JP7124671B2 - Signal analysis device and signal analysis method - Google Patents

Description

The present invention relates to a signal analysis device and signal analysis method for tracking a signal.

Conventionally, FFT (Fast Fourier Transform) is widely used as an analysis technique for narrowband signal processing. On the other hand, FOS (Fast Orthogonal Search) has been proposed as a technique that enables signal detection even in a low SNR (Signal-to-Noise Ratio) environment (see, for example, Non-Patent Document 1).

FOS can prepare a large number of basis function sets regardless of the data length, and performs frequency analysis by repeating the selection of basis functions from the sets, the calculation of residuals, and the selection of basis functions.

Abdalla Osman, Aboelamgd Nourledin, Naser El-Sheimy, Jim Theriault and Scott Campbell, “Improved target detection and bearing estimation utilizing fast orthogonal search for real-time spectral analysis”, Measurement Science and Technology, 2009

However, in the method disclosed in Non-Patent Document 1, as the signal power and noise power become equal, the probability of selecting both the signal and the noise becomes equal, so continuous detection of the signal becomes difficult. .

A signal analysis apparatus according to the present invention uses a received wave signal and a basis function set to repeat the selection of a basis function from the basis function set and the arithmetic processing of subtracting the selected basis function from the received wave signal. A signal analysis device for estimating a combination of a basis function representing the received wave signal and an amplitude of the basis function for each snapshot, which is an observation time unit, comprising a basis function selected for each snapshot. holding means for storing a basis function list; possibility value calculating means for calculating an existence possibility value indicating the possibility of existence of a signal to be analyzed for an unselected basis function; and calculating the amplitude of the added basis function using additional determination means for determining whether or not to add the unselected basis function to the basis function list, and the basis function list including the added basis function. and re-estimating means.

A signal analysis method according to the present invention uses a received wave signal and a basis function set to repeat selection of a basis function from the basis function set and a calculation process of subtracting the selected basis function from the received wave signal. A signal analysis method for estimating a combination of a basis function representing the received wave signal and an amplitude of the basis function for each snapshot, which is an observation time unit, wherein the basis function selected for each snapshot is included. storing a basis function list, calculating an existence possibility value indicating the possibility of existence of a signal to be analyzed for an unselected basis function, and selecting the unselected basis function based on the calculated existence possibility value; It is determined whether or not to add to the basis function list, and the basis function list including the added basis function is used to calculate the amplitude of the added basis function.

According to the present invention, the amplitude is re-estimated by adding to the basis function list the basis functions in which the signal is likely to exist, so the signal to be tracked can be continuously detected.

It is a figure which shows one structural example of the signal-analysis apparatus based on Embodiment 1 of this invention. 2 is a block diagram showing an example of the hardware configuration of the signal analysis device shown in FIG. 1; FIG. FIG. 4 is a diagram for explaining snapshots in FOS processing; FIG. It is a block diagram which shows one structural example of the signal-analysis apparatus of a comparative example. FIG. 5 is a flowchart showing procedures of a signal analysis method executed by the signal analysis device shown in FIG. 4; FIG. 10 is a diagram showing an example of noise power that fluctuates for each snapshot in FOS processing; FIG. 10 is a diagram showing FOS results for a signal whose amplitude attenuates over time in a comparative example; FIG. 2 is a flowchart showing procedures of a signal analysis method executed by the signal analysis device shown in FIG. 1; FIG. 10 is a diagram showing the result of FOS for a signal whose amplitude attenuates over time in Embodiment 1; It is a figure which shows one structural example of the signal-analysis apparatus based on Embodiment 2 of this invention. FIG. 11 is a flowchart showing procedures of a signal analysis method executed by the signal analysis device shown in FIG. 10; It is a figure which shows one structural example of the signal-analysis apparatus based on Embodiment 3 of this invention. FIG. 13 is a flowchart showing procedures of a signal analysis method executed by the signal analysis device shown in FIG. 12; FIG. 12 is a diagram showing a model in which sounds from S targets are received by R sensors arranged in a straight line at equal intervals in the third embodiment.

Embodiment 1.
A signal analysis device according to the first embodiment will be described. FIG. 1 is a diagram showing a configuration example of a signal analysis device according to Embodiment 1 of the present invention. As shown in FIG. 1 , the signal analysis device 1 has a storage section 11 and a control section 12 . The storage unit 11 has holding means 13 . The control unit 12 has an FOS processing unit 20 , possibility value calculation means 14 , additional determination means 15 , and re-estimation means 16 . The FOS processing unit 20 has basis function selection means 21 , estimation means 22 , residual calculation means 23 and end determination means 24 .

FIG. 2 is a block diagram showing an example of the hardware configuration of the signal analysis device shown in FIG. 1. As shown in FIG. The signal analysis device 1 is, for example, an information processing device including a computer. The storage unit 11 stores results of arithmetic processing executed by the control unit 12 . The storage unit 11 is, for example, an HDD (Hard Disk Drive) device. The control unit 12 has a memory 52 that stores programs, and a CPU (Central Processing Unit) 51 that executes processes according to the programs. By executing the program by the CPU 51, the basis function selecting means 21, the estimating means 22, the residual calculating means 23, the end judging means 24, the possibility value calculating means 14, the additional judging means 15 and the re-estimating means shown in FIG. Means 16 are configured.

Note that some or all of the functions provided by the basis function selection means 21, the estimation means 22, the residual calculation means 23, the end determination means 24, the possibility value calculation means 14, the additional determination means 15, and the re-estimation means 16 are It may be composed of a dedicated circuit. The dedicated circuit is, for example, an ASIC (Application Specific Integrated Circuit). By configuring part or all of the signal processing with a dedicated circuit, it is possible to speed up the signal processing.

