Information processing device, information processing method, program, and information processing system

Abstract

An information processing device comprising: an acquisition unit that acquires a-stage tensor information X that is expressed using an a (a being an integer of at least 2) number of axes that specify each of a plurality of measurement information pertaining to measurement, said tensor information X having, as a component thereof, information on the basis of measurement results corresponding to each of an a number of measurement information; a separation information calculation unit that calculates separation information BX which is the tensor product of tensor information X and a 2a-stage separation tensor B; an updated tensor calculation unit that, using the separation information BX, calculates a 2a-stage updated tensor ΔB on the basis of the sum of the tensor products of the separation tensor B and the 2a-stage weighted tensors corresponding to each measurement information; and an update unit that uses the updated tensor ΔB and updates separation tensor B such that separation tensor B in the separation information BX whitens and makes the tensor information X more independent.

Description

[Technical Field]

[0001] The present invention relates to an information processing device, an information processing method, a program, and an information processing system. [Background technology]

[0002] Traditionally, the analysis of tensor-formatted data using Independent Component Analysis (ICA) has been well-known. One type of ICA is called Multilinear ICA (MICA), which incorporates higher-order tensors. Regarding MICA, the Higher-Order Singular Value Decomposition (HOSVD) and Higher-Order Orthogonal Iteration (HOOI) methods based on the tensor decomposition method proposed by Tucker are well-known

[26] -

[30] . Summary of the Invention [Problem to be solved by the invention]

[0003] However, in the techniques described in

[26] -

[30] , data categorized by each axis of a third-order tensor format is decomposed into matrices, which separates data belonging to one category. For this reason, the techniques described in

[26] -

[30] were unable to effectively utilize the classification of tensor-formatted data.

[0004] The present invention has been made in light of such a situation, and one exemplary purpose of an aspect of the present invention is to provide a technique that enables independent component analysis to be performed using each axis category in tensor-format data. [Means for solving the problem]

[0005] One aspect of the present invention is an information processing device comprising: an acquisition unit that acquires a-th order tensor information X, which is expressed using a (a: integer greater than or equal to 2) axes that respectively identify multiple pieces of measurement information related to the measurements and whose components are information based on the results of measurements corresponding to each of the a pieces of measurement information; a separation information calculation unit that calculates separation information BX, which is the tensor product of the tensor information X and a 2a-th order separation tensor B; an update tensor calculation unit that uses the separation information BX to calculate a 2a-th order update tensor ΔB based on the sum of the tensor product of a 2a-th order weight tensor corresponding to each piece of measurement information and the separation tensor B; and an update unit that uses the update tensor ΔB to update the separation tensor B so that the separation tensor B whitens and isolates the tensor information X in the separation information BX.

[0006] In the above aspect, the acquisition unit acquires tensor information based on signals transmitted from multiple transmitters at different times and received by multiple receivers, and the tensor information may be expressed using an axis that identifies multiple pieces of transmitter information each corresponding to one of the multiple transmitters, and an axis that identifies multiple pieces of receiver information each corresponding to one of the multiple receivers.

[0007] Another aspect of the present invention is an information processing system including a plurality of transmitting units, a plurality of receiving units, and the above-described information processing device.

[0008] Any combination of the above components, and any transformation of the present invention into a method, device, system, recording medium, computer program, etc., are also valid aspects of the present invention. [Effects of the Invention]

[0009] According to the present invention, independent component analysis can be performed using each axis category in tensor-format data. [Brief explanation of the drawings]

[0010] [Figure 1] FIG. 1 is a diagram illustrating an overview of a Doppler radar. [Figure 2]FIG. 1 is a diagram showing the flow of online CF-ICA. [Figure 3] FIG. 3(a) is a diagram showing the type of received data tensor in ICA, and FIG. 3(b) is a diagram showing the type of received data tensor in HOT-ICA. [Figure 4] FIG. 10 is a diagram for explaining separation information. [Figure 5] FIG. 10 is a diagram for explaining the product of separation information and conjugate information. [Figure 6] FIG. 1 shows a fourth-order unit tensor. [Figure 7] FIG. 10 is a diagram for explaining an updated tensor. [Figure 8] FIG. 10 is a diagram illustrating the factors of the weight tensor corresponding to the receiving antenna Rx1. [Figure 9] FIG. 1 illustrates an example of a measurement system. [Figure 10] FIG. 2 is a diagram illustrating an example of the arrangement of transmitting antennas and receiving antennas. [Figure 11] FIG. 1 is a diagram showing the arrangement of an antenna and a target. [Figure 12] Figures 12(a-1) to (a-9) show the spectrum of the mixed signal in the final time interval when there are three transmitting antennas and three receiving antennas, and Figures 12(b-1) to (b-9) show the spectrum of the separated signal by HOT-ICA in the final time interval when there are three transmitting antennas and three receiving antennas. [Figure 13] Figures 13(a-1) to (a-9) show the time variation of the normalized electric field strength at each frequency of the mixed signal when there are three transmitting antennas and three receiving antennas, and Figures 13(b-1) to (b-9) show the time variation of the normalized electric field strength at each frequency of the separated signal by HOT-ICA when there are three transmitting antennas and three receiving antennas. [Figure 14] FIG. 10 shows a spectrogram of a separated signal for target H1. [Figure 15] FIG. 1 shows a spectrogram of a separated signal relative to noise. [Figure 16]FIG. 1 is a diagram showing the arrangement of antennas, targets, and obstacles. [Figure 17] Figures 17(a-1) to (a-4) show the spectrum in the final time interval of the mixed signal when there are two transmitting antennas and two receiving antennas in an obstacle environment, and Figures 17(b-1) to (b-4) show the spectrum in the final time interval of the separated signal by CF-ICA when there are two transmitting antennas and two receiving antennas in an obstacle environment. [Figure 18] Figures 18(a-1) to (a-4) show the time variation of the electric field strength at each frequency of the mixed signal when there are two transmitting antennas and two receiving antennas in an obstacle environment, and Figures 18(b-1) to (b-4) show the time variation of the electric field strength at each frequency of the separated signal by CF-ICA when there are two transmitting antennas and two receiving antennas in an obstacle environment. [Figure 19] Figures 19(a-1) to (a-4) show the spectrum in the final time interval of the mixed signal when there are two transmitting antennas and two receiving antennas in an obstacle environment, and Figures 19(b-1) to (b-4) show the spectrum in the final time interval of the separated signal by HOT-ICA when there are two transmitting antennas and two receiving antennas in an obstacle environment. [Figure 20] Figures 20(a-1) to (a-4) show the time variation of the electric field strength at each frequency of the mixed signal when there are two transmitting antennas and two receiving antennas in an obstacle environment, and Figures 20(b-1) to (b-4) show the time variation of the electric field strength at each frequency of the separated signal by HOT-ICA when there are two transmitting antennas and two receiving antennas in an obstacle environment. [Figure 21] Figures 21(a-1) to (a-4) show the spectrum in the time interval at the end of the mixed signal when there are two transmitting antennas and two receiving antennas in an obstacle environment, and Figures 21(b-1) to (b-4) show the spectrum in the time interval at the end of the separated signal by HOT-ICA when there are two transmitting antennas and two receiving antennas in an obstacle environment and the learning weight for receiving antenna Rx1 is set to 0. [Figure 22] Figures 22(a-1) to (a-4) show the time variation of the electric field strength at each frequency of the mixed signal when there are two transmitting antennas and two receiving antennas in an obstacle environment, and Figures 22(b-1) to (b-4) show the time variation of the electric field strength at each frequency of the separated signal by HOT-ICA when there are two transmitting antennas and two receiving antennas in an obstacle environment, with the learning weight for receiving antenna Rx1 set to 0. [Figure 23] 1 is a diagram showing the overall configuration of an information processing system including an information processing device according to an embodiment of the present invention; [Figure 24] FIG. 2 is a functional block diagram illustrating an example of a configuration of an information processing device according to the embodiment. [Figure 25] FIG. 2 is a functional block diagram for explaining functions of a processing unit according to the embodiment. [Figure 26] 10 is a flowchart illustrating an example of processing by the information processing device according to the embodiment. [Figure 27] FIG. 1 is a diagram showing the arrangement of transmitting and receiving antennas Txm, Rxn and a target Hk. [Figure 28] FIG. 10 is a diagram showing the directivity (gain) of a transmitting and receiving antenna according to an embodiment of the present invention, measured at a distance of about 1.5 mm. [Figure 29] Figures 29(a-1) to (a-9) show the spectrum in the final time interval of the mixed signal when there are three transmitting antennas and three receiving antennas, and Figures 29(b-1) to (b-9) show the spectrum in the final time interval of the separated signal by HOT-ICA when there are three transmitting antennas and three receiving antennas. [Figure 30] FIG. 10 is a diagram showing the settings for estimating the direction of arrival using signal paths of transmitting and receiving antennas Tx1-Rx1 and Tx2-Rx1 for target H1. [Figure 31] FIG. 10 is a diagram showing the estimated position of a target H1. DETAILED DESCRIPTION OF THE INVENTION

[0011] The present invention will be described below based on a preferred embodiment with reference to the drawings. The same or equivalent components, parts, and processes shown in each drawing are designated by the same reference numerals, and redundant descriptions will be omitted where appropriate. Furthermore, the embodiment is merely an example and does not limit the invention, and all features and their combinations described in the embodiment are not necessarily essential to the invention.

