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 Threshold and Envelope Design Method for Earth Proximity Warning System

technical field

The invention relates to a threshold and envelope design method applied to an airborne ground proximity warning system, which belongs to the field of ground proximity warning. the

Background technique

Ground proximity warning system (Ground Proximity Warning System, GPWS) is an avionics device widely used in military and civil aircraft in recent years. When the aircraft is in danger of colliding with the ground, the ground proximity warning system provides warning instructions to the crew to prevent the accident of crashing into the mountain and effectively improving flight safety. the

The core component of the ground proximity warning is the warning calculation, that is, according to the aircraft position and other information provided by the airborne cross-linking equipment, the warning calculation is carried out, and compared with the set warning threshold and the envelope, it is judged whether there is a risk of the plane hitting the ground, and then given Issue various warning indications. The performance of the ground proximity warning system mainly lies in the warning calculation and the design of the warning threshold, that is, to provide timely and appropriate warnings for the current aircraft's ground proximity situation. the

For the performance of the ground proximity warning system, it is necessary to design and optimize the warning threshold and envelope, but due to the complexity and diversity of the design to the terrain height, the design of the warning threshold and envelope is difficult. There are related technical researches on the threshold design of the Earth Proximity Warning System in China, but most of them are based on a large number of repeated simulation tests under different terrain data. and envelope design, as well as real-time envelope modulation during actual flight, etc. the

Contents of the invention

The purpose of the present invention is to improve the limitations of the existing ground proximity warning system threshold and envelope design, on the basis of establishing a statistical model of terrain height and a state transition model, by comparing terrain height and track height, calculate the Probability of ground collision risk; combined with performance analysis of ground proximity warning system, a threshold and envelope design method of ground proximity warning system is provided to provide timely and effective warning information with low false alarm rate for aircraft. the

其中，p_ij＝P(y_t+1＝y_j|y_t＝y_i)，i，j∈1…n，y_i为n时刻的高度状态，y_j为n+1时刻的高度状态，计算经过n时刻的状态转移后地形高度的状态概率向量；D、在飞行过程中，根据计算获取t时刻飞机的高度，找到该时刻地形高度高于飞机高度的状态，对这些高度状态的概率进行求和，即获得碰撞态的概率；对于无告警的情况，对飞机正常航迹进行仿真，可以获得无告警情况下飞机发生碰撞的概率，从而可以计算近地告警系统的误警率；对于有告警的情况，对飞机逃逸航迹进行仿真，可以获得有告警情况下飞机发生碰撞的概率，从而可以计算近地告警系统的成功告警率；根据上述仿真计算，可以获得误警率和成功告警率与不同初始条件的关系曲线，即近地告警系统的性能曲线；E、根据误警率和成功告警率与不同初始条件的关系曲线，寻找近地告警系统性能的最佳收益，即误警率低、成功告警率高，获得一定下降速率时最优的报警高度；根据不同下降速率的最优报警高度，获得系统的一系列告警阈值点，实现告警包线设计。  In order to achieve the above object, the technical solution of the present invention is: a threshold and envelope design method of the ground proximity warning system, characterized in that the method includes the following steps: A, flight track modeling: using the current position and speed of the aircraft information, modeling the pilot’s response delay time and the aircraft’s pull-up process, and calculating the track information of the aircraft’s escape flight after the alarm; B. Statistical modeling of the terrain: the terrain height itself has Markov characteristics, and the Markov The autocorrelation function feature matching method between the model and the actual terrain data directly uses the Markov model to model different terrain types; C, Markov state transition modeling of terrain: divide the terrain height of a certain area into n The state [y ₀ , y ₁ ,..., y _n ], using the Markov property of terrain height, can calculate the probability that the height state y _t at time t will transfer to the height state y t+1 at time t ₊₁ , and establish the state of terrain height transfer matrix