Before describing in detail the configuration of the signal analysis device 1 of the first embodiment, a signal analysis device of a comparative example will be described. The signal analysis device of the comparative example displays the FOS calculation results on a three-dimensional graph such as a spectrogram represented by time, frequency, and signal component intensity.

First, the FOS used in the signal analysis processing performed by the signal analysis device of the comparative example will be described. FOS is the signal received by the sensor

を、事前に用意したＭ個の基底関数からなる基底関数セット

is a basis function set consisting of M basis functions prepared in advance

の中から、受波信号ｘとの誤差を小さくするＬ個の基底関数

L basis functions that reduce the error with the received wave signal x from among

を当てはめて、狭帯域信号の捜索を行う。なお、文章中においては、基底関数Ｐのベクトルを「Ｐ＾」で表す。例えば、任意のｌの基底関数ＰをＰ＾_ｌと表記し、Ｌ個の基底関数ＰのリストをＰ＾_Ｌと表記する。

to search for narrowband signals. In the text, the vector of the basis function P is represented by "P^". For example, denote any _l basis function P as P̂l, and a list of _L basis functions P as P̂L.

The observation time unit for the received signal showing the amplitude that changes in time series is called a snapshot. Here, N is the number of samples of the received wave signal used in the processing of one snapshot. FIG. 3 is a diagram for explaining snapshots in FOS processing. As shown in FIG. 3, one snapshot is set with 0 to less than 100% overlap processing. The fitting of L basis functions to the received signal is represented by Equation (1).

式（１）において、

In formula (1),

は、ｘが式（１）の第１項で構成されると仮定したときの真値との誤差を表す。式（１）におけるａ_ｌは基底関数Ｐ＾_ｌに対する重みである。

represents the error from the true value when x is assumed to be composed of the first term of equation (1). a _l in equation (1) is the weight for the basis function P ^ _l .

An example of a basis function is a pair of sine and cosine functions if the signal to be analyzed is a narrowband signal. At this time, a basis function set P composed of M pairs of sine and cosine functions is represented by the following equation (2).

式（２）において、ω_ｍ＝２πｆ_ｍは角周波数であり、Ｍ、ｆ_ｍは任意に設定することができる値である。式（２）の基底関数を用いる場合、式（１）は次の式（３）で表せる。

In Equation (2), ω _m =2πf _m is an angular frequency, and M and f _m are values that can be set arbitrarily. When using the basis function of the formula (2), the formula (1) can be expressed by the following formula (3).

ＦＯＳは、基底関数セットＰおよび受波信号ｘから、式（３）に示すεを最小とする基底関数

FOS is a basis function that minimizes ε shown in Equation (3) from the basis function set P and the received wave signal x

の組み合わせとその基底関数の個数Ｌとを推定する手法である。

and the number L of its basis functions.

FIG. 4 is a block diagram showing a configuration example of a signal analysis device of a comparative example. A signal analysis apparatus 100 of the comparative example has a storage section 101 including holding means 13 and a control section 102 including an FOS processing section 20 . The control unit 102 has a memory and a CPU (not shown). A basis function selecting means 21, an estimating means 22, a residual calculating means 23, and an end judging means 24 are configured by the CPU executing a program stored in the memory. The storage unit 101 is, for example, an HDD device.

The holding means 13 stores a basis function set including a plurality of basis functions prepared in advance. Further, the holding unit 13 stores a basis function list that stores basis functions selected for each snapshot in the signal analysis processing for which the number of searches for the received wave signal is from 1 to (t−1). The holding means 13 stores the residual signal x _e (t) calculated by the residual calculating means 23 .

The basis function selection means 21 receives the received wave signal x for the first search, and receives the residual signal x _e (t−1) for the second and subsequent searches, and selects the basis function for the search number t. conduct. The basis function selection means 21 outputs a basis function list _P̂t including the selected basis functions, and weights g _t and coefficient matrices α _t for the basis functions.

The estimating means 22 receives the basis function list P̂t, the weight g _t and the coefficient matrix α _t , and calculates the _{amplitude A t of} the selected basis function. The estimation means 22 outputs the basis function list _P̂t and the _amplitudes At. The residual calculator 23 receives the basis function list P̂t and the _amplitude At, calculates the residual with respect to the received wave signal x, and outputs the residual signal _xe ( _t ).

The termination determination means 24 receives the residual signal x _e (t) and determines whether or not the termination condition is satisfied. The termination condition is, for example, that the amplitude estimated in the previous snapshot falls below a predetermined threshold. Another example of the termination condition is a condition that the residual power of the residual signal is equal to or less than a predetermined threshold. If the termination condition is not satisfied as a result of the termination determination, the termination determination means 24 outputs the residual signal x _e (t−1) to the basis function selection means 21 . As a result of the termination determination, when the termination condition is satisfied, the termination determination means 24 outputs P̂L at the number of times _L at the end of the search and the amplitude _AL .

FIG. 5 is a flowchart showing procedures of a signal analysis method executed by the signal analysis device shown in FIG. An outline of the procedure shown in FIG. 5 will be described.

The signal analysis apparatus 100 searches for a tracking target signal from narrowband signals by selecting a basis function (step S501), calculating an amplitude (step S502), and calculating a residual signal (step S503). The signal analysis apparatus 100 successively updates the number of searches and repeats the processing of steps S501 to S503 until it is determined in step S504 that there is no basis function component to be detected. After the search is finished, the signal analysis device 100 outputs the spectrum as the analysis result. After outputting the spectrum, the signal analysis apparatus 100 updates the snapshot k to (k+1) as shown in FIG. repeat. k is any positive integer. After that, the signal analysis device 100 displays the spectrum on a three-dimensional graph such as a spectrogram for each snapshot (step S505).

