KR102061228B1 - Method and system for determining location using Newton iteration - Google Patents

Abstract

A method of determining the position of a target using a plurality of transmitters and a plurality of receivers includes a plurality of transmitters and a propagation delay time, which is a time required for the radio wave sent from the transmitter to be reflected by the surface of the target and received by the receiver. Determining a position of a target according to a linear estimation technique, based on the determination of each combination between the plurality of receivers and the position at which the plurality of elliptic trajectories determined corresponding to each of the determined plurality of propagation delay times intersect. It may include.

Description

Location and system for determining location using Newton iteration}

The present invention relates to a positioning method and system using Newton iteration that increases accuracy while reducing computational throughput.

The basic beamforming algorithm and the capon beamforming algorithm can be used to estimate the Direction of Departure (DOD) and the Direction of Arrival (DOA) in a bistatic radar environment.

To ensure the accuracy of DOD / DOA estimation, the search range is equal to the full azimuth range for Uniform Linear Array (ULA), and the search range is equal to the full azimuth range for Uniform Circular Array (UCA). This is possible only by setting the full elevation angle and setting the search interval very tightly.

In monostatic environment with one transmitter and one receiver, DOA is estimated by two-dimensional search when considering only azimuth angle and two-dimensional search when considering azimuth elevation angle, so calculation and execution time are not long. In the case of a bistatic environment, even when only the azimuth angle is considered, the two-dimensional search is performed, thereby increasing the amount of computation and the execution time.

It is to provide a method and system for positioning using Newton iteration.

The technical problem to be achieved by the present embodiment is not limited to the technical problems as described above, and other technical problems may be inferred from the following embodiments.

According to an aspect, a method of determining a position of an object may include: a receiving antenna array including a plurality of receiving antennas, in which a signal sent from the transmitting antenna array including a plurality of transmitting antennas is reflected from the object; Receiving, determining a cost function used to determine DOA and DOD according to the received signal, and calculating the DOA, which is an angle between the DOD and the receiving antenna array, the object between the transmitting antenna array and the object. Determining according to a function, and updating the determined DOD and the determined DOA based on a Newton iteration scheme.

According to another aspect, a system for determining a position of an object includes a transmit antenna array including a plurality of transmit antennas for transmitting a signal, and a plurality of receive antennas for receiving a signal reflected from the object by the transmitted signal An array, and a cost function used to determine DOA and DOD according to the received signal, and the DOA, which is an angle between the DOD and the receiving antenna array, the object between the transmit antenna array and the object, to the cost function. And a processor for determining accordingly and for updating the determined DOD and the determined DOA based on a Newton iteration scheme.

1 is a view for explaining a bistatic radar system.
2 is a flowchart illustrating a method of determining a position of an object according to an exemplary embodiment.
3 is a diagram illustrating a system for determining a position of an object, according to an exemplary embodiment.
4A and 4B are graphs illustrating MSE values of an estimate according to a beamforming DOD / DOA estimation algorithm with respect to SNR, with and without applying Newton iteration according to an embodiment.

Hereinafter, only exemplary embodiments will be described in detail with reference to the accompanying drawings. The following examples are intended to embody the technical idea, but do not limit or limit the scope. From the detailed description and examples, what can be easily inferred by the experts in the relevant technical field is interpreted as belonging to the scope of rights.

As used herein, the term “consisting of” or “comprising” should not be construed as including all of the various elements, or steps, described in the specification, and some or some of them may be included. Should not be included, or should be construed to further include additional components or steps. In addition, the terms "... unit", "module", etc. described in the specification mean a unit for processing at least one function or operation, which may be implemented in hardware or software or a combination of hardware and software. .

In addition, terms including ordinal numbers, such as “first” or “second”, as used herein may be used to describe various components, but these terms may distinguish one component from another or It can be used for convenience.

Hereinafter, exemplary embodiments will be described in detail with reference to the accompanying drawings.

Throughout the specification, it is assumed that the number of transmitters is M (M> 1 is an integer) and the number of receivers is N (an integer of N> 1).

Variables dependent on any transmitter are represented using index m and variables associated with any receiver are represented using index n. At this time, m is an index assigned so as not to overlap with each transmitter as an arbitrary integer from 1 to M. In addition, n is an arbitrary integer from 1 to N, which is an index assigned to each receiver so as not to overlap. In addition, a variable that depends on both the transmitter and the receiver is defined as mn by enumerating the index m for the transmitter and the index n of the receiver, and signals sent from the M transmitters may be orthogonal with each other.

1 is a view for explaining a bistatic radar system.

Referring to FIG. 1, a transmitter and a receiver are separated in a bistatic radar system.

