RU2729459C1 - Method of determining spatial coordinates and speeds of objects using a scanning multiposition radio system - Google Patents

Abstract

FIELD: radio equipment.SUBSTANCE: invention can be used for creation of multi-position radio systems for direction finding of objects in radio range of wavelengths at short range. Essence of invention consists in that method of determining spatial coordinates and speeds of objects scanning multi-position radio system involves placing in space several radio receivers, scanning a viewing area and mutually oriented by rotation arrays and basic vectors connecting receiver coordinate systems, forming, in one scanning period, vectors of vectors of directions to objects, distribution of said boxes as per belonging to specific objects, taking into account moments of time of formation of boxes and finding estimates of distances to objects and coordinates of velocity vectors by solving a system of equations of linear dependence of vectors, wherein an external radio transmitter is added, and scanning of antennae of receivers is carried out electronically in sequence of periods with time delay, wherein in each scanning period signals transmitted by the transmitter and received by the receivers are converted into complex spectra, selecting spectral components, amplitudes of which exceed threshold of useful signal detection and upon exceeding of threshold are determined by amplitude-phase method angular coordinates of azimuth and elevation of position of objects, after which, based on angular coordinates, vectors of direction vectors on objects in coordinate systems of receivers are found, groups are grouped according to membership of specific objects, then from coordinates of units of each group and differences of time moments of scanning make, by a certain rule, matrix A, calculating a matrix of weight coefficients W=(AA)A, where "T" and "-1" are symbols of transposition and matrix inversion, matrix W is multiplied from the left by vector B of coordinates of basic vectors and vector X=W·B of estimates of distances and coordinates of the velocity vector is obtained for each group of conjugated vectors, estimates of distances are multiplied by units and a vector of spatial coordinates of the object is obtained.EFFECT: possibility of determining coordinates of direction vectors of objects by measuring angular coordinates of objects and finding spatial coordinates of objects together with estimates of vectors of movement thereof by increasing time between scanning periods in receivers when a transmitter is available.1 cl

Description

SUBSTANCE: invention relates to multi-position radio systems for direction finding of objects in radio wavelength range at short range.

The radio system consists of several n (n≥2) mutually distant and space-oriented radio receivers with antenna arrays (AR) composed of several receiving elements that receive the radio signal reflected from objects. The receivers carry out electronic scanning of the general viewing area with a narrow antenna pattern (antenna pattern) of the order of 1 ° -3 °, changing the position of the line of sight (bisector of the antenna pattern) in the raster (line-by-line) mode by the value of the specified steps in azimuth and elevation that make up a certain part of the antenna pattern width ...

The radio transmitter, located separately from the radio receivers and changing its position in space, sends at certain times t a periodic radio signal s (t) towards the coverage area of the radio receivers, in which there are several objects of observation (air or ground, stationary or moving).

проходят тракт первичной обработки, преобразуются в измерительных каналах в комплексные спектры. После чего выделяются спектральные составляющие на тех частотах, на которых амплитуды превышают порог обнаружения полезного сигнала одновременно во всех каналах.At each position of the lines of sight of the antennas scanning sequentially in time, the signals s _k (t) received in k-th receivers,

pass through the primary processing path, are converted in measuring channels into complex spectra. After that, spectral components are identified at those frequencies at which the amplitudes exceed the detection threshold of the useful signal simultaneously in all channels.

начала периодов сканирования.The task is to determine the spatial coordinates and velocity vectors of all objects, taking into account the moments of time t _k ,

the beginning of the scanning periods.

Known methods [1-3] for determining the spatial coordinates of several objects in a multi-position receiver system. The methods are based on the distribution of direction vectors to the alleged objects by belonging to specific objects, that is, finding the conjugate vectors. The calculation of the spatial coordinates of objects is carried out through estimates of the distances to objects, which are found by solving a system of equations for the linear dependence of conjugate vectors.

However, all these methods do not show how the coordinates of the direction vectors to objects are found. Let us take as a prototype a method for determining the spatial position, velocity and acceleration of an object in a passive scanning vision system [3], which in relation to several objects of observation is algorithmically reduced to the following.

