coordinate system in which the components of the three coordinate axes can be represented as v, respectively xR 、v yR And v zR 。
Specifically, in step S1, calculating the total lead angle based on the gaze inclination angle, the gaze offset angle, and the velocity vector includes:
s11, calculating a direction cosine matrix from the reference coordinate system to the sight line coordinate system according to the sight line inclination angle and the sight line deflection angle;
Specifically, according to the formula
Direction cosine matrix for calculating base reference coordinate system to sight line coordinate system>
S12, calculating the components of the speed vector in the sight line coordinate system based on the direction cosine matrix;
the components of the velocity vector in the line-of-sight coordinate system are
Wherein v is xL 、v yL And v zL Representing the coordinate components of the velocity vector in the line of sight coordinate system, respectively.
S13, calculating a total lead angle according to the following formula:
wherein v is xL 、v yL And v zL Respectively representing the components of the velocity vector in three coordinate axes of a sight line coordinate system, eta z Represents the prepositive dip angle eta y Represents the lead angle, and η represents the total lead angle.
In practice, the pre-angle segment quantity constant may take a smaller quantity, e.g., Δ η 2 ° may be taken. When the total lead angle eta 0 ＞Δ η When the vehicle is in the turning flight, judging that the current flight is the turning flight, namely, the vehicle is in the turning flight at the current predicted moment of the residual flight; otherwise, judging the current flying behavior to fly linearly.
If the current flight is turning flight, segmenting the turning section according to the total lead angle according to the formula
The number of segments of the turning section is calculated as NumP, and floor (·) represents a rounding down. And predicting the flight time of each turn section in sequence to obtain the residual flight time of the turn section, then calculating the range of the residual straight line section according to the total lead angle and the target distance of the starting point of the straight line section, segmenting the straight line section according to the range of the residual straight line section, and predicting the flight time of each straight line section in sequence to obtain the residual flight time of the straight line section, wherein the total residual flight time is the sum of the residual flight time of the turn section and the residual flight time of the straight line section. Wherein the starting point of the straight line segment is the ending point of the turning segment.
If the current flight is straight-line flight, the straight-line segment is segmented directly according to the remaining straight-line segment range. According to the formula
Calculating the remaining straight line range according to the formula +.>
Calculating the segmentation number NumL+1 of the straight line segment, and predicting the flight time for each segment in sequence to obtain the residual flight time of the straight line segment, namely the predicted total residual flight time.
Wherein D is tc Aircraft representing predicted moments of remaining flightThe linear distance between the targets, η, represents the total lead angle at which the remaining flight prediction is performed, K N For the navigational ratio of the proportional navigational method employed, L represents the remaining straight-line segment voyage at the time of the remaining flight prediction.
Specifically, predicting the residual flight time of the turning section by adopting piecewise iteration or predicting the residual flight time of the straight line section by adopting piecewise iteration comprises the following steps:
s21, for each segment, acquiring a state variable of the starting point of the current segment, wherein the state variable comprises a speed module value v i Inclination angle theta of sight line L,i Sight line deflection angle psi L,i Front tilt angle eta z,i Front deflection angle eta y,i Ground level y i ；
If the current segment is in the turning segment, the state variable further comprises a total lead angle eta i And target distance D tc,i The method comprises the steps of carrying out a first treatment on the surface of the If the current segment is in a straight line segment, the state variables further comprise the remaining straight line segment voyage L i 。
If the current flight is turning flight, for the first segment of the turning segment, the state variable of the starting point of the first segment of the straight line segment is the state variable of the ending point of the last segment of the turning segment, wherein the state variable of the starting point of the first segment of the straight line segment is the state value of the predicted moment of the remaining flight
D tc,Nump+1 And eta Nump+1 Is the distance and total lead angle of the target at the end point of the last leg of the turn.
And if the current flight is straight-line flight, the state variable of the first segmentation starting point of the straight-line segment is the state value of the rest flight prediction moment.
S22, if the current segment is in the turning segment, according to
Calculating the initial flight time predicted value of the current segment +.>
If the current segment is in the straight line segment, then according to +.>
Calculating the initial flight time predicted value of the current segment +.>
Wherein Δη i Representing the variation of the total lead angle of the current segment, delta L representing the range variation of the remaining straight line segment of the current segment, K N Representing a navigation ratio;
specifically, if the current segment is in the turning segment, the change amount Δη of the total lead angle of the current segment i Calculated according to the following formula
I.e. when i=nump, i.e. NumP segment takes Δη i ＝-(η i -NumP·Δ η ) In the 1 st to NumP-1 th paragraphs, Δη is taken i ＝-Δ η 。
para eta i ＝arccos(cosη y,i cosη z,i ) Differentiation is performed to obtain
And because of
The movement of the aircraft in three-dimensional space thus has a movement pattern of
The elimination time variable is +.>
Then in interval t i ,t]Upper integration and reduction->
Therefore there is->
Then to sin eta t One-order Taylor expansion, sin η t ＝sinη i +Δη t ·cosη t Substituted with +.>
Then at->
Upper integral is available->
According to the formula
Predicting the flight time of the current segment to obtain an initial flight time predicted value +.>
If the current segment is in the straight line segment, then according to
Predicting the time of flight of the pre-segment to obtain an initial time of flight prediction value for the current segment>
S23, calculating the initial speed change rate of the current segment according to the dynamics equation of the movement of the mass center of the aircraft based on the state variable of the starting point of the current segment
S24, based on the initial speed change rate
An initial time-of-flight prediction value for said current segment>
Correcting to obtain a current segment flight time correction value +.>
S25, based on the state variable of the current segment start point and the current segment flight time correction value
Predicting a state variable of a current segment end point, wherein the state variable of the current segment end point is a state variable of a next segment start point;
If the current segment is the last segment of the straight line segment, the corrected value of the flight time of the current segment is obtained
The total remaining time of flight is obtained and the state variable of the current segment end point is no longer predicted. />
All segmented time of flight correction values
And the remaining time of flight as a predicted turn or straight line segment.
