CN103903481A - Design method for threshold value and envelop wire of near-earth alarm system - Google Patents

Abstract

The invention provides a design method for a threshold value and an envelop wire of a near-earth alarm system, and aims at improving limitation in design of the threshold value and the envelop wire of the existing near-earth alarm systems. Probability of generation of earth collision danger in the flight process is calculated via comparison of landform height and flight track height on the basis of establishment of a landform height statistic model and a state transfer model; and the design method for the threshold value and the envelop wire of the near-earth alarm system is provided in combination with performance analysis of the near-earth alarm system so that timely and effective alarm information with low false alarm rate is provided for airplanes.

Description

A kind of threshold value of ground proximity warning system and envelope curve method for designing

Technical field

The present invention is a kind of threshold value and envelope curve method for designing that is applied to airborne ground proximity warning system, belongs to near-earth alarm field.

Background technology

Ground proximity warning system (Ground Proximity Warning System, GPWS) be the Aerial Electronic Equipment that is widely used in recent years dual-use aircraft, its major function is to judge that whether aircraft exists that to hit ground dangerous, hits ground accident thereby reduce controllable flight.In the time that ground danger is hit in aircraft existence, ground proximity warning system provides alarm instruction to crew, prevents from hitting the born accident in mountain and occurs, and effectively improves flight safety.

The core component of near-earth alarm is that alarm is calculated, and the information such as the aircraft position providing according to Airborne Interface Equipment, carry out alarm calculating, with alarm threshold and the envelope curve comparison set, judge whether aircraft exists to hit ground danger, and then provides various alarms and indicate.The performance quality of ground proximity warning system is mainly the design of alarm calculating and alarm threshold, for the near-earth situation of current aircraft, provides timely, suitable alarm.

For the performance of ground proximity warning system, need to carry out design and optimization to alarm threshold and envelope curve, but owing to being designed into the complicated variety of Terrain Elevation, alarm threshold and envelope curve design caused to certain difficulty.The domestic correlation technique research that has ground proximity warning system threshold design, but be to be mostly based upon on the basis of a large amount of repetition l-G simulation tests under different terrain data, process is loaded down with trivial details, complicated and time consumption, is not easy to real-time envelope curve modulation in the threshold value of diversified type ground proximity warning system and envelope curve design and practical flight process etc.

Summary of the invention

The object of the invention is to improve the limitation of existing ground proximity warning system threshold value and envelope curve design, setting up on the statistical model of Terrain Elevation and the basis of state transition model, by the comparison of Terrain Elevation and flight path height, calculate the probability that hits the dangerous generation in ground in flight course; In conjunction with the performance evaluation of ground proximity warning system, provide a kind of threshold value and envelope curve method for designing of ground proximity warning system, for aircraft provides timely and effective, the lower warning information of the alert rate of mistake.

To achieve these goals, technical scheme of the present invention is: a kind of threshold value of ground proximity warning system and envelope curve method for designing, it is characterized in that the method comprises the following steps: A, flight track modeling: utilize the current position of aircraft and velocity information, response time to pilot and aircraft pull-up process are carried out modeling, calculate the flight path information of aircraft escape flight after reporting to the police; The statistical property modeling of B, landform: Terrain Elevation itself possesses markov characteristic, utilizes the auto-correlation function characteristics matching process of Markov model and actual landform data, directly adopts Markov model to carry out modeling to different terrain type; The markov state transitions modeling of C, landform: the Terrain Elevation of certain area coverage is divided into n state [y ₀, y ₁..., y _n], utilize the Markov property of Terrain Elevation can calculate t moment height state y _ttransfer to t+1 moment height state y _t+1probability, set up the state-transition matrix of Terrain Elevation

wherein, p _ij=P (y _t+1=y _j| y _t=y _i), i, j ∈ 1 ... n, y _ifor the height state in n moment, y _jfor the height state in n+1 moment, calculate the state probability vector of Terrain Elevation after the state transitions in n moment; D, in flight course, obtain the height of t moment aircraft according to calculating, find the state of this moment Terrain Elevation higher than aircraft altitude, these height shape probability of states are sued for peace, obtain collision probability of state; For the situation of no alarm, the normal flight path of aircraft is carried out to emulation, the no alarm situation probability bumping of getting off the plane can be obtained, thereby the alert rate of mistake of ground proximity warning system can be calculated; For the situation that has alarm, aircraft escape flight path is carried out to emulation, the alarm situation probability bumping of getting off the plane can be obtained, thereby the successful alarm rate of ground proximity warning system can be calculated; According to above-mentioned simulation calculation, can obtain the relation curve of the alert rate of mistake and successful alarm rate and different starting condition, i.e. the performance curve of ground proximity warning system; E, relation curve according to the alert rate of mistake and successful alarm rate with different starting condition, find the optimal benefit of ground proximity warning system performance, and low, the successful alarm rate of by mistake alert rate is high, and while obtaining certain fall off rate, the warning of optimum highly; Report to the police highly according to the optimum of different fall off rates, obtain a series of alarm threshold points of system, realize the design of alarm envelope curve.