1. Place in space several mutually oriented receivers scanning the field of view.

в системах координат приемников с запоминанием моментов времени t_k (i) их образования.2. In one scanning period, unit vectors a _k (i) of vectors of ix directions to objects are formed

in the coordinate systems of receivers with memorizing the moments of time t _k (i) of their formation.

3. Write down a sufficient condition for vector conjugation in the coordinate system of the 1st receiver, taking into account the time moments t _k (i) as a system of linear equations in matrix form, the unknowns of which are the distances r _k (i) to objects and the coordinates of the velocity vectors.

до объектов решением системы уравнений методом обратной матрицы.4. The unit vectors of the directions are distributed by belonging to specific objects by checking the fulfillment of the sufficient condition for the conjugation of vectors, and estimates of the distances are found

to objects by solving a system of equations by the inverse matrix method.

на орты a_k(i) векторов направлений и получают оценки пространственных координат объектов

в системах координат приемников

Дополнительно составляют векторы скоростей из оценок их координат.5. Multiply range estimates

on the unit vectors a _k (i) of the direction vectors and obtain estimates of the spatial coordinates of the objects

in receiver coordinate systems

Additionally, velocity vectors are made from the estimates of their coordinates.

This method has the following disadvantages.

1. The method does not show how the coordinates of the unit vectors of the direction vectors to the objects are found.

2. As applied to a radio system with electronic scanning, small differences in the times of fixing the unit vectors in the receivers during one common scanning period lead to instability of the process of inversion of the system matrix, whose column elements turn out to be close to zero. This leads to large errors in the estimates of the coordinates of the velocity vectors. For this reason, it becomes impossible to find the velocity vectors for one period during electronic scanning.

The proposed technical solution is aimed at eliminating these shortcomings, namely, determining the coordinates of the unit vectors of directions to objects by measuring the angular coordinates of objects and finding the spatial coordinates of objects together with estimates of their motion vectors by increasing the time between scanning periods in receivers in the presence of a transmitter.

The technical result of the proposed technical solution is achieved by using a method for determining the spatial coordinates and velocities of objects by a scanning multi-position radio system, which consists in placing several radio receivers in space, scanning the viewing area and mutually oriented by rotation matrices and base vectors connecting the coordinate systems of the receivers, forming unit vectors in one scanning period vectors of directions to objects, the distribution of these unit vectors by belonging to specific objects, taking into account the moments of formation of unit vectors and finding estimates of distances to objects and coordinates of the vectors of velocities by solving a system of equations of linear dependence of vectors, characterized in that an external radio transmitter is added, and the scanning of receiver antennas is carried out electronically in a sequence of periods with a time delay, while in each scanning period, the signals transmitted by the transmitter and received by the receivers, are converted into complex spectra, spectral components are isolated, the amplitudes of which exceed the detection threshold of the useful signal and, upon exceeding the threshold, the angular coordinates of the azimuth and elevation of the objects are determined by the amplitude-phase method, after which, based on the angular coordinates, the unit vectors of the direction vectors to the objects in coordinate systems are found receivers, group the unit vectors according to their belonging to specific objects, then from the coordinates of the unit vectors of each group and the differences of the scanning times, they compose matrix A according to a certain rule, calculate the matrix of weight coefficients W = (A ^T A) ^-l A ^T , where "T" and "- 1 "- symbols of transposition and inversion of the matrix, multiply the matrix W on the left by the vector B of the coordinates of the base vectors and obtain the vector X = W⋅В of the estimates of the distances and coordinates of the velocity vector for each group of conjugate vectors, multiply the estimates of the distances by the unit vectors and obtain the vector of the spatial coordinates of the object ...

Calculated part. Algorithmically, the method is reduced to the following.

Ориентацию систем координат осуществляют с помощью способа [1], где в качестве контрольных объектов используются несколько пространственно распределенных радиомаяков.1. Place n receivers (n≥3) in space, oriented by matrices P _{k of} rotation of coordinate axes with respect to the first receiver and base vectors b _k connecting the centers of coordinate systems

The orientation of the coordinate systems is carried out using the method [1], where several spatially distributed radio beacons are used as control objects.