Among them, p _ij =P(y _t+1 =y _j |y _t =y _i ), i, j∈1...n, y _i is the height state at time n, y _j is the height state at time n+1, Calculate the state probability vector of the terrain height after the state transition at the n moment; D, in the flight process, obtain the altitude of the aircraft at the t moment according to the calculation, find the state that the terrain height is higher than the aircraft altitude at this moment, and carry out the probability of these altitude states The sum is to obtain the probability of the collision state; for the case of no warning, the simulation of the normal track of the aircraft can obtain the probability of the collision of the aircraft without the warning, so that the false alarm rate of the ground proximity warning system can be calculated; In the case of an alarm, the aircraft escape track is simulated to obtain the probability of an aircraft collision in the event of an alarm, so that the successful alarm rate of the ground proximity warning system can be calculated; according to the above simulation calculation, the false alarm rate and the successful alarm rate can be obtained The relationship curve with different initial conditions, that is, the performance curve of the Earth Proximity Warning System; E. According to the relationship curve between the false alarm rate and the successful alarm rate and different initial conditions, find the best benefit of the performance of the Earth Proximity Warning System, that is, the false alarm rate Low, high success alarm rate, obtain the optimal alarm height at a certain rate of descent; according to the optimal alarm height of different rate of descent, obtain a series of alarm threshold points of the system to realize the design of the alarm envelope.

Wherein in step A, the track information of the escape flight after the alarm is: when t<t _yc , h=h ₀ +v ₀ sinθ ₀ ·t; when t _yc <t<t _yc +t _1q , $h=h_0+v_0*{\sin \mathrm{\&theta;}}_0*t_{\mathrm{yc}}+{\&Integral;}_{t_{\mathrm{yc}}}^t(v_0*\sin ({\mathrm{\&theta;}}_0+\stackrel{\&Center\; Dot;}{\mathrm{\&theta;}}(\mathrm{\&tau;}-t_{\mathrm{yc}})))\mathrm{d\&tau;};$ When t＞t _yc +t _1q ,

$\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; yc</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; \&Integral;</span>}_{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; yc</span>}}}^{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; yc</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; lq</span>}}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; yc</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d\&tau;</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; *</span>$

$<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; yc</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; lq</span>}}<span\; class="notranslate">\; )</span>$

为飞机拉起时的航迹角变化率，θ_τ为飞机拉起结束后的航迹角。  , where, t is the flight time, v ₀ is the initial flight speed, θ ₀ is the initial track angle, l ₀ is the initial horizontal distance, h ₀ is the initial height, t _yc is the pilot response delay time, t _1q is the aircraft pull-up time ,

is the change rate of the track angle when the aircraft pulls up, and θ _τ is the track angle after the aircraft pulls up.

Among them, in steps B and C, the one-dimensional terrain height is modeled in the flight path profile as follows:

的正态分布；  y _n+1 ＝e ^-β y _n +ξ _n , its mean value is 0, variance is σ ² , ξ _n obeys

normal distribution of

Thus, the transition probability between the various states of terrain height can be expressed in the form of state transition matrix:

其中，转移概率p_ij(n)表示n时刻由i状态转移到j状态的概率， $p_{\mathrm{ij}}\left(n\right)={\&Integral;}_{h_{n+1}-\mathrm{\&Delta;h}/2}^{h_{n-1}+\mathrm{\&Delta;h}/2}\frac{1}{\sqrt{{2\mathrm{\&pi;\&sigma;}}^2(1-e^{-2\mathrm{\&beta;}})}}\&CenterDot;e^{\frac{{(y-e^{-{\mathrm{\&beta;}}_{h_n}})}^2}{{2\mathrm{\&sigma;}}^2(1-e^{-2\mathrm{\&beta;}})}}\mathrm{dy},$ 其中，h_n为转移初始高度状态，h_n+1为转移目标高度状态，Δh为一个地形状态的高度区间，给定地形高度的初始状态概率向量y₀，经过n时刻的状态转移后，地形高度的状态概率向量如下：y_n＝T_n-1T_n-2…T₀y₀，获取n时刻地形高度的状态概率向量后，即可计算飞机碰撞发生的概率。 

Among them, the transition probability p _ij (n) represents the probability of transitioning from state i to state j at time n, $p_{\mathrm{ij}}\left(\mathrm{no}\right)={\&Integral;}_{h_{\mathrm{no}+1}-\mathrm{\&Delta;h}/2}^{h_{\mathrm{no}-1}+\mathrm{\&Delta;h}/2}\frac{1}{\sqrt{{2\mathrm{\&pi;\&sigma;}}^2(1-e^{-2\mathrm{\&beta;}})}}\&Center\; Dot;e^{\frac{{(\mathrm{the\; y}-e^{-{\mathrm{\&beta;}}_{h_{\mathrm{no}}}})}^2}{{2\mathrm{\&sigma;}}^2(1-e^{-2\mathrm{\&beta;}})}}\mathrm{dy},$ Among them, h _n is the initial height state of the transfer, h _n+1 is the transfer target height state, Δh is the height range of a terrain state, given the initial state probability vector y ₀ of the terrain height, after the state transfer at time n, the terrain The state probability vector of altitude is as follows: y _n =T _n-1 T _n-2 ...T ₀ y ₀ , after obtaining the state probability vector of terrain height at time n, the probability of aircraft collision can be calculated.