The procedure shown in FIG. 5 will be described in detail below. Note that in the first embodiment, the spectrum is the amplitude for each frequency f _l

のことである。

It's about.

[Selection of Basis Function (Step S501)]
The basis function selection means 21 selects the best fit from the residual signal x _e (t−1) calculated in step S503 (x _e (t−1)=x at t=0) at the search times (t−1) A basis function is selected from the basis function set P.
Here, the basis function list containing the basis functions selected by the search times (t-1)

は、次のように表される。

is expressed as

また、捜索回数（ｔ－１）まで、基底関数Ｐうち、未選択の基底関数を含む未選択基底関数リストＵは、以下の通りである。

Further, the unselected basis function list U including unselected basis functions among the basis functions P up to the number of searches (t−1) is as follows.

In the unselected basis function list U, Q is the number of unselected basis functions among the M prepared basis functions, and Q=M-(t-1). When searching for the q-th basis function from the unselected basis function list U, the basis function selection means 21 creates a matrix Zq of the following equation.

ただし、

however,

is. Here, the basis functions in the basis function set P may have a correlation between basis functions. Correlation causes spectral leakage, and weak signals may be buried in leaked components and missed. Assuming that the matrix obtained by orthogonalizing the basis functions in Zq is Wq, the basis function selecting means 21 attempts to orthogonalize the basis functions as follows.

この行列Ｗｑにおいて、

In this matrix Wq,

である。式（３）の直交化後の式を、式（４）に示す。

is. Equation (4) shows the equation after orthogonalization of equation (3).

In Equation (4), g _q,l represents the weight given to the orthogonalized w _q,l . e represents the error ε after orthogonalization. When the coefficients α _q,l,r are defined, the basis function selection means 21 does not directly obtain w _q,l for speeding up, but g _q,l and α _q,l,r are as follows: , recursively.

Here, {l=0, 1, . . . , 2t+1} in equations (5) to (8).
The basis function selection means 21 selects a basis function that minimizes the error power with the residual signal from the unselected basis function list U.

を選択する。誤差パワーｅ^２は次式で算出する。

to select. ^The error power e2 is calculated by the following equation.

xe(t-1) in equation (9) is the residual signal, which will be described in detail in step S503. The basis function selection means 21 selects the basis function

を用いて、次式のように基底関数リストＰ＾_ｔを更新する。

is used to update the basis function list _P̂t as follows.

このとき、基底関数リストＰ＾_ｔ内の各基底関数に対応した重み

At this time, the weight corresponding to each basis function in the basis function list P^ _t

および係数

and coefficient

はステップＳ５０２の処理で用いられる。そのため、基底関数選択手段２１は、

is used in the process of step S502. Therefore, the basis function selection means 21 is

を重みベクトルとして

as a weight vector

を保持手段１３に保存し、

is stored in the holding means 13,

を次式の下三角行列α_ｔとして保持手段１３に保存する。

is stored in the holding means 13 as a lower triangular matrix α _t of the following equation.

[Calculation of amplitude (step S502)]
FOS is the basis function list selected in step S501

に対応する周波数

frequency corresponding to

のみに推定された振幅

estimated amplitude only

をもち、ステップＳ５０１で未選択の基底関数に対応する周波数の振幅値はゼロである。
推定手段２２は、選択された各周波数に対する振幅

, and the amplitude value of the frequency corresponding to the unselected basis function in step S501 is zero.
The estimator 22 estimates the amplitude

を、直交化後の重みｇ_ｔと係数の行列α_ｔとを用いて、次の式（１１）のように再帰的に求める。

is recursively obtained by the following equation (11) using the weight g _t after orthogonalization and the matrix α _t of coefficients.

式（１１）において、

In formula (11),

である。式（１１）で求められたａ_ｌは振幅ベクトルＡｔとして保持手段１３に、以下のように保存される。

is. The al obtained by the equation (11) is stored in the holding means 13 as the amplitude _vector At as follows.

[Calculation of residual signal (step S503)]
The residual calculation means 23 uses the basis function list P̂t selected in step S501 and the amplitude A _t estimated in step S502 to _remove the components of the selected basis function list from the received wave signal x. to calculate the residual signal x _e (t). Calculation of x _e (t) is performed by the following equation.

[End determination (step S504)]
Since the FOS is an operation process for selecting the basis function that minimizes the error power between the received wave signal and the residual signal, there is a high possibility that only noise is present at the end of the search. If the number of searches is increased more than necessary, it becomes a factor of unnecessary calculations and false alarms. Therefore, it is appropriate to set termination conditions and terminate the search in the middle. The termination determination means 24 determines whether or not termination conditions are satisfied (step S504).

In step S504, if the termination condition is satisfied, the termination determination means 24 _{converts the frequency corresponding to the basis function list P̂t selected in step S501 and the amplitude A t estimated} in step S502 into a three-dimensional image such as a spectrogram. It is displayed on the graph (step S505). The total number of basis functions selected for the number of searches t at this time is L=t. On the other hand, if the termination condition is not satisfied in step S504, the termination determination means 24 instructs the basis function selection means 21 to perform the next search (step S501). The residual signal x _e (t) calculated in step S503 is used in subsequent steps S501 to S503.

FOS can finely set the frequency resolution with the same number of samples as compared to FFT. Furthermore, FOS does not require a window function, thus avoiding SNR degradation. Therefore, FOS can be expected to improve signal detection capability in a low SNR environment compared to FFT. As a result, an improvement in narrowband signal detection can be expected.

However, continuous signal detection is difficult for FOS in a low SNR environment because noise is more likely to be selected even if signal components remain.

