JP3513645B2 - Narrowband signal detection method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To make arbitrarily settable the transition probability by calculating a route certainly and a detecting certainty by a specific formula at each sampling time and for every frequency pin, and judging that a narrow band signal has come if the detecting certainly exceeds a threshold value. SOLUTION: A value ν of maximum certainly γ (ν, m, k) at each sampling time (k) and for every frequency pin (m) is ν0. The γ (ν0, m, k) is stored is Γ(m, k), and Λ (m, k) is calculated from Λ (m, k) = log P (X(m, k)) + Λ(ν0, k-1). The Γ (m, k) is a route certainty, and the Λ(m, k) is a detecting certainty. After the above process is finished for all sampling times (k) and the pins (m), the maximum value Λ (m0, k) of the certainty Λ (m, k) is obtained, compared with a preset threshold value. If it exceeds it, information of detecting a narrow band signal in the pin m0 is output. Thus, any transition probability is used, a signal detection judgement can be performed.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a narrow band signal for detecting the arrival of a narrow band signal by using a frequency space distribution of the input signal intensity obtained by performing frequency analysis on an input signal such as a sound wave. The present invention relates to a signal detection method.

[0002]

2. Description of the Related Art Conventionally, as a narrow band signal detecting method of this kind, there has been one described in the following documents. “Detection and Estimation of Frequency-Random Sig
nals ”RD Short and JPToomey, IEEE Transactions o
n Information Theory, Vol. IT-28, No. 6, Nov. 1982 Next, the operation of the conventional narrow band signal detection method will be described. FIG. 4 is a flow chart showing the operation of the conventional narrow band signal detection method, and for the input acoustic signal, predetermined sampling times k = 1, 2 ,. ． ． , K, the frequency bins m = 1, 2 ,. ． ． , M, a narrow band signal is detected after estimating the frequency transition path by the maximum posterior probability method based on the signal strength X (m, k).

First, the signal intensity distribution X (m, k) (m =
1, 2 ,. ． ． , M; k = 1, 2 ,. ． ． , K) is input (S100), and for each sample time k, each frequency bin m, and for each ν one sample time before, γ (ν, m, k shown in the following equation (1). ) Is calculated (S10
1, S102, S103, S104, S105). This γ is an index representing the probability of passing through the point (ν, k−1) one sample time before, if a narrow band signal passing through the point (m, k) exists.

The certainty factor indicates the certainty of "there is a narrow band signal passing through the point (ν, k-1) and the point (m, k)". γ (ν, m, k): = log P (X (m, k)) + log a (m | ν) + Γ (ν, k−1) (1)

However, P (X (m, k)) is a likelihood ratio when a signal exists and when it does not exist. P (X (m, k)) = p ₁ (X (m, k)) / p ₀ (X (m, k)) (2) where p ₀ (X (m, k)) is Probability density distribution that the observed value X (m, k) follows when there is no signal, p ₁ (X
(M, k)) is the observed value X (m,
k) is the probability density distribution followed.

Further, a (m | ν) represents the probability that a narrow band signal having a frequency corresponding to the frequency bin ν at a certain sample time will transit to the frequency bin m after one sample time. Further, in the conventional example, it is usually assumed that the signal transits at most one frequency bin at one sample time, and that the probability of transiting from ν to ν-1, ν, ν + 1 is uniform. That is, The condition is used.

Ν which maximizes γ (ν, m, k)
Is selected as ν ₀ (S106). This means that if there is a narrowband signal passing through the point (m, k), its past path has the highest probability of passing through the point (ν ₀ , k−1). Then, the certainty factor γ (ν ₀ , m, k) corresponding to the selected route is set to Γ (m,
It is stored in k) (S107).

After the above processing is completed for all sample times k and frequency bins m (S108, S
109), the maximum value Γ (m ₀ , K) of Γ (m, K) is calculated and compared with a predetermined threshold value T. If Γ (m ₀ , K) exceeds the threshold value T, the frequency bin Information that a narrow band signal is detected is output to m ₀ (S110, S111,
S112).

Further, by recording which route is selected in S106 and S107 and tracing the route in reverse from the point (m ₀ , K), the narrow band signal is traced at each sample time. The frequency bins {m ₁ , m ₂ , ..., M _K-1 , m _K (= m ₀ )} are output.

[0010]

Neyman P is one of the methods for detecting a signal in the conventional narrow band signal detection method.
There is an earson method. This is to determine that a signal is present when the likelihood ratio exceeds a predetermined threshold value, and if applied to the operation of the above-mentioned conventional example, a method of comparing the index λ shown in the following equation (4) with the threshold value is used. is there. λ = Σ _{k = 1,2, ..., K} {log P (X (m _k , k))} (4) And the Neyman Pearson method has a detection capability when the false alarm probability is constant. It is used in many applications because it has the advantage of being excellent.

