JP2013120127A - Target tracking device - Google Patents

Abstract

PROBLEM TO BE SOLVED: To obtain a target tracking device capable of quickly detecting a target without being affected by the estimation accuracy of exercise specifications.SOLUTION: A track extraction determination part 11 for executing a correlation determination between an observation value of a beat frequency obtained from a radar 1 and a target track candidate to determine whether a target exists in an observation area on the basis of the existence/absence of a track candidate whose correlation is recognized is provided. The track extraction determination part 11 determines whether the target exists in the observation area before an exercise specifications estimation part 13 estimates target exercise specifications.

Description

  The present invention relates to a target tracking device that estimates target motion parameters (target position, velocity, etc.) from observed beat frequency values obtained by an FM modulation (frequency modulation) type radar.

For example, in a sensor system such as a radar, the presence or absence of a target is determined from a time series of observation values obtained from a sensor that observes the target position, and if a target exists, the target is detected by a tracking process that estimates the target position and speed. It may be necessary to extract the wake.
Techniques for tracking targets using observation values obtained from sensors have been taken up in many papers and patent documents, and various proposals have been made for devices and methods for realizing them.

From the radar, clutter caused by reflected signals other than the target is obtained in addition to the observed value of the target.
When target tracking processing is performed using this clutter, an estimated value of an incorrect motion specification is calculated, and it is necessary to remove this clutter.
As a method for removing this clutter, there is known a pulse Doppler method for discriminating between a target and a clutter by performing frequency analysis by signal processing before the tracking process while transmitting pulses from a radar at a high frequency.

In the radar system in which the radar transmission signal is a pulse signal, target distance information can be calculated from the time difference between the transmission pulse and the reception pulse, as shown in FIG. Hereinafter, the target distance information is referred to as “in-PRI distance”.
However, when pulses are transmitted at a high frequency, it is impossible to specify which transmitted pulse corresponds to which transmitted pulse, and there are a plurality of candidates in the PRI distance, which is target distance information. Will occur.
The occurrence of a plurality of candidates is called ambiguity. When ambiguity occurs in the PRI intra-distance, the observed value of the PRI intra-distance cannot be used in the tracking process in the latter stage of the signal processing.

式（１）において、Ｒ_ｋは第ｋサンプリング時刻における目標の距離、Ｒ_ｋドット（ここでは、電子出願の都合上、Ｒの上部に・の記号を表記することができないため、Ｒ_ｋドットのように表記している）は第ｋサンプリング時刻における目標の距離変化率である。
また、ＢはＦＭ変調の帯域幅、ｃは光速、Ｔは観測時間、ｆ_０は送信周波数である。 As one of the transmission waveforms of the radar, there is FM modulation that changes the frequency linearly with respect to time, as shown in FIG.
The difference in the frequency of the transmitted and received waves at the same time when this transmission waveform is applied is called the beat frequency, and this beat frequency fb _k is the target distance and the distance change rate as shown in the following equation (1). Therefore, the target distance can be obtained by substituting the distance change rate determined from the Doppler frequency.

In Equation (1), R _k is a target distance at the k-th sampling time, R _k dots (here, because of the electronic application, the symbol of • cannot be expressed above R, so that R _k dots Is the target distance change rate at the k-th sampling time.
B is the FM modulation bandwidth, c is the speed of light, T is the observation time, and f ₀ is the transmission frequency.

Here, it is considered to calculate the target distance and the distance change rate from the beat frequencies fb _{k of a} plurality of scans obtained when this transmission waveform is applied.
A method for estimating a target distance and a distance change rate by a Kalman filter using an observed value of the beat frequency fb _k is disclosed in Patent Document 1 below.
This method can be applied to a radar having a high pulse repetition frequency, which is the premise of the invention of the present application, with a device configuration as shown in FIG.

ただし、Δｔはサンプリング間隔である。上記の例では、サンプリング間隔分の時間内での目標の距離変化率の変化が極めて小さいと仮定している。 In this method, first, an initial estimated value of the target distance and distance change rate is calculated by solving the following simultaneous equations from the observed values zfb ₀ and zfb ₁ of the beat frequency for the initial two sampling times.

However, Δt is a sampling interval. In the above example, it is assumed that the change in the target distance change rate within the time corresponding to the sampling interval is extremely small.