The present invention starts from the warning performance requirements of the ground proximity warning system, and based on the Markov property of the terrain height, carries out the Markov state transition modeling of the terrain height, and combines the normal flight track and escape flight track models of the aircraft to provide different The successful alarm rate and false alarm rate under the initial descent rate and initial flight altitude conditions, the alarm threshold point is obtained by selecting the best performance gain point of the system, and then the alarm envelope is designed to improve the alarm performance of the ground proximity warning system. For different aircraft types and characteristics, different terrain feature types, different flight characteristics, etc., using the method of the present invention, by changing different condition settings, the design of the warning threshold and envelope can be realized, and the design results can adapt to Complicated and diverse actual use requirements, the present invention has strong engineering application value. the

Attached to the manual

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

Fig. 2 is a schematic diagram of a threshold design method based on a Markov state transition process. the

Figure 3 is a schematic diagram of a normal flight path and an escape flight path. the

Fig. 4 is a schematic diagram of the Markov state transition process of terrain height state. the

Fig. 5 is the relationship curve between successful alarm rate and false alarm rate of the ground proximity warning system. the

Fig. 6 is the relation curve of successful warning rate, false warning rate and flight parameters of the ground proximity warning system. the

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

Detailed ways

The threshold and envelope design of the traditional ground proximity warning system is based on a large number of repeated simulation experiments under different terrain data, as shown in Figure 1. In each simulation test, terrain information is randomly established through a random process, and the test results have certain limitations and one-sidedness. In the design of a new product envelope, or in some special environments or conditions, when the envelope needs to be modulated, it is necessary to repeat the above-mentioned a large number of simulation tests. The design of the alarm envelope is complicated and cumbersome, and it is not convenient for the envelope Adaptive adjustment, also not suitable for real-time envelope modulation during actual dynamic flight. the

The invention improves on the basis of the performance analysis of the ground proximity warning system, and analyzes the warning performance of the ground proximity warning system by adopting a state transfer model based on a Markov chain through a systematic modeling method. And use the performance analysis results to further calculate and establish the alarm threshold of the ground proximity warning system, and complete the design of the alarm envelope. The basic principle is shown in Figure 2. the

In order to complete the threshold and envelope design of the ground proximity warning system, the following work needs to be completed. the

A. Flight path modeling steps

A flight trajectory model is established, including a normal trajectory model without an alarm and an escape trajectory model after an alarm, as shown in Figure 3. the

In the case of no alarm, the flight track is a normal flight track. Assuming that the aircraft does not run other maneuvering flight procedures during this process, that is, the aircraft moves at a constant speed, the aircraft track is a straight line, and its horizontal distance and altitude are shown in the following formula:

h＝h ₀ +v ₀ sinθ ₀ t (1)

l＝l ₀ +v ₀ ·cosθ ₀ ·t

Among them, t is the flight time, v ₀ is the initial flight speed, θ ₀ is the initial track angle (downward is positive), l ₀ is the initial horizontal distance, h ₀ is the initial height.

For the escape flight trajectory, it is assumed that it moves at a constant speed before pulling up, pitches at a constant speed when pulling up, stops pitching when pulling up to a certain track angle, and starts to move at a constant speed again. The horizontal distance and height are shown below. the

When the pilot does not respond to the alarm, the aircraft still keeps moving in a straight line, and its horizontal distance and altitude are shown in the following formula:

h＝h ₀ +v ₀ sinθ ₀ t (2)

l＝l ₀ +v ₀ ·cosθ ₀ ·t

当飞行员对报警作出响应，对飞机实施拉起操纵后，飞机航迹方向由向下飞行逐渐变为向上飞行，其水平距离与高度如下式所示： 

When the pilot responds to the alarm and pulls up the aircraft, the direction of the aircraft's flight path gradually changes from downward flight to upward flight, and its horizontal distance and altitude are shown in the following formula:

$\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; yc</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; \&Integral;</span>}_{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; yc</span>}}}^{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; yc</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d\&tau;</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

$\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; yc</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; \&Integral;</span>}_{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; yc</span>}}}^{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; yc</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d\&tau;</span>}$

