JP3142489B2 - Target motion analysis method and target motion analysis device - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for receiving a sound radiated from a target object by a receiver sensor array attached to a movable observation object, and obtaining a position of the moving target object from an observation amount disturbed by noise. TECHNICAL FIELD The present invention relates to a target motion analysis method and a target motion analysis device for measuring an internal state quantity related to, for example, velocity, sound source natural frequency, and the like.

[0002]

2. Description of the Related Art FIG. 2 is a geometrical explanatory view showing an observation system and a motion system in a target motion analysis method.

In FIG. 2, (X, Y) is a fixed coordinate system at the origin o, 1 is an observation object, 2 is a target object, x ₁ (t) is a position vector of the observation object 1 at time t, x ₂ (t ) Is the position vector of target 2 at time t, r (t) is the distance {x ₂ (t) −x ₁ (t)} between target 1 and target 2 at time t,
θ (t) is the azimuth of the target 2 with respect to the Y-axis as viewed from the observer 1 at time t. Note that {} represents the norm of the vector.

The target motion analysis method is based on the assumption that the target body 2 is performing a linear motion at a constant velocity, and determines the position and velocity of the target body 2 from the observation time series of the azimuth and frequency of the target sound source disturbed by noise. And the like. First, the operation principle of the target motion analysis method will be described below.

The observed value of the azimuth angle θ (t) at time t and the observed value of the Doppler shift frequency ν _k (t) of the k-th natural frequency component f _k of the sound source are expressed by the following equations (1). θ _m (t) = θ (t) + n (t) ν _km (t) = ν _k (t) + η _k (t) (1) where n (t) and η _k (t) are respectively This is the observation noise for the azimuth angle θ (t) and the observation noise for the Doppler shift frequency ν _k (t) at time t.

[0006] A relative position vector x (t) with respect to the target 2 as viewed from the observation body 1 is represented by the following equation (2).
t _1, ..., the internal state vector X at t _n (t),
(3) Defined by equation. In the expression (3), T represents the transposition of a vector. Hereinafter, similarly, in this specification, the transposition of a matrix or a vector is represented by adding T. Represents a time derivative.

[0007]

(Equation 1) It should be noted that, in this specification, in the notation of the expression read by the image reader, the vector is underlined and the matrix is double underlined, which is different from the notation in the text. Also in the drawing notation, vectors are underlined, and matrices are double underlined.

Now, when the internal state quantity vector at time t = t ₀ is X ₀ = X (t ₀ ), the internal state quantity vector X (t) at time t and the internal state quantity vector at time t = t ₀ The relationship with the vector X ₀ is given by a state transition expression shown in Expression (4).

[0009]

(Equation 2) The estimation of the internal state quantity vector X (t) is performed at time t = t ₁ ,
.., T _n are obtained by obtaining an initial internal state quantity vector X ₀ that minimizes the evaluation function L (X ₀ ) shown in Expression (5) composed of a set of observation values at t _n . The evaluation function L (X ₀ ) shown in the equation (5) is based on the assumption that the motion speeds of the observation object 1 and the target object 2 are much lower than the speed of sound. Each element of the expression (5) is represented by the expression (6). E [] in the equation (6) indicates an ensemble average.

[0010]

(Equation 3) Evaluation In the minimization of the function _{L (X 0), (7} ) must be solved using iterative method of non-linear equations in the expression, the initial values for ^ X ₀₀ (Note, indicating an estimated value ^ a sign In addition to the case where it is shown at the top, it may be necessary to determine the case where it is shown before the code in some cases).

[0011]

(Equation 4) Therefore, assuming that the observed value error is very small,
An equation shown in equation (8) expressed as shown in equation (9) is derived, and an approximate weight matrix ＾ obtained by replacing unknown elements of the weight matrix W (X (t)) of this equation with appropriate set values. The initial value を X ₀₀ of the target motion analysis is determined by solving the pseudo-linear equation shown in Expression (10) for the initial internal state quantity vector X ₀ using W (see Document 1). Here, + represents a general inverse matrix.