初期の推定値である式（４）の各成分は式（２）（３）の連立方程式の解であるため、初期２サンプリング時刻のビート周波数の観測値ｚｆｂ_０，ｚｆｂ_１の線形結合となる。
このため、以降のカルマンフィルタに基づく処理で必要となる推定誤差共分散行列の初期値Ｐ_１（＋）の各成分は、ビート周波数の観測誤差標準偏差より算出することができる。 The estimated value is updated using the Kalman filter every time an observed value zfb _k of the beat frequency is obtained using the initial estimated value as a starting point.
The state variables of this Kalman filter are as follows.

Since each component of the equation (4), which is the initial estimated value, is a solution of the simultaneous equations of the equations (2) and (3), it becomes a linear combination of the observed values zfb ₀ and zfb ₁ of the beat frequency at the initial two sampling times. .
For this reason, each component of the initial value P ₁ (+) of the estimated error covariance matrix required for the subsequent processing based on the Kalman filter can be calculated from the observation error standard deviation of the beat frequency.

ただし、Φ_ｋは状態遷移行列であり、下記の式（６）で定義される。

また、ｗ_ｋは運動に加わる外乱であり、以下の共分散を持つガウス分布に従うものとする。

ただし、Ｑ_ｋは事前に設定されるパラメータである。 Hereinafter, the update process of the estimated value using the beat frequency fb _k at the sampling time k (≧ 2) will be described.
The estimation value update process performs a prediction process, but the Kalman filter assumes the following state transition model.

However, (PHI) _k is a state transition matrix and is defined by the following formula | equation (6).

W _k is a disturbance applied to the motion, and follows a Gaussian distribution having the following covariance.

However, Q _k is a parameter set in advance.

Based on the above state transition model, the predicted value x _k (−) hat at sampling time k (≧ 2) (Here, the symbol “^” cannot be written above x for convenience of electronic application. Is expressed from the smoothed value x _k-1 (+) hat at the previous sampling time k−1, as shown in the following equation (8), and the sampling time k ( The prediction error covariance matrix P _k (−) of ≧ 2) is obtained from the smoothing error covariance matrix P _k−1 (+) at the previous sampling time k−1, as shown in the following equation (9). Calculated.

ただし、Ｈは観測行列であり、下記の式（１１）で定義される。

また、ｅ_ｆｂはビート周波数の観測誤差であり、その分散Ｒ_ｆｂがパラメータとして事前に与えられる。

A smoothing process after the prediction process is performed to calculate a final estimated value. Here, the following observation model is assumed.

However, H is an observation matrix and is defined by the following formula (11).

E _fb is an observation error of the beat frequency, and its variance R _fb is given in advance as a parameter.

ただし、Ｉは単位行列、Ｋ_ｋはカルマンゲインであり、下記の式（１５）から算出される。

Based on this observation model, the smooth values x _k (+) hat and P _k (+) at the sampling time k (≧ 2) are the predicted values x _k (−) hat and the prediction error covariance matrix P _{k at} the sampling time. (−) And an observed value zfb _k of the beat frequency are calculated as in the following formulas (13) and (14).

However, I is a unit matrix, _Kk is a Kalman gain, and is calculated from the following equation (15).

In a situation where there are a plurality of targets in the observation area or a situation where an unnecessary signal such as a false alarm is obtained together with the target signal, it is common to obtain a plurality of observed values of the beat frequency in each scan.
In such a case, it is necessary to determine whether or not there is a target in the observation region, and if it is determined that the target exists, the motion specifications must be output.
In this case, it is possible to determine the presence / absence of the target based on the likelihood of the wake candidate while selecting the observed value of the beat frequency in each scan and estimating the motion specifications by the tracking processing of the above-described conventional technique. .

ただし、ｄは事前に設定されるゲートサイズパラメータである。また、Ｓ_ｋは残差共分散行列であり、下記の式（１７）で算出される。

上記の式（１６）を満たす観測値が複数ある場合、式（１６）の左辺の値が最も小さくなる観測値を選択して、航跡候補に割り当てる方法や、複数の割り当てを考えて、航跡候補を複数生成するといった観測値の割り当て方法がある。 The possibility of correlation between the wake candidate and the observation value can be determined as follows.

Here, d is a gate size parameter set in advance. S _k is a residual covariance matrix, and is calculated by the following equation (17).