[0012] 0. Overview This paper proposes Higher-Order Tensor Independent Component Analysis (HOT-ICA), a tensor ICA method that effectively exploits the inter-axis relationships of separated tensors. Conventional tensor-based ICA, such as multilinear ICA (MICA), does not fully utilize the high dimensionality of tensors. In such cases, matrixing invalidates data classification. HOT-ICA improves generalization by incorporating information about the transmission and reception paths of signals rather than processing all acquired signals in parallel. Within the framework of non-contact measurement, we develop a system that can effectively measure and separate biological signals using microwaves in environments with obstacles, which are typically difficult to achieve. We set up a simulation environment that takes into account the antenna and target placement, as well as electromagnetic factors. We then demonstrate the effectiveness of HOT-ICA through numerical experiments simulating non-contact measurements of human respiration and heart rate.

[0013] 1. Introduction Traditionally, heart rate monitoring has involved contact-based measurement, where electrodes are attached to the body to record an electrocardiogram. However, in recent years, research has attempted to measure vital signs without contacting the human body. Lin [1] was the first to detect respiration using microwaves. Since then, there has been a lot of research into measuring respiration and heart rate using Doppler radar. Some studies do not take into account the presence of obstacles [2]-[5], while others use obstacles in experiments to simulate measurements during disasters [6]-

[11] .

[0014] By using a MIMO (Multi-Input Multi-Output) configuration with multiple transmitting and receiving antennas in a Doppler radar, it is possible to detect multiple targets and increase the amount of information available, such as which transmitting and receiving antennas the electromagnetic waves passed through. For example, there is a system

[12] that detects breathing and heartbeats for each target. This system uses a 24 GHz millimeter-wave, frequency-modulated continuous wave (FMC) MIMO radar and performs signal separation using target ranging. However, due to its high frequency band, it can only perform well at short distances without obstacles. Therefore, the use of a 2.5 GHz microwave CW Doppler radar with a high signal-to-noise ratio is expected to be more effective.

[0015] In environments with obstacles and multiple targets, it is necessary to separate and measure target signals from other targets and noise. As an example of source separation, Sakamoto et al.

[13] conducted an experiment using an X-band array radar to separate a target's heartbeat signal from other targets using beamforming. However, in environments with obstacles, the resolution is low because microwaves are used, which can propagate between obstacles and travel between the target and the antenna. In such cases, other source separation techniques are required, and blind source separation (BSS) is commonly used. BSS is a method for estimating the original signal from multiple mixed signals. Independent Component Analysis (ICA) is a representative BSS technique. ICA aims to remove noise by linearly transforming mixed signals into separated signals based on statistical properties, and calculates a separation matrix that performs this linear transformation. The first paper on ICA was published by Herault and Ans et al.

[14] . The history of ICA is described in detail in

[15] , and mathematical analysis and the numerous algorithms studied are summarized in

[16] . ICA is also frequently used in the field of frequency domain speech signal processing

[17] -

[19] .

[0016] In reference [9], the in-phase and quadrature components obtained by quadrature detection were treated as two independent real signals, and ICA was performed. However, based on the framework of complex-valued neural networks

[20] -

[22] , the set of in-phase and quadrature components obtained by quadrature detection is essentially a single complex signal. This specification also deals with complex signals as a whole. In addition, we would like to be able to adaptively process changes in the properties of complex signals over time due to changes in the measurement environment, such as target movement or the presence or absence of obstacles. To this end, online ICA

[23] ,

[24] , which adaptively processes data each time a new data sample is given, has been proposed.

[0017] In MIMO remote sensing systems, data can be categorized by utilizing information about the data acquisition environment (physical characteristics), such as the origin of the received signal from the transmitting and receiving antennas. Therefore, it is possible to effectively use higher-order tensors in ICA calculations. MICA has been proposed as an effective method. The most commonly used MICA methods, such as Higher-Order Singular Value Decomposition (HOSVD) and Higher-Order Orthogonal Iteration (HOOI), are based on the tensor decomposition method proposed by Tucker

[25] and have been evaluated for their effectiveness

[26] -

[30] . This method first creates a core tensor by applying singular value decomposition (SVD) to each mode of a third-order tensor. The core tensor is equivalent to the diagonal singular value matrix in conventional SVD. A prediction tensor is then constructed using the core tensor and the factor matrices generated by SVD for each mode of the matrix decomposition. The prediction tensor is then iteratively updated until the error between the prediction tensor and the original data tensor is sufficiently small.

[0018] For example, there is MICA, which treats EEG as waveform data

[31] -

[33] . In

[32] , a method is proposed in which frequency bins, time frames, and cases are set on the axes of a data tensor, and MICA and clustering are used to identify symptoms from patient data. MICA is also frequently used in the field of image data analysis, including magnetoencephalography

[33] , as well as EEG

[34] ,

[35] . A method that extends MICA to higher dimensions has also been proposed

[36] .

[0019] In the MICA framework described above, if we were to handle data tensors in which the properties of each axis category are independent, we could have processed them using methods such as HOSVD and HOOI, which are based on the Tucker decomposition. However, these methods do not effectively utilize the fact that the tensor is a third-order tensor, and are based on the premise that the tensor axes are separated by matrix conversion. By using a higher-order method, it should be possible to maintain the relationships between each axis and achieve more meaningful tensor ICA processing.

[0020] This paper proposes Higher Order Tensor Independent Component Analysis (HOT-ICA) as a tensor ICA process that effectively utilizes the axis categories of the received signal data tensors from multiple targets in order to realize non-contact measurement of the respiration and heart rate of multiple people in an environment where obstacles exist. We construct a continuous wave (CW) multi-input multi-output (MIMO) Doppler radar and demonstrate the effectiveness of HOT-ICA processing.

[0021] HOT-ICA has the advantage of being able to manipulate the contribution of each component according to its origin when evaluating independence. HOT-ICA with weighting of the separation tensor is expected to improve the effectiveness of MIMO-based remote sensing. In this paper, we conducted numerical experiments in which the instability of the received signal caused by the installation of obstacles in the measurement environment was reflected in a simulation environment. The effectiveness of HOT-ICA with weighting of the separation tensor was demonstrated by comparing the separation results of the conventional CF-ICA

[11] and HOT-ICA before and after weighting of the separation tensor.

[0022] This specification is structured as follows. Section 2 introduces the theory of Doppler radar and ICA as a conventional method. Section 3 introduces the theory of HOT-ICA proposed in this specification. Section 4 explains the method and data settings used in the experiment. Section 5 presents the experimental results. Section 6 summarizes Sections 2 to 5. Section 7 explains an example of the configuration of a system using HOT-ICA, and Section 8 explains an example of the processing performed by that system. Sections 9 and 10 explain direction-of-arrival estimation based on HOT-ICA.

[0023] 2.Physical / mathematical background 2-1. Doppler radar Figure 1 shows a measurement scene in an environment with no obstacles. First, microwaves transmitted from transmitting antenna Tx1 propagate to the target, are backscattered by the body surface, and are received by receiving antennas Rx1, Rx2, .... Next, microwaves are transmitted from transmitting antenna Tx2, and measurement is carried out in the same way. In this way, measurement proceeds while changing the transmitting antenna that transmits the microwave. The proposed CW Doppler radar is a radar system that detects chest displacement due to breathing using the above method. Frequency f t The microwaves are transmitted, scattered on the body surface, and received, but due to the Doppler effect, the phase Φ(t) of the received radio waves depends on the target's displacement x(t) and is expressed as follows:

number

[0024] Here, λ and φ0 represent the wavelength and steady-state phase offset, respectively. The signal is a complex amplitude consisting of the in-phase component I(t) and quadrature component Q(t) obtained by quadrature detection. If the steady-state phase offset is ignored, it can be written as follows:

number

[0025] To observe human breathing, a displacement of about 1 cm is detected by the phase change shown in (1).

[0026] 2-2.ICA ICA is a method to estimate the original signal before mixing from only multiple mixing matrices in which multiple statistically independent signals are mixed.

number

number

number

[0027] The mixed signal x(t) is divided into statistically independent signals

number

number

[0028] y(t)=Bx(t) (4) Each of these signals is the original signal

number

[0029] Basically, the ICA algorithm consists of two parts: whitening and independence. The first part, whitening, is a transformation that makes the data uncorrelated with each other, with a mean of 0 and a variance of 1. This is closely related to Principal Component Analysis (PCA).

[0030] First, consider a linear transformation on the sample vector x(t). TIFF0007770042000009.tif997

[0031] PCA is the first principal component y1(t)=v1 T The choice of v1 that maximizes the variance of x(t) and the i-th principal component y i (t) is y k (t)(1≦k≦i-1) and v that are uncorrelated and have the maximum variance i To select the transformation V=[v i The solution to this problem is the covariance matrix C of x. x =E{xx T} is given by the eigenvalue decomposition of C x The eigenvalues ​​d1,d2, ,d n (d1≧d2≧ ≧d n ) and the corresponding eigenvectors e1, e2, TIFF0007770042000010.tif9146. y i =e i (6)

[0032] Whitening can essentially be thought of as a combination of decorrelation achieved by PCA and normalization to set the variance to 1. We want to find a whitening matrix V such that the following z becomes a white signal. z=Vx(7) C xThe diagonal matrix D=diag(d1, ,d n ) and the matrix E=(e1, ,e n ), for example, V below defines one of the whitening matrices.