[0012]

(Equation 5)

(Equation 6) Reference 1 [JMPasserieux, D. Pillion, P. Blanc-Benon and
C. Jauffret, “Target Motion Analysis with Bearin
g and Frequencies Measurements vis Instrumental Va
riable Estimator ”, ACASSP, pp.2645-2648, 1989” In the subsequent target motion analysis, ＾ X ₀₀ given by equation (10)
Is used as an initial value, an appropriate internal state quantity vector ＾ X ₀ that minimizes the evaluation function L (X ₀ ) of Expression (5) is obtained by solving the nonlinear equation of Expression (7).

The estimated information matrix of the estimated value vector ＾ X ₀ of the internal state quantity vector X ₀ obtained from the set of observation values at times t = t ₁ ,..., T _n is defined by equation (11). , At time t = t ₁ ,..., T _n , the estimated information matrix of the estimated state quantity vector ＾ X _t is expressed by Expression (12) from the relationship of Expression (4).

[0014]

(Equation 7) At time t = t ₁ ,..., T _{n + m} , the target body 2
When the maneuver by shifting is performed, the assumption condition of the target motion analysis is not satisfied, and the time t = t _{n + 1} ,.
The statistical distribution of the prediction residual vector ε defined by the equation (13) for the observation value of _{n + m} deviates from the assumed statistical distribution. Therefore, Manila detection can be performed by examining the distribution of the prediction residual (see Document 2).

[0015]

(Equation 8) Reference 2 “JCHassab,“ Underwater signal and data p
rocessing ", CRCPress, Inc., 1990" Hereinafter, a method for detecting a maneuver in the conventional target motion analysis method will be described in detail.

Assuming that the distribution of observation noise at time t = t ₁ ,..., T _{n + m} is a normal distribution with mean 0 and a variance-covariance matrix given by equation (6), time t = t ₁ ,. , T
time t = t based on the estimated value vector ＾ X ₀ of the internal state quantity vector X ₀ obtained from the set of observation values at _{n
n + 1,} ..., the t n ₊ (13) with respect to the observed value of the _m estimated variance-covariance matrix sigma _epsilon prediction residual vector epsilon of formula given by (14). However, each element in the equation (14) is a time t = t _{n + 1} ,
..., various quantities corresponding to the observed value of t _{n + m} .

[0017]

(Equation 9) Now, the average of each component of the prediction residual vector ε is 0,
Assuming that they are independent of each other, the m-dimensional probability vector ε
The variance-covariance matrix of _j is as shown in equation (15). Therefore, each component of the m-dimensional probability vector ε _j independently follows a multivariate normal distribution, and the average value μ of the sum of the components is
_j follows the normal distribution shown in equation (16).

[0018]

(Equation 10) Manual - If server occurs, with departing from a normal distribution the average value mu _j is assumed to detect the maneuver. That is, when H0: μ _j = 0 is assumed as a null hypothesis, a standardized test statistic z _j is given by Expression (17), and z _{α / 2} is defined as the upper α / 2 point of the standard normal distribution, and the rejection area is determined. According to the expression (18), the maneuver can be detected at the significance level α.

[0019]

[Equation 11] When a maneuver is detected, since it is not satisfied that the target body 2 assumed by the conventional target motion analysis method is performing a constant-velocity linear motion, the observation value time series after the maneuver detection is used. The analysis is restarted from the beginning.

FIG. 3 is a functional block diagram of a maneuver detecting section in a target motion analysis device to which a conventional target motion analysis method is applied.

The maneuver detecting section 10 includes a prediction residual calculating section 11 for calculating a residual between the observed value and the observed value estimated from the internal state quantity, an estimated internal state quantity and estimation information of the estimated internal state quantity. A prediction value calculation unit 12 that calculates a variance-covariance matrix of a predicted value of an observation value and a prediction residual from a matrix, and a test statistic calculation that calculates a test statistic from a variance-covariance matrix of a prediction residual and a prediction residual It comprises a unit 13 and a threshold comparing unit 14 for comparing a test statistic with a threshold to determine a maneuver.