Wherein, in steps A, after reporting to the police, the flight path information of aircraft escape flight is: t < t _yctime, h=h ₀+ v ₀sin θ ₀t; t _yc< t < t _yc+ t _1qtime, $h=h_0+v_0*{\sin \mathrm{\&theta;}}_0*t_{\mathrm{yc}}+{\&Integral;}_{t_{\mathrm{yc}}}^t(v_0*\sin ({\mathrm{\&theta;}}_0+\stackrel{\&CenterDot;}{\mathrm{\&theta;}}(\mathrm{\&tau;}-t_{\mathrm{yc}})))\mathrm{d\&tau;};$ T > t _yc+ t _1qtime,

$h=h_0+v_0*{\sin \mathrm{\&theta;}}_0*t_{\mathrm{yc}}+{\&Integral;}_{t_{\mathrm{yc}}}^{t_{\mathrm{yc}}+t_{\mathrm{lq}}}(v_0*\sin ({\mathrm{\&theta;}}_0+\stackrel{\&CenterDot;}{\mathrm{\&theta;}}(\mathrm{\&tau;}-t_{\mathrm{yc}})))\mathrm{d\&tau;}+v_0*{\sin \mathrm{\&theta;}}_t*$

$(t-t_{\mathrm{yc}}-t_{\mathrm{lq}})$

, wherein, t is the flight time, v ₀for initial flying speed, θ ₀for initial flight-path angle, l ₀initial level distance, h ₀for elemental height, t _ycfor pilot's response time, t _1qfor the aircraft pull-up time,

flight-path angle rate of change during for aircraft pull-up, θ _τfor the flight-path angle of aircraft pull-up after finishing.

Wherein, in step B and C, in flight track section, one dimension Terrain Elevation is carried out to modeling as follows:

Y _n+1=e ^-βy _n+ ξ _n, its average is 0, variance is σ ², ξ _nobey

normal distribution;

Thereby the transition probability obtaining between each state of Terrain Elevation can be expressed by the form of state-transition matrix:

wherein, transition probability p _ij(n) represent the n moment by i state transitions to j shape probability of state, $p_{\mathrm{ij}}\left(n\right)={\&Integral;}_{h_{n+1}-\mathrm{\&Delta;h}/2}^{h_{n-1}+\mathrm{\&Delta;h}/2}\frac{1}{\sqrt{{2\mathrm{\&pi;\&sigma;}}^2(1-e^{-2\mathrm{\&beta;}})}}\&CenterDot;e^{\frac{{(y-e^{-{\mathrm{\&beta;}}_{h_n}})}^2}{{2\mathrm{\&sigma;}}^2(1-e^{-2\mathrm{\&beta;}})}}\mathrm{dy},$ Wherein, h _nfor shifting elemental height state, h _n+1for the height state that diverts the aim, Δ h is the height interval of a landform state, the original state probability vector y of given Terrain Elevation ₀, after the state transitions in n moment, the state probability vector of Terrain Elevation is as follows: y _n=T _n-1t _n-2t ₀y ₀, obtain after the state probability vector of n moment Terrain Elevation, can calculate the probability that aircraft collision occurs.

The present invention starts with from the alarm performance demand of ground proximity warning system, based on the Markov property of Terrain Elevation, carry out the Markov state transitions modeling of Terrain Elevation, in conjunction with normal flight flight path and the escape flight flight path model of aircraft, successful alarm rate and the alert rate of mistake under different initial fall off rates and Initial Flight Level condition are provided, obtain alarm threshold point by selecting system optimum performance income point, and then carry out the design of alarm envelope curve, improve the alarm performance of ground proximity warning system.For different type of airplanes and feature, the different demand such as terrain feature type, different flight characteristics, utilize the method in the present invention, by changing different condition setting, all can realize the design of alarm threshold and envelope curve, its design result can adapt to complicated and diversified actual user demand, and the present invention has very strong engineering using value.