当飞机拉起到一定航迹角后，即完成拉起机动，飞机转为直线飞行，其水平距离与高度如下式所示： 

When the aircraft pulls up to a certain track angle, the pull-up maneuver is completed, and the aircraft turns to fly in a straight line. The horizontal distance and height are shown in the following formula:

$\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; yc</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; \&Integral;</span>}_{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; yc</span>}}}^{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; yc</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; lq</span>}}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; yc</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d\&tau;</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; *</span>$

$<span\; class="notranslate">\; *</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; yc</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; lq</span>}}<span\; class="notranslate">\; )</span>$

$\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; yc</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; \&Integral;</span>}_{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; yc</span>}}}^{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; yc</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; lq</span>}}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; yc</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d\&tau;</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; *</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

$<span\; class="notranslate">\; *</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; yc</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; lq</span>}}<span\; class="notranslate">\; )</span>$

为飞机拉起时的航迹角变化率，θ_τ为飞机拉起结束后的航迹角。  Among them, t _yc is the pilot response delay time, t _1q is the aircraft pull-up time,

is the change rate of the track angle when the aircraft pulls up, and θ _τ is the track angle after the aircraft pulls up.

The above-mentioned flight trajectory derivation simplifies the flight movement. If the authenticity of the flight is considered, the simplification is not required. The parameters of the complex movement can also be derived and calculated according to the flight rules to obtain the normal flight trajectory and escape trajectory of the aircraft. the

B. Statistical characteristics modeling steps of terrain

In the terrain height description, the Markov model is used to model the terrain height. the

Terrain refers to the ups and downs of the earth's surface, which is a continuous geometric surface, and its height variation characteristics satisfy the Gauss-Markov property. First, the terrain is classified according to the degree of undulation of the terrain. Divide the terrain height span value within 60 nautical miles into 5 intervals, and accordingly divide the terrain into 5 different types, as shown in Table 1. the

Table 1 Terrain type

The advantage of this classification method is that its classification method has nothing to do with the terrain area, but only with the characteristics of the terrain itself, so it is applicable to all terrains in the world. the

Since the terrain height itself has Markov properties, after the terrain is classified, the Markov model can be directly used to model different terrains. In the ground proximity warning simulation, only the collision situation in the plane where the aircraft track is located is analyzed, so it is only necessary to establish a one-dimensional terrain model in the section. the

A Markov model with a mean of 0 and a variance of ^σ2 is shown in formula (5).

y _n+1 ＝e ^-β y _n +ξ _n (5)

的正态分布。  where ξ _n obeys

normal distribution of .

For different types of terrain, the key to terrain modeling lies in the model parameters. Collect a certain number of data points in the real terrain database, and perform fitting and feature extraction on the sampled data to obtain the relevant parameters in the model, as shown in Table 2. the

Table 2 Model parameters of different terrain types

C. Modeling steps of Markov state transition of terrain

In the description of terrain height state, the transfer process of terrain height state is established by using Markov chain. the

The initial terrain height is divided into m intervals. According to different terrain types, each height interval has different values, and the terrain height corresponds to m states.

${\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; =</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}\\ {\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\\ <span\; class="notranslate">\; .</span>\\ <span\; class="notranslate">\; .</span>\\ <span\; class="notranslate">\; .</span>\\ {\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

The defined state vector y _n represents the probability that each state is at a certain height value at time n, x _n :

${\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; =</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>\\ <span\; class="notranslate">\; .</span>\\ <span\; class="notranslate">\; .</span>\\ <span\; class="notranslate">\; .</span>\\ {\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

The transition probability between the various states of terrain height can be expressed in the form of state transition matrix:

Among them, the transition probability p _ij (n) represents the probability of transitioning from state i to state j at time n.

${\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; \&Integral;</span>}_{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&Delta;h</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}^{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&Delta;h</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\sqrt{{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;\&sigma;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&beta;</span>}}<span\; class="notranslate">\; )</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{\frac{{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&beta;</span>}}<span\; class="notranslate">\; )</span>}}\mathrm{<span\; class="notranslate">\; dy</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$

Among them, h _n is the initial height state of the transfer, that is, the height of state i, h _n+1 is the transfer target height state, that is, the height of state j, and Δh is the height range of a terrain state.