When there are a plurality of observation values satisfying the above equation (16), the observation candidate having the smallest value on the left side of the equation (16) is selected and assigned to a wake candidate, or a plurality of assignments are considered. There is a method of assigning observation values such as generating multiple.

ただし、γ_ｋ−１は１サンプリング時刻前の当該航跡候補の尤度である。尤度の初期値γ_１は事前に設定されるパラメータである。 Among the wake candidates generated in this way, if the likelihood γ _k of a wake candidate exceeds a preset likelihood threshold for wake extraction, the existence of the target is determined, and at that time Outputs the estimated values of motion specifications.
Here, the likelihood γ _k is calculated by the following equation (18) when it is updated using a certain observation value.

However, γ _k-1 is the likelihood of the wake candidate one sampling time before. The initial likelihood value γ ₁ is a parameter set in advance.

JP 2010-19824 A

  Since the conventional target tracking device is configured as described above, it is determined whether or not the target exists while estimating the motion specifications of the target. For this reason, when the accuracy rate of the correlation determination is reduced due to the estimation error of the target motion specification, there is a problem that the detection of the target is delayed.

  The present invention has been made to solve the above-described problems, and an object thereof is to provide a target tracking device that can quickly detect a target without being affected by the estimation accuracy of motion specifications. .

  The target tracking device according to the present invention performs a correlation determination between the observed value of the beat frequency obtained by the frequency modulation type radar and the target wake candidate, and the target is set in the observation region based on the presence or absence of the wake candidate in which the correlation is recognized. Target presence / absence determination means for determining whether or not the target exists, and if the target presence / absence determination means determines that the target exists in the observation area, the target motion specifications according to the prior information indicating the radar observation conditions An initial value setting means for setting an initial value of the motion specification state search used for estimating the motion specification, and the motion specification estimation means uses the initial value set by the initial value setting means to search the motion specification state. The target motion parameters are estimated by performing a motion parameter state search using the time series of the observed values of the beat frequency.

  According to this invention, the correlation determination between the observed value of the beat frequency obtained by the frequency modulation type radar and the target wake candidate is performed, and the target exists in the observation region based on the presence or absence of the wake candidate where the correlation is recognized. A target presence / absence determination means for determining whether or not the target exists in the observation area before the motion specification estimation means estimates the target motion specifications. Since the determination is made, it is possible to quickly detect the target without being affected by the estimation accuracy of the motion specification, and to increase the estimation accuracy of the target motion specification.

It is a block diagram which shows the target tracking apparatus by Embodiment 1 of this invention. It is a flowchart which shows the processing content of the target tracking apparatus by Embodiment 1 of this invention. It is explanatory drawing which shows the example of a setting of the initial value of the state search of the motion specification by the initial value setting part. It is explanatory drawing which shows the example of a setting of the initial value of the state search of the motion specification by the initial value setting part. It is explanatory drawing which shows the search process of the estimated value of the motion specification by Newton method. It is a block diagram which shows the target tracking apparatus by Embodiment 2 of this invention. It is a flowchart which shows the processing content of the target tracking apparatus by Embodiment 2 of this invention. It is explanatory drawing which shows the example which ambiguity generate | occur | produces in the distance in PRI. It is explanatory drawing which shows the transmission waveform control by FM modulation. It is a block diagram which shows the conventional target tracking apparatus.

Embodiment 1 FIG.
1 is a block diagram showing a target tracking apparatus according to Embodiment 1 of the present invention.
In FIG. 1, a radar 1 is an FM modulation type (frequency modulation type) radar, observes a beat frequency fb _k as an observation value, and outputs the observation value to the target tracking device 2.
The wake extraction determination unit 11 of the target tracking device 2 extracts a target wake candidate from the observed value of the beat frequency fb _k obtained by the radar 1 and determines the correlation between the observed value of the beat frequency fb _k and the target wake candidate. A process for determining whether or not the target exists in the observation area is performed based on the presence or absence of a wake candidate in which a correlation is recognized.
Further, the wake extraction determination unit 11 outputs a determination result indicating the presence / absence of the target to the initial value setting unit 12 and, for example, displays the determination result on a display (not shown) to determine the presence / absence of the target. Perform a process to inform the user.
The wake extraction determination unit 11 constitutes a target presence / absence determination unit.