Figure of description

Fig. 1 is the schematic diagram of the threshold design method based on a large amount of statistical tests.

Fig. 2 is the schematic diagram of the threshold design method based on markov state transitions process.

Fig. 3 is normal flight flight path and escape flight flight path schematic diagram.

Fig. 4 is the markov state transitions process schematic diagram of Terrain Elevation state.

Fig. 5 is the successful alarm rate and the alert rate relation curve of mistake of ground proximity warning system.

Fig. 6 is the alert rate of successful alarm rate, mistake and the flight parameter relation curve of ground proximity warning system.

Fig. 7 is the schematic diagram of alarm threshold point and alarm envelope.

Embodiment

Traditional ground proximity warning system threshold value and envelope curve design are to be based upon on the basis of a large amount of repetition l-G simulation tests under different terrain data, as shown in fig. 1.In each l-G simulation test, terrain information is set up at random by stochastic process, and test findings has some limitations and one-sidedness.In the time of new product envelope curve design, or in some particular surroundings or condition situation, need to modulate envelope curve time, need to repeat above-mentioned a large amount of l-G simulation tests, the design of alarm envelope curve is comparatively complicated loaded down with trivial details, be not easy to the accommodation of envelope curve, be not also suitable for the real-time envelope curve modulation in actual dynamic flying process simultaneously.

The present invention improves on the basis of the performance evaluation of ground proximity warning system, by systematic modeling method, adopts the state transition model based on Markov chain, and the alarm performance of ground proximity warning system is analyzed.And utility analysis result, further calculate and the alarm threshold of establishing ground proximity warning system, complete the design of alarm envelope curve, its ultimate principle is as shown in Figure 2.

In order to complete threshold value and the envelope curve design of ground proximity warning system, need to complete following work.

A, flight track modeling procedure

Set up flight path model, comprise the escape locus model after normal trace model and the warning in alarm free situation, as shown in Figure 3.

In alarm-free situation, flight track is normal flight track, supposes that aircraft does not move other maneuvering flight programs in this process, and aircraft carries out uniform motion, and aircraft trace is straight line, its horizontal range be highly shown below:

h＝h ₀+v ₀·sinθ ₀·t (1)

l＝l ₀+v ₀·cosθ ₀·t

Wherein, t is the flight time, v ₀for initial flying speed, θ ₀for initial flight-path angle (downwards for just), l ₀for initial level distance, h ₀for elemental height.

For escape flight track, suppose pull-up previous crops uniform motion, when pull-up, do at the uniform velocity pitching, while being pulled up to certain flight-path angle, stop pitching, restart uniform motion, its horizontal range is with highly as follows.

when pilot not to report to the police respond, aircraft still maintains rectilinear motion, its horizontal range be highly shown below:

h＝h ₀+v ₀·sinθ ₀·t (2)

l＝l ₀+v ₀·cosθ ₀·t

when pilot responds to reporting to the police, after aircraft is implemented pull-up and handled, aircraft track direction gradually becomes upwards flight by downward flight, its horizontal range be highly shown below:

$h=h_0+v_0*{\sin \mathrm{\&theta;}}_0*t_{\mathrm{yc}}+{\&Integral;}_{t_{\mathrm{yc}}}^t(v_0*\sin ({\mathrm{\&theta;}}_0+\stackrel{\&CenterDot;}{\mathrm{\&theta;}}(\mathrm{\&tau;}-t_{\mathrm{yc}})))\mathrm{d\&tau;}---\left(3\right)$

$l=l_0+v_0*{\cos \mathrm{\&theta;}}_0*t_{\mathrm{yc}}+{\&Integral;}_{t_{\mathrm{yc}}}^t(v_0*\cos ({\mathrm{\&theta;}}_0+\stackrel{\&CenterDot;}{\mathrm{\&theta;}}(t-t_{\mathrm{yc}})))\mathrm{d\&tau;}$

when aircraft is pulled up to after certain flight-path angle, complete pull-up motor-driven, aircraft transfers rectilinear flight to, its horizontal range be highly shown below:

$h=h_0+v_0*{\sin \mathrm{\&theta;}}_0*t_{\mathrm{yc}}+{\&Integral;}_{t_{\mathrm{yc}}}^{t_{\mathrm{yc}}+t_{\mathrm{lq}}}(v_0*\sin ({\mathrm{\&theta;}}_0+\stackrel{\&CenterDot;}{\mathrm{\&theta;}}(\mathrm{\&tau;}-t_{\mathrm{yc}})))\mathrm{d\&tau;}+v_0*$

$*(t-t_{\mathrm{yc}}-t_{\mathrm{lq}})$

$l=l_0+v_0*{\cos \mathrm{\&theta;}}_0*t_{\mathrm{yc}}+{\&Integral;}_{t_{\mathrm{yc}}}^{t_{\mathrm{yc}}+t_{\mathrm{lq}}}(v_0*\cos ({\mathrm{\&theta;}}_0+\stackrel{\&CenterDot;}{\mathrm{\&theta;}}(t-t_{\mathrm{yc}})))\mathrm{d\&tau;}+v_0*---\left(4\right)$

$*(t-t_{\mathrm{yc}}-t_{\mathrm{lq}})$

Wherein, t _ycfor pilot's response time, t _1qfor the aircraft pull-up time,

flight-path angle rate of change during for aircraft pull-up, θ _τfor the flight-path angle of aircraft pull-up after finishing.

Above-mentioned flight path is simplified sporting flying in deriving, if consider flight authenticity, can not simplify, equally can be according to flithg rules, and carry out the parameter of compound movement and derive and calculate, obtain normal flight flight path and the escape flight path of aircraft.

The statistical property modeling procedure of B, landform

In Terrain Elevation is described, adopt Markov model to carry out modeling to Terrain Elevation.

Landform refers to that the height of earth surface rises and falls, and is continuous geometric curved surfaces, and its height change characteristic meets Gauss-Markov property.First according to the fluctuating quantity of landform, landform is classified.Terrain Elevation span value in 60 nautical miles is divided into 5 intervals, accordingly landform is divided into 5 kinds dissimilar, as shown in table 1.

Table 1 terrain type

The advantage of this sorting technique is that its mode classification and landform region have nothing to do, only relevant with the feature of landform itself, is therefore applicable to worldwide all landform.

Because Terrain Elevation itself possesses Markov property, after therefore landform being classified, can directly adopt Markov model to carry out modeling to different terrain.In near-earth alarm emulation, only aircraft track institute collision situation is planar analyzed, therefore need to set up the one dimension relief block in this section.

Average is 0, variance is σ ²markov model as shown in formula (5).

y _n+1＝e ^-βy _n+ξ _n (5)

Wherein, ξ _nobey

normal distribution.

For dissimilar landform, the key of terrain modeling is model parameter.In real terrain database, gather the data point of some, sampled data is carried out to matching and feature extraction, can obtain the correlation parameter in model, as shown in table 2.

The model parameter of table 2 different terrain type

The markov state transitions modeling procedure of C, landform

In the description of Terrain Elevation state, adopt Markov chain to set up the transfer process of Terrain Elevation state.

Initial Terrain Elevation be divided into m interval, according to terrain type difference, each height interval value not etc., Terrain Elevation correspondence m state,

$x_n=\left[\begin{array}{c}{h}_m\\ h_{m-1}\\ .\\ .\\ .\\ h_1\end{array}\right]---\left(6\right)$

The state vector y of definition _nbe illustrated in moment n, x _nin the probability of each state in some height values:

$y_n=\left[\begin{array}{c}{p}_m\left(n\right)\\ p_{m-1}\left(n\right)\\ .\\ .\\ .\\ p_1\left(n\right)\end{array}\right]---\left(7\right)$

Transition probability between each state of Terrain Elevation can be expressed by the form of state-transition matrix:

Wherein, transition probability p _ij(n) represent the n moment by i state transitions to j shape probability of state.

$p_{\mathrm{ij}}\left(n\right)={\&Integral;}_{h_{n+1}-\mathrm{\&Delta;h}/2}^{h_{n-1}+\mathrm{\&Delta;h}/2}\frac{1}{\sqrt{{2\mathrm{\&pi;\&sigma;}}^2(1-e^{-2\mathrm{\&beta;}})}}\&CenterDot;e^{\frac{{(y-e^{-{\mathrm{\&beta;}}_{h_n}})}^2}{{2\mathrm{\&sigma;}}^2(1-e^{-2\mathrm{\&beta;}})}}\mathrm{dy}---\left(9\right)$

Wherein, h _nbe the height of i state for shifting elemental height state, h _n+1for the height state that diverts the aim, the i.e. height of j state, Δ h is the height interval of a landform state.