After step S21, before step S24, further comprising:
s201, if the current segment is in the turning segment, calculating the prepositioning inclination angle eta of the end point of the current segment according to the following formula z,i+1 Front deflection angle eta y,i+1 And a total lead angle eta i+1 ：
η y,i+1 ＝η y,i +Δη y,i ，η z,i+1 ＝η z,i +Δη z,i ，η i+1 ＝arccos(cosη y,i+1 cosη z,i+1 )；
According to the formula
Calculating a target distance D of the end point of the current segment tc,i+1 ；
If the current segment is in the straight line segment, calculating the remaining straight line segment range L of the ending point of the current segment according to the following formula i+1 Front tilt angle eta z,i+1 And a prepositive deflection angle eta y,i+1 ：
L i+1 ＝L i -ΔL，
Wherein K is N Represents the navigation ratio, delta η Representing the lead angle segment quantity constant.
In step S23, based on the state variable of the starting point of the current segment, the initial speed change rate of the current segment is calculated according to the dynamics equation of the centroid motion of the aircraft, including steps S231-S237:
s231 based on the sight inclination angle theta L,i Sight line deflection angle psi L,i Front tilt angle eta z,i Front deflection angle eta y,i And velocity module v i Calculating components of the speed vector in each coordinate axis in the base reference coordinate system; calculating the component of each coordinate axis in the basic reference coordinate system based on the velocity vector to obtain the ballistic inclination angle theta of the current segment i ；
Specifically, the ballistic tilt θ is calculated according to the following formula:
wherein, the liquid crystal display device comprises a liquid crystal display device,
direction cosine matrix representing base reference coordinate system to line-of-sight coordinate system, v represents velocity module value, eta z Represents the prepositive dip angle eta z Represents the prepositive deflection angle theta L Represents the inclination of the sight line, ψ L Representing the angle of deflection of the line of sight, v px ,v py ,v pz Representing the component sum v of the velocity vector on each axis of the line-of-sight coordinate system qx ,v qy ,v qz Representing the components of the velocity vector on each axis of the reference frame, respectively.
The above formula for calculating the ballistic tilt angle θ is expressed as θ=f θ (θ L ,ψ L ,η y ,η z ,v)。
The state variable line-of-sight inclination angle theta according to the current segment start point L,i Sight line deflection angle psi L,i Velocity module v i Front tilt angle eta z,i And a prepositive deflection angle eta y,i Carry-in θ=f θ (θ L ,ψ L ,η y ,η z V) the initial trajectory of the current segment can be calculatedInclination angle theta i 。
S232, if the current segment is in the turning segment, according to the formula
Calculating the component of the current acceleration in a ballistic coordinate system; if the current segment is in the straight line segment, then according to the formula +.>
Calculating the component of the current acceleration in a ballistic coordinate system;
a y Y representing acceleration in ballistic coordinate system v Component of axis, a z Z representing acceleration in ballistic coordinate system v Component of the axis.
S233, according to the ground height y i Interpolation to obtain the atmospheric density ρ and the sound speed aT, and Mach number is calculated according to the atmospheric density ρ and the sound speed aT
And dynamic pressure->
Specifically, according to the U.S. standard atmosphere model, the atmosphere density ρ and the sound speed aT can be obtained by interpolating according to the height of the current segment from the ground
Mach number is calculated according to +.>
Dynamic pressure is calculated.
S234, calculating a lift coefficient C according to the following formula Ld,i ：
F y ＝MT·g tc cosθ i +MT·a y,i ，F z ＝MT·a z,i
Wherein MT represents aircraft mass, ST represents aircraft reference area, g tc Represents the gravitational constant, sign represents the sign function, F L Representing total lift force, F y Y representing lift in ballistic coordinate system v Component of axis, F z Z representing lift in ballistic coordinate system v A component of the shaft; according to the calculation principle of lift force: lift = lift coefficient x dynamic pressure x aircraft reference area, calculate lift coefficient C Ld,i 。
S235, based on Mach number and lift coefficient C Ld,i Calculating the attack angle command alpha by Newton iteration method c,i 。
Specifically, the iteration formula of the newton iteration method is as follows:
the iteration initial value is 5 DEG, namely alpha 0 At 5 deg., the iteration accuracy meets the accuracy requirement, e.g. 1e-5, or a maximum number of iterations is reached, e.g. 100, the iteration is ended.
Specifically, the function f (α) and derivative f '(α) used by newton's iterative method are as follows:
f(α)＝k Cl_00 +k Cl_10 α+k Cl_01 Mach+k Cl_20 α 2 +k Cl_11 α·Mach+k Cl_02 Mach 2 +k Cl_30 α 3
+k Cl_21 α 2 ·Mach+k Cl_12 α·Mach 2 +k Cl_03 Mach 3 +k Cl_31 α 3 ·Mach+k Cl_22 α 2 ·Mach 2
+k Cl_13 α·Mach 3 +k Cl_04 Mach 4 +k Cl_32 α 3 ·Mach 2 +k Cl_23 α 2 ·Mach 3
+k Cl_14 α·Mach 4 +k Cl_05 Mach 5 -C Ld
f'(α)＝k Cf_00 +k Cf_10 α+k Cf_01 Mach+k Cf_20 α 2 +k Cf_11 α·Mach+k Cf_02 Mach 2
+k Cf_21 α 2 ·Mach+k Cf_12 α·Mach 2 +k Cf_03 Mach 3 +k Cf_22 α 2 ·Mach 2
+k Cf_13 α·Mach 3 +k Cf_04 Mach 4
wherein k is Cl_00 、k Cl_10 、k Cl_01 、k Cl_20 、k Cl_11 、k Cl_02 、k Cl_30 、k Cl_21 、k Cl_12 、k Cl_03 、k Cl_31 、k Cl_22 、k Cl_13 、k Cl_04 、k Cl_32 、k Cl_23 、k Cl_14 、k Cl_05 ，k Cf_00 、k Cf_10 、k Cf_01 、k Cf_20 、k Cf_11 、k Cf_02 、k Cf_21 、k Cf_12 、k Cf_03 、k Cf_22 、k Cf_13 、k Cf_04 Is a coefficient fitted in advance according to aerodynamic parameters of the aircraft.