[0033] V=D -1 / 2 E T (8) Here, D -1 / 2 =diag(d1 -1 / 2 ,···,d n -1 / 2 )

[0034] The second method of independence is to convert data that has become uncorrelated due to whitening into independent data. Note that uncorrelation does not necessarily mean independence. When whitened data normalized to variance 1 is transformed by the rotation matrix W, we find W such that independence is maximized. Nonlinear uncorrelation can be used as a measure of independence. If any variables y1 and y2 are independent, then the following theorem holds for any two functions h1 and h2. E{h1(y1)h2(y2)}=E{h1(y1)}E{h2(y2)} (9)

[0035] According to the theorem, if nonlinear functions are appropriately selected for h1 and h2, a measure of independence can be determined. In other words, if h1(y1) and h2(y2) are uncorrelated, then y1 and y2 are presumed to be independent. In actual algorithms, kurtosis, a fourth-order statistic, hyperbolic functions (tanh), and other polynomials have been used.

[0036] 2-3. Online CF-ICA Online CF-ICA (Complex-valued Frequency-domain Independent Component Analysis: CF-ICA) is an ICA that uses online processing to handle complex signals in the frequency domain. The processing flow is shown in Figure 2. As mentioned in Section 1, the fractional bandwidth of microwave CW radar signals used to detect respiration is very small, so the algorithm below assumes that the ICA model does not have frequency dependence. Generally, online ICA learns the following equation for sequentially input time series signals: B(t+1) = B(t) + ΔB. The online algorithm for online CF-ICA is based on Equivariant Adaptive Separation via Independence (EASI)

[24] . EASI is a method that simultaneously performs the two operations of ICA described in Subsection 2-2, whitening and independence, based on a single update equation. First, let V be the whitening matrix that gives the linear transformation used for whitening. z=Vx(10)

[0037] where z is the white signal. The update formula for the whitening matrix V is given by: ΔV=μ v (I-zz T ) (11)

[0038] μ v is the learning rate (also called the "update parameter"). Now z = VAs, so considering the meaning of whitening, the matrix VA is an orthogonal matrix that gives the rotation.

[0039] Furthermore, if we introduce an independence matrix W that gives the separation y = Wz for the white signal z, the inverse matrix of VA determines one of W. Therefore, W is also an orthogonal matrix. It includes a nonlinear function g(·) to incorporate the measure of independence.

number

number

[0040] If we assume that D is small, then by first approximation, D=-D T We redefine D to satisfy this and derive the update formula for W.

number

[0041] The serial processing of the above whitening and isolation is y = Wz = WVx, so the separation matrix can be written as B = WV.

[0042] The learning rule for the separation matrix B is derived by combining the update equations (11) and (14).

number

[0043] Here, the learning rates in (11) and (14) are set to be equal, μv = μw = μ. Also, the complex EASI represents the transpose [·] T Transpose conjugate [·] H can be obtained by changing

number

[0044] This operation is extended to the frequency domain and is called online CF-ICA. By using the frequency domain, it is possible to easily narrow down the learning bandwidth.

[0045] In online CF-ICA, the time domain signal is converted to the frequency domain using the Short Time Fourier Transform (STFT). Since respiration is one of the measurement targets, the frequency band f min =0.17Hz to f max =Up to 2.0Hz.

[0046]

number

number

[0047] L fft is the length of the Fourier window, S is the window movement step, t d represents discrete time. For instantaneous mixtures, the linearity of the Fourier transform allows the ICA model (4) in the time domain to be applied directly to the frequency domain. That is, 2πf min <ω<2πf max For ω, the following separation learning is possible:

number

[0048] In theory, signal separation can be achieved by updating B according to (20). However, in practice, it is necessary to determine the range that the separated signal Y or separation matrix B can take. There are two reasons for this. First, the value of B updated according to (20) may exceed the limits of the computer. Second, this is to effectively utilize the nonlinear region of the nonlinear function g(·). To achieve this, the following method was used.

number

number

number

[0049] For learning, we use Y = BX using the scaled B. This allows us to calculate Y in this section. i The RMS of (t) becomes 1. Using this Y, learning within the interval is performed according to (20). By repeating this process, it is possible to always efficiently use the nonlinearity of g(·) without being affected by the absolute magnitude of the received signal.

[0050] 3. Proposal of Higher Order Independent Component Analysis (HOT-ICA) Overview As mentioned in Section 1, we propose HOT-ICA as an ICA method that does not use tensor decomposition. HOT-ICA is an effective method when using a measurement system based on a MIMO configuration. Furthermore, the data tensor type acquired by the MIMO antennas used in HOT-ICA is expressed as shown in Figure 3(b), compared to the data tensor type used in ICA (Figure 3(a)).

[0051] 3(b) shows an example of a data tensor 400. The data tensor 400 is expressed using a transmission axis 412 that specifies multiple pieces of transmitter information and a reception axis 414 that specifies multiple pieces of receiver information. The transmitter information is information that specifies, for example, transmitting antennas Tx1, Tx2, and Tx3. The receiver information is information that specifies, for example, receiving antennas Rx1, Rx2, and Rx3.

[0052] 3(b) has a configuration in which 3-row, 3-column matrix information 410, whose components are signals received by a plurality of receiving units, is arranged in the direction of a time axis 416. The nine components included in the matrix information are signals corresponding to the corresponding transmitting axis information and receiving axis information. For example, the component in row m and column n of matrix information 410 corresponding to time t may be a signal transmitted from transmitting antenna Txm at time t and received by receiving antenna Rxn.

[0053] The microwaves transmitted from the transmitting antenna Tx1 propagate to the target, are backscattered by the body surface, and are received by the receiving antennas Rx1, Rx2, .... After that, measurements are similarly performed on the microwaves transmitted from the transmitting antennas Tx2, Tx3, .... If the number of transmitting antennas is p t , and the number of receiving antennas is p r The mixed signal obtained at the receiving antenna is

number

[0054] Referring to equation (4), the separation tensor

number

number

number

[0055] In addition, similar to online CF-ICA, we apply the time-domain HOT-ICA model (23) to the frequency domain using STFT.

number

[0056] We extend the update formula (20) to the HOT-ICA calculation. In this case, we can construct the following update formula by referring to formula (20).

number

[0057] Here,

number

number

[0058] Also,

number

number

[0059] When using a MIMO configuration, it is inevitable that the environment will differ for each antenna. In this case, it is thought that the robustness of the overall learning can be improved by reducing the learning weights related to antennas with relatively large noise or malfunctions. To make this possible, HOT-ICA decomposes the update equation (25). The update tensors related to each transmit antenna Tx1, Tx2,...,TxM are

number

number

number

[0060] Here,

number

number

[0061] Also, update tensor weights

number

number

[0062] For example, the weight of the update tensor for the receiving antenna Rx1

number

number

[0063] As described above, HOT-ICA's unique technique, which allows for individual manipulation of the learning weights for each antenna in the separation tensor, is expected to be effective for measurements using MIMO configuration systems. This manipulation was not possible with the conventional online CF-ICA (see Subsection 2-3). Furthermore, unlike MICA, which is based on the Tucker decomposition method and requires manipulations such as matrixing, HOT-ICA's tensor calculations can process the data while preserving the structure of each categorized data without destroying the original tensor shape. Therefore, adaptive source separation training is possible each time received signal data is acquired, which involves changes in the measurement environment, and this is expected to improve generalization performance.

[0064] 3-2. Examples of various tensors With reference to FIGS. 4 to 8, examples of various tensors when the number of transmitting antennas (Tx1, Tx2, Tx3) is three and the number of receiving antennas (Rx1, Rx2, Rx3) is three will be described.

[0065] Fig. 4 is a diagram for explaining the separation information Y = BX. On the right side of Fig. 4, a tensor information group 500 in which nine pieces of tensor information 502 are arranged by frequency is shown. Each of the nine pieces of tensor information 502 is expressed using a transmission axis 504 that specifies three pieces of transmitting antenna information and a reception axis 506 that specifies three pieces of receiving antenna information. The tensor information group 500 is configured by arranging the nine pieces of tensor information 502 in the direction of a frequency axis 508.

[0066] The tensor information 502 is data of a matrix with 3 rows and 3 columns. The subscripts included in the components of the tensor information 502 indicate the corresponding transmitting antenna and receiving antenna. For example, X mn corresponds to the transmitting antenna Txm and the receiving antenna Rxn. Note that the number of tensor information 502 included in the tensor information group 500 is not limited to nine, and may be eight or less, or ten or more.

[0067] As shown in Fig. 4, separation tensor 510 is expressed as a fourth-order tensor. Specifically, separation tensor B is expressed as a configuration in which rooms 512, each expressed as a three-row, three-column matrix, are arranged in a three-row, three-column arrangement. Note that the method of expressing a fourth-order separation tensor is not limited to this. Also, for simplicity, Fig. 4 shows all components of only room 512 in the first row and first column of the nine rooms included in separation tensor 510.

[0068] The subscript of a component contained in room 512 indicates the position of the component. Specifically, the first two characters of the subscript indicate the position of room 512, and the last two characters of the subscript indicate the position of the component in room 512. For example, the first half of the subscript of a component contained in the room located i-th from the top and j-th from the left is ij. Similarly, the last half of the subscript given to the component k-th from the top and l-th from the left in a room is kl.

[0069] The separation information 520 shown at the bottom of FIG. 4 is the tensor product of the fourth-order separation tensor 510 and the second-order tensor information 502. The separation information 520 is expressed as a 3-row, 3-column matrix (i.e., a second-order tensor), just like the tensor information 502. Therefore, the separation information 520 includes nine components. For simplicity, in FIG. 4, the component Y 11 Only the following is shown.