The use of Markovian process,, with the variation of flight course, follows the tracks of the variation of Terrain Elevation.From initial Terrain Elevation, apply above-mentioned state-transition matrix, can calculate the probability of landform in a certain certain height.Be the original state probability vector y of given Terrain Elevation ₀, after the state transitions in n moment, the state probability vector of Terrain Elevation is as follows:

y _n＝T _n-1T _n-2…T ₀y ₀ (10)

Obtain after the state probability vector of n moment Terrain Elevation, can calculate the probability that aircraft collision occurs.As shown in Figure 4, once Terrain Elevation state is transferred to the state higher than flight path, to cause collision, these state transitions will merge to and shift as collision probability of state, hit the probability of ground accident, therefore n moment aircraft is all Terrain Elevation state probability sums higher than aircraft altitude in collision probability of state.In the n moment, from the state probability vector of above-mentioned Terrain Elevation, find Terrain Elevation to exceed all states of aircraft trace, by its probability summation be this moment hit the probability of accident.

Any Terrain Elevation state, once exceed aircraft altitude, will cause collision, be marked as collision state, and collision has occurred for aircraft and landform, and other Terrain Elevation states are non-collision state.All Terrain Elevations are unified and are labeled as a collision status higher than the state of aircraft altitude, and this state is absorbing state, once Terrain Elevation enters this state, this state will remain collision state, no longer shift.

The performance evaluation step of D, ground proximity warning system

Success alarm and misunderstanding are the important performance indexes of ground proximity warning system.If etching system sends alarm when t, and within the scope of certain hour, aircraft hits ground accident, and the alarm in t moment is successful alarm; If etching system does not send alarm when t, within the scope of certain hour, aircraft does not hit ground accident yet, if send alarm in the t moment so, this alarm is mistake police.

Adopt successful alarm rate P(SA) with the alert rate P of mistake (UA), ground proximity warning system is carried out to quantitative Performance Evaluation, provide successfully the definition of alarm probability and the alert rate of mistake below:

A) successful alarm rate P (SA)=1-P (send after alarm, within the scope of certain time interval T, aircraft still hits the probability of ground accident)

B) the alert rate P of mistake (UA)=1-P (do not send alarm, within the scope of certain time interval T, aircraft hits the probability of ground accident)

A key index in this definition is time range T, and it is corresponding to best alarm time.Best alarm time is necessary for pilot's response delay, the aircraft pull-up safety time that retains enough time surplus such as motor-driven.Time range T is less, and the degree that aircraft faces a danger is just higher, arrange and notice that the best alarm time of level and alarm level is respectively 60 seconds and 30 seconds, if in 60s aircraft normal flight and do not hit time, identification alarm is now unnecessary.

The elemental height of given initial time aircraft and speed, can obtain normal flight flight path and the escape flight flight path of aircraft, on this basis, carries out following performance calculating.

A) given initial time aircraft is in each height shape probability of state, according to the normal flight flight path of aircraft and the state transition model of system, can obtain in no alarm situation, t moment aircraft is in non-collision probability of state, at initial time aircraft without alarm, this probability is the alert rate of mistake.

B) given initial time aircraft is in each height shape probability of state, according to the escape flight flight path of aircraft and the state transition model of system, can obtain and have in alarm situation, t moment aircraft is in non-collision probability of state, i.e. the probability of system success alarm.

The threshold value of E, ground proximity warning system and envelope curve design procedure

The initial position of given aircraft, by changing the simulated conditions of initial velocity, can obtain successful alarm rate and the alert rate of mistake of system under different initial velocity conditions, obtain the warning system performance curve shown in Fig. 5 and Fig. 6, be the relation curve of successful alarm rate and the alert rate of mistake, and the relation curve of successful alarm rate, the alert rate of mistake and initial velocity.

In order to make near-earth alarm performance the highest, need system success alarm probability high, the alert rate of mistake is low, obtains the optimal benefit of alarm, and as shown in the optimal benefit line in the ideal value point of Fig. 5 and Fig. 6, the alarm threshold of selecting meets the following conditions:

P(SA)-P(UA)＝(P(SA)-P(UA)) _max (12)

At the optimal benefit place of alarm performance, can obtain now corresponding system starting condition speed (elemental height and speed), when aircraft is during at this initial position, if when speed reaches this speed restriction condition, system is sent alarm, obtain the most at last best alarm performance, obtained a best alarm threshold (v ₁, h ₁).

