RU2499278C1 - Method of tracking path of moving ship - Google Patents

Abstract

FIELD: radio engineering, communication.

SUBSTANCE: method involves radar measurement of coordinates of the ship at the present moment in time and then smoothing parameters of the path of the ship using an α-β filter. In order to select smoothing coefficients α and β, a procedure for simulating tracking of the ship at different values of α and β is performed, wherein the selected values of smoothing coefficients provide minimum mean-square deviation of the difference between current measurements of the coordinates of the ship and values calculated when simulating tracking.

EFFECT: high accuracy of estimating current coordinates and the velocity vector of a ship when movement thereof includes areas of both rectilinear uniform and manoeuvring movement.

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Description

The invention relates to the field of external observation of moving ships by radar stations and is intended to accompany the ship's trajectory by estimating its coordinates and the velocity vector along its entire trajectory.

One of the tasks of modern maritime transport is to increase traffic safety. To achieve this, automated marine traffic control systems use radar information. After the primary processing of radar information, the process of its secondary digital processing is carried out, which is usually performed using programmed algorithms. As a result of the secondary processing, the current coordinates and the velocity vector of each vessel are calculated. To control the movement and prevent collisions and other dangerous situations, based on the data on the coordinates and speed vector of each vessel, teams (recommendations) are generated for correcting the motion path. Moreover, the quality of traffic control depends on the reliability and accuracy of the algorithms for estimating the current coordinates and the velocity vector of each vessel.

Currently, methods are widely used to estimate the current coordinates and the velocity vector of the vessel, in which at the current time using the radar station measure the coordinates of the vessel and smooth the parameters of the trajectory of the vessel using the α-β filter.

In the case of rectilinear and uniform movement of the vessel, the smoothing coefficients α and β must be given small positive values close to zero, while when maneuvering with the smoothing coefficients α and β, values close to unity should be set. If the tracking of the ship's trajectory, implemented with small positive values of the smoothing coefficients α and β, is used for a maneuvering ship, or, conversely, the indicated tracking, implemented with the values of the smoothing coefficients α and β, close to unity, is used for rectilinear uniform motion of the ship, estimate the current coordinates and the velocity vector in both cases occurs with a big error. Thus, since the magnitude of the smoothing coefficients α and β depends on the nature of the vessel’s movement, the algorithms for tracking the ship’s trajectory should include the calculation of the values of the smoothing coefficients taking this character into account.

A known method of tracking the trajectory of a moving vessel, described in (Farina A., Student F. Digital processing of radar information. Target tracking. M: Radio and communication. 1993, p. 182), in which, based on the calculation of the difference between the current coordinate measurements the vessel and their extrapolated values (measurement discrepancies) and comparing this difference with the threshold value, reveal the maneuver of the vessel, and then take the values of the smoothing coefficients α and β equal to one (alpha-beta algorithm with a maneuver detector). The lack of accuracy of the known method is determined by the fact that with this approach to the choice of smoothing coefficients, only the fact of the presence of the maneuver of the vessel is taken into account and its intensity is not taken into account. Thus, the presence of maneuvering areas in the vessel’s movement leads to a significant error in estimating the current coordinates and the velocity vector, since the maneuvering intensity, and, accordingly, the values of the smoothing coefficients α and β, which provide the best tracking, remain unknown.

Closest to the claimed is a method of tracking a maneuvering air target (US Pat. RF No. 2048684, publ. 1995.11.20), including radar measurements of coordinates and assessment of the current parameters of the trajectory by smoothing using a - (3 filters. In the known method, the probability of , that the target is maneuvering, and the values of the smoothing coefficients α and β, which provide the best support, are calculated from the value of this probability. Since the radar image of a small air target is a single value of the amplitude of the reflected echo, for a small target the variance of coordinate measurement errors corresponds to the known instrumental error of the radar.