In the conventional example, the index Γ (m, K) for determining whether or not a signal exists can be expressed by the following equation (5). Γ (m, K): = Σ _{k = 1,2, ..., K} {= log P (X (m _k , k)) + log a (m _k | m _k-1 )} (5) Here, if the transition probability a (m _k | m _k-1 ) is always a constant value, Γ (m, K) will be equal to the above λ without bias, and thus Γ (m, K). The signal is detected when () exceeds the threshold, which is equivalent to using the Neyman Pearson method.

However, this does not hold when the transition probability is not a constant value, so that there is a constraint that the transition probability must be uniform as long as the Neyman Pearson method is followed. However, in reality, the transition probabilities of signals are not always uniform, and many signals have the property of having a high probability of going straight. If such a signal is processed on the assumption that the transition probabilities are uniform, performance deterioration due to the difference between the reality and the model cannot be avoided. Therefore, conventionally, the transition probability can be freely set, and the signal detection judgment is performed by the Neyman Pea.
There was a demand for a technique that follows a method equivalent to the rson method.

[0013]

A narrow band signal detecting method according to the present invention is applied to a predetermined sampling time k = 1, 2 ,. ． ． , K, the frequency bins m = 1, 2 ,. ． ． , N based on the signal strength X (m, k) at N, the narrowband signal detection method for estimating the narrowband signal after estimating the frequency transition path by the maximum posterior probability method. The frequency of the narrowband signal corresponding to
Transition probability a of transition to frequency bin m after sample time
(M | ν) and the likelihood defined by the ratio of the probability density distribution p ₁ (z) of the signal strength when the signal exists to the probability density distribution p ₀ (z) of the signal strength when the signal does not exist Using the ratio P (z) = p ₁ (z) / p ₀ (z), for each sample time k and each frequency bin m, the route certainty factor Γ
(M, k) and the detection certainty factor Λ (m, k) are calculated by the following equations, and when the detection certainty factor Λ (m, k) exceeds a preset threshold value, the narrowband signal is calculated. Is determined to have arrived. For each frequency bin ν, γ (ν, m, k): = log P (X (m, k)) + log a
(M | ν) + Γ (ν, k−1) · ν ₀ : = {frequency bin ν that maximizes γ (ν, m, k)} · Γ (m, k): = γ (ν ₀ , m , K) · Λ (m, k): = log P (X (m, k)) + Λ
(Ν ₀ , k-1)

[0014]

BEST MODE FOR CARRYING OUT THE INVENTION Embodiment 1. FIG. 1 is a flowchart showing the operation of a narrowband signal detection method according to an embodiment of the present invention. In this embodiment, as in the conventional example, the frequency bin transition is limited to at most 1 bin.
However, in this embodiment, the transition probability may be arbitrarily determined according to the property of the signal to be detected. a (m | ν) = a ₁ (if m = ν−1) (6) a ₂ (if m = ν) a ₃ (if m = ν + 1) 0 (otherwise) where a ₁ + a ₂ + a ₃ = 1.0

First, as in the conventional example, each sample time k
And for each frequency bin m, ν that maximizes the certainty factor γ (ν, m, k) shown in the above equation (1) is selected and set as ν ₀ (S10 to S16). Then, γ (ν ₀ , m, k) is
It is stored in Γ (m, k) (S17), and Λ (m, k) is calculated according to the following equation (7) (S18). Λ (m, k): = log P (X (m, k)) + Λ (ν ₀ , k−1) (7) where Γ (m, k) specifies the path taken by the signal. Λ (m, k) is a certainty factor for determining whether or not a signal exists.

In the following description, Γ (m, k) is called a route certainty factor and Λ (m, k) is called a detected certainty factor.

After the above processing is completed for all sample times k and frequency bins m (S19, S2).
0), the maximum value Λ (m ₀ , K) of the detection certainty Λ (m, K)
Is calculated and compared with a predetermined threshold value T, and if Λ (m ₀ , K)
Is greater than the threshold T, the information that the narrow band signal is detected in the frequency bin m ₀ is output (S21, S22,
S23). In addition, as in the conventional example, the frequency bins {m ₁ , m ₂ , ..., M _K-1 , m that the narrowband signal has followed.
_K (= m ₀ )} may be output.