The cause of this problem is considered to be the termination determination in step S504 shown in FIG. Termination conditions include a threshold determination for the amplitude value estimated in the previous snapshot and a threshold determination for the residual power. These threshold determinations can be expected to end the search early in situations where no signal is included in the residual signal. However, even with stationary noise, the local noise power fluctuates for each snapshot. FIG. 6 is a diagram showing an example of noise power that fluctuates for each snapshot in FOS processing. As shown in FIG. 6, there may be snapshots where the noise exceeds the signal power, and at such snapshots the above threshold may be reached before the signal is searched.

FIG. 7 is a diagram showing the results of FOS for a signal whose amplitude attenuates over time in a comparative example. In the signal analysis method of the comparative example, as the amplitude of the signal becomes smaller, the search often ends before the frequency at which the signal exists is selected, and as shown in FIG. signal is difficult to detect.

Relaxing the FOS termination condition leads to selection of the frequency where the signal exists, but simply increasing the number of searches as described in the explanation of the signal analysis method of the comparative example does not lead to an increase in erroneous detection. Connect. The first embodiment solves the problem of the conventional FOS by selecting a frequency where the signal to be analyzed continuously exists without relaxing the search termination condition.

The configuration of the signal analysis device 1 according to the first embodiment will be described in detail with reference to FIG. The same reference numerals are given to the same configurations as those of the signal analysis apparatus 100 of the comparative example, and detailed description thereof will be omitted. As shown in FIG. 1, the signal analysis apparatus 1 of Embodiment 1 includes the signal analysis apparatus 100 described with reference to FIGS. It is a configuration in which means 16 is added.

The possibility value calculation means 14 receives as input the basis function list P̂L for which the search has been completed and the basis function set P including all basis functions, _counts the number of frequency bin _detections for the basis function list P̂L, Output the basis function list _P̂L and the weighted number of detections DT _mean .

The addition determination unit 15 receives the basis function list P^ _L and the weighted detection count DT _mean , and determines whether or not to newly add an unselected basis function based on the weighted detection count DT _mean . When adding an unselected basis function, the addition determining means 15 updates the basis function list _P̂L and outputs the updated basis function list _P̂L .

The re- _estimator 16 receives the updated basis function list _P̂L and estimates the amplitude _AL based on the basis function list P̂L. Then, the re-estimating means 16 displays the estimation result on a three-dimensional graph such as a spectrogram.

Next, the operation of the signal analysis device 1 of Embodiment 1 will be described. FIG. 8 is a flowchart showing procedures of a signal analysis method executed by the signal analysis apparatus shown in FIG. 1; Since the processing of steps S101 to S104 and S108 shown in FIG. 8 is the same as steps S501 to S505 described with reference to FIG. 5, detailed description thereof will be omitted.

[Counting the number of detections (step S105)]
The possibility value calculation means 14 uses a set of M basis functions prepared in advance.

に対して、ステップＳ１０４の終了判定で得られた基底関数リスト

, the basis function list obtained by the end determination in step S104

を用いて、どの基底関数が検出されたか、検出回数をカウントする。具体的には、

is used to count which basis functions are detected. In particular,

の関係であるため、

Since the relationship is

に一致する

matches

の周波数ｆ_ｍに対し、可能性値算出手段１４は、次式のように検出回数バッファＤＴへ検出回数をカウントする。

The possibility value calculation means 14 _counts the number of detections in the detection number buffer DT as shown in the following equation.

ここで、ｋはスナップショット番号である。可能性値算出手段１４は、α個前までのスナップショットのＤＴを用いて、ｋ番目のスナップショットで検出されていない基底関数の（ｋ－１）から（ｋ－α）番目までの検出回数を次式のように見積もる。

where k is the snapshot number. The possibility value calculation means 14 uses the DT of the snapshots up to α-th previous to calculate the number of detections of the basis functions not detected in the k-th snapshot from the (k-1)th to the (k-α)th. is estimated as follows.

式（１４）において、｜ＤＴ（ｆ_ｍ，ｋ）－１｜は現スナップショットのＦＯＳで選択済みの基底関数を除くための演算である。β（ｋ）は重み係数であり、過去α個の平均的な検出回数で、可能性値算出手段１４は、分析対象となる狭帯域信号の存在を判定する。この方法に限らず、直近の検出回数の重みの比率を上げるなどして、直近の検出回数を重視するなど自由に設定できる。重み付き検出回数ＤＴ_ｍｅａｎは、分析対象信号の存在の可能性を示す存在可能性値に相当する。

In equation (14), |DT(f _m ,k)−1| is an operation to remove the basis functions already selected in the FOS of the current snapshot. β(k) is a weighting factor, and the possibility value calculating means 14 determines the existence of the narrowband signal to be analyzed based on the average number of past α detections. It is not limited to this method, and can be set freely, for example, by increasing the ratio of the weight of the most recent number of detections, for example, to emphasize the most recent number of detections. The weighted number of detections DT _mean corresponds to an existence possibility value indicating the possibility of the existence of the signal to be analyzed.

[New addition to basis function list (step S106)]
The weighted detection count generated by the possibility value calculation means 14 in step S105 using equation (14)

に基づいて、追加判定手段１５は、新しく基底関数を追加して基底関数リストを更新する。具体的には、追加判定手段１５は、新規追加する基底関数として、ＤＴ_ｍｅａｎを用いて重み付き検出回数が多い周波数ｆ_ｍに対応する基底関数

Based on , the addition determining means 15 adds a new basis function and updates the basis function list. Specifically, the addition determining means 15 uses DT _mean as the basis function to be newly added, and uses the weighted basis function corresponding to the frequency _fm with a large number of detections.