The initial value setting unit 12 is a motion used when estimating the motion specifications of the target according to the prior information indicating the observation conditions of the radar 1 when the wake extraction determining unit 11 determines that the target is present in the observation region. A process for setting the initial value of the state search of the specification is performed. The initial value setting unit 12 constitutes an initial value setting unit.
The motion specification estimation unit 13 sets the initial value set by the initial value setting unit 12 as an initial point for the state search of the motion specification, and uses the time series of the observed values of the beat frequency fb _k to determine the motion specification. By performing the state search, a process for estimating the target motion specifications is performed. The motion specification estimation unit 13 constitutes motion specification estimation means.

In the example of FIG. 1, each of the wake extraction determination unit 11, the initial value setting unit 12, and the motion specification estimation unit 13, which are components of the target tracking device, has dedicated hardware (for example, a semiconductor integrated circuit that implements a CPU). Although it is assumed that the circuit is configured with a circuit or a one-chip microcomputer, the target tracking device may be configured with a computer.
When the target tracking device is configured by a computer, a program describing the processing contents of the wake extraction determination unit 11, the initial value setting unit 12, and the motion specification estimation unit 13 is stored in the memory of the computer, The CPU may execute the program stored in the memory.
FIG. 2 is a flowchart showing the processing contents of the target tracking device according to Embodiment 1 of the present invention.

Next, the operation will be described.
The state variables, state transition model, and observation model of the Kalman filter used by the target tracking device 2 are as follows.
State variables, as shown in the following equation (19), the beat frequency fb _k, is composed of a rate of change of the beat frequency fb _k.

ただし、Φ_ｋは状態遷移行列であり、下記の式（２１）で定義される。

また、ｗ_ｋは運動に加わる外乱であり、下記の共分散を持つガウス分布に従うものとする。

ただし、Ｑ_ｋは事前に設定されるパラメータである。 The state transition model is as shown in the following equation (20).

However, (PHI) _k is a state transition matrix and is defined by the following formula | equation (21).

W _k is a disturbance applied to the motion, and follows a Gaussian distribution having the following covariance.

However, Q _k is a parameter set in advance.

ただし、Ｈ_ｆｂは観測行列であり、下記の式（２４）で定義される。

また、ｅ_ｆｂはビート周波数の観測誤差であり、その分散Ｒ_ｆｂがパラメータとして事前に与えられる。

The observation model is as shown in the following formula (22).

However, H _fb is an observation matrix and is defined by the following formula (24).

E _fb is an observation error of the beat frequency, and its variance R _fb is given in advance as a parameter.

Hereinafter, processing for one sampling time will be described in detail.
The wake extraction determination unit 11 extracts a target wake candidate from the observed value of the beat frequency fb _k obtained by the radar 1 and performs a correlation determination between the observed value of the beat frequency fb _k and the target wake candidate. Whether or not the target exists in the observation area is determined based on the presence or absence of a wake candidate that is recognized.
Specifically, it is as follows.

ただし、ｘ_ｋ（−）ハットは航跡候補の予測値であり、下記の式（２７）で算出される。

また、Ｓ_ｋは残差共分散行列であり、下記の式（２８）で算出される。

ただし、Ｐ_ｋ（−）は予測誤差共分散行列であり、下記の式（２９）で算出される。

First, track extraction determination unit 11 as a "gate outside judgment", the step of the correlation determination to implement (Figure 2 between the observed value and the target track candidates the beat frequency fb _k as shown in equation (26) below ST1).

However, x _k (−) hat is a predicted value of a wake candidate, and is calculated by the following equation (27).

S _k is a residual covariance matrix and is calculated by the following equation (28).

However, P _k (−) is a prediction error covariance matrix, and is calculated by the following equation (29).

When the wake extraction determination unit 11 determines the correlation between the observation value of the beat frequency fb _k and the target wake candidate, the wake extraction determination unit 11 selects the observation value in the gate as “wake candidate correlation determination” (step ST2). .
Select the observation value that minimizes the value on the left-hand side of Equation (26) and assign it to the wake candidate as the observation value selection method, or generate multiple wake candidates assigned to each of the observation values in the gate. Possible ways to do this.