In addition, the radar system includes a transmit antenna array 110 including a plurality of transmit antennas 111, 112, 113, and 114 and a receive antenna array 130 including a plurality of receive antennas 131, 132, 133, and 134. It may include. The transmitting antenna array and the receiving antenna array may be, for example, a uniform linear array in which a distance between adjacent transmitting antennas and adjacent receiving antennas is constant and arranged in a straight line, but is not limited thereto.

The plurality of transmit antennas 111, 112, 113, and 114 may transmit signals that are orthogonal to each other. The signal sent from each of the plurality of transmission antennas 111, 112, 113, and 114 may constitute a transmission signal of the transmission antenna array 110 as a whole.

The signal sent from the transmit antenna array 110 may be reflected on the surface of the object 120. The object 120 may have a unique radar cross section (RCS). RCS means an average area defined to represent the amount of reflection when a predetermined signal is reflected on an object that is a reflector.

The reception antenna array 130 may receive a signal transmitted from the transmission antenna array 110 and reflected from the object. In this case, each of the plurality of reception antennas 131, 132, 133, and 134 constituting the reception antenna array 130 may receive a signal reflected from the object.

는 송신 안테나 어레이(110)를 기준으로 할 때, 대상체의 방위각을 나타낼 수 있다. DOA(Direction of Arrival)는

은 수신 안테나 어레이(130)를 기준으로 할 때, 대상체의 방위각을 나타낼 수 있다. Direction of Departure (DOD)

May represent an azimuth angle of the object when the transmission antenna array 110 is referred to. DOA (Direction of Arrival)

May represent an azimuth angle of the object when the reception antenna array 130 is referred to.

2 is a flowchart illustrating a method of determining a position of an object according to an exemplary embodiment.

In operation 210, the positioning apparatus may receive a signal, which is transmitted by using a transmission antenna array including a plurality of transmission antennas, reflected from the object using a reception antenna array including a plurality of reception antennas.

In addition, a receive antenna array consisting of N receive antennas may receive a signal sent from a transmit antenna array consisting of M transmit antennas and reflected on the surface of the target.

Hereinafter, it is assumed that the number of subjects is P (an integer of P> 1). The index p, which is an integer from 1 to P, is used for the variable associated with the object.

  A receive antenna array consisting of N receive antennas may receive a signal sent from a transmit antenna array consisting of M transmit antennas and reflected on the surface of the target.

및

로 나타낼 수 있다.Both the transmit antenna array and the receive antenna array may be equally spaced linear arrays (ULA). In addition, the DOD (Direction of departure) and the DOA (Directon of arrival) for the p-th subject, respectively

And

It can be represented as.

In this case, an array vector including information on the phase difference of the reception antenna may be defined as in Equation 1. dr represents the distance between adjacent receiving antennas.

In addition, an array vector including information about a phase difference of a transmitting antenna may be defined as in Equation 2. dt represents the distance between adjacent transmit antennas.

과 송신 안테나 응답

을 각각 수학식 3과 수학식 4와 같이 나타낼 수 있다.In addition, a reception antenna response corresponding to an array vector of a transmission antenna and a reception antenna for a plurality of objects using equations (1) and (2).

And transmit antenna response

May be represented as in Equation 3 and Equation 4, respectively.

는 각각 P 개의 대상체들의 RCS나타내며 P 개의 대상체들의 RCS들에 나타내는

가 정의될 수 있다. 이 때, 수신 안테나 어레이에 의하여 수신된 수신 신호는 수학식 5 및 수학식 6과 같이 정의될 수 있다.

Each represents the RCS of P objects and represents the RCSs of P objects.

Can be defined. In this case, the reception signal received by the reception antenna array may be defined as Equation 5 and Equation 6.

In Equations 5 and 6, L represents the number of snapshots for the received signal, and S represents the coded pulse matrix sent from the transmit antenna array.

인 복소수 가우시안 랜덤 벡터(complex Gaussian random vector)이다.In addition, in order to distinguish signals sent from each of the plurality of transmit antennas constituting the transmit antenna array, signals sent from the plurality of transmit antennas may be orthogonal to each other. In addition, E represents the noise component, the mean of the real part and the imaginary part is 0, respectively, and the variance is

Is a complex Gaussian random vector.

In addition, matched filtering may be performed on the received signals in order to distinguish the signals sent from each of the plurality of transmitting antennas in the receiving antenna array. The matched filtered reception signal may be defined as shown in Equation 7.

In order to model the matched filtered signal in the bistatic multiple input / output radar system, if the transform is converted into an independent sufficient statistic vector using Equation 7, a transform equation such as Equation 8 is obtained. Can be.