At the maneuver detector 10, the time t
= M _n observation azimuths θ at t _{n + 1} ,..., T _{n + m
m} (t) and Doppler shift observation frequency component ν _km (t) (k
,..., P) are input to the prediction residual calculation unit 11, and the prediction value calculation unit 12 performs the following processing.
That is, the predicted value calculating unit 12 calculates the estimated value vector {X} of the internal state quantity transmitted from the internal state quantity estimating unit (not shown).
_{Using 0} , the observation azimuth angle θ _m (t) and the Doppler shift observation frequency component ν _km (t) (k = 1,..., P) at time t = t _{n + 1} ,..., _Tm (> t _n ) Is calculated and sent to the prediction residual calculating unit 11, and the prediction residual is calculated from the estimated value vector か ら X ₀ of the internal state quantity and the estimation information matrix of the estimated value of the internal state quantity by using equation (14). The estimated variance-covariance matrix of the difference is calculated, and the result is sent to the test statistic calculation unit 13. The prediction residual calculation unit 11 calculates a prediction residual from the prediction value sent from the prediction value calculation unit 12 and the already input observation azimuth and Doppler shift observation frequency component, and calculates a test statistic calculation unit 13. Send to The test statistic calculation unit 13 calculates a statistic z _j (j =
0, 1,..., P) and sends the result to the threshold value comparison unit 14. The threshold comparing unit 14 compares the test threshold z _{α / 2} set from a threshold setting terminal (not shown) with the test statistic z _j, and when the expression (18) is satisfied, determines that the maneuver is detected. , An initialization instruction signal is sent to an initial value calculating unit (not shown), and the target motion analysis is started again from the initial value calculation.

[0023]

However, in the conventional target motion analysis method and the maneuver detection method in the target motion analysis device, the average value of m prediction residuals is used. The effect is smoothed,
There was a problem that the fluctuation of the prediction residual was not immediately reflected in the test statistic, and the detection sensitivity of the maneuver was low.

Therefore, there is a need for a target motion analysis method and a target motion analysis device having high maneuver detection sensitivity.

[0025]

According to a first aspect of the present invention, a sound radiated from a target is received by a receiver sensor array attached to a movable observation object. From the observable time series consisting of the azimuth observable time series, which is the azimuth angle measurement result of the target body, and the frequency observable time series, which is the frequency measurement result, under the assumption that the target body performs a uniform linear motion, In the target motion analysis method for estimating the state quantity related to the sound source natural frequency of the target body together with the state quantity related to the position and the speed, the following is characterized.

That is, the determination of the presence or absence of a maneuver such as a change in the course of a target, a shift, or the like, for which the assumption that the target performs a constant velocity linear motion, is determined by applying a linear regression equation to the normalized prediction residual for the observation time series. The coefficient of the regression equation is estimated using the estimated coefficient, and the significance of the regression equation expressed by the estimated coefficient is used to determine whether there is a bias in the normalized prediction residual.

According to a second aspect of the present invention, a sound radiated from a target object is received by a receiver sensor array attached to a movable observation object, and an azimuth observation amount obtained as an azimuth angle measurement result of the target object is obtained. From the observable time series consisting of the series and the frequency observable time series that is the frequency measurement result, the sound source of the target body along with the state quantities related to the position and speed of the target body under the assumption that the target body performs a uniform linear motion. A target motion analysis for estimating a state quantity related to a natural frequency and having maneuver detecting means for judging presence / absence of a maneuver such as a change of a course or a speed change of the target body in which it is not assumed that the target body performs a uniform linear motion. In the apparatus, the maneuver detection means has the following units.

That is, the maneuver detecting means comprises: (1) a normalized prediction residual calculating section for calculating a normalized prediction residual for the observed time series; and (2) a linear regression equation for the calculated normalized prediction residual. And (3) the significance test of the regression equation expressed by the estimated coefficients to determine the presence or absence of bias in the normalized prediction residuals, and A testing unit for detecting presence / absence.

According to the first and second aspects of the present invention, it is possible to detect a maneuver from the time when a maneuver is generated and the normalized prediction residual begins to be biased. Even if a maneuver is generated, its influence is smoothed. Thus, the conventional problem that the detection sensitivity of the maneuver is low can be solved.

[0030]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, an embodiment of a target motion analysis method and a target motion analysis device according to the present invention will be described with reference to the accompanying drawings.

First, the principle of maneuver detection in the target motion analysis method of this embodiment will be described.