In this embodiment, the detection certainty factor Λ (m _K , E), which is an index of signal detection, is expressed by the following equation (8). Λ (m ₀ , K) = Σ _{k = 1,2, ..., K} {log P (X (m _k , k))} (8) This is exactly shown in the above equation (4). A signal detection method that is equal to λ and therefore compares the detection certainty with a threshold is Neym
It is nothing but the an Pearson method.

That is, according to this embodiment, it is possible to perform signal detection determination according to the Neyman Pearson method, regardless of the transition probability used. In other words, the transition probability a (m _k | m _k-1 ) can be set arbitrarily, and the detection performance can be kept high when the false alarm probability is constant.

Embodiment 2. FIG. 2 is a flowchart showing the operation of the narrowband signal detection method according to another embodiment of the present invention. In this embodiment, according to the first embodiment, time k = {1, 2 ,. ． ． , K}, the signal is detected within the range, whereas this embodiment does not particularly limit the number of data input samples, and theoretically can be operated semipermanently and continuously. Is.

First, the signal intensity distribution X (m, k) (m =
1, 2 ,. ． ． , M; k = 1, 2 ,. ． ． , K) is input (S30), and for each sample time k, each frequency bin m, and for each ν one sample time before, the path certainty factor γ (ν, m, k) is calculated (S31, S32, S33, S34, S35). γ (ν, m, k): = α × {log P (X (m, k)) + log a (m | ν)} + (1-α) × {Γ (ν, k-1)} ... (9) However, α is a predetermined time constant and is in the following range. 0.0 <α <1.0 (10)

Then, ν that maximizes γ (ν, m, k)
Is selected as ν ₀ (S36), and the certainty factor γ (ν ₀ , m, k) corresponding to the selected route is set to Γ (m, k).
(S37). Then, the detection certainty factor is calculated according to the following equation (11) (S38). Λ (m, k): = α × {log P (X (m, k))} + (1-α) × {Λ (ν ₀ , k-1) (11)

After the above processing is completed for all frequency bins m (S39), the detection certainty factor Λ (m,
The maximum value Λ (m ₀ , K) of K) is calculated and compared with a predetermined threshold T. If Λ (m ₀ , K) exceeds the threshold T,
Information that a narrow band signal has been detected is output to the frequency bin m ₀ (S40, S41, S42). Then, the time samples k = {1, 2 ,. ． ． , K} are not processed after all the data have been processed, but the judgment is performed every sample time (S43). The initial values Γ (m, 0) and Λ (m, 0) of the route certainty factor and the detected certainty factor are initialized to appropriate values, for example, 0.

Here, in the actual operation of signal detection,
The time when a signal is input is not always known. There is a demand for a method that can be operated under the circumstances where a signal may appear or disappear and the time is difficult to predict. In this embodiment, a method of forgetting past information by introducing a time constant α in the calculation of the path certainty factor and the detection certainty factor is adopted, and it is decided to detect the signal at each sample time. It is possible to perform the signal detection processing that is approximately equivalent to the method described in the first embodiment consecutively in time.

Further, conventionally, although the input signal is not completely clear, the detection process has to be repeated because it is necessary to detect the signal in real time. It is possible to perform the detection. The signal detection method of this embodiment has different characteristics depending on the magnitude of the time constant α. If α
If is larger, the degree of forgetting is larger, so that it is possible to react promptly to the appearance and disappearance of a signal. On the other hand, if α is small, signal detection is performed based on long-term data, so that the ability to detect weak signals is excellent.

Embodiment 3. FIG. 3 is a flowchart showing the operation of the narrowband signal detecting method according to another embodiment of the present invention. First, the signal intensity distribution X (m, k) (m =
1, 2 ,. ． ． , M; k = 1, 2 ,. ． ． , K) is input (S50), and for each sample time k, the average value μ of the input data X (m, k) (m = 1, 2, ..., M) and the standard difference σ are calculated. Then, for each frequency bin m, using the average value μ and standard deviation σ, input data X (m, k) (m
= 1, 2 ,. ． ． , M) is standardized, and Y (m, k) (m = 1, 2, ..., M) is generated by the following equation (12) (S51, S52, S53, S54). Y (m, k): = {X (m, k) -μ} / σ ... (12)

For each ν one sample time before,
The logarithmic value Q of the likelihood ratio shown in the following equation (13) and the certainty factor γ (ν, m, k) shown in the following equation (14) are calculated (S55, S56, S57, S58). Q: = Λ (ν, k−1) × {Y (m, k) −Λ (ν, k−1) / 2} (13) γ (ν, m, k): = α × {Q + log a (m | ν)} + (1-α) × {Γ (ν, k-1)} (14)