в каждом приемнике выполняют следующие операции.A radio transmitter, randomly located in space relative to the receivers, periodically emits a signal s (t) at a certain radio frequency. In a sequence of time instants t _k scanning periods of k-th receivers

in each receiver, the following operations are performed.

в комплексные спектры

на j-x промежуточных частотах ƒ_j. После чего выделяют спектральные составляющие

на тех частотах ƒ_jk, на которых максимум амплитуды

превышает порог обнаружения полезного сигнала одновременно во всех q-x каналах. Запоминают угловые координаты азимута ϕ_k(i) и угла места θ_k(i) по факту обнаружения каждого i-го полезного сигнала

за период сканирования зоны обзора. Тем самым находят угловые координаты объектов методом максимума амплитуды.2. In the k-th time period, an electronic scanning of the antenna of the k-th receiver with a narrow antenna pattern is carried out along the goniometric space of the viewing area. At each position of the line of sight, the received signal s _k (t) passes through the primary processing path and is converted into qx measuring channels

to complex spectra

at jx intermediate frequencies ƒ _j . Then the spectral components are isolated

at those frequencies ƒ _jk at which the maximum amplitude

exceeds the detection threshold of a useful signal simultaneously in all qx channels. The angular coordinates of the azimuth ϕ _k (i) and the elevation angle θ _k (i) are memorized upon detection of each i-th useful signal

during the scanning period of the view area. Thus, the angular coordinates of objects are found by the method of maximum amplitude.

выделяют аргументы - фазы

в q-x каналах

и методом разности фаз находят более точные оценки угловых координат. При этом совместное применение амплитудного и фазового методов устраняет проблему неоднозначности измерения фазы за счет приема сигнала в направлении, близком к биссектрисе узкой ДНА с шириной порядка 1°-3°. Кроме того, если в зоне обзора находятся несколько объектов, не различимых по скорости и доплеровской частоте, то амплитудный метод позволяет их обнаружить.3. To reduce the measurement error of angular coordinates, which in the amplitude method is half the scanning step Δϕ / 2 and Δθ / 2, additionally from the complex components

highlight arguments - phases

in qx channels

and the phase difference method is used to find more accurate estimates of the angular coordinates. In this case, the combined application of the amplitude and phase methods eliminates the problem of ambiguity in measuring the phase by receiving a signal in a direction close to the bisector of a narrow beam pattern with a width of the order of 1 ° -3 °. In addition, if there are several objects in the field of view that are indistinguishable in speed and Doppler frequency, then the amplitude method allows them to be detected.

In the case of moving objects, the maximum amplitudes are recorded at Doppler frequencies.

векторов направлений на объекты по формуле4. Based on the angular coordinates ϕ _k (i) = ϕ _k and θ _k (i) = θ _k determine the unit vectors a _k (i),

vectors of directions to objects by the formula

a _k (i) = (a _kx , a _ky , a _kz ) = (cosθ _k sinϕ _k , sinθ _k , cosθ _k cos ϕ _k ),

in local coordinate systems O _k , X _k , Y _k , Z _k , where the O _k Z _k axes are directed towards the object, the O _k X _k and O _k Z _k axes are located in the horizontal plane, the O _k Y _k axis is in the vertical , the angle ϕ _{k is} measured from the axis O _k Z _k in the plane O _k , X _k , Z _k , the angle θ _k is in the vertical plane relative to

i_k∈{1, 2, …, m}. Для каждой группы векторов а₁, а₂, …, a_n, предположительно принадлежащих одному объекту, линейная зависимость векторов записывается в виде векторного уравнения в системе координат 1-го приемника с учетом возможного перемещения объекта на промежутке [t₁, t_k]:5. Make up non-repeating combinations of n vectors a _k (i _k ),

i _k ∈ {1, 2,…, m}. For each group of vectors а ₁ , а ₂ , ..., a _n , presumably belonging to one object, the linear dependence of the vectors is written in the form of a vector equation in the coordinate system of the 1st receiver, taking into account the possible movement of the object in the interval [t ₁ , t _k ]:

where r _k is the distance to the proposed object; V ₁ = (ν _1x , ν _ly , ν _lz ) ^T is the velocity vector in the coordinate system of the 1st receiver; e _k - vectors of conjugation errors а ₁ , а ₂ ,…, a _n. In matrix form for the case n = 3, the vector equation is written as:

According to the criterion of the minimum squared norm of the vector E of the conjugation errors:

J = || E || ² = (AX-B) ^T (AX-B)

дальностей и скоростей:find OLS estimates

ranges and speeds:

W=(A^TA)^-lA^T.

W = (A ^T A) ^-l A ^T.

When the matrix is inverted, a regularization procedure is provided.

и вычисляют векторы оценок пространственных координат объектов

в системах координат k-х приемников. Устанавливают векторы скоростей

в системе координат 1-го приемника.6. Choose m non-repeating combinations a ₁ (i), a ₂ (i), ..., a _n (i) with the smallest values of the coupling indices

and calculate vectors of estimates of spatial coordinates of objects

in coordinate systems of k-th receivers. Set the velocity vectors

in the coordinate system of the 1st receiver.

7. In the particular case of using two receivers (n = 2), the matrix A of the system of equations is reduced to the size of the first three rows and two columns, and the vector X contains estimates of two ranges. In this case, the speed of objects is estimated by two observation periods. On the contrary, with an increase in the number of receivers (n> 3), the dimensions of the matrix A increase.

Conclusion. The proposed method can be used in existing radio systems for the direction finding of stationary and moving objects at short range with the accuracy of determining the angular coordinates, which is characteristic of amplitude-phase methods. The implementation of the method does not require binding to the terrain map and allows detecting objects that are not resolvable by the Doppler frequency, due to the better spatial resolution of objects when scanning the view area with a narrow beam antenna.

Literature

1. Patent RU 2682382. Method for orientation of observer coordinate systems in a passive vision system. Publ. 03/19/19. Bul. No. 8.

2. Patent RU 2694023. A method for finding conjugate vectors of directions to moving objects. Publ. 07/08/2019. Bul. No. 19.

3. Patent RU 2700275. Method for determining the spatial position, speed and acceleration of an object in a passive scanning vision system Publ. 16.09.2019. Bul. No. 26.

Claims (1)

A method for determining the spatial coordinates and velocities of objects by a scanning multi-position radio system, which consists in placing several radio receivers in space, scanning the viewing area and mutually oriented by rotation matrices and base vectors connecting the coordinate systems of the receivers, forming unit vectors of direction vectors to objects in one scanning period, distributing these unit vectors by belonging to specific objects, taking into account the moments of time of formation of unit vectors and finding estimates of distances to objects and coordinates of velocity vectors by solving a system of equations of linear dependence of vectors, characterized in that an external radio transmitter is added, and scanning of receiver antennas is carried out electronically in a sequence of periods with a time delay , while in each scanning period the signals transmitted by the transmitter and received by the receivers are converted into complex spectra, spectral components are separated, the amplitudes of which x exceed the detection threshold of the useful signal and upon exceeding the threshold, the angular coordinates of the azimuth and the elevation of the objects are determined by the amplitude-phase method, after which, on the basis of the angular coordinates, the unit vectors of the direction vectors to the objects in the receiver coordinate systems are found, the unit vectors are grouped by belonging to specific objects, then from the coordinates of the unit vectors of each group and the differences of the scanning times, they compose the matrix A according to a certain rule, calculate the matrix of weight coefficients W = (A ^T A) ^-1 A ^T , where “T” and “-1” are symbols of transposition and matrix inversion, multiply the matrix W on the left by the vector B coordinates of the base vectors and obtain the vector X = W⋅В of the estimates of the ranges and coordinates of the velocity vector for each group of conjugate vectors, multiply the estimates of the distances by the unit vectors and obtain the vector of the spatial coordinates of the object.