In the maneuver detection method of this embodiment,
In order to solve the problem of the conventional maneuver detection method in which the influence of a maneuver is smoothed and the detection sensitivity of the maneuver is low, a linear regression equation is applied to the normalized prediction residual, and the regression equation is calculated. By coefficient significance test,
The presence or absence of a bias in the normalized prediction residual is determined to detect a maneuver.

The prediction residual vector ε _j in the above equation (13) is normalized using the estimated variance-covariance matrix Σ _j as shown in the equation (19). Here, Σ _j ^-1/2 is an upper triangular square root matrix of Σ _j ^-1 . In the following description, the suffix j is omitted to simplify the description.

Y _mj = Σ _j ^-1/2 ε _j (19) When the target 2 is performing a constant velocity linear motion, the normalized prediction residual has a unit variance, and is statistically The amplitude is constant. However, when a maneuver occurs, a bias occurs in the distribution, so that the normalized prediction residual sequence has a slope. Therefore, it is possible to detect a maneuver by checking whether or not the inclination is zero. However, as described above, in the conventional maneuver detection method, since the influence of the inclination is detected as a change in the average value of the entire m time-series sections, there has been a problem that the detection sensitivity of the maneuver is low. .

[0035] Now, (19) with respect to normalized predicted residual vector series y _m given by equation fitting a linear regression equation as a variable time t as shown in equation (20). Here, the vector ζ is a residual vector from the regression equation vector y, and it is assumed that each component follows a normal distribution having a mean of 0 and mutually independent and equal variances.

[0036]

(Equation 12) At this time, the estimated values of the regression coefficients a and b for minimizing the evaluation function J shown in Expression (21) are given by Expression (22). Note that the value with an overline indicates an average value of the corresponding values.

[0037]

(Equation 13) At this time, under the null hypothesis H0: a = 0 that the normalized prediction residual has no bias, the F value shown in the equation (23) follows the F distribution with (1, m−2) degrees of freedom. Is known.
Therefore, the value of the F distribution table for the significance level α is represented by F _α (1,
m-2), if the F value satisfies the expression (24), the null hypothesis H0 is rejected at the risk factor (significance level) α, and the normalized prediction residuals are biased, that is, a maneuver occurs. Can be determined.

[0038]

[Equation 14] In this way, since the slope of the regression line changes from the time the maneuver occurs and the bias of the normalized prediction residual starts to be biased, the bias of the prediction residual is detected using the average value in the observation section. The maneuver detection sensitivity is higher than that of the conventional method.

FIG. 4 is a functional block diagram showing the overall configuration of a target motion analysis device to which the maneuver detection method according to the above-described principle is applied.

The target motion analyzer includes a signal input terminal 21 from a receiver sensor (not shown), an azimuth information calculator 22 for calculating the arrival direction of the target signal from the received signal, and a frequency component of the target signal from the received signal. Frequency information calculating section 23 for calculating, initial value calculating section 24 for calculating an initial state quantity from azimuth information and frequency information, maneuver detecting section 25 for detecting maneuver of target 2, internal state for analyzing motion of target 2 It has an amount estimating unit 26, an output terminal 27 for outputting a target motion analysis result, and an input terminal 28 for a threshold value for maneuver detection.

Here, the maneuver detecting section 25 includes a prediction residual calculating section 31 for calculating a residual between the observed value and the observed value predicted from the internal state quantity, an estimated internal state quantity, and the estimated internal state quantity. A prediction value calculation unit 32 that calculates a variance-covariance matrix of a prediction value of an observation value and a prediction residual from the estimation information matrix, and a normalization that calculates a normalized prediction residual from the variance-covariance matrix of the prediction residual and the prediction residual Generalized prediction residual calculation unit 33, a regression line estimation unit 34 that applies a linear regression equation to the normalized prediction residual, and estimates coefficients, and calculates a test statistic using various quantities obtained from the regression line estimation unit 34. And a threshold comparison unit 36 that compares the test statistic with its threshold value and determines a maneuver.

Next, the operation of the target motion analyzer will be described. The received signal from the signal source received by the receiving sensor array input from the input terminal 21 is sent to the azimuth information calculating unit 22 and the frequency information calculating unit 23, respectively. When the received signal is input to the azimuth information calculation unit 22 and the frequency information calculation unit 23, the azimuth information calculation unit 22 calculates the observation azimuth angle θ _m (t). Frequency component ν _km (t) (k = 1,
.., P), and sends the result to the initial value calculation unit 24 and the maneuver detection unit 25.

