RU2616107C9 - Method for determination aircraft landing trajectory based on registered trajectories data using cosine measures to measure trajectory similarities (versions) - Google Patents

Abstract

FIELD: aviation.

SUBSTANCE: determination of effective landing trajectory of an aircraft (AC) comprises recording spatial coordinates of the AC movement per time unit at the appropriate time, calculating multidimensional spatial landing trajectory of AC movement based on the recorded characteristics, determining a cone of multidimensional spatial landing trajectories under cosine measures asymptotically converging with a threshold parameter, determining effective AC landing trajectory in a certain way. In addition to the above steps the minimum allowed landing trajectory in a cone (release) is also calculated in order to determine the minimum allowed AC trajectory under the following conditions: the minimum allowed landing trajectory is most distant from the effective one at the cosine measure and on the landing plane the distance from the end point of the effective AC landing trajectory to the end point of the minimum allowed AC landing trajectory does not exceed the width of the runway.

EFFECT: improving safety and reducing the number of accidents during landing of the aircraft.

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Description

The invention relates to the field of data analysis, in particular, multidimensional trajectories of aircraft detected by radar in the airport area, and can be used to sectorize airspace, design air corridors, simulate and determine the optimal (normal) trajectories of aircraft approach, design automatic (unmanned) approach systems (in particular, in a complex geographical landscape, as well as in the absence of glide path planning) and and solving the problems of identifying and preventing potential conflicts.

Due to the growing workload of airports, to optimize the work of dispatching services, the task of dividing the airport's airspace into sectors and designing air corridors for flights with similar trajectories is relevant. For this, it is necessary to take into account the established separation of airspace along routes and the dynamics of air traffic.

Statistics from the International Civil Aviation Organization (ICAO) show that approach and landing are the most critical phases of aircraft flight. Most accidents involving large aircraft occur after the aircraft enters the runway (runway) and within 19 km of it. An analysis of the civil aviation safety of the Russian Federation, conducted by the Federal Air Transport Agency (flight safety inspection department), shows that there are cases of failure to maintain a safe descent path at the final stage of approach, maneuvering at the stage of landing (increased speed, deviations from the glide path) and rolling out Runways pose the greatest threat to flight safety, since even a slight deviation from a safe route can lead to an airplane crash, especially If the airport is located in the area of complex geographical landscape.

Currently, approaches, methods and systems are being actively developed that simplify piloting aircraft at the final stage of landing. For this, both flight management systems and automatic landing route selection devices are used (see US 8489261). At the final stage of the flight, the crew can ask the on-board system one of the approach options. In this case, the on-board system automatically determines the coordinates of the selected trajectory.

The analysis of aircraft trajectories is used in air traffic control and safety systems. In particular, based on the analysis of data on successful landings of the same type of aircraft, further trajectories are displayed (see US 9020662) and trajectories that are most optimal in the given meteorological conditions (see US 8977484) are determined.

The tasks of analysis, classification and clustering of aircraft motion paths (LA) are becoming increasingly relevant for research, organization and optimization of movement in the airport area. An integral part of these tasks is the grouping of similar trajectories into clusters, accompanied by measuring the distance between the trajectories. However, it should be noted that in practice the problems of combining similar trajectories are solved either by directly analyzing the similarity of the current trajectory with the trajectories from the database, or by clustering the trajectories using geometric models of the proximity of the trajectories, using, in particular, Euclidean distances as a measure of proximity.

In clusters obtained by dividing airspace into sectors or grouping similar trajectories, it is possible to distinguish bundles of trajectories (for example, trajectories corresponding to landings on a given runway), in which central trajectories are simulated, hereinafter referred to as centroids. The determination of centroids for bundles of multidimensional trajectories can be performed in various ways.

Currently, for separation of airspace in the airport zone, for grouping similar trajectories and determining centroids for multidimensional bundles, in particular, methods based on Voronoi diagrams [1] and K-means clustering are used.

определяются кластерами C_k,

, полученными в результате геометрического разбиения пространства векторов

, d>>1 на ячейки «в стиле диаграмм Воронова», то центроиды пучков, полученных таким образом, определяются алгоритмом разбиения на заданное число кластеров (K-means algorithm) [2].The first of these methods assumes that the space (for example, the airspace in the airport area or the space of vectors representing the motion paths) is divided into a given number of sectors or cells. If the sheaves N _k ,

defined by clusters C _k ,

obtained as a result of geometric partitioning of the vector space

, d >> 1 into cells “in the style of Voronov diagrams”, then the centroids of the beams obtained in this way are determined by the algorithm for splitting into a given number of clusters (K-means algorithm) [2].