を選択し、次式のように基底関数リストＰ＾_Ｌを更新する。

and update the basis function list _P̂L as follows.

ここで、θ_ＤＴは閾値である。追加判定手段１５は、閾値θ_ＤＴよりも重み付き検出回数の多い周波数ｆ_ｍに対応する基底関数は分析対象信号が存在する可能性が高いと判断し、その基底関数をＰ＾_Ｌに追加する。

where θ _DT is the threshold. The additional determination means 15 determines that there is a high possibility that the signal to be analyzed exists in the basis function corresponding to the frequency f _m with a greater number of weighted detections than the threshold _{θ DT} , and adds this basis function to P̂L. .

[Recalculation of amplitude (step S107)]
The re-estimator 16 applies the amplitude of the basis function newly added to the basis function list in step S106 to the basis function list P̂ _L updated in step S106 and the equations (5) to (8) and (11). ) to formula (12). The re- _estimator 16 displays the frequencies corresponding to the basis functions of the updated basis function list P̂L and the _amplitudes At corresponding to the basis functions of the updated basis function list P̂L on a three-dimensional graph such as a _spectrogram . .

The signal analysis apparatus 1 of the first embodiment includes an FOS processing unit 20 for estimating a combination of a basis function representing a received wave signal and an amplitude of the basis function for each snapshot, a holding unit 13, and a possibility value calculation unit. 14 , additional determination means 15 , and re-estimation means 16 . The holding means 13 stores a basis function list including basis functions selected for each snapshot. The possibility value calculating means 14 calculates an existence probability value indicating the possibility of the existence of the analysis target signal for the unselected basis functions. The addition determining means 15 determines whether or not to add an unselected basis function to the basis function list based on the calculated existence possibility value. The re-estimator 16 uses the basis function list containing the added basis functions to calculate the amplitudes of the added basis functions.

In the first embodiment, the number of detections for each frequency bin of FOS is used to determine the presence or absence of a signal in order to continuously detect the frequency at which the signal exists. Assuming uncorrelated noise, the detection frequency differs for each snapshot when noise is erroneously detected as a signal. Therefore, the detection frequency for noise becomes unstable over time. On the other hand, even if it is difficult to continuously detect the frequency where the signal exists, the detected frequency is temporally stable. Therefore, by counting the number of detections for each frequency bin, the number of detections for frequency bins where signals exist increases, and the number of detections for frequency bins containing only noise does not increase as compared to frequency bins where signals exist. it is conceivable that. The signal analysis apparatus 1 according to the first embodiment can preferentially search for frequency bins in which signals are likely to exist by using the number of detections based on the search of a plurality of past snapshots. Therefore, temporal continuity of signal detection is improved.

FIG. 9 is a diagram showing the result of FOS for a signal whose amplitude attenuates over time in the first embodiment. Comparing FIG. 9 with FIG. 7 reveals that signals can be detected more continuously than in FIG. In the first embodiment, the amplitude is re-estimated by adding to the basis function list the basis functions that are highly likely to contain the signal without relaxing the search termination conditions. can be effectively detected.

Embodiment 2.
In the signal analysis method described in the first embodiment, the second embodiment excludes the added basis function from the basis function list when the added basis function is not the object of signal analysis.

The configuration of the signal analysis device according to the second embodiment will be described. In the second embodiment, the same reference numerals are assigned to the same configurations as those described in the first embodiment, and detailed description thereof will be omitted. FIG. 10 is a diagram showing a configuration example of a signal analysis device according to Embodiment 2 of the present invention.

As shown in FIG. 10, the signal analysis device 1a has a storage unit 11 and a control unit 12. The control unit 12 includes an FOS processing unit 20 , possibility value calculation means 14 , addition determination means 15 , re-estimation means 16 and exclusion determination means 31 . The holding means 13 stores an amplitude value buffer in which the statistic of the amplitude of the basis function selected in the past is stored.

The exclusion determining means 31 receives the basis function list _{P̂L, the amplitude A L ,} and the amplitude value buffer as inputs, performs exclusion determination of the added basis function, and determines the basis function list _P̂L and the amplitude reflecting the determination result. _Output AL.

Next, the operation of the signal analysis device 1a according to the second embodiment will be described. FIG. 11 is a flowchart showing procedures of a signal analysis method executed by the signal analysis apparatus shown in FIG. 10; Since the processes of steps S201 to S204 and S210 shown in FIG. 11 are the same as steps S501 to S505 described with reference to FIG. 5, detailed description thereof will be omitted. Further, since the processing of steps S205 to S207 shown in FIG. 11 is the same as steps S105 to S107 described with reference to FIG. 8, detailed description thereof will be omitted.

After step S204, the end determination means 24 outputs the basis function list _{P̂L and the amplitude A L ,} and then outputs the amplitude value buffer.

への振幅値の保存を、次式のように行う。

store the amplitude value in the following formula:

[Determination of Exclusion of Added Basis Function (Step S208)]
The exclusion determination means 31 uses the basis function list P̂L updated in step S206, the amplitude A _L for the basis function list _P̂L calculated in step _S207 , and the amplitude value buffer Amp. Eliminate basis functions. Specifically, the exclusion determination means 31 uses the added basis function

に対する過去の振幅の統計量として平均および分散を、振幅値バッファＡｍｐから次式のように計算する。

Calculate the mean and variance as past amplitude statistics for , from the amplitude value buffer Amp as follows.