Then, ν that maximizes γ (ν, m, k)
Is selected as ν ₀ (S59), and the certainty factor γ (ν ₀ , m, k) corresponding to the selected route is set to Γ (m, k).
(S60). Then, the detection certainty factor is calculated according to the following equation (15) (S61). Λ (m, k): = α × {Y (m, k)} + (1-α) × {Λ (ν0, k-1)} (15)

After the above processing is completed for all frequency bins m (S62), the detection certainty factor Λ (m,
The maximum value Λ (m ₀ , K) of K) is calculated and compared with a predetermined threshold T. If Λ (m ₀ , K) exceeds the threshold T,
Information that a narrow band signal has been detected is output to the frequency bin m ₀ (S63, S64, S65). Then, the time samples k = {1, 2 ,. ． ． , K} are not processed after all the data have been processed, but the judgment is performed every sample time (S66). The initial values Γ (m, 0) and Λ (m, 0) of the route certainty factor and the detected certainty factor are initialized to appropriate values, for example, 0.

Here, when it can be considered that the distribution of the input signal X (m, k) in which only noise is input follows a normal distribution,
The standardized input Y (m, k) follows a standard normal distribution with an average value of 0 and a standard deviation of 1. That is, the probability density function p of the distribution that Y (m, k) follows when there is no signal
₀ (Z) is expressed by the following equation (16). _{p 0 (Z) = exp (} -Z 2/2) ...... (16) Similarly, under the assumption that a narrow-band signal of the signal intensity A is _{present, p 1 (Z) = exp} (- (Z ^{-A) 2/2) ...... (} 17)

From this, the logarithmic value Q of the likelihood ratio is expressed by the following equation (18). Q = log P (Y (m , k)) = log p 1 (Y (m, k)) - log p 0 (Y (m, k)) = -Y (m, k) 2/2 + (Y ( ^{m, k) -A) 2/} 2 = A × Y (m, k) -A 2/2 ...... (18)

Since the signal strength A is positive, Q is Y (m, k)
Is a monotonically increasing function of. Therefore, performing the threshold determination on Q is equivalent to performing the threshold determination on Y (m, k). Based on this idea, as shown in the equation (15), the temporal integration of Y (m, k) is set as the detection certainty factor A (m, k), and the detection certainty factor exceeds the threshold value. I decided to judge the existence of the signal.

It should be noted that the detection certainty factor Λ (m, k) obtained as described above is also an estimated value of the signal strength. That is, if it is assumed that a narrowband signal of signal strength A is constantly input to the frequency bin m, and signal tracking is ideally performed for a sufficiently long time, the detection confidence Λ ( The expected value of m, k) is equal to the signal strength A. Therefore, in the above equation (18) expressing the logarithmic value of the likelihood ratio, the signal strength A is detected with the detection certainty Λ (m,
What is replaced by k) is the above formula (13). However, since the signal strength A cannot be negative, safety measures may be taken, such as assuming that A = 0 when the detection certainty factor Λ (m, k) is negative.

As described above, in this embodiment, the route certainty factor is calculated according to the above equations (13) and (14), and the detected certainty factor is calculated according to the equation (15). Was only addition, subtraction, multiplication and division. That is, since a calculation process such as a logarithmic function is not included, it is possible to realize a signal detection method based on the maximum posterior probability method with a relatively small calculation resource.

[0035]

As described above, according to the present invention, the transition probability a (m | ν) that the frequency of the narrowband signal corresponding to the frequency bin ν given in advance transits to the frequency bin m after one sample time, And the likelihood ratio P (z) = defined by the ratio of the probability density distribution p ₁ (z) of the signal strength when the signal exists and the probability density distribution p ₀ (z) of the signal strength when the signal does not exist. Using p ₁ (z) / p ₀ (z), for each sample time k and each frequency bin m, the path certainty factor Γ
(M, k) and the detection confidence Λ (m, k): γ (ν, m, k): = log P (X (m, k)) + log a for each frequency bin ν.
(M | ν) + Γ (ν, k−1) · ν ₀ : = {frequency bin ν that maximizes γ (ν, m, k)} · Γ (m, k): = γ (ν ₀ , m , K) · Λ (m, k): = log P (X (m, k)) + Λ
Since it is calculated by each equation of (ν ₀ , k−1) and the detection certainty factor Λ (m, k) exceeds a preset threshold value, it is determined that a narrowband signal has arrived. Since the signal detection determination according to the Neyman Pearson method can be performed regardless of any transition probability, the transition probability a (m _k | m _k-1 ) can be set arbitrarily and the false alarm probability is constant. This has the effect that the detection performance can be maintained at a high level.

[Brief description of drawings]

FIG. 1 is a flowchart showing an operation of a narrowband signal detecting method according to an embodiment of the present invention.