Mach number Mach calculated in step S232 and lift coefficient C calculated in step S234 Ld,i Carrying out iterative calculation to obtain attack angle command alpha c,i . The Newton iteration method is high in convergence speed, and a more accurate numerical solution can be obtained by setting convergence conditions, so that a common attack angle instruction can be calculated rapidly and accurately.
S236, based on Mach number and angle of attack instruction alpha c,i Calculating a resistance coefficient C according to the fitting formula D,i ；
Specifically, the drag coefficient is calculated according to the following formula:
wherein k is tc_00 、k tc_10 、k tc_01 、k tc_20 、k tc_11 、k tc_02 、k tc_30 、k tc_21 、k tc_12 、k tc_03 、k tc_40 、k tc_31 、k tc_22 、k tc_13 、k tc_04 、k tc_50 、k tc_ 41、k tc_32 、k tc_23 、k tc_14 、k tc_05 Is a coefficient fitted in advance according to aerodynamic parameters of the aircraft. The aerodynamic characteristics of the aircraft are generally described by a large amount of discrete data, and by fitting the data, an approximate fitting relation between the drag coefficient and the attack angle and Mach number can be obtained, so that the method is simple, and the calculation speed is high.
Mach number Mach calculated in step S232 and attack angle command alpha calculated in step S236 c, i carrying out iterative calculation to obtain a resistance coefficient C D,i 。
S237, according to the formula
The initial rate of speed change is calculated.
In particular, according to the kinetic equation of the movement of the aircraft mass centre 
And calculating to obtain the initial speed change rate. The stress of the unpowered aircraft mainly comes from resistance and gravity, so the dynamic equation is expressed as
Wherein->
Represents the effect of resistance on the rate of change of speed g tc sinθ i The effect of gravity on the rate of change of speed is shown.
Wherein MT represents the mass of the aircraft, ST represents the reference area of the aircraft, g tc Representing the gravitational constant.
The method of calculating the rate of change of speed in steps 233-237 is represented as
v denotes the velocity modulus in the base reference frame, a y Y representing acceleration in ballistic coordinate system v Component of axis, a z Z representing acceleration in ballistic coordinate system v The component of the axis, θ, represents the ballistic dip and y represents the ground level.
Specifically, step S24 is based on the initial speed change rate
Initial time-of-flight predictions for the current segment
Correcting to obtain a current segment flight time correction value +.>
Including steps S241-S244.
S241, based on the initial speed change rate
And said initial time of flight prediction value +.>
According to the formula
Obtaining a first speed predictive value v of the segment end point p,i ；
S242, predicting value v of first speed based on the segment ending point p,i And the initial time-of-flight prediction value
Calculating a first rate of change of velocity from the kinetic equation of the movement of the aircraft centroid >
/>
Specifically, in step S242, a first velocity prediction value v based on the segment end point p,i And the initial time-of-flight prediction value
Calculating a first rate of change of velocity from the kinetic equation of the movement of the aircraft centroid>
Comprises steps S2421-S2424:
s2421 based on the first speed predictor v p,i And the initial time-of-flight prediction value
Correcting the sight inclination angle and the sight deflection angle of the current segment to respectively obtain a first corrected sight inclination angle theta Lp,i And a first corrected line-of-sight offset angle ψ Lp,i ；
Specifically, according to the first speed predictor v p,i And the initial time-of-flight prediction value
Correcting the sight inclination angle and the sight deflection angle of the current segment to respectively obtain a first corrected sight inclination angle theta Lp,i And a first corrected line-of-sight offset angle ψ Lp,i Comprising:
correcting the sight inclination angle of the current segment according to the following formula to obtain a first corrected sight inclination angle theta Lp,i ：
If the current segment is in the turning segment, according to
Calculating the initial gaze tilt rate +.>
And a first corrected line of sightInclination angle change Rate->
If the current segment is in the straight line segment, then according to
Calculating the initial gaze tilt rate +.>
And a first corrected gaze inclination rate of change +>
According to the formula
Calculating a first corrected line of sight tilt angle theta Lp,i 。
If the current segment is the last segment of the straight line segment, L is i+1 0, thus the first corrected gaze inclination change rate
Directly taking 0.
Line-of-sight inclination rate of a current segment start point
And a first corrected gaze inclination rate of change +>
Averaging to obtain the average inclination angle change rate +.>
Whereby according to the initial time of flight prediction value +.>
Correcting the sight inclination angle of the current segment to obtain a first corrected sight inclination angle theta Lp,i 。
Correcting the sight line deflection angle of the current segment according to the following formula to obtain a first corrected sight line deflection angle phi Lp,i ：
If the current segment is in the turning segment, according to
Calculating the initial line of sight deflection change rate +.>
And a first corrected line-of-sight angle change rate
If the current segment is in the straight line segment, then according to +.>
Calculating the initial line of sight deflection change rate +.>
And a first corrected gaze angle change rate +>
According to the formula
Obtaining a first corrected sight offset angle psi Lp,i 。
If the current segment is the last segment of the straight line segment, L is i+1 Is 0, thus the first corrected line of sight offset angle change rate
Directly taking 0.