Unlike a small air target, the ship is an extended object, as a result of which the radar image at high resolution of the radar is not a single value of the amplitude of the reflected echo signal, but a matrix of such amplitudes that are difficult to distribute and depend on the orientation of the ship and the location of local sources of reflected echo signal, as well as the state of the underlying surface (sea waves) and weather conditions (Dorozhko V.M. Simulation model of a radar echo signal // Far Eastern Mathematical Journal. - 2001. - No. 1. - S.98-113). At the same time, the probabilistic characteristics of the measurement errors of the coordinates of a particular ship in specific conditions cannot be determined based on the known instrumental error of the radar. The actual variance of the measurements of the coordinates of the ship will always be unknown and will be much higher than the variance of the instrumental error of the radar. Thus, when implementing the known tracking method for the vessel, the determination of the probability of maneuver occurs with a big error, which leads to the fact that, in the presence of sections of the vessel in the movement of both rectilinear uniform and maneuverable movement, the current coordinates and the vector of the vessel’s speed are also estimated significant mistake.

The objective of the invention is to provide a method for tracking the trajectory of a moving vessel, with high accuracy, providing the specified tracking in the presence of straight, uniform, as well as maneuvering motion in the vessel when the probabilistic characteristics of coordinate measurement errors are unknown.

The technical result of the invention is to increase the accuracy of estimating the current coordinates and the vector of the vessel’s speed in the presence of straight and uniform sections, as well as maneuverable movement in its movement.

и $${\beta }_{k_{\min }},$$

соответствующие минимальному среднеквадратичному отклонению разности между текущими измерениями координат судна и их вычисленными при моделировании траектории сопровождения значениями, и сглаживают параметры траектории судна с помощью α-β фильтра с выбранными коэффициентами $${\alpha }_{k_{\min }}$$

и $${\beta }_{k_{\min }}$$

. Схематично реализация предлагаемого способа показана на фиг.1, где приведена блок-схема его последовательных операций:The specified technical result is achieved by the method of tracking the trajectory of a moving vessel, including radar measurement of coordinates, estimation of the current parameters of the motion path by smoothing with the help of an α-β filter, in which, unlike the known one, the vector of current measurements of the coordinates of the vessel is additionally formed and stored, and storing the vector of possible values of the smoothing coefficients a and p, simulate the tracking of the trajectory with each of the possible values the smoothing coefficients α and β, the formation and storage of the vector of standard deviations of the difference between the current measurements of the coordinates of the vessel and their values calculated by modeling tracking, then choose from the vector of possible values of the smoothing coefficients α and β values $${\alpha }_{k_{\min }}$$

and $${\beta }_{k_{\min }},$$

corresponding to the minimum standard deviation of the difference between the current measurements of the ship’s coordinates and their values calculated when modeling the tracking path, and smooth the parameters of the ship’s trajectory using an α-β filter with selected coefficients $${\alpha }_{k_{\min }}$$

and $${\beta }_{k_{\min }}$$

. Schematically, the implementation of the proposed method is shown in figure 1, which shows a block diagram of its sequential operations:

1) radar measurement of the coordinates of the vessel;

2) the formation and storage of the vector of current measurements of the coordinates of the vessel;

3) the formation and storage of the vector of possible values of the smoothing coefficients α and β;

4) modeling trajectory tracking with each of the possible values of the smoothing coefficients α and β;

5) the formation and storing of the vector of standard deviations of the difference between the current measurements of the coordinates of the vessel and their values calculated during the modeling of tracking;

и $${\beta }_{k_{\min }}$$

, которые соответствуют минимальному среднеквадратичному отклонению разности между текущими измерениями координат судна и их вычисленными при моделировании сопровождения значениями;6) selection from the vector of possible values of the smoothing coefficients α and β of such values $${\alpha }_{k_{\min }}$$

and $${\beta }_{k_{\min }}$$

that correspond to the minimum standard deviation of the difference between the current measurements of the coordinates of the vessel and their values calculated during the simulation of tracking;

и $${\beta }_{k_{\min }}$$

, выбранных на этапе 6.7) smoothing the parameters of the ship's trajectory using the α-β filter using smoothing coefficients $${\alpha }_{k_{\min }}$$

and $${\beta }_{k_{\min }}$$

selected in step 6.