Equation 8 is for the case where the number of objects is one. In this case, by expanding Equation 8 to the case where the number of objects is P, the received signals for the plurality of targets may be defined as in Equations 9 to 11.

In Equation 10, a matrix K for P objects is defined by merging the column vectors κ for each object. In Equation 11, a column vector H is defined by merging RCSs for P objects.

In step 220, the positioning device may determine the cost function used for DOA and DOD determination according to the received signal.

The cost function is a function of the first angle variable corresponding to any DOD and the second angle variable corresponding to any DOA, wherein the value of the cost function when the first and second angle variables are the DOD and DOA of the object. This can be maximum or minimum.

및 케이폰DOD/DOA 추정 알고리즘(Capon Beamforming DOD/DOA estimation algorithm)에 이용되는

이 정의된다.According to Equations 12 and 13, the cost function used for the Conventional Beamforming DOD / DOA estimation algorithm

And a Capon Beamforming DOD / DOA estimation algorithm.

Is defined.

은 수학식 14와 같이 산출된다. Where the covariance matrix

Is calculated as shown in equation (14).

In operation 230, the positioning apparatus may determine a DOD, which is an angle of the object with respect to the transmitting antenna array, and a DOA, which is an angle of the object with respect to the receiving antenna array, according to a cost function.

가 최대인 제 1 각도 변수 및 제 2 각도 변수 값이 대상체의 DOD 및 DOA로 결정된다. 또한, 케이폰 빔형성DOD/DOA 추정 알고리즘에 의하면, 수학식 16에 따라

비용함수가 최소인 제 1 각도 변수 및 제 2 각도 변수 값이 대상체의 DOD 및 DOA로 결정된다.According to the classical beamforming DOD / DOA estimation algorithm, the cost function

The first angle variable and the second angle variable value of which are maximum are determined as the DOD and DOA of the object. In addition, according to the Keppon beamforming DOD / DOA estimation algorithm,

The first and second angle variable values having a minimum cost function are determined as the DOD and DOA of the object.

The positioning device substitutes a predetermined number of search values into each of the first and second angle variables, so that each of the search values of the first angle and the search value of the second angle has a maximum or minimum value of the cost function. Can be determined by DOD and DOA. For example, in the classical beamforming DOD / DOA estimation algorithm, the first angle search value and the second angle search value having the maximum value of the cost function may be estimated as the DOD and DOA of the object. In addition, in the case of the KEPCO beamforming DOD / DOA estimation algorithm, the first angle search value and the second angle search value having the minimum value of the cost function may be estimated as the DOD and DOA of the object. The predetermined number of search values may be values selected at predetermined angular intervals from -90 degrees to 90 degrees.

In operation 240, the positioning apparatus may update the determined DOD and the determined DOA for the object based on the Newton iteration method.

As the Newton iteration technique is repeatedly performed on the initial estimate obtained based on the wide interval search values, the error of the initial estimate may be reduced.

In the beamforming DOD / DOA estimation algorithm, the partial derivative of the corresponding cost function to the DOD or DOA of the object can be used to obtain a Newton iteration equation using the property of having a value of zero. Since Newton iteration can be applied to both classical and kapon estimation algorithms, the cost function can be generalized as shown in Equation 17 for convenience.

이고, 케이폰 빔형성 DOD/DOA 추정 알고리즘의 경우 C는

일 수 있다.In Equation 17, C for the classical beamforming DOD / DOA estimation algorithm

In the case of the Keppon beamforming DOD / DOA estimation algorithm, C

Can be.

Newton iteration for simultaneously estimating DOD and DOA of an object in a bistatic system may be performed as in Equation 18.

Equation 18 may be specifically derived according to Equations 19 to 26.

In the existing bistatic multi-input / output radar system, the DOD and DOA are estimated first through the DOD / DOA estimation algorithm. For accurate DOD / DOA estimation and performance analysis, the full azimuth range must be explored in detail. However, in the present disclosure, since the correct DOD / DOA is estimated through the Newton iteration technique, the DOD / DOA search may be performed at a wide interval.

3 is a diagram illustrating a system 300 for determining a position of an object, according to an exemplary embodiment.

The system 300 according to an embodiment may include a transmit antenna array 110, a receive antenna array 130, and a positioning device 140.

The transmit antenna array 110 may be an equally spaced linear array (ULA) including a plurality of transmit antennas. A plurality of transmit antennas included in the transmit antenna array may transmit signals that are orthogonal to each other. The signal sent from each of the plurality of transmit antennas may constitute the transmit signal of the transmit antenna array as a whole.