, представляющих многомерные траектории движения (L>>1 - длина траектории), при Евклидовой мере расстояния решается задача идентификации центроидов

пучков многомерных траекторий, ассоциируемых с кластерами C_k,

. В этом случае для набора центроидов сумма квадратов Евклидовых расстояний до векторов в соответствующих кластерах C_k,

является минимальной. Для решения этой задачи в результате итеративного процесса минимизируется целевая функция алгоритма K-means, которая имеет вид:The K-means clustering method assumes that for multidimensional vectors

representing multidimensional motion trajectories (L >> 1 is the length of the trajectory), with the Euclidean measure of distance, the problem of identifying centroids is solved

bundles of multidimensional trajectories associated with clusters C _k ,

. In this case, for a set of centroids, the sum of the squares of the Euclidean distances to the vectors in the corresponding clusters C _k ,

is minimal. To solve this problem as a result of an iterative process, the objective function of the K-means algorithm is minimized, which has the form:

- набор бинарных индикаторных переменных принадлежности траектории кластеру. Если вектор x[i] назначен кластеру k, то r[i;k]=1, в противном случае r[i;k]=0, что также может быть записано в виде

.where "⋅" denotes the scalar product of vectors in the state space R ^{3 × L} and

- a set of binary indicator variables of the trajectory belonging to the cluster. If the vector x [i] is assigned to the cluster k, then r [i; k] = 1, otherwise r [i; k] = 0, which can also be written as

.

используются векторы

. Минимизация J (1) осуществляется последовательными итерациями, состоящими из двух шагов: оценки

при фиксированных

в замкнутой формеIn the K-means algorithm for initializing centroids

vectors are used

. Minimization of J (1) is carried out by successive iterations consisting of two steps: estimates

at fixed

in closed form

при фиксированных

and assessments

at fixed

in closed form

until convergence is achieved.

In relation to the problems of determining centroids for bundles of aircraft landing trajectories (i.e., when considering the airspace of an airport zone), the limitations and disadvantages of these methods are that:

, d>>1 на ячейки в стиле диаграмм Воронова не отражает характер пучков траекторий (например, пучков посадочных траекторий самолетов);the distinguished regions of the state space R ^{3 × d} have a different number of faces; therefore, the concept of the geometric partition of the vector space

, d >> 1 on cells in the style of Voronov diagrams does not reflect the nature of the trajectory bundles (for example, aircraft landing path bundles)

The Euclidean measure of the distance between the trajectories (as a whole) in the state space R ^{3 × d} poorly reflects the similarity (difference) of the shape (profiles) of the trajectories in 3-dimensional space. It is great for spatially spaced but similar trajectories and does not separate intersecting but different in geometry trajectories;

(2) вычисляется Евклидово расстояние между каждым вектором μ[k],

и каждым вектором x[i],

.in practice, in R ^{3 the} bundles of trajectories intersect. When using the Euclidean measure of distance, the features of spatial geometry (for example, possible intersections in space, curvature and torsion) of multidimensional trajectories are not taken into account. In addition, the direct implementation of the K-means algorithm is relatively slow, since at each step of determining r [i; k],

(2) the Euclidean distance between each vector μ [k] is calculated,

and each vector x [i],

.

In general, the use of the Euclidean metric as a measure of proximity between multidimensional spatial motion trajectories is a common significant drawback of the above-mentioned and other well-known approaches to the analysis of multidimensional motion trajectories.

Thus, the problem to be solved when creating the present invention is aimed at further improving the methods of dividing airspace in the airport zone into sectors, taking into account established traffic flows, automatic (unmanned) approach systems and designing air corridors for flights with similar landing paths, in in particular, to increase the accuracy of the aircraft’s landing (aiming) for landing, while the technical result achieved by solving such a problem consists in increasing the safety bout their dangers flights and reducing the number of freelance (emergency) situations with regard to the cases of the approach and landing.

The stated result in the first of the declared variants is achieved by the proposed method for determining the optimal landing paths of an aircraft (LA) for multidimensional spatial landing paths asymptotically converging with the threshold parameter using a cosine measure that includes collecting and recording data on the characteristics of the aircraft’s motion per unit time, calculating on based on the recorded characteristics of multidimensional spatial landing trajectories of the aircraft, determination, at least measure of one beam of multidimensional spatial landing trajectories asymptotically converging with the threshold parameter with respect to cosine, containing at least two multidimensional spatial landing trajectories and determining the optimal one for which the optimal trajectory (centroid) is the trajectory, the sum of the squares of the distances from which to all the beam paths calculated by the cosine measure, it is minimal, and the threshold parameter for asymptotic beam convergence does not exceed the width of the runway.