Technically, the method is as follows.

Using a measuring device based on the radar at exact times t _j, the values of the Cartesian coordinates of the vessel are measured z ^x (t _j ), z ^y (t _j ), where z ^x (t _j ) is the measurement of the Cartesian coordinates of the vessel x, az ^y (t _j ) - measurement of the Cartesian coordinate of the vessel y.

After that, the vector Z of the current measurements of the Cartesian coordinates of the vessel is formed and stored. This is as follows.

Let N be the number of times at which the current measurements of the Cartesian coordinates of the vessel z ^x (t _j ) and z ^y (t _j ) were made. Then the vector Z of the current measurements of the Cartesian coordinates of the vessel is formed from the N last current measurements of the Cartesian coordinates of the vessel in this way:

Z = (z ^x (t _jN ), x ^y (t _jN ), z ^x (t _{j-N + 1} ), z ^y (t _{j-N + 1} ), ..., z ^x (t _j-1 ), z ^y (t _j-1 ), z ^x (t _j ), z ^y (t _j ))

At the same time, a vector of possible values of the smoothing coefficients α and β is formed. This is as follows

Let α be the smoothing coefficient used in calculating the ship's coordinates x, y, α β be the smoothing coefficient used in calculating the components of the ship's velocity vector v _x , v _y . It is known that the smoothing coefficients air can take values in the range from 0 to 1, and there is a relation β = α ² / (2-α) (Farina A., Studer F. Digital processing of radar information. Target tracking. M: Radio and communication. 1993, p. 177).

The vector A of possible values of the smoothing coefficients a by condition includes the following components

A = (α ₁ , α ₂ , ..., α ₁₀ ) = (0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9,1.0) - only 10 components. The components of the vector B of the possible values of the smoothing coefficients β are conditionally calculated from the components of the vector A in such a way that B = (β ₁ , β ₂ , ..., β ₁₀ ) are also only 10 components, and β _k = α _k ² / (2- α _k ).

After that, the trajectory tracking is simulated with each of the possible values of the smoothing coefficients α _k and β _k using the well-known algorithm: when simulating the trajectory tracking at each time t _{i, the} current coordinates and components of the ship's velocity vector are calculated by implementing an iterative procedure

. $${\widehat{s}}_{i+\mathrm{one}}=F{\widehat{s}}_i+K\left(z_{i+\mathrm{one}}-HF{\widehat{s}}_i\right)\left(\mathrm{one}\right)$$

.

, $${\widehat{s}}_i$$

- оценка вектора s_i, который равенHere i is the number of time points of the corresponding measurements from the vector of current measurements of the Cartesian coordinates of the vessel Z, and $$i=\overline{\mathrm{one,}N}$$

, $${\widehat{s}}_i$$

is an estimate of the vector s _i , which is equal to

$$s_i=\Vert \begin{array}{l}x\left(t_i\right)\\ v_x\left(t_i\right)\\ y\left(t_i\right)\\ v_y\left(t_i\right)\end{array}\Vert ,$$

Z _i - a vector of measurements of the current coordinates of the vessel, formed from the values of the vector Z in such a way that

$$z_i=\Vert \begin{array}{l}{z}^x\left(t_i\right)\\ z^y\left(t_i\right)\end{array}\Vert ,$$

Φ and H are matrix coefficients equal to

$$F=\Vert \begin{array}{cccc}\mathrm{one}& t_i-t_{i-\mathrm{one}}& 0& 0\\ 0& \mathrm{one}& 0& 0\\ 0& 0& \mathrm{one}& t_i-t_{i-\mathrm{one}}\\ 0& 0& 0& \mathrm{one}\end{array}\Vert ,$$

$$H=\Vert \begin{array}{cccc}\mathrm{one}& 0& 0& 0\\ 0& 0& \mathrm{one}& 0\end{array}\Vert .$$