ただし、Δｔはサンプリング間隔である。
２つのビート周波数の観測値ｚｆｂ_０，ｚｆｂ_１の線形結合であるため、以降のカルマンフィルタに基づく処理で必要となる推定誤差共分散行列の初期値Ｐ_１（＋）の各成分は、ビート周波数の観測誤差標準偏差より算出することができる。 When selecting the observation value in the gate, the wake extraction determination unit 11 updates the state estimation value of the Kalman filter with the observation value assigned to the wake candidate as “update state in filter” (step ST3).
For example, when the current process is the second sampling time for the wake candidate, the state estimated value is the observed values zfb ₀ and zfb ₁ of the beat frequencies for two sampling times as shown in the following equation (30). Can be calculated.

However, Δt is a sampling interval.
Since each of the observed values zfb ₀ and zfb ₁ of the two beat frequencies is a linear combination, each component of the initial value P ₁ (+) of the estimated error covariance matrix required in the subsequent processing based on the Kalman filter is It can be calculated from the observation error standard deviation.

ただし、Ｉは単位行列、Ｋ_ｋはカルマンゲインであり、下記の式（３３）で算出される。

For the current process trajectory candidate, if a third and subsequent sampling time, the state estimation value, as shown in the following equation (31) can be calculated from the observed value Zfb _k beat frequency.

However, I is a unit matrix, _Kk is a Kalman gain, and is calculated by the following equation (33).

ただし、γ_ｋ−１は１サンプリング時刻前の当該航跡候補の尤度であり、尤度の初期値γ_１は事前に設定されるパラメータである。 The wake extraction determination unit 11 updates the likelihood γ _{k of the} wake candidate when the state estimation value of the Kalman filter is updated (step ST4).
The likelihood γ _{k of the} wake candidate is calculated by the following equation (34) when updated using a certain observation value.

However, γ _k−1 is the likelihood of the wake candidate one sampling time before, and the initial value γ _{1 of the} likelihood is a parameter set in advance.

If the likelihood γ _{k of the} wake candidate does not exceed the preset threshold th (step ST5), the processing for one sampling time is terminated at this point.
On the other hand, when the likelihood γ _{k of the} wake candidate exceeds a preset threshold th (step ST5), the process proceeds to the “motion parameter estimation initial value generation” process of step ST6.
That is, when the likelihood γ _{k of the} wake candidate exceeds a preset threshold th, the wake extraction determining unit 11 determines that the target is present in the observation region, and the “motion estimation” in step ST6 is performed. The process proceeds to “initial value generation”.

When the wake extraction determination unit 11 determines that the target is present in the observation region, in steps ST6 and ST7 described later, when the observed value of the beat frequency fb _k accumulated in the wake candidate so far is used. Using the sequence, the position and velocity of the target in the three-dimensional space are estimated. The motion parameters to be estimated are the following position and velocity in the three-dimensional space at the current sampling time n.

The initial value setting unit 12 is used when estimating the motion parameters of the target according to the prior information indicating the observation condition of the radar 1 when the wake extraction determining unit 11 determines that the target exists in the observation region. An initial value x _{n — 1} hat for motion condition state search is set (step ST6).
That is, as shown in FIG. 3, the initial value setting unit 12 determines the maximum search distance of the radar 1, the direction in which the beam of the radar 1 is directed, and the observed value of the beat frequency at the initial search time (the beat frequency at the first sampling time). Is used to set an initial value x _{n — 1} hat for the state search of the motion specification using the observed value zfb ₀ ).
As shown in FIG. 3, when the distance _R0 to the target is the maximum search distance of the radar 1 and the elevation angle and azimuth are the beam center, the three-dimensional position of the target is determined.
Also, the target distance change rate R ₀ dot is calculated from the distance R ₀ to the target and the observed beat frequency zfb ₀ at the first sampling time of this wake candidate as shown in the following equation (36). be able to.

The traversal component of the target speed is set to 0, and the motion specifications at the first search time are determined. From the motion parameters at the first search time, extrapolation is made to the latest time n assuming a constant-velocity linear motion, and used as the initial value of the search.
When the elevation angle cannot be obtained from the radar 1, it is difficult to set the initial value as described above. In this case, assuming that the target altitude is 0, as shown in FIG. 4, the initial value is calculated from the boundary of the observable region calculated from the roundness of the earth.
That is, the initial value x _{n — 1} hat for the state search of the motion specification is set using the observation values of the line-of-sight angle, the azimuth angle, and the beat frequency at the initial search time obtained from the installation altitude of the radar 1.