FIG. 2 is a flowchart showing an operation of a narrowband signal detecting method according to another embodiment of the present invention.

FIG. 3 is a flowchart showing an operation of a narrowband signal detecting method according to another embodiment of the present invention.

FIG. 4 is a flowchart showing an operation of a conventional narrowband signal detection method.

─────────────────────────────────────────────────── ─── Continuation of the front page (58) Fields surveyed (Int.Cl. ⁷ , DB name) G01R 23/16 G10L 11/00

Claims (3)

(57) [Claims] 1. Predetermined sample times k = 1, 2 ,. ． ． , K, the frequency bins m = 1, 2 ,. ． ． , N in the narrowband signal detection method for determining the narrowband signal detection after estimating the frequency transition path by the maximum posterior probability method based on the signal strength X (m, k). The probability of a transition of the frequency of the narrow band signal corresponding to the transition to the frequency bin m after one sample time, a (m | ν), and the probability density distribution p ₁ (z) of the signal strength when the signal exists and the signal exist. When the likelihood ratio P (z) = p ₁ (z) / p ₀ (z) defined by the ratio of the probability density distribution p ₀ (z) of the signal intensity when not using each sample time k and each frequency bin For each m, the route certainty factor Γ (m, k) and the detected certainty factor Λ (m, k) are calculated by the following equations, and the detected certainty factor Λ (m, k) is set to a preset threshold value. Narrowband signal is judged to have arrived when Narrowband signal detection method characterized by and. For each frequency bin ν, γ (ν, m, k): = log P (X (m, k)) + log a
(M | ν) + Γ (ν, k−1) · ν ₀ : = {frequency bin ν that maximizes γ (ν, m, k)} · Γ (m, k): = γ (ν ₀ , m , K) · Λ (m, k): = log P (X (m, k)) + Λ
(Ν ₀ , k-1) 2. A predetermined sampling time k = 1, 2 ,. ． ． , K, the frequency bins m = 1, 2 ,. ． ． , N, the narrowband signal detection method for determining the narrowband signal detection after estimating the frequency transition path by the maximum posterior probability method based on the signal strength X (m, k) at The transition probability a (m | ν) that the frequency of the narrowband signal corresponding to ν transits to the frequency bin m after one sampling time, the probability density distribution p ₁ (z) of the signal strength when the signal exists, and the signal exist The likelihood ratio P (z) = p ₁ (z) / p ₀ (z) defined by the ratio of the probability density distribution p ₀ (z) of the signal intensity when not and the integration coefficient α given in advance are used. , The route confidence Γ (m, k) and the detection confidence Λ (m, k) are calculated for each sample time k and each frequency bin m by the following equations, and the detection confidence Λ (m, k k) exceeds a preset threshold, Narrowband signal detecting method characterized by determining a narrow-band signal arriving at. -For each frequency bin ν: γ (ν, m, k): = α (log P (X (m, k)) + lo
g a (m | ν)) + (1−α) Γ (ν, k-1) · ν ₀ : = {frequency bin ν that maximizes γ (ν, m, k)} · Γ (m, k) ): = Γ (ν ₀ , m, k) ・ Λ (m, k): = α log P (X (m, k)) + (1-
α) Λ (ν ₀ , k-1) 3. Predetermined sample times k = 1, 2 ,. ． ． , K, the frequency bins m = 1, 2 ,. ． ． , N based on the signal strength X (m, k) at N, the narrowband signal detection method for determining the narrowband signal detection after estimating the frequency transition path by the maximum posterior probability method. The transition probability a (m | ν) that the frequency of the narrowband signal corresponding to ν transits to the frequency bin m after one sample time, the predetermined integration coefficient α, and the signal strength observed when only noise is input. Using the average value μ and the standard deviation σ of each, the route confidence Γ (m, k) and the detection confidence Λ (m, k) are calculated for each sample time k and each frequency bin m by the following equations. Then, the narrowband signal detection method is characterized in that when the detection certainty factor Λ (m, k) exceeds a preset threshold value, it is determined that a narrowband signal has arrived. For each frequency bin ν: Q: = Λ (ν, k−1) × {((X (m, k) −μ) /
σ) −Λ (ν, k−1) / 2} γ (ν, m, k): = α (Q + log a (m | ν)) +
(1-α) Γ (ν, k-1) ν ₀ : = {Frequency bin ν that maximizes γ (ν, m, k) ・ Γ (m, k): = γ (ν ₀ , m , K) · Λ (m, k): = α (X (m, k) −μ) / σ + (1
−α) Λ (ν ₀ , k−1)