[0070] Each component Y included in the separation information 520 ij The subscripts of the components correspond to the room positions of the separation tensor 510. Specifically, the subscript ij of each component corresponds to the room in the ith row and jth column of the separation tensor 510. Furthermore, the component Y ij is the sum of the products of the components included in the corresponding room and the components of the tensor information 502 corresponding to that room. Specifically, each component of the separation information 520 is expressed as Y ij =Σ 3 k=1 Σ 3 l=1 (B ijkl X kl ) is expressed as

[0071] The update tensor ΔB is expressed as follows using the separation information Y, the separation tensor B, the transformation tensor W, and the learning rate μ:

number

[0072] Here, referring to Fig. 5, the product of separation information Y and a second-order tensor (hereinafter referred to as "conjugate information") expressed by the complex conjugate of separation information Y will be described. Tensor product 530 shown in Fig. 5 is a fourth-order tensor expressed by the product of separation information 520 and conjugate information 525 of separation information 520. Like the separation tensor, tensor product 530 is expressed by a configuration in which rooms expressed by a 3-row, 3-column matrix are arranged in a 3-row, 3-column format. The component YY in the k-th row and j-th column of the tensor product 530 is included in the room in the ith row and j-th column, and the component YY in the k-th row and l-th column of the room is* ijkl (* indicates complex conjugate) is a component of the separation information Y ij and the conjugate information component Y * kl Using Y ij Y * kl For simplicity, in FIG. 5, of the nine rooms included in the tensor product 530, all components are shown for only the room 512 in the first row and first column.

[0073] Fig. 6 is a diagram showing a fourth-order unit tensor 540. As shown in Fig. 6, the fourth-order unit tensor 540 is expressed by arranging second-order unit tensors 542 in a 3-row, 3-column arrangement. Here, the second-order unit tensor 542 is a 3-row, 3-column unit matrix.

[0074] Fig. 7 is a diagram illustrating the update tensor ΔB. As shown in Fig. 7, the update tensor 560 may be expressed as a tensor product of the separation tensor 510 and the transformation tensor 550. The separation tensor 510 has the same configuration as the separation tensor 510 described with reference to Fig. 4. The transformation tensor 550 is a fourth-floor tensor, and is expressed as a configuration in which rooms, each represented by a 3-by-3 matrix, are arranged in a 3-by-3 matrix.

[0075] The updated tensor 560 is a fourth-order tensor, and is expressed by arranging rooms, each expressed as a 3-row, 3-column matrix, in a 3-row, 3-column configuration. The nine rooms in the updated tensor 560 each have nine components. The component ΔB in the γ-th row and δ-th column contained in the room in the α-th row and β-th column in the updated tensor 560 is αβγδ is the component W of the transformation tensor 550 αβεζ and component B of separation tensor 510 εζγδ Using ΔB αβγδ =Σ 3 ε=1 Σ 3 ζ=1 W αβεζ B εζγδ For simplicity, in FIG. 7, the component ΔB 1111Only the following is shown.

[0076] Here, when performing the weighting shown in equation (33), ΔB can be expressed as the sum of the tensor products of the second-order weight tensors corresponding to the transmitting antennas (Tx1, Tx2, Tx3) and the receiving antennas (Rx1, Rx2, Rx3) and the separation tensor B, as shown in the following equation.

number

[0077] Therefore, ΔB can be decomposed into weight tensors corresponding to the three transmit antennas and the three receive antennas, where the weight tensors are η for each of the transmit antennas (Tx1, Tx2, Tx3) and receive antennas (Rx1, Rx2, Rx3). Tx1 W Tx1 , η Tx2 W Tx2 , η Tx3 W Tx3 , η Rx1 W Rx1 , η Rx2 W Rx2 and η Rx3 W Rx3 The weighting parameter η Tx1 , η Tx2 , η Tx3 , η Rx1 , η Rx2 and η Rx3 By adjusting the above, it becomes possible to perform more appropriate signal processing in accordance with the operating conditions and noise of the transmitting antennas (Tx1, Tx2, Tx3) and receiving antennas (Rx1, Rx2, Rx3).

[0078] The factors of the weight tensor are expressed by the above formulas (31) and (32). An example of the factors of the weight tensor will be described with reference to Fig. 8. Fig. 8 shows the weight tensor η corresponding to the receiving antenna Rx1. Rx1 W Rx13 is a diagram showing a factor 580 of the above-mentioned antennas. As shown in equation (32), for each of the nine rooms 582 included in the factor 580, the components in the first row are the corresponding components of W shown in equation (26), and the components other than the first row are 0. The weight tensors corresponding to the other antennas are also expressed by the above-mentioned equation (31) or equation (32), and the update tensor ΔB can be decomposed into weight tensors corresponding to the respective antennas.

[0079] 4. Numerical experiment method and data settings Measurements were taken using a CW MIMO Doppler radar (Figure 9), and signal source separation processing was performed by applying online HOT-ICA to the resulting received signals through simulation. As shown in Figure 9, three transmitting antennas (Tx1, Tx2, Tx3) and three receiving antennas (Rx1, Rx2, Rx3) are arranged in a substantially straight line. Continuous microwaves are generated by a VNA (Virtual Network Analyzer) shown in Figure 9. A PC (Personal Computer) can acquire data, perform calculations, and perform plotting. In addition, a control board (not shown) controls switches to switch antennas as needed. For example, the transmitting antenna that transmits the signal may be switched as needed.

[0080] The arrangement of the transmitting antennas and receiving antennas is not limited to the example shown in Fig. 9. By devising an antenna arrangement as necessary, it is possible to increase the independence of received signals. For example, the transmitting antennas and receiving antennas may be arranged so as to be alternately positioned within a rectangular frame, as shown in Fig. 10.

[0081] The antenna may be, for example, a patch antenna (also called a "microstrip antenna")

[11] . The frequency band of the microwaves transmitted by the transmitting antenna may be, for example, the 2.5 GHz band. Microwaves are more likely to propagate through obstacles than millimeter waves.

[0082] Figure 11 shows the arrangement of antennas and targets. Here, there are three transmitting antennas Tx and three receiving antennas Rx, and four targets (humans: H). A human's chest constantly moves periodically due to breathing and heartbeat, and the displacement caused by this body movement is detected by Doppler radar, resulting in a complex signal (see Subsection 2-1). The complex signal obtained contains not only the original signal from the target, but also various noises.

[0083] The average distance from the transmitting antenna Txm (1≦m≦3) to the target Hk (1≦k≦4) is

number

number

[0084] Original signal model

number

number

[0085] Here, w H1 , w H2 , w H3 , w H4 is expressed as follows:

number

[0086] The received signal can be expressed by, for example, the sum of the product of various factors and Gaussian noise. The various factors may include, for example, the transmission directivity of the transmitting antenna, the electric field strength on the outbound path which is inversely proportional to the distance, the degree of radio wave scattering by the human body, the electric field strength on the return path which is inversely proportional to the distance, and the reception directivity of the receiving antenna.

[0087] Received Signal Model

number

number

[0088] Here, L Txm-Hk (t), L Hk-Rxn (t) is expressed as follows:

number

[0089] In this simulation experiment, the received signal model Erec is

number

number

[0090] Here, ρ is a coefficient that determines the magnitude of noise (Noise coefficient).

number

[0091] Table 1 shows the respiratory and cardiac parameters for each target. [Table 1]

[0092] The parameters of online HOT-ICA are shown in Table 2. [Table 2]

[0093] 5. Numerical Experiment Results 5-1. Signal source separation results using online HOT-ICA We evaluate the performance of source separation using online HOT-ICA. Figure 12 shows the signal obtained as a result of learning for the mixed signal x(t). d =T d The vertical axis represents the electric field strength normalized to 1, with the maximum electric field strength in each stage being 1, and the horizontal axis represents the frequency.

[0094] The spectrum in the top row is the received signal spectrum X(ω,T d ) In this graph, the mixed signal spectrum, which is the sum of the original signals from the four targets and noise from the measurement environment and amplifier, is shown.

[0095] The spectrum in the lower part is the mixed signal spectrum X(ω,T d) after online HOT-ICA. Note that the spectrum in the lower panel is not in the same order as the spectrum in the upper panel. This is due to the permutation problem introduced in Section 1. Figures 12(b-2), (b-5), (b-6), and (b-8) show one large first peak and one small second peak in the field strength. Referring to Table 1, the frequencies of the first and second peaks correspond to the respiration and heartbeat frequencies of each target, with the first peak representing respiration and the second peak representing heartbeat. It is noteworthy that the respiration and heartbeat signals of the same target appear simultaneously in a single spectrum. The remaining spectra, Figures 12(b-1), (b-3), (b-4), (b-7), and (b-9), represent noise.

[0096] Figure 13 shows the time variation of the electric field strength for each frequency for all spectra in Figure 12. The vertical axis represents the electric field strength normalized with the maximum electric field strength of each signal in the final time interval set to 1, the horizontal axis represents time, and the color bar represents frequency. Looking at Figures 13(b-2), (b-5), (b-6), and (b-8), the first peak is already determined to be a single frequency after about 5 seconds, demonstrating the speed of HOT-ICA's separation learning. However, the second peak in Figure 13 is difficult to discern because the normalized electric field strength is close to the noise value.