The stated result in the second of the declared variants is achieved by the proposed method for determining the minimum permissible landing trajectories of an aircraft (LA) for multidimensional spatial landing trajectories asymptotically converging with the threshold parameter using a cosine measure, including collecting and recording data on the characteristics of the aircraft’s motion per unit time, calculating based on the recorded characteristics of multidimensional spatial landing trajectories of the aircraft, and determine at least one bundle of multidimensional spatial landing trajectories asymptotically converging with the threshold parameter with respect to cosine, while one of the trajectories in the beam is optimal (centroid), in which the minimum path (ejection) is the path in the beam that is farthest as cosine from the optimal one, and the spread of the endpoint of such a potentially dangerous trajectory relative to the optimal endpoint does not exceed the threshold parameter equal to the width of the runway.

The invention is illustrated by an example of the practical determination of centroids of bundles of trajectories of aircraft landing on the aerodrome strip (Fig. 1), as well as a flowchart showing the stages of the execution of variants of the method (Fig. 2).

The possibility of achieving the claimed result is due to the use of the cosine measure as an experimental measure of the similarity of multidimensional spatial landing trajectories of aircraft (for example, aircraft) to evaluate asymptotically converging bundles of multidimensional trajectories of motion, their centroids and emissions (the meaning of the terms will be explained below). Outliers can be considered the trajectories of the beam of multidimensional trajectories that are farthest from the corresponding centroids with the cosine when solving the conditional problem of optimizing the estimation of centroids of asymptotically converging bundles of multidimensional landing trajectories. In other words, the cosine measure is used to estimate the proximity of possibly intersecting spatial motion trajectories in potentially intersecting beams of multidimensional trajectories.

Unlike the Euclidean distance measure, the cosine measure used as an experimental measure of the similarity of multidimensional spatial trajectories (for example, landing trajectories of an aircraft) takes into account the spatial geometry of multidimensional trajectories (their potential spatial intersections, curvature and torsion) and allows you to separate overlapping but different in geometry, multidimensional trajectories of motion.

Revealing the possibility of realizing the claimed purpose and practical feasibility of the solution, it is established in the present description that multidimensional landing trajectories of the aircraft, represented by multidimensional vectors, are calculated on the basis of metadata recorded at the corresponding time points, including, in particular, the spatial coordinates of the aircraft (for example, the coordinates of the center position mass) and the speed of the aircraft. The sequence of meta-data recorded by the radar in the airport area determines the multidimensional trajectories of the aircraft (which are hereinafter briefly referred to as multidimensional trajectories). Multidimensionality is determined by the long trajectory and the number of meta-data parameters used (for example, the spatial coordinates of the aircraft, speed at the corresponding time instants, etc.).

The flight paths of the aircraft, in particular, in the airport area, are divided into take-off and landing paths, which in turn form bundles of multidimensional paths. Multidimensional landing paths on the aerodrome stripes form bundles of multidimensional landing paths. In this case, the trajectories in the beams can intersect in space. A beam of multidimensional motion trajectories is considered convergent if multidimensional trajectories in the beam have a common target and are close in finite coordinates (for example, on the landing plane). In particular, sets of three-dimensional spatial trajectories of airplanes when approaching a given runway are an example of converging beams of multidimensional trajectories. The convergence of the beam of multidimensional trajectories is determined by the threshold parameter, which does not exceed the width of the runway.

By centroid or optimal (normal, support) trajectory, one should understand the possible trajectory of the aircraft, associated with the asymptotic behavior of the trajectories of a converging beam of multidimensional trajectories of motion for a given value of the threshold parameter.

Outliers should be understood as the trajectories of asymptotically converging beams of multidimensional trajectories that are farthest from the corresponding centroids as the cosine. In the context of solving security problems, we can say that the trajectory of an asymptotically converging bundle of multidimensional trajectories distinguished in this way is boundary (minimally admissible), i.e. potentially dangerous trajectory.

, представляющих пучок многомерных траекторий N_k,

(K₀ - эмпирический параметр), выполняется условие асимптотического схождения пучкаA beam of multidimensional trajectories is considered asymptotically converging with the threshold parameter if, for vectors

representing a bundle of multidimensional trajectories N _k ,

(K ₀ is an empirical parameter), the condition of asymptotic beam convergence

- евклидова мера расстояния в трехмерном пространстве R³, ε - порог, не превосходит ширины взлетно-посадочной полосы в случае настоящего изобретения.where (∀i ∈ N _k , x [L _i ; i] are the coordinates of the points of the trajectories that almost coincide, that is, the parameters L _i , i∈N _k are to be determined,

- the Euclidean measure of distance in the three-dimensional space R ³ , ε is the threshold, does not exceed the width of the runway in the case of the present invention.