According to an embodiment, the receiving antenna array 130 may be an equally spaced linear array (ULA) including a plurality of transmitting antennas. The reception antenna array 130 may receive a signal transmitted from the transmission antenna array 110 and reflected from the object. At this time, each of the plurality of receiving antennas constituting the receiving antenna array 130 may receive a signal reflected from the object.

According to an embodiment, the positioning device 140 may include a processor.

Processors should be interpreted broadly to include general purpose processors, central processing units (CPUs), microprocessors, digital signal processors (DSPs), controllers, microcontrollers, state machines, and the like. In some circumstances, a “processor” may refer to an application specific semiconductor (ASIC), a programmable logic device (PLD), a field programmable gate array (FPGA), or the like. The term "processor" refers to a combination of processing devices such as, for example, a combination of a DSP and a microprocessor, a combination of a plurality of microprocessors, a combination of one or more microprocessors in conjunction with a DSP core, or a combination of any other such configuration. May be referred to.

The processor may determine a cost function used to determine DOA and DOD of the object according to the signal received by the receive antenna array 130.

The cost function is a function of the first and second angle variables, where the value of the cost function may be the maximum or minimum when the first and second angle variables are DOD and DOA of the object.

For example, the processor may perform matched filtering on the received signal. In addition, the processor may determine the cost function based on the matched filtered signal.

In addition, the processor may determine the DOD, which is the angle of the object with respect to the transmit antenna array 110, and the DOA, which is the angle of the object with respect to the receive antenna array 130, according to the cost function.

The processor assigns a predetermined number of search values to each of the first angle variable and the second angle variable, so that each of the search values of the first angle and the search value of the second angle whose value of the cost function is the maximum or minimum is respectively an object. Can be determined by DOD and DOA. The predetermined number of search values may be values selected at predetermined angular intervals from -90 degrees to 90 degrees.

In addition, the processor may update the determined DOD and the determined DOA based on the Newton iteration scheme.

The processor may determine the location of the object using the updated DOA and the updated DOD.

4A and 4B are graphs illustrating an MSE value of an estimate according to a beamforming DOD / DOA estimation algorithm with respect to SNR, with and without applying Newton iteration according to an embodiment.

In FIGS. 4A and 4B, it is assumed that the number of objects is two, and the simulation is performed. At this time, the DOD and DOA of the first object are 30 degrees and 0 degrees, respectively, and the DOD and DOA of the second object are 50 degrees and 30 degrees, respectively.

4A and 4B, the graphs 410 and 510 are for the first object, and the graphs 420 and 520 are for the second object.

In addition, in FIGS. 4A and 4B, the indexes DOD and DOA are cases where Newton iteration is not applied, and the NT DOD and NT DOA are cases where Newton iteration is applied.

In this case, when the Newton iteration technique is not applied, the interval of DOD / DOA search values is set to 1 degree interval, and in the case of the simulation using the Newton iteration technique, the search interval is set to 3 degrees.

In FIG. 4A, the graph 410 and the graph 420 are classical beamforming DOD / DOA algorithms to which Newton iteration is applied as the SNR increases from -5 dB to 15 dB at 5 dB intervals for each of the first object and the second object. The MSE value for an estimate of.

In FIG. 4B, the graph 510 and the graph 520 each show a kapon beamforming DOD / DOA to which Newton iteration is applied as the SNR increases from -5 dB to 15 dB at 5 dB intervals for each of the first object and the second object. Represents an MSE value for an estimate of an estimation algorithm.

In the case of the classical beamforming DOD / DOA estimation algorithm in FIG. 4A, as the graphs 410 and 420 show, when the Newton iteration is not applied, the MSE has a value close to 1, and the MSE is increased even though the SNR is increased. On the other hand, when Newton iteration is applied, it has a smaller MSE value in all SNRs than when Newton iteration is not applied, and as the SNR increases, the MSE decreases significantly, and when the SNR is 15 DB, it decreases below 0.01. .

In the case of the Keppon beamforming DOD / DOA estimation algorithm in FIG. 4B, as the graphs 510 and 520 show, when the Newton iteration is not applied, the MSE value is approximately 1, and the MSE becomes large even if the SNR increases. Without decreasing, the MSE value converges to one. However, when Newton iteration is applied, it has a smaller MSE value in all SNRs than when Newton iteration is not applied, and as the SNR increases, the MSE decreases significantly and decreases below 0.01 when the SNR is 15 DB.

The foregoing description of the present invention is intended for illustration, and it will be understood by those skilled in the art that the present invention may be easily modified in other specific forms without changing the technical spirit or essential features of the present invention. will be. Therefore, it should be understood that the embodiments described above are exemplary in all respects and not restrictive. For example, each component described as a single type may be implemented in a distributed manner, and similarly, components described as distributed may be implemented in a combined form.