[0097] Figure 14 shows the spectrogram of the separated signal for target H1. The vertical axis is frequency, the horizontal axis is time, and the color bar represents the normalized field strength of each signal, with the maximum field strength of each signal in the final time interval set to 1. Looking at this graph, the second peak, which was difficult to see in Figure 13, appears as a light yellow-green (gray) straight line, making it easier to observe. Figure 15 shows the spectrogram of the separated signal for noise. Looking at the breathing frequencies of targets H1, H2, H3, and H4 at 0.40 Hz, 0.31 Hz, 0.71 Hz, and 0.53 Hz, a dark green (gray) straight line appears. This means that HOT-ICA strongly suppresses the target frequencies in the separated signal from noise. This indicates that the original signals derived from the targets are statistically independent of the normally distributed noise, demonstrating that HOT-ICA works well.

[0098] 5-2. Experimental results comparing online CF-ICA with online HOT-ICA after weighting of separation tensors Figure 16 shows an obstacle placed between target H1 and receiving antenna Rx1. To simplify the situation, we set two transmitting antennas Tx and two receiving antennas Rx. We will add two effects of this obstacle to the received signal model x. The first is that the signals backscattered from all transmitting antennas by target H1 and received by receiving antenna Rx1 are attenuated by -50 dB from the original signal of target H1 only. The second is that the signal received by receiving antenna Rx1 generates +16 dB noise compared to the signals received by the other receiving antennas. This is due to the constant influence of radio waves reflected by obstacles. It can also imply a situation where some kind of malfunction has occurred with a specific receiving antenna Rx1.

[0099] Figure 17 shows the received signal affected by an obstacle after signal source separation processing using online CF-ICA. The mixed signal spectrum in the upper part is the mixed signal spectrum X(ω,T d ) It can be seen that the mixed signal spectrum (Fig. 17(a-1) and (a-3)) via the receiving antenna Rx1 shows a large amount of noise. In Fig. 17(b-2), the breathing frequencies of targets H1 and H2 appear simultaneously and are not well separated, and Fig. 17(b-4) shows a spectrum of only noise.

[0100] In Figure 18(b-2), the breathing signal of target H1 is determined to be a peak, but the breathing signal of target H2 also appears significantly. In Figure 18(b-4), the breathing signal of target H2 sometimes peaks during learning, but noise is generally dominant. This shows that in scenes where obstacles are present, separation learning using online CF-ICA before adjusting the weighting of the separation tensor becomes unstable.

[0101] 5-3. Experimental results comparing before and after weighting of separation tensors in online HOT-ICA As in Subsection 5-2, the environment shown in Figure 16 is used, in which an obstacle is placed between the target H1 and the receiving antenna Rx1. Figure 19 shows the received signal affected by the obstacle after undergoing signal source separation processing using online HOT-ICA. The mixed signal spectrum in the upper part is the mixed signal spectrum X(ω,T d) It can be seen that the mixed signal spectrum (Fig. 19(a-1) and (a-3)) via the receiving antenna Rx1 shows a large amount of noise. In Fig. 19(b-1), the breathing frequencies of targets H1 and H2 appear simultaneously and are not well separated, resulting in a spectrum of only noise in Fig. 19(b-2).

[0102] In Figure 20(b-1), the breathing signal of target H1 is determined to be a peak, but the breathing signal of target H2 also appears significantly. In Figure 20(b-2), the breathing signal of target H2 sometimes peaks during learning, but noise is generally dominant. This shows that in scenes where obstacles are present, separation learning using online HOT-ICA before adjusting the weighting of the separation tensor becomes unstable.

[0103] Fig. 21 shows the result of applying online HOTICA to the mixed signals in the same environment as Fig. 19, with weighting operation for the receiving antenna Rx1. Specifically, in Equation (33), η Rx1 = 0. Compared to Figure 19, it can be seen that the signal peaks in each spectrum (bx) of the separated signals in Figure 21 are narrowed down to one, and the signals of each target are separated into each spectrum.

[0104] Looking at Figure 22, we can see that all of the separated spectra in the lower row are ultimately determined to have a single peak frequency. Compared to the case where no obstacles are assumed (Figure 13), the completion of separation learning is delayed due to the influence of the obstacles, but it does not reach a situation where the target cannot be separated and the signal is dominated by noise, as shown in Figure 20(b-2). This demonstrates the effectiveness of manipulating the weighting of separation learning for some antennas in online HOT-ICA.

[0105] 6. Conclusion We proposed online HOT-ICA as a novel method suitable for measuring human respiration and heart rate using CW MIMO Doppler radar and its signal source separation. We then conducted simulation experiments to verify the source separation performance of online HOT-ICA. As a preprocessing step, we narrowed the useful bandwidth of the short-time Fourier transform of the received signal model, and then performed online source separation training for each time interval. Online HOT-ICA demonstrated successful separation of each target from noise. Furthermore, to investigate the effectiveness of weighting for separation training for some antennas, a key feature of online HOT-ICA, we modified the simulation environment and conducted experiments. We incorporated noise increases and target signal attenuation due to obstacles and specific antenna defects into the simulation environment, and compared the separation performance with and without weighting using the resulting received signal model. The results showed that online HOT-ICA with weighting manipulation was more robust in source separation training. This suggests that online HOT-ICA is capable of flexible measurements in any environment.

[0106] 7. Information Processing System Configuration FIG. 23 is a diagram showing the overall configuration of an information processing system 1 including an information processing device 10 according to one embodiment of the present invention. The information processing system 1 according to this embodiment includes the information processing device 10, M (M: an integer of 2 or greater) transmitters 20-1,...,20-M, and N (N: an integer of 2 or greater) receivers 30-1,...,30-N. Hereinafter, when the transmitters 20-1,...,20-M are not distinguished from one another, they will be collectively referred to simply as "transmitter 20." Furthermore, when the receivers 30-1,...,30-N are not distinguished from one another, they will be collectively referred to simply as "receiver 30." The information processing device 10, transmitters 20, and receivers 30 are connected to one another via various known networks so as to be able to transmit or receive information as needed.

[0107] The information processing device 10 acquires a-th order tensor information X, which is expressed using a (a: integer equal to or greater than 2) axes that respectively identify a plurality of pieces of measurement information related to the measurements, and whose components are information based on the results of measurements corresponding to the a pieces of measurement information. The information processing device 10 also calculates separation information BX, which is the tensor product of the tensor information X and a 2a-th order separation tensor B, and uses the separation information BX to calculate a 2a-th order update tensor ΔB based on the sum of the tensor products of the 2a-th order weight tensors corresponding to each piece of measurement information and the separation tensor B. Furthermore, the information processing device 10 uses the update tensor ΔB to update the separation tensor B such that the separation tensor B whitens and separates the tensor information X in the separation information BX. Details of the configuration and functions of the information processing device 10 will be described later with reference to FIGS. 24 and 25.

[0108] The transmitting unit 20 transmits various signals. The signals may be electromagnetic waves such as microwaves, or may be audio signals. In this embodiment, the transmitting unit 20 is, for example, an antenna capable of transmitting microwaves. The M transmitting units 20 can transmit signals at different timings. For example, the M transmitting units 20-1, . . . , 20-M may transmit signals in sequence at predetermined time intervals. In this embodiment, the signals transmitted from the transmitting units 20 are irradiated onto the measurement objects 40a and 40b.

[0109] The receiving unit 30 can receive various signals. In this embodiment, the receiving unit 30 is an antenna that can receive microwaves. For example, the receiving unit 30 receives a signal x∈C transmitted from the transmitting unit 20 and reflected by the measurement targets 40a and 40b. M×N can be received.

[0110] The measurement targets 40a and 40b are measurement targets in this embodiment and may be, for example, people, etc. The number of measurement targets 40a and 40b may be one, or three or more.

[0111] 24 is a functional block diagram illustrating an example of the configuration of the information processing device 10 according to this embodiment. As shown in FIG. 24, the information processing device 10 according to this embodiment includes an input unit 110, an output unit 120, a storage unit 130, a communication unit 140, a control unit 150, and a processing unit 160.

[0112] The input unit 110 can receive various operations and transmit signals corresponding to the operations to other functional units. The input unit 110 may be, for example, a mouse, a keyboard, or a touch panel.

[0113] The output unit 120 outputs various types of information. For example, the output unit 120 may output the results of processing by the processing unit 160. The output unit 120 may be, for example, a liquid crystal display.

[0114] The storage unit 130 stores various types of information. The information stored in the storage unit 130 may be referenced by other functional units such as the control unit 150 and the processing unit 160 as necessary. The storage unit 130 may be configured with various types of memory such as a ROM (Read Only Memory) and a RAM (Random Access Memory).

[0115] The storage unit 130 may store various types of information, such as a control program for implementing control by the control unit 150, a processing program for implementing processing by the processing unit 160, and results of processing by the processing unit 160. The processing program is a program for acquiring tensor information, calculating various tensors, and updating separation tensors, and is a program for implementing various processing contents described below with reference to FIG. 25. The storage unit 130 may also store information based on signals received by the receiving unit 30. For example, the storage unit 130 may store matrix information whose components are signals received by N receiving units 30, and which is expressed using a transmitting axis that identifies M pieces of transmitter information and a receiving axis that identifies N pieces of receiver information.