The trajectories in asymptotically converging beams have a typical shape (profile) and a characteristic geometric asymptote in the region of convergence of the trajectories (4) [3].

The geometric asymptote of a converging beam of multidimensional landing trajectories of aircraft is a line in R ³ (three-dimensional coordinate space) that satisfies condition (4).

The trajectories in asymptotically convergent sheaves have a tangent in the neighborhood of the endpoints ∀i ∈ N _k , x [L _i ; i] of all the trajectories of the pencil with threshold ε (4)) [3].

асимптотически сходящихся пучков также удовлетворяют условию типа (4) в видеCentroids

asymptotically converging bundles also satisfy a condition of type (4) in the form

подлежат определению.where the parameters L _i , i∈N _k and L _k ,

to be determined.

и каждым вектором x[i],

.It should be noted that at present, when determining centroids for converging bundles of multidimensional trajectories, there is a strict interdependence between the definition of centroids and the corresponding asymptotically converging bundles of multidimensional trajectories. As mentioned above, two-step methods for the independent determination of convergent beams and the subsequent determination of centroids for already defined beams of multidimensional motion trajectories are known. For example, the determination of centroids and bundles of multidimensional trajectories using the K-means algorithm. However, this method has a significant drawback: the determination of centroids for asymptotically converging bundles of multidimensional trajectories turns out to be unstable to random outliers. Also, the disadvantages of this method are related to a possible unsuccessful initialization, as a result of which the algorithm can converge not to a global but to a local minimum, and to the relatively slow implementation of the K-means algorithm associated with the calculation of the Euclidean distance between each vector μ [k],

and each vector x [i],

.

It should be noted that for the exact determination of centroids and bundles of multidimensional landing trajectories, when solving the problem of determining clusters representing bundles of trajectories, the minimization of the objective function (1) should be carried out taking into account conditions (5) in the form

- евклидова мера расстояния в трехмерном пространстве R³.Where

- Euclidean measure of distance in three-dimensional space R ³ .

модели полиномиальной регрессии [4-5] или представление векторов

, L>>1 в пространствах абстрактных характеристик

с евклидовой мерой расстояния [6-8]. При этом, вектора, представляющие пучки многомерных траекторий, которые геометрически неразделимы в исходном пространстве состояний R^3×L, в пространствах абстрактных характеристик становятся разделимыми, поэтому в этих пространствах используется евклидова мера расстояния [9-10]. При отображении в исходное пространство состояний эта метрика становится неевклидовой.There are ways to adapt the conditional optimization problem (1), (6) to the analysis of bundles of spatial trajectories. Possible use for centroids

polynomial regression models [4-5] or representation of vectors

, L >> 1 in spaces of abstract characteristics

with the Euclidean measure of distance [6-8]. At the same time, vectors representing bundles of multidimensional trajectories that are geometrically inseparable in the original state space R ^{3 × L} in spaces of abstract characteristics become separable, therefore, the Euclidean distance measure is used in these spaces [9-10]. When mapped to the original state space, this metric becomes non-Euclidean.

An example of a non-Euclidean measure of distance for trajectory vectors in a state space is, for example, the cosine measure:

, L>>1 в пространстве состояний, представляющих пучки траекторий определенного профиля [11]. Поэтому, можно модифицировать задачу оптимизации (1), (6), заменив в (1) скалярное произведение на общую меру расстояния.The indicated measure most adequately reflects the proximity of vectors

, L >> 1 in the space of states representing bundles of trajectories of a certain profile [11]. Therefore, it is possible to modify the optimization problem (1), (6) by replacing the scalar product in (1) with a common measure of distance.

Thus, the objective function is generalized by introducing a general measure of the distance ρ (x, x ') between two vectors x, x'∈R ^{3 × L} and minimizing the objective function

(K-medoids algorithm) [12].

шаг оценки

включает назначение каждого вектора x[i],

кластеру C_k,

, для которого расстояние ρ(x[i],μ[k]) с соответствующим центроидом минимальноWith given centroids

evaluation step

includes the assignment of each vector x [i],

cluster C _k

for which the distance ρ (x [i], μ [k]) with the corresponding centroid is minimal

является потенциально более сложным.with an estimate of the computational complexity O (K⋅N). However, the assessment step

is potentially more complex.

Under the standard constraint, where each centroid is one of the vectors assigned to the corresponding cluster, condition (6) is satisfied automatically, which allows us to implement an algorithm for any choice of distance measure ρ (x [i], μ [k:]), which is directly calculated.