このとき、

At this time,

の平均と分散は非零成分のみで算出され、αは非零のみの過去のスナップショット数とする。除外判定手段３１は、算出した平均と分散に基づいて次式のような

The mean and variance of are calculated with only nonzero components, and α is the number of past snapshots with only nonzero components. Exclusion determination means 31, based on the calculated average and variance, such as the following equation

に対する除外判定を行う。

Perform exclusion judgment for

ここで、Ｖは重みである。２つの関係式のうち、上段の関係式が満たされる場合、除外判定手段３１は、追加された基底関数を基底関数リストＰ＾_Ｌから除外する（ステップＳ２０９）。一方、下段の関係式が満たされる場合、除外判定手段３１は、追加された基底関数を基底関数リストＰ＾_Ｌに維持する。除外判定手段３１は、基底関数リストＰ＾_Ｌの基底関数に対応する周波数と基底関数リストＰ＾_Ｌの基底関数に対する振幅Ａ_Ｌとをスペクトログラム等の三次元グラフ上に表示する（ステップＳ２１０）。

where V is the weight. If the upper relational expression of the two relational expressions is satisfied, the exclusion determining means 31 excludes the added basis function from the basis function list P̂L (step _S209 ). On the other hand, if the lower relational expression is satisfied, the exclusion determining means 31 maintains the added basis function in the basis function list _P̂L . The exclusion determining means 31 displays the frequencies corresponding to the basis functions of the basis function list _{P̂L and the amplitudes A L corresponding} to the basis functions of the basis function list P̂L on a three-dimensional graph such as a spectrogram ₍ step S210).

Based on the amplitude calculated by the re-estimator 16 and the statistic of the amplitude of the past basis function, the signal analysis device 1a of the second embodiment determines whether or not to exclude the added basis function from the basis function list. It has exclusion determination means 31 for determining whether or not.

In Embodiment 1, basis functions satisfying the conditions are added in the additional judgment, but no judgment is made as to whether or not the signal of the added basis functions is noise. So it is possible that the added basis function signal is noise in the current snapshot. Therefore, since the narrowband signal is a stationary signal, the signal analysis device 1a of the second embodiment calculates the statistic of the added basis function from the amplitude value of the basis function detected in the past, Based on the statistics, it is determined whether the added basis function signal is noise. If the signal subjected to signal analysis is noise, it does not follow the calculated statistic of the signal. Therefore, in the second embodiment, it can be determined whether or not the signal is noise. Therefore, not only can the same effect as in the first embodiment be obtained, but false alarms can be suppressed when the signal of the added basis function is noise. As a result, an increase in false alarms can be avoided.

Embodiment 3.
Embodiment 3 is obtained by applying Embodiment 1 to signal arrival azimuth estimation by phasing processing.

The configuration of the signal analysis device according to the third embodiment will be described. In the third embodiment, the same reference numerals are assigned to the same configurations as those described in the first and second embodiments, and detailed description thereof will be omitted. FIG. 12 is a diagram showing a configuration example of a signal analysis device according to Embodiment 3 of the present invention.
As shown in FIG. 12, the signal analysis device 1b has a storage unit 11 and a control unit 12. The storage unit 11 has holding means 13 . The control unit 12 has an FOS processing unit 20 , possibility value calculation means 14 , additional determination means 15 , and re-estimation means 16 . A sensor array 50 having a plurality of sensors is connected to the signal analysis device 1 b via a fast Fourier transform section (FFT section) 40 . A signal observed by each sensor of the sensor array 50 is Fourier transformed by the FFT section 40 and then input to the control section 12 . The shape of the sensor array 50 is, for example, a linear equidistant array.

If the sensor array 50 is a linear equidistant array, the basis function may be the steering vector (SV), as an example. The steering vector will be described in the explanation of the operation of the signal analysis device 1b. A holding means 13 stores an SV set containing a plurality of steering vectors.

The basis function selection means 21 receives the received wave signal X(f) of each sensor for the first search, and receives the residual signal X _e (f, t−1) for the second and subsequent searches. Select a steering vector from the SV set at t. The basis function selection means 21 outputs the SV list _P̂t containing the selected steering vectors, the weight g _t and the coefficient matrix α _t for each steering vector.

The estimating means 22 receives the SV list _P̂t , the weight _gt , and the coefficient matrix _αt , and outputs the SV list _P̂t and the _amplitude At. In Embodiment 3, the estimating means 22 may calculate the phasing output A _t including the arrival direction of the signal using the input SV list P^ _t . Estimation of the phasing output will be described later. The residual calculation means 23 receives the SV list P^ _t and the amplitude A _t as inputs and calculates the residual signal X _e (f, t). The residual calculation means 23 may receive the SV list P̂t and the phasing output At as inputs to calculate the residual signal _Xe ( _f , _t ).

The termination determination means 24 receives the residual signal X _e (f, t) and determines whether or not the termination condition is satisfied. The termination determination means 24 outputs the residual signal X _e (f, t−1) to the basis function selection means 21 if the termination condition is not satisfied, and if the termination condition is satisfied, the SV list P^ Output _L and amplitude A _L. The end determination means 24 may output the result of phasing the signal to the estimated azimuth instead of the amplitude _AL .

The possibility value calculation means 14 receives the SV list P̂L for which the search has been completed and the _SV set P including all the steering vectors, counts the number of frequency bin detections for the _SV list P̂L, and calculates the SV list P Output _̂L and the weighted number of detections DT _mean .

The addition determining means 15 receives the SV list _P̂L and the weighted detection count DT _mean , and determines whether or not to newly add an unselected steering vector based on the weighted detection count DT _mean . When adding an unselected steering vector, the addition determining means 15 updates the SV list _P̂L and outputs the updated _SV list P̂L.