[0116] The communication unit 140 is a communication interface that transmits and receives information to and from an external device. The communication unit 140 may, for example, instruct the transmission unit 20 to transmit a signal, or may receive a signal received by the reception unit 30 from the reception unit 30. The signal received by the communication unit 140 is transmitted to, for example, the storage unit 130, the processing unit 160, etc.

[0117] The control unit 150 controls the operation of the transmission unit 20. For example, the control unit 150 may transmit an instruction to the communication unit 140 to cause the transmission unit 20 to transmit a signal. As a result, the instruction is sent to the transmission unit 20, and the transmission unit 20 transmits a microwave signal. The control unit 150 may be configured by a processor such as a CPU (Central Processing Unit), for example.

[0118] The processing unit 160 can perform various types of information processing. Functions of the processing unit 160 will be described later with reference to Fig. 25. The processing unit 160 may be configured with various types of processors such as a CPU and a GPU (Graphics Processing Unit).

[0119] 25 is a functional block diagram for explaining functions of the processing unit 160 according to this embodiment. As shown in FIG. 25, the processing unit 160 according to this embodiment includes a generating unit 162, an acquiring unit 164, a separation information calculating unit 166, an updated tensor calculating unit 168, an updating unit 169, a setting unit 170, and an estimating unit 172.

[0120] The generation unit 162 performs a Fourier transform on the time-series matrix information to generate tensor information X for each frequency expressed using the transmission axis and the reception axis. The tensor information X generated by the generation unit 162 is transmitted to the acquisition unit 164.

[0121] The time-series matrix information may be, for example, information in which a plurality of pieces of matrix information are arranged in the time axis direction, like the data tensor 400 described with reference to FIG. 3(b). The matrix information may have a configuration similar to that of matrix information whose components are signals received by M receivers, and which is expressed using, for example, a transmission axis that identifies M pieces of transmitter information and a reception axis that identifies N pieces of receiver information. In this case, the matrix information may be, for example, a matrix with M rows and N columns. In this embodiment, the components included in the matrix information are signals transmitted from the M transmitters 20 at different timings and received by the N receivers 30.

[0122] The components of the generated tensor information X are values ​​obtained by Fourier transforming the time-series matrix information. The tensor information X calculated by Fourier transforming the time-series matrix information may be a matrix with M rows and N columns, similar to the matrix information.

[0123] The acquisition unit 164 acquires a-level tensor information X, which is expressed using a number of axes that respectively identify a plurality of pieces of measurement information related to the measurement and has information based on the measurement results corresponding to the a pieces of measurement information as components. The acquired tensor information X is transmitted to the separation information calculation unit 166.

[0124] In this embodiment, a is assumed to be 2. Therefore, in this embodiment, the tensor information X is expressed as a matrix. Furthermore, in this embodiment, the tensor information X is assumed to be an M-row, N-column matrix expressed using an axis specifying a plurality of pieces of transmitter information corresponding to any of the N transmitters 20 and an axis specifying a plurality of pieces of receiver information corresponding to any of the M receivers 30. Note that, in this embodiment, the measurement information will be described as being transmitter information or receiver information, but the measurement information is not limited to these pieces of information.

[0125] In this embodiment, the measurement results are signals transmitted from N transmitters 20 at different timings and received by M receivers 30. Also, in this embodiment, the tensor information X is information generated by the generator 162 described above.

[0126] The separation information calculation unit 166 calculates the tensor information X and the 2a-th order separation tensor B (in this embodiment, B∈C M×N×M×N ), and transmits the calculated separation information Y to the updated tensor calculation unit 168. Specifically, the separation information calculation unit 166 calculates the separation information Y by the following equation.

number

[0127] The update tensor calculation unit 168 uses the separation information BX to calculate a 2a-th order update tensor ΔB based on the sum of the tensor products of the 2a-th order weight tensors corresponding to each piece of measurement information and the separation tensor B. The update tensor calculation unit 168 also transmits the calculated update tensor ΔB to the updating unit 169.

[0128] Here, the updated tensor ΔB is a fourth-order tensor ΔB corresponding to the transmitter 20-m (1≦m≦M). m and a fourth-order tensor ΔB corresponding to the receiving unit 30-n (1≦n≦N) n (1≦n≦N)

number

[0129] Also, ΔB m and ΔB n The components of are the weight tensor W' m and W´ n (In this embodiment, W' m ,W´ n ∈C M×N×M×N ) and

number

[0130] Furthermore, the weight tensor W' m and W´ nis the fourth-order transformation tensor W and the weighting parameter η m and η n Using

number

[0131] Here, the components of the transformation tensor W are expressed as follows, for example, using the update parameter μ and the separation information BX=Y:

number

[0132] Furthermore, the components of the unit tensor I are

number

[0133] Furthermore, the separation information calculation unit 166 may calculate the separation information Y using the separation tensor B updated by the update unit 169, which will be described later. This allows the calculation of separation information Y that includes statistically independent signals. Furthermore, the separation information calculation unit 166 performs an inverse Fourier transform on the separation information Y in the frequency domain to obtain a separated signal y in the time domain (in this embodiment, y∈C M×N ) can be converted to

[0134] The update unit 169 uses the update tensor ΔB to update the separation tensor B so that the separation tensor B whitens and makes independent the tensor information X in the separation information BX. That is, the separation tensor B is updated so that the separation information Y includes statistically independent signals. Note that it is not necessary to generate the separation tensor B that whitens and makes independent the tensor information X by a single update. The update may be repeatedly performed as necessary to generate the separation tensor B that whitens and makes independent the tensor information X.

[0135] Furthermore, in this embodiment, the updating unit 169 adds the updated tensor ΔB to the separation tensor B before the update, and sets the resulting tensor as the updated separation tensor B. The updated separation tensor B is transmitted to the separation information calculation unit 166.

[0136] The setting unit 170 has a function as a first setting unit or a second setting unit. Specifically, the setting unit 170 can set weighting parameters and transmit the set weighting parameters to the update tensor calculation unit 168.

[0137] The setting unit 170 can set the weighting parameters of the corresponding weight tensor based on the noise intensity included in the measurement result corresponding to any of the measurement information. For example, the setting unit 170 may compare the S / N ratio or noise intensity of the signal received by a specific receiving unit 30 with a predetermined threshold, and set the weighting parameters of the weight tensor corresponding to that receiving unit 30 based on the comparison result.

[0138] For example, when the noise intensity of a signal received by a specific receiving unit 30 exceeds a predetermined threshold, the setting unit 170 may set the weighting parameter of the corresponding weight tensor to 0. This suppresses a decrease in analysis accuracy due to the signal received by the receiving unit 30 receiving strong noise, enabling more accurate independent component analysis. Note that when a signal based on a specific transmitting unit 20 contains a large amount of noise, the weighting parameter of the weight tensor corresponding to that transmitting unit 20 may be set to, for example, 0.

[0139] Furthermore, the setting unit 170 may set weighting parameters of the weight tensor corresponding to each of the transmitter information and receiver information based on the respective operating states of the M transmitters 20 and the N receivers 30. For example, suppose that a malfunction occurs in the operation of a specific receiver 30. In this case, the setting unit 170 may set the weighting parameters of the weight tensor corresponding to that receiver 30 to, for example, 0. This suppresses a decrease in analysis accuracy due to the received signal of the malfunctioning receiver 30, enabling more accurate independent component analysis. Note that if a malfunction occurs in a specific transmitter 20, the weighting parameters of the weight tensor corresponding to that transmitter 20 may be set to, for example, 0.

[0140] The estimation unit 172 can estimate the position information of the object based on the updated separation tensor B updated by the update unit 169. Specifically, the estimation unit 172 can estimate the position information of the object based on the tensor components corresponding to the object contained in the updated separation tensor B and the tensor product components corresponding to the object contained in the tensor product BX of the updated separation tensor B and tensor information X.

[0141] The position information is information about the position of the target object, and may be, for example, information indicating the direction from the receiving unit to the target object, or information indicating the distance from the receiving unit to the target object, etc. In this embodiment, an example will be described in which the target object is mainly a person, but the target object is not limited to this and may be, for example, an animal or various movable objects.

[0142] Here, each component of the tensor information X is a value obtained by Fourier transforming data in which signals transmitted by a corresponding transmitter and received by a corresponding receiver are arranged in time series. The multiple transmitters include a first transmitter and a second transmitter.

[0143] The estimation unit 172 determines the phase Φm by the following equation, where Bm is the tensor component corresponding to the mth (m=1, 2) transmitter among the M transmitters, Yo is the tensor product component corresponding to the target, and

number

[0144] According to the information processing device 10 of this embodiment, by calculating the tensor product of the updated 2a-th order separation tensor B and the tensor information X, separation information Y including statistically independent signals can be generated. At this time, the structure of the categorized data is maintained without destroying the form of the 2a-th order tensor. Therefore, the information processing device 10 can perform independent component analysis using each axis category in the tensor-format data. In other words, the information processing device 10 of this embodiment can perform independent component analysis using the structure of the axis category in the tensor-format data.

[0145] Furthermore, the MICA described in Reference

[34] requires a temporally coherent data set. Therefore, the technique described in Reference

[34] cannot perform adaptive processing in response to changes in the measurement environment, and is therefore unsuitable for online processing. On the other hand, the information processing device 10 according to this embodiment can adaptively update the separation tensor B each time new data (e.g., a microwave reception signal) is provided. Therefore, the information processing device 10 according to this embodiment can perform adaptive online processing in response to changes in the measurement environment, such as target movement and the presence or absence of obstacles. Note that the information processing device 10 does not necessarily need to perform processing, such as updating the separation tensor B, online.