включает дискретный поиск по всем N_k векторам, назначенным этому кластеру C_k,

, и требует O(N_k ²) оценок меры расстояния ρ(x[i],μ[k]).Definition step

includes a discrete search on all N _k vectors assigned to this cluster C _k ,

, and requires O (N _k ² ) estimates of the measure of the distance ρ (x [i], μ [k]).

навязана логикой алгоритма K-средних и его обобщениями и, в принципе, центроиды

и кластеры C_k,

, представляющие пучки траекторий N_k,

, могут определяться независимо.Note that the relationship of centroids and clusters

imposed by the logic of the K-means algorithm and its generalizations and, in principle, centroids

and clusters C _k ,

representing bundles of trajectories N _k ,

, can be determined independently.

используются скрытые компоненты линейных и нелинейных динамических моделей (см. [13-14]), и скрытые последовательности Марковских моделей (см. [15-16]) при условии (6), затем пучки траекторий определяются по схеме

на основе однократного применения формулы (9) с мерой косинуса (7).As independent methods for evaluating centroids

hidden components of linear and nonlinear dynamic models are used (see [13-14]), and hidden sequences of Markov models (see [15-16]) under condition (6), then the bundles of trajectories are determined according to the scheme

based on a single application of formula (9) with the cosine measure (7).

определяются по схеме

на основе однократного применения формулыOptimization of the objective function of the K-means algorithm with the condition of asymptotic convergence of the beam allows us to determine centroids for bundles of spatial trajectories. To estimate the bundles of trajectories, geometric triangulation methods can be used, for example [17, 18], then centroids

determined by the scheme

based on a single use of the formula

under condition (6) using the squared measure of cosine (7).

и

в исходном пространстве состояний.Estimate (10) is effective in representing vectors

and

in the original state space.

As an example, using the claimed method, the centroids of the bundles of trajectories of aircraft landing on the aerodrome strip shown in the figure are determined. The bundles of multidimensional aircraft landing trajectories are shown, obtained using the cosine measure as a measure of the proximity of the trajectories based on the analysis of data (sampling) of the trajectories of aircraft going for landing at the international airport of San Francisco (USA). The origin coincides with the position of the radar, the time interval between the registration points is about 5 s. In order to exclude accidental aircraft maneuvers before landing, trajectories with a length of 160 points were considered. For selected beams (cyan, green, and blue), their centroids are shown by thick red lines. It can be seen that the trajectories in the beams substantially intersect and twist.

Thus, the use of the cosine measure as a proximity measure between multidimensional spatial trajectories (for example, aircraft landing trajectories) allows us to separate intersecting, but different in geometry, multidimensional motion trajectories and provides an accurate determination of centroids for asymptotically converging (potentially intersecting) bundles of multidimensional trajectories when solving conditional optimization problem, in which the standard deviation of the centroid from all trajectories in the beam is minimal as the cosine.

In addition, by using the cosine measure as a measure of proximity between multidimensional trajectories in the beam, it is possible to determine the so-called outliers, i.e. beam paths farthest from the centroid as the cosine.

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Claims (5)

1. A method for determining the optimal landing path of an aircraft (LA), in which the spatial coordinates of the movement of the aircraft per unit time are recorded at appropriate points in time, multidimensional spatial landing paths of the movement of the aircraft are calculated based on the recorded characteristics, at least one asymptotically converging with the parameter is determined threshold, a bundle of multidimensional spatial landing trajectories with respect to cosine, containing at least two multidimensional spatial landing paths, and determine the optimal landing path of the aircraft (centroid) from the condition that the centroid is the path, the sum of the squares of the distances from which to all the beam paths, calculated with respect to the cosine, is minimal, and the threshold parameter for asymptotic beam convergence does not exceed the width runway (runway). 2. A method for determining the minimum allowable trajectory of an aircraft (LA), in which the spatial coordinates of the movement of the aircraft per unit time are recorded at appropriate times, the multidimensional spatial landing trajectories of the aircraft are calculated on the basis of the recorded characteristics, and at least one asymptotically converging threshold parameter is extracted a beam of multidimensional spatial landing trajectories with respect to cosine, containing at least two multidimensional spatial n sedimentary path determine, as the cosine in the selected beam, the optimal landing trajectory (centroid) of the aircraft, determine the minimum permissible landing trajectory in the beam (ejection) from the following conditions: the minimum permissible landing trajectory is the most distant from the optimal one as the cosine; on the landing plane, the distance from the end point of the aircraft’s optimal landing path to the end point of the minimum acceptable aircraft landing path does not exceed the threshold parameter equal to the runway width.

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