The re- _estimator 16 receives the updated SV list P̂L as an input, estimates the amplitude _AL based on the SV list P̂L on a three-dimensional graph of time, orientation and _phasing output, and outputs the estimation result as indicate. The re-estimator 16 may calculate the _phased output A _L using the updated SV list P̂t.

Next, the operation of the signal analysis device 1b according to the third embodiment will be described. FIG. 13 is a flowchart showing procedures of a signal analysis method executed by the signal analysis apparatus shown in FIG. 12; Here, the estimating means 22 and the re-estimating means 16 will be explained in the case of outputting the result of phasing the signal to the estimated azimuth instead of the amplitude for A _t and A _L .

In step S301, the basis function selection means 21 receives the received wave signal X(f) of each sensor for the first search, and selects a steering vector from the SV set for the search number t. The basis function selection means 21 outputs the SV list _P̂t containing the selected steering vectors, the weight g _t and the coefficient matrix α _t for each steering vector. From the second search onwards, in step S301, the basis function selection means 21 receives the residual signal X _e (f, t−1).

In step S302, the estimating means 22 receives the SV list _P̂t , the weight _gt , and the coefficient matrix _αt , and outputs the SV list _P̂t and the _phased output At. In step S303, the residual calculator 23 receives the SV list P̂t and the phasing output At, and calculates the residual signal _Xe ( _f , _t ). In step S304, when the residual signal X _e (f, t) is input, the termination determination means 24 determines whether or not the termination condition is satisfied.

As a result of the determination in step S304, if the termination condition is not satisfied, the termination determination means 24 outputs the residual signal X _e (f, t−1) to the basis function selection means 21 (step S301). On the other hand, if the termination condition is satisfied as a result of the determination in step S304, the termination determination means 24 outputs the SV list P̂L and the _phasing output _AL at the end of the search.

In step S305, the possibility value calculation means 14 receives the SV list P̂L for which the search has been completed and the SV set P including all steering _vectors , and counts the number of frequency bin _detections for the SV list P̂L. . Then, the possibility value calculation means 14 outputs the SV list _P̂L and the weighted number of detections DT _mean .

In step _S306 , the addition determining means 15 receives the SV list P̂L and the weighted detection count DT _mean , and determines whether or not to newly add an unselected steering vector based on the weighted detection count DT _mean . judge. When adding an unselected steering vector, the addition determining means 15 updates the SV list _P̂L and outputs the updated _SV list P̂L.

In step _S307 , the re-estimator 16 receives the updated SV list P̂L and estimates the _phasing output _AL based on the SV list P̂L. The re-estimator 16 outputs the spectrum of the estimation result on a three-dimensional graph of time, azimuth and phased output (step S308). After step S308, the signal analysis apparatus 1b repeats the processing of steps S301 to S308 for the received signal of the next snapshot.

FIG. 14 is a diagram showing a model in which sounds from S targets are received by R sensors linearly arranged at equal intervals in the third embodiment. Consider the case of the model shown in FIG. At this time, the received wave signal Xr(f _n ), {r= ₁ , 2, .

ここで、ａ_ｒｓはｒ番目のセンサで受波したｓ番目のターゲットの振幅、ｄはセンサ間隔、θ_ｒｓはｒ番目のセンサからみたｓ番目のターゲットの到来方向である。φ_ｓはｓ番目のターゲットの初期位相、ｃは音速、ｎｏｉｓｅはｒ番目のセンサで受波した雑音である。同様に得られたＲ個のセンサ出力

Here, ars is the amplitude of the sth target received by the rth sensor, d is the sensor interval, and _θrs is the direction of arrival of the sth target viewed from the _rth sensor. φ _s is the initial phase of the sth target, c is the speed of sound, and noise is the noise received by the rth sensor. Similarly obtained R sensor outputs

を用いて、θ_ｐ方向へ整相した出力Ｙ（θ_ｐ，ｆ_ｎ）は次式で表される。

, the output Y(θ _p , f _n ) phased in the θ _p direction is expressed by the following equation.

ここで、ｂ（θ_ｐ，ｆ_ｎ）は各センサの受波信号をθ_ｐ方向へ整相するステアリングベクトルであり、

Here, b(θ _p , f _n ) is a steering vector for phasing the received wave signal of each sensor in the θ _p direction,

と表される。出力Ｙ（θ_ｐ，ｆ_ｎ）は、θ_ｐがセンサアレイからみたｓ番目のターゲットの到来方向θ_ｓに一致した場合に大きくなるので、Ｙ（θ_ｐ，ｆ_ｎ）のピーク方向が推定方位となり、ピークの数が推定ターゲット数となる。Ｘ（ｆ_ｎ）は，ステアリングベクトルを用いて以下のように表すことができる。

is represented. The output Y(θ _p , _{f n} ) becomes large when θ _p coincides with the direction of arrival θ _s of the s- _th target seen from the sensor array. , and the number of peaks is the estimated number of targets. X(f _n ) can be expressed as follows using a steering vector.

ここで、

here,

であり、

and

である。式（１）と式（１８）を比較すると、ステアリングベクトルｂが基底関数に対応していることがわかる。また、周波数解析における１スナップショットの受波信号

is. A comparison of equations (1) and (18) reveals that the steering vector b corresponds to the basis function. In addition, the received wave signal of one snapshot in frequency analysis

は、推定手段２２および再推定手段１６によって行われる信号到来方位推定では、各センサの受波信号

In the signal arrival direction estimation performed by the estimation means 22 and the re-estimation means 16, the received wave signal of each sensor is

に対応していることがわかる。以上より、基底関数セットＰは、次式に示すような整相方向θ_ｍを任意に設定可能なステアリングベクトルのセットＢに置き換えられる。

It can be seen that it corresponds to As described above, the basis function set P is replaced with a steering vector set B in which the phasing direction _θm can be arbitrarily set as shown in the following equation.