The use of a Markov process, which tracks changes in terrain height as the flight progresses. From the initial terrain height, the probability that the terrain is at a certain height can be calculated by applying the above state transition matrix. That is, given the initial state probability vector y ₀ of the terrain height, after the state transition at time n, the state probability vector of the terrain height is as follows:

y _n = T _n-1 T _n-2 ... T ₀ y ₀ (10)

After obtaining the state probability vector of terrain height at time n, the probability of aircraft collision can be calculated. As shown in Figure 4, once the terrain altitude state is transferred to a state higher than the track, it will lead to a collision, and these state transitions will be combined into the probability of transitioning to a collision state, that is, the probability of a ground collision accident. Therefore, the aircraft is in The probability of a collision state is the sum of the probabilities of all terrain altitude states above the aircraft altitude. That is, at time n, find all the states whose terrain height exceeds the trajectory of the aircraft from the state probability vector of the above terrain height, and sum their probabilities to obtain the probability of a ground collision accident at this moment. the

Any terrain height state, once exceeding the aircraft height, will cause a collision, that is, it is marked as a collision state, that is, the aircraft has collided with the terrain, and other terrain height states are non-collision states. All states where the terrain height is higher than the aircraft altitude are uniformly marked as a collision state, which is an absorbing state, that is, once the terrain height enters this state, the state will always remain in the collision state and no transfer will occur. the

D. Performance analysis steps of the ground proximity warning system

Successful warning and misinterpretation are important performance indicators of the ground proximity warning system. If the system issues an alarm at time t and the aircraft does not collide with the ground within a certain time range, then the alarm at time t is a successful alarm; if the system does not issue an alarm at time t, the plane does not collide with the ground within a certain time range accident, then if an alarm is issued at time t, the alarm is a false alarm. the

The successful alarm rate P(SA) and the false alarm rate P(UA) are used to quantitatively evaluate the performance of the ground proximity warning system. The definitions of the successful alarm probability and false alarm rate are given below:

a) Successful alert rate P(SA)=1-P (after the alert is issued, within a certain time T range, the probability that the aircraft still has a ground collision accident) 

b) False alarm rate P(UA)＝1-P (the probability of an aircraft crashing into a terrain accident within a certain time T range without issuing an alarm) 

A key metric in this definition is the time horizon T, which corresponds to the optimal alarm time. The optimal warning time must be a safe time with sufficient time margin for pilot reaction delay, aircraft pull-up maneuver and so on. The smaller the time range T, the higher the degree of danger faced by the aircraft. The optimal alarm time for setting the attention level and the warning level are 60 seconds and 30 seconds respectively, that is, if the aircraft is flying normally and does not hit the ground within 60 seconds, it is determined that at this time warnings are unnecessary. the

Given the initial altitude and speed of the aircraft at the initial moment, the normal flight path and escape flight path of the aircraft can be obtained, and on this basis, the following performance calculations are performed. the

a) Given the probability that the aircraft is in each altitude state at the initial time, according to the normal flight path of the aircraft and the state transition model of the system, the probability that the aircraft is in a non-collision state at time t without warning can be obtained, that is, at the initial time The aircraft does not need to alert, and this probability is the false alarm rate. the

b) Given the probability that the aircraft is in each altitude state at the initial moment, according to the escape flight path of the aircraft and the state transition model of the system, the probability that the aircraft is in a non-collision state at time t under the condition of an alarm can be obtained, that is, the system successfully alarms The probability. the

E. Threshold value and envelope design steps of the ground proximity warning system

Given the initial position of the aircraft, by changing the simulation conditions of the initial speed, the successful alarm rate and false alarm rate of the system under different initial speed conditions can be obtained, and the performance curves of the alarm system shown in Figure 5 and Figure 6 are obtained, that is, the successful alarm rate The relationship curve between rate and false alarm rate, and the relationship curve between successful alarm rate, false alarm rate and initial speed. the

In order to achieve the highest ground proximity warning performance, it is necessary for the system to have a high probability of successful warning and a low false alarm rate, that is, to obtain the best benefit of the warning. The alarm threshold meets the following conditions:

P(SA)-P(UA)＝(P(SA)-P(UA)) _max (12)

At the point where the warning performance is optimal, the corresponding system initial condition speed (initial altitude and speed) can be obtained at this time, that is, when the aircraft is at the initial position, if the speed reaches the speed limit condition, the system will issue an alarm, and eventually the The best alarm performance is obtained, that is, an optimal alarm threshold (v ₁ , h ₁ ) is obtained.

By changing the initial condition settings, the above simulation can be repeated to obtain a series of optimal alarm thresholds (v ₂ , h ₂ ), (v ₃ , h ₃ ), ..., (v _n , h _n ), and this group of alarm threshold points can be It constitutes the best alarm envelope of the alarm 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.

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