[0146] 8. Examples of processing by information processing systems Fig. 26 is a flowchart showing an example of processing by the information processing device 10 according to this embodiment. While the processing shown in Fig. 26 is being performed, it is assumed that M transmitters 20 transmit signals at different timings at predetermined time intervals, and N receivers 30 receive the transmitted signals. Furthermore, it is assumed that the signals received by the receivers 30 are received by the communication unit 140 of the information processing device 10, and the signals received by the communication unit 140 are sequentially stored in the storage unit 130. An example of processing by the information processing device 10 will be described below with reference to the flowchart of Fig. 26.

[0147] First, the setting unit 170 sets weighting parameters of weight tensors corresponding to the transmitter information and the receiver information, respectively, based on the operation states of the M transmitters 20 and the N receivers 30 (step S101). Note that the setting unit 170 may set weighting parameters of corresponding weight tensors based on noise intensity in addition to or instead of the operation states, as necessary.

[0148] Next, the generating unit 162 acquires matrix information whose components are the signals received by the M receiving units 30 (step S103). At this time, the generating unit 162 may acquire a plurality of pieces of matrix information arranged in chronological order from the storage unit 130.

[0149] Next, the generating unit 162 generates tensor information X for each frequency expressed using the transmission axis and the reception axis by performing a Fourier transform on the time-series matrix information acquired in step S103 (step S105).

[0150] Next, the acquiring unit 164 acquires the tensor information X for each frequency generated by the generating unit 162 in step S105 (step S107).

[0151] Next, the separation information calculation unit 166 calculates separation information BX, which is the separation tensor product of the tensor information X acquired in step S107 and the 2a-th order separation tensor B (step S109). Here, if the separation tensor B has been updated in step S113, which will be described later, the separation information calculation unit 166 may use the updated separation tensor B. On the other hand, if the separation tensor B has not been updated, the separation information calculation unit 166 may use the separation tensor B having an initialized arbitrary component.

[0152] Next, the update tensor calculation unit 168 uses the separation information BX calculated in step S109 to calculate a 2a-th order update tensor ΔB based on the sum of the tensor products of the 2a-th order weight tensors corresponding to each piece of measurement information and the separation tensor B (step S111). At this time, the update tensor calculation unit 168 may calculate the update tensor ΔB using a weight tensor including the weighting parameters set in step S101.

[0153] Next, the update unit 169 uses the updated tensor ΔB calculated in step S111 to update the separation tensor B so that the separation tensor B whitens and separates the tensor information X in the separation information BX (step S113). The updated separation tensor B is transmitted to the separation information calculation unit 166.

[0154] Next, the updating unit 169 determines whether to end the updating of the separation tensor B (step S115). For example, the updating unit 169 may determine to end the updating of the separation tensor B when the receiving unit 30 has finished receiving a signal. Alternatively, for example, the updating unit 169 may determine not to end the updating of the separation tensor B when the receiving unit 30 is receiving a signal.

[0155] When the update unit 169 determines that the update of the separation tensor B has not been completed (step S115: NO), the process returns to step S103, and the processes from step S103 to S115 are repeatedly executed, and the separation tensor B is updated. On the other hand, when the update unit 169 determines that the update of the separation tensor B has been completed (step S115: YES), the process proceeds to step S117.

[0156] When it is determined as YES in step S115, the separation information calculation unit 166 calculates the separation information Y using the separation tensor B updated in step S113 (step S117). Next, the separation information calculation unit 166 calculates the separated signal y in the time domain by performing an inverse Fourier transform on the separation information Y in the frequency domain calculated in step S117 (step S119).

[0157] <Estimation of Direction of Arrival Based on HOT-ICA> Hereinafter, a method for estimating information regarding the position of a target using HOT-ICA will be described. The method described by referring to Sections 9 and 10 may be performed by, for example, the estimation unit 172 or the like.

[0158] 9. Numerical Experiment A. Settings in the Experiment Measurement by a CW MIMO Doppler radar and signal source separation processing by applying HOT-ICA to the obtained received signal are performed by numerical experiments. The experiment is assumed to be performed in the far field. The frequency of the radar is 2.5 GHz. FIG. 27 shows the arrangement of the antennas and the targets. Here, both the transmitting antenna Tx and the receiving antenna Rx are assumed to be three, and the number of targets (humans: H) is set to four. Since a human's chest always moves periodically due to breathing and heartbeat, the displacement due to the body movement is detected by the Doppler radar, and a complex signal can be obtained. The obtained complex signal contains not only the original signal from the target but also various noises.

[0159] The arrangement of the target, transmitting antenna Tx, and receiving antenna Rx shown in Figure 27 is substantially the same as that shown in Figure 11, so a description thereof will be omitted here. Figure 28 is a diagram showing the directivity (gain) of a transmitting and receiving antenna according to an embodiment of the present invention, measured at a position about 1.5° away. The original signal model s(t) is defined by the above-mentioned equation (34). The w in equation (34) H1 ,w H2 ,w H3 ,w H4 are expressed by equations (35) to (38), which represent the breathing and heart rate signals of four targets with the amplitudes and frequencies shown in Table 1. In addition, the received signal model E rec is shown in equations (39) to (41). In this experiment, the received signal model E rec Noise V n Let the mixed signal x(t) be the equation (42) taking into account the above.

[0160] The parameters of HOT-ICA are shown in Table 2. The signal is received for 70 seconds. The sampling frequency is f s = 11.3Hz, so there are 790 data points. STFT = 256, and the step size S = 2, the total number of outputs is 267. d is from 0 to T d = The range is up to 267.

[0161] B. Experimental Results We evaluate the performance of source separation using HOT-ICA. Figure 29 shows the results of the measurement of the mixed signal x(t) in the last time window (t d =T d ) are spectra obtained as a result of learning. The upper row shows the mixed signal, and the lower row shows the separated signals. The vertical axis represents the magnitude of the signal normalized so that the maximum magnitude of the signal in the upper and lower rows is 1, and the horizontal axis represents frequency.

[0162] The spectra in the top row of Figure 29 are the mixed signal spectrum X(ω,T d ) are shown in the graphs. The mixed signal spectrum, which is the sum of the original signals from the four targets and noise from the measurement environment and amplifier, is shown in each graph. The spectrum in the bottom row is the separated signal spectrum Y(ω,T d ) In each of Figures 29(b-3), (b-4), (b-7), and (b-9), a large first peak and a small second peak can be observed in the signal magnitude. In Figure 29, it can be seen that the frequencies of the first and second peaks correspond to the respiration and heartbeat of each target, with the first peak representing respiration and the second peak representing heartbeat. It is noteworthy that the respiration and heartbeat signals of the same target appear simultaneously in one spectrum. The other spectra, Figures 29(b-1), (b-2), (b-5), (b-6), and (b-8), represent only noise.

[0163] 10. Numerical experiments on direction of arrival estimation A. Experimental Setup We propose a method for estimating direction of arrival using HOT-ICA. In this section, as a concrete example, in Figure 27, we identify the direction in which target H1 exists as seen from transmitting antenna Tx2, and estimate the target position using multiple such results.

[0164] As shown in Figure 30, points A, B, C, D, and E are set. ABC is the signal path where microwaves are emitted from transmitting antenna Tx1, reach target H1, and are received by Rx1 after backscattering. DBC is the signal path where microwaves are emitted from transmitting antenna Tx2, reach target H1, and are received by Rx1 after backscattering. Furthermore, if point F where AB = FB is placed on BD, the difference between these two paths is expressed as DF. This path difference DF can be calculated using the phase difference between the signal received at receiving antenna Rx1 via signal path ABC and the signal received at receiving antenna Rx1 via signal path DBC.

number

[0165] where Φ H1 Tx2-Rx1 , Φ H1 Tx1-Rx1 represent the phase of the signal received by receiving antenna Rx1 via signal path ABC, and the phase of the signal received by receiving antenna Rx1 via signal path DBC, respectively. λ is the microwave wavelength, which is set to 11.6 cm. Furthermore, if the long side of triangle ADF is AD, and the quotient obtained by dividing AD by the microwave wavelength λ is n', then 0≦n≦n' holds.

[0166] In this experiment, taking into consideration the placement of the antenna and target, the distance between the antenna and target was assumed to be relatively far enough that ∠AFD could be approximated as π / 2. In this case, the triangle ADF is a right triangle with the hypotenuse AD and ∠AFD=π / 2. If the direction angle to the target H1 as seen from the transmitting antenna Tx2 is ∠ADB=∠ADF, then

number

[0167] Source separation in HOT-ICA is a process of converting mixed signals into separated signals using a separation tensor (Equation (24)). After updating the separation tensor, the signal of target H1 is represented by spectrum (b-3) in Figure 29. In this case, α = 1 and β = 3 in Equation (24), and the separated signal of target H1 is Y H1 =Y(ω,T d ) (1,3) In addition, the elements of the separation tensor corresponding to the signal passing through the signal path DBC are B Tx2-Rx1 =B(T d ) (1,3,2,1) Using these, we express the following equation:

number

[0168] Finally, Φ H1 Rx2-Rx1 X H1 Tx2-Rx1 The phase of is expressed as follows:

number

[0169] Also, Φ H1 Tx1-Rx1 Similarly,

number

[0170] B. Experimental Results We evaluate the direction of arrival estimation capability using HOT-ICA. In Figure 30, the objective is to derive ∠ADF. Here, we first find the theoretical value of ∠ADF. The angle ADF is ∠ADF=π / 2-∠BDE, and ∠BDEtan -1 = (BE / DE). Here, BE = 130 (cm) and DE = 150 (cm), so the theoretical value of the angle ADF is 0.856 rad.