In this way, FOS can be applied to signal direction-of-arrival estimation. The operation principle of steps S101 to S108 described with reference to FIG. 8 in Embodiment 1 and steps S301 to S308 shown in FIG. 13 are the same. In the third embodiment, as in the first embodiment, the second embodiment can also be applied.

The resolution in the conventional phasing direction is (π/M) and depends on the number of sensors. Therefore, many sensors are required for detailed azimuth estimation. If the object to be analyzed is divided into more than the number of sensors, the orthogonal relationship between the steering vectors cannot be maintained, and leakage occurs in directions other than the phasing direction. Since the component leaks from the direction adjacent to the phasing direction, the component related to the phasing direction cannot be distinguished from the leaked component, and the resolution is not improved. On the other hand, in the signal analysis device 1b of the third embodiment, since the steering vector is orthogonalized to the residual calculation by the FOS processing, improvement in the accuracy of azimuth estimation can be expected without increasing the number of sensors.

Although the signal analysis method using FOS has been described in the first to third embodiments, OMP (Orthogonal Matching Pursuit) may be used instead of FOS. OMP is a method similar to FOS. Briefly describe OMP. First, the OMP selects the basis function that has the highest correlation with the residual signal (the received signal in the first search) from the basis function set. Subsequently, the OMP performs orthogonalization with the already selected basis function list after selection, and calculates a residual signal from the orthogonalized basis function list and the received signal. The result of selecting the basis function list can be applied to the first to third embodiments described above in the same manner as the FOS. The end of the loop is determined from the residual signal as in the case of FOS.

Further, in the first to third embodiments, sine and cosine functions are used as examples of basis functions for frequency analysis, but other basis functions such as wavelet functions are used in addition to sine and cosine functions. may Further, in Embodiments 1 to 3, the estimating means 22 and the re-estimating means 16 were described as means for estimating the amplitude, signal arrival azimuth and phasing output for the sake of explanation. It may have 16 functions.

Reference Signs List 1, 1a, 1b Signal analysis device 11 Storage unit 12 Control unit 13 Holding unit 14 Possibility value calculation unit 15 Additional determination unit 16 Re-estimation unit 20 FOS processing unit 21 Basis function selection unit 22 Estimation unit 23 Residual calculation unit 24 End Determination Means 31 Exclusion Determination Means 40 FFT Section 50 Sensor Array 51 CPU
52 memory 100 signal analyzer 101 storage unit 102 control unit.

Claims (12)

Using a received wave signal and a basis function set, by repeating a calculation process of selecting a basis function from the basis function set and subtracting the selected basis function from the received signal, a snapshot that is an observation time unit A signal analysis device for estimating a combination of a basis function representing the received wave signal and an amplitude of the basis function,
holding means for storing a basis function list including basis functions selected for each snapshot;
possibility value calculation means for calculating an existence probability value indicating the possibility of existence of the signal to be analyzed for an unselected basis function;
addition determining means for determining whether or not to add the unselected basis function to the basis function list based on the calculated existence possibility value;
re-estimating means for calculating amplitudes of the added basis functions using a basis function list containing the added basis functions;
A signal analyzer having The holding means stores amplitude statistics of previously selected basis functions,
2. The method according to claim 1, further comprising exclusion determining means for determining whether or not to exclude the added basis function from the basis function list based on the amplitude calculated by the re-estimating means and the statistic. A signal analyzer as described. the basis function set consists of a pair of sine and cosine functions,
3. A signal analysis device according to claim 1 or 2, wherein the received signal belongs to a narrowband signal. 3. The signal analysis apparatus according to claim 1, wherein said received signal is a signal observed by a sensor array including a plurality of sensors. the basis functions are steering vectors;
wherein the sensor array is a linear equidistant array;
further comprising estimating means for estimating the amplitude based on the steering vector representing the received signal for each snapshot;
5. The signal analyzing apparatus according to claim 4, wherein said estimating means estimates the direction of arrival of said received wave signal. The possibility value calculation means is
The signal analysis device according to any one of claims 1 to 5, wherein said existence probability value for said unselected basis function is calculated from a weighted average value of previously selected basis functions. Using a received wave signal and a basis function set, by repeating the selection of a basis function from the basis function set and the arithmetic processing of subtracting the selected basis function from the received signal, a snapshot that is an observation time unit A signal analysis method for estimating a combination of a basis function representing the received signal and an amplitude of the basis function for each
storing a basis function list containing basis functions selected for each of said snapshots;
calculating a presence probability value indicating the possibility of the presence of the signal to be analyzed for the unselected basis functions;
determining whether to add the unselected basis function to the basis function list based on the calculated existence possibility value;
calculating amplitudes of the added basis functions using a basis function list containing the added basis functions;
Signal analysis method. store the statistics of the amplitudes of the previously selected basis functions;
8. The signal analysis method according to claim 7, wherein it is determined whether or not to exclude the added basis function from the basis function list based on the amplitude of the added basis function and the statistic. the basis function set consists of a pair of sine and cosine functions,
9. A signal analysis method according to claim 7 or 8, wherein said received signal belongs to a narrowband signal. 9. The signal analysis method according to claim 7, wherein said received wave signal is a signal observed by a sensor array including a plurality of sensors. the basis functions are steering vectors;
wherein the sensor array is a linear equidistant array;
11. The signal analysis method according to claim 10, wherein when estimating the amplitude based on the steering vector representing the received signal for each snapshot, an arrival direction of the received signal is estimated. The signal analysis method according to any one of claims 7 to 11, wherein said existence probability value for said unselected basis function is calculated from a weighted average value of previously selected basis functions.

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