N sets of observation azimuth angles θ _m (t) and Doppler shift observation frequency components ν at time t = t ₁ ,..., T _{n
When km} (t) is input to the initial value calculating unit 24, the initial value calculating unit 24 obtains the initial value ＾ X ₀₀ of the motion analysis using Expression (10), and sends the result to the internal state quantity estimating unit 26. send. When the initial value ＾ X ₀₀ of the motion analysis is input to the internal state quantity calculation unit 26, the internal state quantity calculation unit 26 sets the value ＾ X ₀₀ as the initial value of the motion analysis by using the nonlinear minimum value given by the equation (5). The square problem is solved to obtain an estimated value ＾ X ₀ of the internal state quantity, an estimated quantity ＾ x ₂ (t) of the internal state quantity x ₂ (t) of the target body motion is calculated, and the result is sent to the output terminal 27. And the estimated value of the internal state quantity ＾ X ₀
And the estimated information matrix calculated by the equation (11) is sent to the maneuver detector 25.

In the next step, the maneuver detecting section 25 sets m observation azimuths θ _m (t) and Doppler shift observation frequency components ν at times t = t _{n + 1} ,..., T _{n + m} .
_In synchronization with the input of _km (t) (k = 1,..., p) to the prediction residual calculation unit 31, the prediction value calculation unit 32 transmits the internal state quantity sent from the internal state quantity estimation unit 26. using an estimated value ^ X ₀ of the time _{t n + 1, ..., t} m observation azimuth in _{(> t n) θ m (} t) and the Doppler shift observed frequency components ν
A predicted value for _km (t) (k = 1,..., p) is calculated and sent to the prediction residual calculation unit 31, and the estimated value of the internal state quantity ＾
The estimated variance-covariance matrix of the prediction residual is calculated from X ₀ and the estimated information matrix of the estimated state quantity by using Expression (14), and the result is sent to the normalized prediction residual calculation unit 33.

The prediction residual calculation unit 31 includes a prediction value calculation unit 32
The prediction residual is calculated from the transmitted prediction value and the already input observation azimuth angle and Doppler shift observation frequency component, and sent to the normalized prediction residual calculation unit 33. The normalized prediction residual calculation unit 33 calculates the normalized prediction residual according to the equation (20), and sends the result to the regression line estimation unit 34.

The regression line estimation unit 33 applies a linear regression equation to the normalized prediction residual, estimates its coefficient, calculates various quantities given by the equations (22) and (23), and The result is sent to the test statistic calculation unit 35. Test statistic calculation unit 3
5 calculates the statistic F by using the equation (23), and sends the result to the threshold comparing unit 36. The threshold comparing unit 36 includes a threshold setting terminal 28
The test statistic F is compared with the test threshold value F _α (1, m−2) set from the above. If the expression (24) is satisfied, it is determined that the maneuver is detected, and the initialization instruction signal is initialized. The value is sent to the value calculation unit 24.

According to the above embodiment, a linear regression equation is applied to the normalized prediction residual, and the
Since the maneuver is detected by determining the presence or absence of the bias of the prediction residual by the significance test, the maneuver can be detected from the time when the maneuver occurs and the bias begins to occur in the normalized prediction residual, Even if a maneuver is generated, its influence is smoothed, and the conventional problem that the detection sensitivity of the maneuver is low can be solved.

In the above embodiment, the maneuver detection based on the prediction residual is performed in a state where the observation azimuth and the Doppler shift observation frequency component are fused, but the maneuver detection based on the prediction residual regarding the observation azimuth is performed. Perform maneuver detection and maneuver detection based on the prediction residual for the Doppler shift observation frequency component as separate series,
When one or both of the results are maneuver detection, the final detection result may be maneuver detection.

In the above embodiment, the maneuver detection is performed by using the regression equation. In addition, the maneuver detection is performed in the same manner as in the related art, and at least one of the detection results indicates that the maneuver is detected. In this case, the final detection result may be the maneuver detection.

Further, in the above embodiment, the threshold setting terminal 2
Although the maneuver detection is performed using the threshold value for maneuver detection from No. 8, the threshold value (therefore, the significance level α of detection) may be arbitrarily changed.