[0171] Table 3 shows the parameters for HOT-ICA-based direction-of-arrival estimation for target H1 using transmitting antennas Tx1 and Tx2 and receiving antenna Rx1. In Fig. 29(b-3), the separated signal Y H1 =Y(ω,Td) (1.3) , elements of the separation tensor B Tx2-Rx1 =B(T d ) (1,3,2,1) , B Tx1-Rx1 =B(T d ) (1,3,1,1) The values ​​of are as shown in Table 3. Using these values, equation (45) is solved. As a result, the experimental value of angle ADF is 0.845 rad. Therefore, the experimental value is almost identical to the theoretical value. Furthermore, although the distance between the antenna and the target in this experiment is not infinite, it was found that it is acceptable to approximate angle ADF as π / 2. [Table 3]

[0172] C. Target Localization The experiment in Section B was similarly performed using other transmitting antennas Tx2 and Tx3 and receiving antenna Rx2. Table 4 shows the parameters for direction-of-arrival estimation based on HOT-ICA for target H1 using transmitting antennas Tx2 and Tx3 and receiving antenna Rx2. Separation signal Y of target H1 H1=Y(ω,T d ) (α,β) , elements of the separation tensor B Tx3-Rx2 =B(T d ) (α,β,3,2) , B Tx2-Rx2 =B(T d ) (α,β,2,2) The values ​​of each are as shown in Table 4. The theoretical value for the direction angle of H1 relative to the transmitting antenna Tx3 is 0.779 rad, while the experimental value is 0.768 rad. Here too, the experimental value is almost the same as the theoretical value. [Table 4]

[0173] By estimating the direction angle of target H1 relative to transmitting antenna Tx2 and the direction angle of target H1 relative to transmitting antenna Tx3, the position of target H1 can be estimated as shown in Figure 31. In other words, by performing two direction of arrival estimations for different antenna sets, the target position can be estimated as the intersection of the two directions of arrival, and the distance from the antenna to the target can also be determined.

[0174] 11. Supplementary Information The present invention has been described above based on one embodiment. This embodiment is merely an example, and it will be understood by those skilled in the art that various modifications are possible in the combination of the components and treatment processes, and that such modifications are also within the scope of the present invention.

[0175] In the above embodiment, an example has been described in which the information processing device 10 performs independent component analysis on a microwave signal, but the information processing device 10 is not limited to this, and may perform independent component analysis on various types of signals such as an audio signal.

[0176] In the above embodiment, the tensor information X is a second-order tensor (i.e., a matrix), but the present invention is not limited to this and the tensor information X may be a third-order or higher tensor.

[0177] In the above embodiment, an example has been described in which the weight tensor includes a weighting parameter. However, the present invention is not limited to this, and the weight tensor does not need to include a weighting parameter. Alternatively, the weighting parameter included in the weight tensor may be 1.

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[0179] The present invention can be used in an information processing device, an information processing method, a program, and an information processing system. [Explanation of symbols]

[0180] 1 Information processing system, 10 Information processing device, 130 Storage unit, 160 Processing unit, 162 Generation unit, 164 Acquisition unit, 166 Separation information calculation unit, 168 Updated tensor calculation unit, 169 Update unit, 170 Setting unit, 172 Estimation unit, 20 Transmission unit, 30 Reception unit, 502 Tensor information, 510 Separation tensor, 520 Separation information

Claims

1. an acquisition unit that acquires a-th order tensor information X, which is expressed using a number of axes (a: an integer of 2 or more) that respectively identify a plurality of pieces of measurement information related to the measurement, and has information based on the results of the measurement corresponding to each of the a pieces of measurement information as components; A separation information calculation unit that calculates separation information BX, which is a tensor product of the tensor information X and a 2a-th order separation tensor B; an update tensor calculation unit that calculates a 2a-th order update tensor ΔB based on the sum of a tensor product of a 2a-th order weight tensor corresponding to each of the measurement information and the separation tensor B using the separation information BX; an updating unit that updates the separation tensor B using the updated tensor ΔB so that the separation tensor B whitens and separates the tensor information X in separation information BX; An information processing device comprising:

2. The weight tensors each include a weighting parameter, Further comprising a first setting unit that sets the weighting parameters. The information processing device according to claim 1 .

3. the first setting unit sets weighting parameters of a corresponding weight tensor based on noise intensity included in a measurement result corresponding to any of the measurement information. The information processing device according to claim 2 .

4. a is 2, the tensor information X is expressed using a first axis specifying M (M: an integer of 2 or more) pieces of first measurement information and a second axis specifying N (N: an integer of 2 or more) pieces of second measurement information, The updated tensor ΔB is a fourth-order tensor ΔB ｍ (1 ≦ m ≦ M) and ΔB ｎ (1≦n≦N) [Equation 1] It is expressed as ΔB ｍ and ΔB ｎ The components of W' are the weight tensor ｍ and W' ｎ Using [Equation 2] It is expressed as W' ｍ and W' ｎ is the fourth-order transformation tensor W and the weighting parameter η ｍ and η ｎ Using [Equation 3] It is expressed as, The information processing device according to claim 1 .

5. The components of the transformation tensor W are expressed as follows using the update parameter μ and the separation information BX=Y: [Equation 4] where g(·) is a nonlinear function, and the components of the unit tensor I are [Equation 5] The components of the separation information Y are expressed as follows: [Equation 6] It is expressed as the updating unit updates the separated tensor B by adding the updated tensor ΔB to the separated tensor B before the update, and sets the resulting tensor as the separated tensor B after the update. The information processing device according to claim 4 .

6. the acquisition unit acquires tensor information based on signals transmitted from a plurality of transmission units at different timings and received by a plurality of reception units; The tensor information is expressed using an axis specifying a plurality of pieces of transmitter information each corresponding to one of the plurality of transmitters, and an axis specifying a plurality of pieces of receiver information each corresponding to one of the plurality of receivers. The information processing device according to claim 1 .

7. The weight tensors corresponding to the plurality of pieces of transmitter information and the plurality of pieces of receiver information each include a weighting parameter; a second setting unit that sets weighting parameters of weight tensors corresponding to the transmitter information and the receiver information, based on the operation states of the transmitters and the receivers, respectively; The information processing device according to claim 6 .

8. a storage unit configured to store matrix information, the matrix information being expressed using a transmission axis that identifies the plurality of pieces of transmitter information and a reception axis that identifies the plurality of pieces of receiver information, and having signals received by the plurality of receivers as components; a generation unit that generates tensor information for each frequency expressed using the transmission axis and the reception axis by Fourier transforming the time-series matrix information, 8. The information processing device according to claim 6 or 7.

9. An estimation unit that estimates position information of an object based on the updated separation tensor B updated by the update unit, a is 2, the tensor information X is expressed using a first axis that identifies each of M (M: an integer of 2 or more) transmitters that transmit signals to the object and a second axis that identifies each of N (M: an integer of 2 or more) receivers, Each component of the tensor information X is a value obtained by Fourier transforming data in which signals transmitted by a corresponding transmitter and received by a corresponding receiver are arranged in time series, the estimation unit estimates position information of the object based on tensor components corresponding to the object contained in the updated separated tensor B and tensor product components corresponding to the object contained in a tensor product BX of the updated separated tensor B and the tensor information X. The information processing device according to claim 1 .

10. the M transmitters include a first transmitter and a second transmitter; When the tensor component corresponding to the m-th (m=1, 2) transmitter among the M transmitters is Bm, the tensor product component is Yo, and the phase Φm is expressed by the following equation, [Equation 7] Phase Φ １ and phase Φ ２ and estimating the position information based on the difference between the The information processing device according to claim 9 .

11. An information processing method by an information processing device including a processor, the processor: Acquiring a-th order tensor information X, which is expressed using a number of axes (a: an integer of 2 or more) that respectively identify a plurality of pieces of measurement information related to the measurement, and has information based on the results of the measurement corresponding to each of the a pieces of measurement information as components; Calculating separation information BX, which is a tensor product of the tensor information X and a 2a-th order separation tensor B; Using the separation information BX, calculate a 2a-th order update tensor ΔB based on the sum of a tensor product of a 2a-th order weight tensor corresponding to each of the measurement information and the separation tensor B; Using the updated tensor ΔB, update the separation tensor B so that the separation tensor B whitens and separates the tensor information X in separation information BX; An information processing method, including:

12. On the computer, Acquiring a-th order tensor information X, which is expressed using a number of axes (a: an integer of 2 or more) that respectively identify a plurality of pieces of measurement information related to the measurement, and has information based on the results of the measurement corresponding to each of the a pieces of measurement information as components; Calculating separation information BX, which is a tensor product of the tensor information X and a 2a-th order separation tensor B; Using the separation information BX, calculate a 2a-th order update tensor ΔB based on the sum of a tensor product of a 2a-th order weight tensor corresponding to each of the measurement information and the separation tensor B; Using the updated tensor ΔB, update the separation tensor B so that the separation tensor B whitens and separates the tensor information X in separation information BX; A program to execute.

13. the plurality of transmitters; the plurality of receiving units; An information processing device according to any one of claims 6 to 8; An information processing system comprising:

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