Change starting condition setting, can repeat above-mentioned emulation, obtain a series of best alarm threshold (v ₂, h ₂), (v ₃, h ₃) ..., (v _n, h _n), this group alarm threshold point can form the best alarm envelope of warning system.

Claims (4)

1. the threshold value of a ground proximity warning system and envelope curve method for designing, it is characterized in that the method comprises the following steps: A, flight track modeling: utilize the current position of aircraft and velocity information, response time to pilot and aircraft pull-up process are carried out modeling, calculate the flight path information of aircraft escape flight after reporting to the police; The statistical property modeling of B, landform: utilize the auto-correlation function characteristics matching process of Markov model and actual landform data, directly adopt Markov model to carry out modeling to different terrain type; The markov state transitions modeling of C, landform: the Terrain Elevation of certain area coverage is divided into n state [y ₀, y ₁..., y _n], utilize the Markov property of Terrain Elevation can calculate t moment height state y _ttransfer to t+1 moment height state y _t+1probability, set up the state-transition matrix of Terrain Elevation

wherein, p _ij=P (y _t+1=y _j| y _t=y _i), i, j ∈ 1 ... n, y _ifor the height state in n moment, y _jfor the height state in n+1 moment, calculate the state probability vector of Terrain Elevation after the state transitions in n moment; D, in flight course, obtain the height of t moment aircraft according to calculating, find the state of this moment Terrain Elevation higher than aircraft altitude, a little height shape probability of states are sued for peace, obtain collision probability of state; For the situation of no alarm, the normal flight path of aircraft is carried out to emulation, the no alarm situation probability bumping of getting off the plane can be obtained, thereby the alert rate of mistake of ground proximity warning system can be calculated; For the situation that has alarm, aircraft escape flight path is carried out to emulation, the alarm situation probability bumping of getting off the plane can be obtained, thereby the successful alarm rate of ground proximity warning system can be calculated; According to above-mentioned simulation calculation, can obtain the relation curve of the alert rate of mistake and successful alarm rate and different starting condition, i.e. the performance curve of ground proximity warning system; E, relation curve according to the alert rate of mistake and successful alarm rate with different starting condition, find the optimal benefit of ground proximity warning system performance, and low, the successful alarm rate of by mistake alert rate is high, and while obtaining certain fall off rate, the warning of optimum highly; Report to the police highly according to the optimum of different fall off rates, obtain a series of alarm threshold points of system, realize the design of alarm envelope curve.

2. method for designing according to claim 1, is characterized in that in step B and C, in flight track section, one dimension Terrain Elevation is carried out to modeling as follows: y _n+1=e ^-βy _n+ ξ _n, its average is 0, variance is σ ², ξ _nobey

normal distribution; Thereby the transition probability obtaining between each state of Terrain Elevation can be expressed by the form of state-transition matrix:

wherein, transition probability p _ij(n) represent the n moment by i state transitions to j shape probability of state,

wherein, h _nfor shifting elemental height state, h _n+1for the height state that diverts the aim, Δ h is the height interval of a landform state, the original state probability vector y of given Terrain Elevation ₀, after the state transitions in n moment, the state probability vector of Terrain Elevation is as follows: y _n=T _n-1t _n-2t ₀y ₀, obtain after the state probability vector of n moment Terrain Elevation, can calculate the probability that aircraft collision occurs.

3. method for designing according to claim 1, it is characterized in that in step D, adopt successful alarm rate P (SA) and the alert rate P of mistake (UA) to carry out quantitative Performance Evaluation to ground proximity warning system, given initial time aircraft is in each height shape probability of state, according to the normal flight flight path of aircraft and the state transition model of system, can obtain in no alarm situation, t moment aircraft is in non-collision probability of state, at initial time aircraft without alarm, this probability is the alert rate of mistake; Given initial time aircraft, in each height shape probability of state, according to the escape flight flight path of aircraft and the state transition model of system, can obtain and have in alarm situation, and t moment aircraft is in non-collision probability of state, i.e. the probability of system success alarm.

4. method for designing according to claim 1, it is characterized in that in step e, for certain Initial Flight Level and speed, its best alarm threshold is the optimal benefit point with the difference maximum of the alert rate of mistake corresponding to successful alarm rate, change starting condition setting, obtain a series of best alarm threshold, this group alarm threshold point can form the best alarm envelope of warning system.

Images