S2422, if the current segment is in the turn segment, according to equation y p,i ＝-D tc,i+1 sin(θ Lp,i ) Calculating a first corrected ground height y p,i The method comprises the steps of carrying out a first treatment on the surface of the If the current segment is in a straight line segment, then according to formula y p,i ＝-L i+1 sin(θ Lp,i ) Calculating a first corrected ground height y p,i 。
S2423, based on the first corrected gaze inclination angle θ Lp,i First corrected line-of-sight offset angle ψ Lp,i And a first speed predictive value v p,i Calculating the components of the first speed vector in all coordinate axes in the base reference coordinate system; calculating a first corrected ballistic inclination angle theta based on the components of each coordinate axis of the first velocity vector in the base reference coordinate system p,i ；
Specifically, the ballistic tilt angle θ is calculated according to the formula in step S231 as θ=f θ (θ L ,ψ L ,η y ,η z V) correcting the inclination angle theta of the sight line Lp,i First corrected line-of-sight offset angle ψ Lp,i First speed predictive value v p,i Pretilt η of the end point of the current segment z,i+1 And the pre-bias angle eta of the end point of the current segment y,i+1 Carry in f θ Calculating to obtain a first corrected trajectory inclination angle theta p,i 。
Wherein the pretilt η of the end point of the current segment z,i+1 And the pre-bias angle eta of the end point of the current segment y,i+1 Can be calculated according to step S201.
S2424, based on the first speed predictive value v p,i First corrected ground height y p,i First corrected ballistic tilt angle theta p,i Calculating a first corrected speed change rate according to a kinetic equation of the mass center motion of the aircraft
Specifically, if the current segment is in the turn segment, the method is according to the formula
Calculating components of acceleration in a ballistic coordinate system; if the current segment is in the straight line segment, then according to the formula +. >
The components of acceleration in the ballistic coordinate system are calculated.
It should be noted that, if the current segment is the last segment of the straight line segment, then due to L i+1 0, so a is not calculated using the above formula yp,i And a zp,i Directly convert a yp,i And a zp,i Set to 0.
Wherein the pretilt η of the end point of the current segment z,i+1 Front offset angle eta of current segment end point y,i+1 Target distance D of current segment end point tc,i+1 Remaining straight-line segment voyage L of current segment end point i Can be calculated according to step S201.
According to the formula for calculating the speed change rate in steps S233-S237
First corrected ballistic inclination angle theta p,i First speed predictive value v p,i 、a yp,i 、a zp,i And a first corrected ground height y p,i Carry in->
Calculating to obtain a first corrected speed change rate->
S243, according to the formula
Calculating to obtain a first average correction speed +.>
/>
I.e. for initial rate of speed change
And a first corrected speed change rate->
Averaging to obtain an average speed change rate
According to the initial velocity v i Average rate of speed change->
And an initial time-of-flight prediction value->
Correcting the speed to obtain a first average corrected speed +.>
The accuracy of the estimation is improved by taking the average value.
S244, if the current segment is in the turning segment, according to
According to the first average correction speed
Recalculating the time of flight of the current segment to obtain a current time of flight correction value +.>
The predicted value of the flight time is further corrected by correcting the line-of-sight inclination angle, the line-of-sight deflection angle and the trajectory inclination angle according to the initial speed change rate, so that the prediction is more accurate.
Step S25, based on the state variable of the current segment start point and the current segment flight time correction value
Predicting a state variable for a current segment end point, comprising:
s251, according to the initial speed change rate of the current segment
And said current segment time of flight correction value +.>
According to the formula->
Obtaining a second speed predicted value v of the current segment end point q,i ；
And calculating the speed predicted value again by using the corrected flight time estimated value, thereby improving the estimation accuracy.
S252, second speed predicted value v based on the segment end point q,i And the current segment time of flight correction value
Calculating a second rate of change of velocity from the kinetic equation of the movement of the aircraft centroid>
In particular, according to
Calculating a second corrected line of sight tilt angle θ Lq,i According to
Calculating to obtain a second sight offset angle phi Lq,i The method comprises the steps of carrying out a first treatment on the surface of the According to y q,i ＝-D tc,i+1 sinθ Lq,i Calculating a second corrected ground height y q,i ；
The ballistic tilt angle θ is calculated according to the formula in step S231 as θ=f θ (θ L ,ψ L ,η y ,η z V), the second velocity prediction value v q,i Second corrected line of sight tilt angle theta Lq,i Second corrected line-of-sight offset angle ψ Lq,i Pretilt η of the end point of the current segment z,i+1 And the pre-bias angle eta of the end point of the current segment y,i+1 Carry in f θ Calculating to obtain a second corrected trajectory inclination angle theta q,i 。
According to calculation a in step S2424 yp,i And a zp,i Will be v p,i Replaced by v q,i Calculating to obtain a yq,i And a zq,i
According to the formula for calculating the speed change rate in steps S233-S237
Second corrected ballistic tilt angle theta q,i Second speed predictor v q,i 、a yq,i 、a zq,i And a second corrected ground height y q,i Carry in->
Calculating a second corrected speed change rate +.>
S253, for initial speed change Rate
And a second corrected speed change rate->
Averaging to obtain a second average correction speed +.>
/>
S254, based on the second average correction speed
Calculating a third speed predicted value of the end point of the current segment
The third speed predicted value is the predicted speed v of the ending point of the current segment i+1 ；
S255, according to the sight inclination angle theta of the current segmentation starting point L,i Speed v of end point of current segment i+1 And said current segment time of flight correction value 
Calculating the sight inclination angle theta of the end point of the current segment L,i+1 The method comprises the steps of carrying out a first treatment on the surface of the Line-of-sight offset angle psi according to the current segment start point L,i Speed v of end point of current segment i+1 And said current segment time of flight correction value +.>
Calculating to obtain the sight offset angle psi of the end point of the current segment L,i+1 。
Specifically, the line-of-sight inclination angle θ of the end point of the current segment is calculated according to the following formula L,i+1 ；
If the current segment is in the turning segment, according to the formula
Calculating a second corrected gaze angle change rate +.>
If the current segment is in the straight line segment, according to the formula +.>
Calculating a second corrected gaze angle change rate +.>
According to the formula
Calculating the line-of-sight inclination angle theta of the end point of the current segment L,i+1 。
If the current segment is in the turning segment, according to the formula
Calculating a second corrected gaze angle change rate +.>
If the current segment is in the straight line segment, according to the formula +.>
Calculating a second corrected gaze angle change rate +.>
According to the formula
Calculating the line-of-sight offset angle psi of the end point of the current segment L,i+1 。
S256, if the current segment is in the turning segment, according to the formula y i+1 ＝-D tc,i+1 sinθ L,i+1 Calculating the ground height of the ending point of the current segment; if the current segment is in a straight lineSegment according to y i+1 ＝-L i+1 sinθ L,i+1 Calculating the ground height y of the end point of the current segment i+1 。
By adopting the segmentation mode, the flight time is predicted for each segment, and the time sum of all segments is the total residual flight time, so that the estimation of the residual flight time is more accurate under the conditions that the speed of the unpowered aircraft is obviously reduced and the total leading angle is greatly changed.