K is the matrix coefficient equal to

$$K=\Vert \begin{array}{cc}{\alpha }_k& 0\\ {\beta }_k/(t_i-t_{i-\mathrm{one}})& 0\\ 0& {\alpha }_k\\ 0& {\beta }_k/(t_i-t_{i-\mathrm{one}})\end{array}\Vert .$$

, выбираемых из векторов А и В.The tracking procedure (1) is implemented for the vector Z of the current measurements of the Cartesian coordinates of the vessel for each of the 10 possible values of the smoothing coefficients α _k and β _k , $$k=\overline{1.10}$$

selected from vectors A and B.

As a result of the simulation, 10 vectors (for each of the selected α _k and β _k ) of differences are formed between the current measurements of the Cartesian coordinates of the vessel and their values calculated during the modeling of tracking. We denote the second factor of the second term in formula (1) as δ _z (t _i ), and $$\delta z\left(t_{i+\mathrm{one}}\right)=\Vert \begin{array}{l}\delta z_x\left(t_{i+\mathrm{one}}\right)\\ \delta z_y\left(t_{i+\mathrm{one}}\right)\end{array}\Vert =\left(z_{i+\mathrm{one}}-HF{\widehat{s}}_i\right).$$

The vector Δ _{k of the} difference between the current measurements of the Cartesian coordinates of the vessel and their calculated values during tracking modeling (with the selected values of α _k and β _k ) will have the following components:

$$\begin{array}{l}{\Delta }_k=\left(\sqrt{{\left(\delta z_x\left(t_{\mathrm{one}}\right)\right)}^2+{\left(\delta z_y\left(t_{\mathrm{one}}\right)\right)}^2},\sqrt{{\left(\delta z_x\left(t_2\right)\right)}^2+{\left(\delta z_y\left(t_2\right)\right)}^2},...,\sqrt{{\left(\delta z_x\left(t_N\right)\right)}^2+{\left(\delta z_y\left(t_N\right)\right)}^2}\right)\\ =\left({\delta }_{\mathrm{one}},{\mathrm{<figure-callout\; id="2"\; label="\delta "\; filenames="00000026.png"\; state="\{\{state\}\}">\delta </figure-callout>}}_2,...,{\delta }_N\right),k=\overline{1.10}.\end{array}$$

Next, the vector R of the standard deviations of the difference between the current measurements of the Cartesian coordinates of the vessel and their values calculated during the modeling of tracking are formed and stored. This is done by calculating the standard deviation for each vector Δ _k so that

$${\delta }_k=\frac{{\displaystyle \sum _{i=\mathrm{one}}^N\left({\delta }_i^2\right)}}{N-\mathrm{one}}.$$

As a result, the vector R is formed: R = (δ ₁ , δ ₂ , ..., δ ₁₀ ).

и $${\beta }_{k_{\min }}$$

, соответствующих индексу k_min.Then, from the vector A, the possible values of the smoothing coefficients α and β are selected, those values that correspond to the minimum standard deviation of the difference between the current measurements of the Cartesian coordinates of the vessel and their values computed with the accompanying. This is done by choosing from the vector R the minimum component δ _k , determining its index k _min , and then choosing from the vectors A and B the components $${\alpha }_{k_{\min }}$$

and $${\beta }_{k_{\min }}$$

corresponding to the index k _min .

и $$\beta ={\beta }_{k_{\min }}$$

, сглаживают параметры траектории судна с помощью α-β фильтра в соответствии с известным способом путем реализации описанной выше итерационной процедуры (1).After that, using the selected coefficient values $$\alpha ={\alpha }_{k_{\min }}$$

and $$\beta ={\beta }_{k_{\min }}$$

smooth the parameters of the trajectory of the vessel using the α-β filter in accordance with the known method by implementing the iterative procedure described above (1).