The scope of the present invention is shown by the following claims rather than the above description, and all changes or modifications derived from the meaning and scope of the claims and their equivalents should be construed as being included in the scope of the present invention. do.

Claims (9)

A method of determining the position of an object in a bistatic system comprising a transmit antenna array and a receive antenna array separated from each other,
Receiving a signal reflected by the transmission signal using the transmission antenna array including a plurality of transmission antennas from the object using the reception antenna array including a plurality of reception antennas;
Determining a cost function used for DOA and DOD determination according to the received signal;
Determining the DOD, which is an angle between the transmitting antenna array and the object, and a DOA, which is an angle between the receiving antenna array and the object, according to the cost function; And
Updating the determined DOD and the determined DOA based on a Newton iteration scheme;
In the receiving step,
The plurality of transmit antennas each transmits a signal orthogonal to each other,
In determining the cost function,
The cost function is a function of a first angle variable corresponding to the DOD and a second angle variable corresponding to the DOA,

Is selected from one of the first cost function used for the classical beamforming estimation algorithm and the second cost function used for the kapon estimation algorithm,
Where P is the cost function,

Is the first angle variable,

Is the second angle variable, K is a column vector having the first angle variable and the second angle variable as elements, H is a column vector having the radar cross section of the object as an element, C is a covariance matrix of the received signal

Is determined based on the classical beamforming estimation algorithm.

In the case of the K- phone estimation algorithm, C is

ego,
Determining according to the cost function,
When the first angle variable and the second angle variable are DOD and DOA of the object, the value of the first cost function is maximum, the value of the second cost function is minimum,
The updating step,
To estimate DOD and DOA of the subject at the same time in the bistatic system

Update the determined DOD and the determined DOA based on the Newton iteration method derived by partial differentiation,
In this case, M is the number of transmit antennas, N is the number of receive antennas, b _h is an array vector including information on the phase difference of the transmit antenna, and a _i includes information about the phase difference of the receive antenna. The array vector. The method of claim 1,
Determining the location of the object using the updated DOA and updated DOD. delete The method of claim 1,
Determining according to the cost function,
Substituting a predetermined number of search values into each of the first and second angle variables, the search value of the first angle and the search value of the second angle having the maximum or minimum value of the cost function are respectively converted into the DOD. And determining with the DOA. The method of claim 4, wherein
Determining according to the cost function
The predetermined number of search values are values selected at predetermined angular intervals of an angle from -90 degrees to 90 degrees. The method of claim 1,
Determining the cost function,
Performing matched filtering on the received signal; And
Determining the cost function based on a matched filtered signal. The method of claim 1,
Wherein the transmit antenna array and receive antenna array are a uniform linear array (ULA). In a bistatic system for determining the position of an object,
A transmit antenna array comprising a plurality of transmit antennas for sending a signal;
A receiving antenna array including a plurality of receiving antennas for receiving the signal from which the transmitted signal is reflected from an object; And
Determine a cost function used for DOA and DOD determination according to the received signal,
The DOD, which is an angle between the transmitting antenna array and the object, and the DOA, which is an angle between the receiving antenna array and the object, are determined according to the cost function.
And a positioning device including a processor for updating the determined DOD and the determined DOA based on a Newton iteration scheme.
The plurality of transmit antennas each transmits a signal orthogonal to each other,
The cost function is a function of a first angle variable corresponding to the DOD and a second angle variable corresponding to the DOA,

Is selected from one of the first cost function used for the classical beamforming estimation algorithm and the second cost function used for the kapon estimation algorithm,
Where P is the cost function,

Is the first angle variable,

Is the second angle variable, K is a column vector having the first angle variable and the second angle variable as elements, H is a column vector having the radar cross section of the object as an element, C is a covariance matrix of the received signal

Is determined based on the classical beamforming estimation algorithm.

In the case of the K- phone estimation algorithm, C is

ego,
When the first angle variable and the second angle variable are DOD and DOA of the object, the value of the first cost function is maximum, the value of the second cost function is minimum,
The processor is
To estimate DOD and DOA of the subject at the same time in the bistatic system

Update the determined DOD and the determined DOA based on the Newton iteration method derived by partial differentiation,
In this case, M is the number of transmit antennas, N is the number of receive antennas, b _h is an array vector including information on the phase difference of the transmit antenna, and a _i includes information about the phase difference of the receive antenna. The array vector. The method of claim 8,
And the positioning device performs matched filtering on the received signal and determines a cost function according to the matched filtered signal.

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