The result of the remaining time of flight estimation using the prediction method and other methods of the present application is shown in fig. 4. It can be seen that the actual remaining time of flight is a straight line with a slope of-1, and the conventional estimation method and the constant-speed small-angle estimation method obviously estimate a large deviation because the speed variation and the large lead angle are not considered. By adopting the residual flight time prediction method, the residual flight time estimation curve is approximately overlapped with the actual residual flight time curve, the approach degree is higher and higher along with the time, and higher estimation precision is displayed.
In another aspect, an embodiment of the present invention provides a system for predicting a remaining time of flight of an unpowered aircraft, including:
the data acquisition module is used for acquiring a target distance, a sight inclination angle, a sight deflection angle and a speed vector of the aircraft at the current moment, calculating a total lead angle based on the sight inclination angle, the sight deflection angle and the speed vector, and judging turning flight or straight line flight of the current flight behavior according to the total lead angle;
the turning flight prediction module is used for segmenting the turning section according to the total front angle if turning flight is performed, and predicting the remaining flight time of the turning section by adopting segmented iteration; calculating the remaining linear segment voyage according to the total lead angle of the starting point of the linear segment and the target distance, segmenting the linear segment according to the remaining linear segment voyage, and predicting the remaining flight time of the linear segment by adopting segmented iteration; the sum of the residual flight time of the turning section and the residual flight time of the straight line section is the predicted total residual flight time;
And the linear flight prediction module is used for calculating a remaining linear segment course according to the total lead angle and the target distance if the linear flight is linear flight, segmenting the linear segment according to the remaining linear segment course, and predicting the remaining flight time of the linear segment by adopting segmentation iteration, wherein the remaining flight time of the linear segment is the predicted total remaining flight time.
The method embodiment and the system embodiment are based on the same principle, and the related parts can be mutually referred to and can achieve the same technical effect. The specific implementation process refers to the foregoing embodiment, and will not be described herein.
In the invention, the technical schemes can be mutually combined to realize more preferable combination schemes. Additional features and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. The objectives and other advantages of the invention may be realized and attained by the structure particularly pointed out in the written description and drawings.
Those skilled in the art will appreciate that all or part of the flow of the methods of the embodiments described above may be accomplished by way of a computer program to instruct associated hardware, where the program may be stored on a computer readable storage medium. Wherein the computer readable storage medium is a magnetic disk, an optical disk, a read-only memory or a random access memory, etc.
The present invention is not limited to the above-mentioned embodiments, and any changes or substitutions that can be easily understood by those skilled in the art within the technical scope of the present invention are intended to be included in the scope of the present invention.
Claims (4)
1. A method of predicting the remaining time of flight of an unpowered aircraft, comprising the steps of:
acquiring a target distance, a sight inclination angle, a sight deflection angle and a speed vector of an aircraft at the current moment, calculating a total lead angle based on the sight inclination angle, the sight deflection angle and the speed vector, and judging turning flight or straight flight of the current flight behavior according to the total lead angle;
if the turning flight is the turning flight, segmenting the turning section according to the total lead angle, and predicting the residual flight time of the turning section by adopting segmented iteration; calculating the remaining linear segment voyage according to the total lead angle of the starting point of the linear segment and the target distance, segmenting the linear segment according to the remaining linear segment voyage, and predicting the remaining flight time of the linear segment by adopting segmented iteration; the sum of the residual flight time of the turning section and the residual flight time of the straight line section is the predicted total residual flight time;
If the straight line flight is performed, calculating a remaining straight line segment course according to the total lead angle and the target distance, segmenting the straight line segment according to the remaining straight line segment course, and predicting the remaining flight time of the straight line segment by adopting segmented iteration, wherein the remaining flight time of the straight line segment is the predicted total remaining flight time;
predicting the residual flight time of a turning section by adopting piecewise iteration or predicting the residual flight time of a straight line section by adopting piecewise iteration comprises the following steps:
for each segment, a state variable of the starting point of the current segment is obtained, wherein the state variable comprises a velocity module value v i Inclination angle theta of sight line L,i Sight line deflection angle psi L,i Front tilt angle eta z,i Front deflection angle eta y,i Ground level y i ；
If the current segment is in the turning segment, the state variable further comprises a total lead angle eta i And target distance D tc,i The method comprises the steps of carrying out a first treatment on the surface of the If the current segment is in a straight line segment, the state variables further comprise the remaining straight line segment voyage L i ；
If the current segment is in the turning segment, according to
Calculating the initial flight time predicted value of the current segment +.>
If the current segment is in the straight line segment, then according to +.>
Calculating the current segmentStart time of flight prediction +.>
Wherein Δη i Representing the variation of the total lead angle of the current segment, delta L representing the range variation of the remaining straight line segment of the current segment, K N Representing a navigation ratio;
calculating the initial speed change rate of the current segment according to the dynamics equation of the mass center motion of the aircraft based on the state variable of the starting point of the current segment
Based on the initial rate of speed change
An initial time-of-flight prediction value for said current segment>
Correcting to obtain a current segment flight time correction value +.>
State variable based on current segment start point and said current segment time-of-flight correction value
Predicting a state variable of a current segment end point, wherein the state variable of the current segment end point is a state variable of a next segment start point;
all segmented time of flight correction values
And remaining time of flight as a predicted turn or straight segment;
based on the initial rate of speed change
An initial time-of-flight prediction value for said current segment>
Correcting to obtain a current segment flight time correction value +.>
Comprising the following steps:
based on the initial rate of speed change
And said initial time of flight prediction value +.>
According to the formula->