Further, in the above embodiment, the output from the internal state quantity estimating unit is that of the absolute position vector on the coordinate system of the target body, but may be another value. For example, it may be a relative position vector from the observation object to the target object.

[0052]

As described above, according to the target motion analysis method and the target motion analysis device of the present invention, a linear regression equation is applied to the normalized prediction residual, and the obtained regression equation (coefficient of) is obtained.
Since the maneuver is detected by judging the presence or absence of the bias of the prediction residual by the significance test of, the maneuver can be detected from the time when the maneuver occurs and the bias of the normalized prediction residual begins to occur. Therefore, even if a maneuver is generated, its influence is smoothed, and the conventional problem that the detection sensitivity of the maneuver is low can be solved.

[Brief description of the drawings]

FIG. 1 is a functional block diagram illustrating a detailed configuration of a maneuver detection unit according to an embodiment.

FIG. 2 is an explanatory diagram showing an observation system and a motion system to which a target motion analysis method is applied.

FIG. 3 is a functional block diagram showing a detailed configuration of a conventional maneuver detector.

FIG. 4 is a functional block diagram illustrating an overall configuration of a target motion analysis device according to the embodiment.

[Description of Signs] 22 ... direction information calculation unit, 23 ... frequency information calculation unit, 24
... Initial value calculation unit, 25 ... Maneuver detection unit, 26 ... Internal state quantity estimation unit, 31 ... Prediction residual calculation unit, 32 ... Prediction value calculation unit, 33 ... Normalized prediction residual calculation unit, 34 ... Regression line estimation Section, 35: Test statistic calculation section, 36: Threshold comparison section.

Continuation of the front page (56) References JP-A-8-160120 (JP, A) JP-A-5-126951 (JP, A) JP-A-2-28704 (JP, A) JP-A-8-82665 (JP) , A) JP-A-7-306251 (JP, A) JP-A-9-133750 (JP, A) (58) Fields investigated (Int. Cl. ⁷ , DB name) G01S 3/80-3/86 G01S 5/18-5/30 G01S 7/52-7/64 G01S 15/00-15/96

Claims (3)

(57) [Claims] 1. An azimuth observable time series and a frequency measurement result, which are azimuth measurement results of an azimuth of a target object, received by a receiver sensor array attached to a movable observation object. From the observable time series consisting of the frequency observable time series that is, under the assumption that the target body performs a uniform linear motion, the state quantity related to the position and speed of the target body, the sound source natural frequency of the target body In the target motion analysis method for estimating a state quantity relating to the target object, the determination of the presence or absence of a maneuver such as a change of course or a speed change of the target object that does not hold the assumption that the target object performs a constant-velocity linear motion is performed by normalizing prediction with respect to the observed quantity time series. Estimating the coefficients of the regression equation by applying the linear regression equation to the residuals, and determining whether there is a bias in the normalized prediction residuals by performing a significance test on the regression equation expressed by the estimated coefficients. Desired motion analysis method according to claim. 2. The presence or absence of a maneuver is also determined by a bias test using the sum or average value of the prediction residuals for the observation time series and the estimated variance of the prediction residuals. 2. The target motion analysis method according to claim 1, wherein a final determination result of presence / absence of a maneuver is generated from the determination result of presence / absence of the used maneuver. 3. A sound radiated from a target object is received by a receiver sensor array attached to a movable observation object, and an azimuth observation time series and a frequency measurement result which are azimuth angle measurement results of the target object are received. From the observable time series consisting of the frequency observable time series that is, under the assumption that the target body performs a uniform linear motion, the state quantity related to the position and speed of the target body, the sound source natural frequency of the target body A target motion analysis having maneuver detection means for judging presence / absence of a maneuver such as a change of a needle or a speed change of the target object in which the assumption that the target object performs a constant velocity linear motion does not hold. In the apparatus, the maneuver detecting means calculates a normalized prediction residual for an observed time series, and applies a linear regression equation to the calculated normalized prediction residual. A regression line estimator that estimates the coefficients of the regression equation by fitting and a significance test of the regression equation expressed by the estimated coefficients to determine whether there is a bias in the normalized prediction residuals and to determine whether there is a maneuver. And a target motion analyzing device.