, $$\widehat{y}\left(t_j\right)$$

и компонент вектора скорости $$\widehat{\nu }\left(t_j\right)$$

, $$\widehat{\nu }\left(t_j\right)$$

.As a result, an estimate of the current coordinates of the vessel is formed. $$\widehat{x}\left(t_j\right)$$

, $$\widehat{y}\left(t_j\right)$$

and component of the velocity vector $$\widehat{\nu }\left(t_j\right)$$

, $$\widehat{\nu }\left(t_j\right)$$

.

An example of a specific implementation of the method

Numerical simulation of tracking the trajectory of a moving vessel using the proposed method is carried out under the following conditions.

Using a measuring device (radar) for a vessel moving along a trajectory having sections of both rectilinear and uniform, as well as maneuvering movement, it is possible to measure the azimuth of the vessel and its distance with a period t _j -t _j-1 = 3 s. The vessel moves at a speed of 20 m / s from point 8 to point 9 (figure 2). At first, its movement is straightforward and uniform, and then the ship makes a maneuver - moves along an arc of a circle with a radius of 300 m, after which it again moves straight and evenly. The dimension of the vector Z of current measurements is limited by the value N = 10.

.The simulation results are presented in figure 2 and 3. Figure 2 shows the simulated trajectory of the vessel. Figure 3 shows a chart of errors in estimating the coordinates of the vessel according to the prototype (10 - dashed line) and the proposed method (11 - solid line). The time t _j from the start of trajectory tracking is plotted along the abscissa, and the value along the ordinate $$\delta \left(t_j\right)=\sqrt{{\left(x\left(t_j\right)-\widehat{x}\left(t_j\right)\right)}^2+{\left(y\left(t_j\right)-\widehat{y}\left(t_j\right)\right)}^2}$$

.

Here 12 is the moment of the start of maneuvering the vessel, 13 (the shaded section of the abscissa axis) is the length of time during which the maneuver of the vessel takes place, 14 is the moment the maneuver of the vessel ends.

In this case, the instrumental mean square errors of measurements of the coordinates of the vessel are taken equal to σ _x = 5 m, σ _y = 5 m, and real (numerically

simulated) root-mean-square errors of measurements of the coordinates of the vessel are taken equal to two times greater than the a priori known instrumental.

From figure 3 it can be seen that in areas of rectilinear uniform motion, the error of the known method of tracking the trajectory of the vessel is much higher than the proposed, and in areas of maneuvering movement the errors of the known and proposed method are comparable.

Thus, the proposed method allows to reduce the error in calculating the current coordinates and the velocity vector of the vessel and provides better tracking quality in comparison with the known method, in particular, in the case when the a priori ideas about the errors of coordinate measurements are unreliable.

Claims (1)

A method for tracking a moving ship’s trajectory, including radar coordinate measurement, estimating the current motion trajectory parameters by smoothing with an α-β filter, characterized in that it additionally generates and stores the vector of current measurements of the ship’s coordinates, generates and stores the vector of possible values of the smoothing coefficients α and β, simulate the tracking of the trajectory with each of the possible values of the smoothing coefficients α and β, the formation and storage the vector of standard deviations of the difference between the current measurements of the ship’s coordinates and their values calculated during the modeling of tracking, then the values are selected from the vector of possible values of the smoothing coefficients α and β $${\alpha }_{k_{\min }}$$

and $${\beta }_{k_{\min }}$$

corresponding to the minimum standard deviation of the difference between the current measurements of the coordinates of the vessel and their values calculated when modeling the tracking path, and smooth the parameters of the ship's trajectory using an α-β filter with selected coefficients $${\alpha }_{k_{\min }}$$

and $${\beta }_{k_{\min }}$$

.

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