Obtaining a first speed predictive value v of the segment end point p,i ；
A first speed predictor v based on the segment end point p,i And the initial time-of-flight prediction value
Calculating a first rate of change of velocity from the kinetic equation of the movement of the aircraft centroid >
According to the formula
Calculating to obtain a first average correction speed +.>
If the current segment is in the turning segment, according to
Calculating the current segment time of flight correction +.>
If the current segment is in the straight line segment, then according to +.>
Calculating a current segment time-of-flight correction value
A first speed predictor v based on the segment end point p,i And the initial time-of-flight prediction value
Calculating a first rate of change of velocity from the kinetic equation of the movement of the aircraft centroid>
Comprising the following steps:
according to the first speed predictive value v p,i And the initial time-of-flight prediction value
Correcting the sight inclination angle and the sight deflection angle of the current segment to respectively obtain a first corrected sight inclination angle theta Lp,i And a first corrected line-of-sight offset angle ψ Lp,i ；
If the current segment is in the turning segment, then according to formula y p,i ＝-D tc,i+1 sin(θ Lp,i ) Calculating a first corrected ground height y p,i The method comprises the steps of carrying out a first treatment on the surface of the If the current segment is in a straight line segment, then according to formula y p,i ＝-L i+1 sin(θ Lp,i ) Calculating a first corrected ground height y p,i The method comprises the steps of carrying out a first treatment on the surface of the Wherein D is tc, i +1 Representing segment i+1Target distance of starting point, L i+1 Representing the rest straight-line segment course of the starting point of the i+1 segment;
based on the first corrected line of sight inclination angle theta Lp,i First corrected line-of-sight offset angle ψ Lp,i And a first speed predictive value v p,i Calculating the components of each coordinate axis of the first speed vector in the base reference coordinate system; calculating a first corrected ballistic inclination angle theta based on the components of each coordinate axis of the first velocity vector in the base reference coordinate system p,i ；
Based on the first speed predictive value v p,i First corrected ground height y p,i First corrected ballistic tilt angle theta p,i Calculating a first speed change rate according to a kinetic equation of the mass center motion of the aircraft
According to the first speed predictive value v p,i And the initial time-of-flight prediction value
Correcting the sight inclination angle and the sight deflection angle of the current segment to respectively obtain a first corrected sight inclination angle theta Lp,i And a first corrected line-of-sight offset angle ψ Lp,i Comprising:
correcting the sight inclination angle of the current segment according to the following formula to obtain a first corrected sight inclination angle theta Lp,i ：
If the current segment is in the turning segment, according to
Calculating the initial gaze tilt rate +.>
And a first corrected gaze inclination rate of change +>
If the current segment is in the straight line segment, then according to
Calculating the initial gaze tilt rate +.>
And a first corrected gaze inclination rate of change +>
According to the formula
Obtaining a first corrected sight inclination angle theta Lp,i ；
Correcting the sight line deflection angle of the current segment according to the following formula to obtain a first corrected sight line deflection angle phi Lp,i ：
If the current segment is in the turning segment, according to
Calculating the initial line of sight deflection change rate +.>
And a first corrected line-of-sight angle change rate
If the current segment is in the straight line segment, then according to
Calculating the initial line of sight deflection change rate +. >
And a first corrected gaze angle change rate +>
According to the formula
Obtaining a first corrected sight offset angle psi Lp,i ；
State variable based on current segment start point and said current segment time-of-flight correction value
Predicting a state variable for a current segment end point, comprising:
initial rate of speed change according to current segment
And said current segment time of flight correction value +.>
According to the formula
Obtaining a second speed predicted value v of the current segment end point q,i ；
A second velocity predictor v based on the segment end point q,i And the current segment time of flight correction value
Calculating a second rate of change of velocity from the kinetic equation of the movement of the aircraft centroid>
For initial rate of speed change
And second rate of change of speed->
Averaging to obtain a second average correction speed +.>
Based on the second average corrected speed
Calculating a third speed predicted value of the end point of the current segment
The third speed predicted value is the predicted speed v of the ending point of the current segment i+1 ；
Line of sight inclination angle theta according to current segment start point L,i Speed v of end point of current segment i+1 And said current segment time of flight correction value
Calculating the sight inclination angle theta of the end point of the current segment L,i+1 The method comprises the steps of carrying out a first treatment on the surface of the Line-of-sight offset angle psi according to the current segment start point L,i Speed v of end point of current segment i+1 And said current segment time of flight correction value +.>
Calculating to obtain the sight offset angle psi of the end point of the current segment L,i+1 ；
If the current segment is in the turning segment, then according to formula y i+1 ＝-D tc,i+1 sinθ L,i+1 Calculating the current segmentThe ground height of the end point; if the current segment is in a straight line segment, then according to y i+1 ＝-L i+1 sinθ L,i+1 Calculating the ground height of the ending point of the current segment;
calculating the initial speed change rate of the current segment according to the dynamics equation of the mass center motion of the aircraft based on the state variable of the starting point of the current segment
Comprising the following steps:
based on the inclination angle theta of the sight line L,i Sight line deflection angle psi L,i Front tilt angle eta z,i Front deflection angle eta y,i And velocity module v i Calculating the components of the speed vector in each coordinate axis in the base reference coordinate system; calculating the component of each coordinate axis in the basic reference coordinate system based on the velocity vector to obtain the initial ballistic inclination angle theta of the current segment i ；
If the current segment is in the turning segment, the method is based on the formula
Calculating components of acceleration in a ballistic coordinate system; if the current segment is in the straight line segment, the method is according to the formula
Calculating components of acceleration in a ballistic coordinate system;
according to the ground height y i Interpolation to obtain the atmospheric density ρ and the sound speed aT, and Mach number is calculated according to the atmospheric density ρ and the sound speed aT 
And dynamic pressure->
Calculating the lift coefficient C according to the following formula Ld,i ：
F y ＝MT·g tc cosθ i +MT·a y,i
F z ＝MT·a z,i
Based on Mach and lift coefficient C Ld,i Calculating the attack angle command alpha by Newton iteration method c,i ；
Based on the Mach number Mach and the angle of attack command alpha c,i Calculating a resistance coefficient C according to the fitting formula D,i ；
According to the formula
The rate of change of the initial velocity is calculated,
wherein MT represents the mass of the aircraft, ST represents the reference area of the aircraft, g tc Representing the gravitational constant.
2. The method of claim 1, wherein the initial rate of change of velocity is based on a state variable of a current segment start point obtained for each segment
An initial time-of-flight prediction value for said current segment>
Before the correction, the method further comprises the following steps:
if the current segment is in the turning segment, thenCalculating the pretilt angle eta of the current segment end point according to the following formula z,i+1 Front deflection angle eta y,i+1 And a total lead angle eta i+1 ：
η y,i+1 ＝η y,i +Δη y,i
η z,i+1 ＝η z,i +Δη z,i
η i+1 ＝arccos(cosη y,i+1 cosη z,i+1 )；
According to the formula
Calculating a target distance D of the end point of the current segment tc,i+1 ；
If the current segment is in the straight line segment, calculating the remaining straight line segment range L of the ending point of the current segment according to the following formula i+1 Front tilt angle eta z,i+1 And a prepositive deflection angle eta y,i+1 ：
L i+1 ＝L i -ΔL
Wherein K is N Represents the navigation ratio, delta η Indicating the pre-angle segment quantity constant and NumP indicates the number of segments of the turn segment.
3. The method of claim 1, wherein calculating a total lead angle based on the line-of-sight inclination, line-of-sight offset, and velocity vector comprises:
calculating a direction cosine matrix from the reference coordinate system to the sight line coordinate system according to the sight line inclination angle and the sight line deflection angle;
calculating a component of the velocity vector in the line-of-sight coordinate system based on the direction cosine matrix;
the total lead angle is calculated according to the following formula:
η＝arccos(cosη y cosη z )
wherein v is xL 、v yL And v zL Respectively representing the components of the velocity vector in three coordinate axes of a sight line coordinate system, eta z Represents the prepositive dip angle eta y Represents the lead angle, and η represents the total lead angle.
4. A system for predicting the remaining time of flight of an unpowered aircraft, comprising the following modules:
the data acquisition module is used for acquiring a target distance, a sight inclination angle, a sight deflection angle and a speed vector of the aircraft at the current moment, calculating a total lead angle based on the sight inclination angle, the sight deflection angle and the speed vector, and judging turning flight or straight line flight of the current flight behavior according to the total lead angle;
the turning flight prediction module is used for segmenting the turning section according to the total front angle if turning flight is performed, and predicting the remaining flight time of the turning section by adopting segmented iteration; calculating the remaining linear segment voyage according to the total lead angle of the starting point of the linear segment and the target distance, segmenting the linear segment according to the remaining linear segment voyage, and predicting the remaining flight time of the linear segment by adopting segmented iteration; the sum of the residual flight time of the turning section and the residual flight time of the straight line section is the predicted total residual flight time;
The linear flight prediction module is used for calculating a remaining linear segment course according to the total lead angle and the target distance if the linear flight is performed, segmenting the linear segment according to the remaining linear segment course, and predicting the remaining flight time of the linear segment by adopting segmented iteration, wherein the remaining flight time of the linear segment is the predicted total remaining flight time;
the turning flight prediction module adopts piecewise iteration to predict the remaining flight time of a turning section or adopts piecewise iteration to predict the remaining flight time of a straight line section, and comprises the following steps:
for each segment, a state variable of the starting point of the current segment is obtained, wherein the state variable comprises a velocity module value v i Inclination angle theta of sight line L,i Sight line deflection angle psi L,i Front tilt angle eta z,i Front deflection angle eta y,i Ground level y i ；
If the current segment is in the turning segment, the state variable further comprises a total lead angle eta i And target distance D tc,i The method comprises the steps of carrying out a first treatment on the surface of the If the current segment is in a straight line segment, the state variables further comprise the remaining straight line segment voyage L i ；
If the current segment is in the turning segment, according to
Calculating the initial flight time predicted value of the current segment +.>
If the current segment is in the straight line segment, then according to +.>
Calculating the initial flight time predicted value of the current segment +.>
Wherein Δη i Representing the variation of the total lead angle of the current segment, delta L representing the range variation of the remaining straight line segment of the current segment, K N Representing a navigation ratio;
calculating the initial speed change rate of the current segment according to the dynamics equation of the mass center motion of the aircraft based on the state variable of the starting point of the current segment
Based on the initial rate of speed change
An initial time-of-flight prediction value for said current segment>
Correcting to obtain a current segment flight time correction value +.>
State variable based on current segment start point and said current segment time-of-flight correction value
Predicting a state variable of a current segment end point, wherein the state variable of the current segment end point is a state variable of a next segment start point;
all segmented time of flight correction values
And remaining time of flight as a predicted turn or straight segment;
based on the initial rate of speed change
An initial time-of-flight prediction value for said current segment>
Correcting to obtain a current segment flight time correction value +.>
Comprising the following steps:
based on the initial rate of speed change
And said initial time of flight prediction value +.>
According to the formula->
Obtaining a first speed predictive value v of the segment end point p,i ；
A first speed predictor v based on the segment end point p,i And the initial time-of-flight prediction value
Calculating a first rate of change of velocity from the kinetic equation of the movement of the aircraft centroid >
According to the formula
Calculating to obtain a first average correction speed +.>
If the current segment is in the turning segment, according to
Calculating the current segment time of flight correction +.>
If the current segment is in the straight line segment, then according to +.>
Calculating a current segment time-of-flight correction value
A first speed predictor v based on the segment end point p,i And the initial time-of-flight prediction value
Calculating a first rate of change of velocity from the kinetic equation of the movement of the aircraft centroid>
Comprising the following steps:
according to the first speed predictive value v p,i And the initial time-of-flight prediction value
Correcting the sight inclination angle and the sight deflection angle of the current segment to respectively obtain a first corrected sight inclination angle theta Lp,i And a first corrected line-of-sight offset angle ψ Lp,i ；
If the current segment is in the turning segment, then according to formula y p,i ＝-D tc,i+1 sin(θ Lp,i ) Calculating a first corrected ground height y p,i The method comprises the steps of carrying out a first treatment on the surface of the If the current segment is in a straight line segment, then according to formula y p,i ＝-L i+1 sin(θ Lp,i ) Calculating a first corrected ground height y p,i The method comprises the steps of carrying out a first treatment on the surface of the Wherein D is tc,i+1 Representing the target distance of the starting point of the i+1 segment, L i+1 Representing the rest straight-line segment course of the starting point of the i+1 segment;
based on the first corrected line of sight inclination angle theta Lp,i First corrected line-of-sight offset angle ψ Lp,i And a first speed predictive value v p,i Calculating the components of each coordinate axis of the first speed vector in the base reference coordinate system; calculating a first corrected ballistic inclination angle theta based on the components of each coordinate axis of the first velocity vector in the base reference coordinate system p,i ；
Based on the first speed predictive value v p,i First corrected ground height y p,i First corrected ballistic tilt angle theta p,i Calculating a first speed change rate according to a kinetic equation of the mass center motion of the aircraft
According to the first speed predictive value v p,i And the initial time-of-flight prediction value
Correcting the sight inclination angle and the sight deflection angle of the current segment to respectively obtain a first corrected sight inclination angle theta Lp,i And a first corrected line-of-sight offset angle ψ Lp,i Comprising:
correcting the sight inclination angle of the current segment according to the following formula to obtain a first corrected sight inclination angle theta Lp,i ：
If the current segment is in the turning segment, according to
Calculating the initial gaze tilt rate +.>
And a first corrected gaze inclination rate of change +>
If the current segment is in the straight line segment, then according to
Calculating the initial gaze tilt rate +.>
And a first corrected gaze inclination rate of change +>
According to the formula
Obtaining a first corrected sight inclination angle theta Lp,i ；
Correcting the sight line deflection angle of the current segment according to the following formula to obtain a first corrected sight line deflection angle phi Lp,i ：
If the current segment is in the turning segment, according to
Calculating the initial line of sight deflection change rate +.>
And a first corrected gaze angle change rate +>
If the current segment is in the straight line segment, then according to
Calculating the initial line of sight deflection change rate +. >
And a first corrected gaze angle change rate +>
According to the formula
Obtaining a first corrected sight offset angle psi Lp,i ；
State variable based on current segment start point and said current segment time-of-flight correction value
Predicting a state variable for a current segment end point, comprising:
initial rate of speed change according to current segment
And said current segment time of flight correction value +.>
According to the formula
Obtaining a second speed predicted value v of the current segment end point q,i ；
A second velocity predictor v based on the segment end point q,i And the current segment time of flight correction value
Calculating a second rate of change of velocity from the kinetic equation of the movement of the aircraft centroid>
For initial rate of speed change
And second rate of change of speed->
Averaging to obtain a second average correction speed +.>
Based on the second average corrected speed
Calculating a third speed predicted value of the end point of the current segment
The third speed predicted value is the predicted speed v of the ending point of the current segment i+1 ；
Line of sight inclination angle theta according to current segment start point L,i Speed v of end point of current segment i+1 And said current segment time of flight correction value
Calculating the sight inclination angle theta of the end point of the current segment L,i+1 The method comprises the steps of carrying out a first treatment on the surface of the Line-of-sight offset angle psi according to the current segment start point L,i Speed v of end point of current segment i+1 And said current segment time of flight correction value +.>
Calculating to obtain the sight offset angle psi of the end point of the current segment L,i+1 ；
If the current segment is in the turning segment, then according to formula y i+1 ＝-D tc,i+1 sinθ L,i+1 Calculating the ground height of the ending point of the current segment; if the current segment is in a straight line segment, then according to y i+1 ＝-L i+1 sinθ L,i+1 Calculating the ground height of the ending point of the current segment;
calculating the initial speed change rate of the current segment according to the dynamics equation of the mass center motion of the aircraft based on the state variable of the starting point of the current segment
Comprising the following steps:
based on the inclination angle theta of the sight line L,i Sight line deflection angle psi L,i Front tilt angle eta z,i Front deflection angle eta y,i And velocity module v i Calculating the components of the speed vector in each coordinate axis in the base reference coordinate system; calculating the component of each coordinate axis in the basic reference coordinate system based on the velocity vector to obtain the initial ballistic inclination angle theta of the current segment i ；
If the current segment is in the turning segment, the method is based on the formula
Calculating components of acceleration in a ballistic coordinate system; if the current segment is in the straight line segment, the method is according to the formula
Calculating components of acceleration in a ballistic coordinate system;
according to the ground height y i Interpolation to obtain the atmospheric density ρ and the sound speed aT, and Mach number is calculated according to the atmospheric density ρ and the sound speed aT 
And dynamic pressure->
Calculating the lift coefficient C according to the following formula Ld,i ：
F y ＝MT·g tc cosθ i +MT·a y,i
F z ＝MT·a z,i
Based on Mach and lift coefficient C Ld,i Calculating the attack angle command alpha by Newton iteration method c,i ；
Based on the Mach number Mach and the angle of attack command alpha c,i Calculating a resistance coefficient C according to the fitting formula D,i ；
According to the formula
The rate of change of the initial velocity is calculated,
wherein MT represents the mass of the aircraft, ST represents the reference area of the aircraft, g tc Representing the gravitational constant.
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