When the initial value setting unit 12 sets the initial value x _{n — 1} hat for the motion _item state search, the motion _item estimation unit 13 sets the initial value x _{n — 1} hat as the initial point for the motion _item state search, The target motion parameters are estimated by performing a motion parameter state search using the time series of the observed values of the beat frequency fb _k accumulated in the wake candidates so far (step ST7). .
As a result, an accurate motion specification is estimated. Hereinafter, the principle of improving the estimation accuracy will be described.

Assuming constant-velocity linear motion as the target motion, if the target motion specifications at the latest time n are determined, the motion parameters at the previous sampling time k are uniquely determined as shown in the following equation (37). In the target detection, it is assumed that a beat frequency sequence is extracted as in the following equation (38).

上記の予測観測値と実際の観測値の差異が最も小さくなる推定値は、非線形最小自乗法により算出される。

ここで、最小とする関数は、下記の式（４１）で定義される。

From the estimated value at the latest time n, the observed value can be predicted as shown in the following equation (39).

The estimated value that minimizes the difference between the predicted observed value and the actual observed value is calculated by the nonlinear least square method.

Here, the function to be minimized is defined by the following equation (41).

The motion specification estimation unit 13 searches for an optimal state according to the Newton method using the initial value set by the initial value setting unit 12 as a starting point.
That is, as shown in FIG. 5, the motion specification estimation unit 13 starts from an initial point x _{n — 1} hat of the state search, and values F (fb ₁ ,..., Fb _n , x _{n — 1} hat of the objective function at the initial point. ) And the inclination of the tangent plane, the next search point x _{n — 2} hat is determined.
For the next search point _{x n_3} hat it is also determined in the same manner as the search point _{x n_2} hat (the search point _{x n_3} hat, a a starting search point _{x n_2} hat instead of the initial point _{x n_1} hat).
By repeatedly determining the search point, the point x _{n_opt} hat at which the objective function is minimized is determined, and the point x _{n_opt} hat is output as an estimated value of the target motion specification.

Note that there are six variables in total because the motion specification estimation unit 13 needs to solve the three-dimensional position and velocity.
Therefore, in order to obtain observability, a scan number of 6 or more is required. Therefore, if the observed value of the beat frequency for 6 scans cannot be obtained, the state variable to be estimated is limited by limiting the tracking target to a target approaching slightly above the sea surface and setting the altitude direction speed to 0, etc. Thus, it is possible to estimate even an observation value with a small beat frequency.

  As is apparent from the above, according to the first embodiment, the correlation between the observed beat frequency value obtained by the radar 1 and the target wake candidate is performed, and the target is determined based on the presence or absence of the wake candidate where the correlation is recognized. A wake extraction determining unit 11 is provided for determining whether or not the target is present in the observation area. The wake extraction determining unit 11 observes the target before the motion specification estimating unit 13 estimates the target motion specification. Since it is configured to determine whether or not it exists in the area, it is possible to quickly detect the target without being affected by the estimation accuracy of the motion specification, and the estimation accuracy of the target motion specification There is an effect that can be enhanced.

That is, according to the first embodiment, the presence / absence of the target is determined from the time series of the observed values of the beat frequency, and the motion specifications are estimated after the existence of the target is determined. Even when the cross-correlation occurs due to the estimation error of the motion specification and the extraction of the target track is delayed, the target track can be extracted early.
Further, the estimated motion is a motion in a three-dimensional space, and more accurate information on motion specifications can be provided to the user as compared with the conventional method for estimating motion only in the distance direction.
In addition, since the initial point of the search in the nonlinear least square method is determined from prior information on the observation conditions of the radar, convergence in the search for the optimum state variable is quick and the estimation accuracy of the generated solution is high.

Embodiment 2. FIG.
6 is a block diagram showing a target tracking apparatus according to Embodiment 2 of the present invention. In the figure, the same reference numerals as those in FIG.
The intra-PRI distance correlation determination unit 21 performs correlation determination between the observed value of the PRI internal distance, which is the distance from the radar 1 to the target, and the target track candidate.
The wake extraction determination unit 22 extracts a target wake candidate from the observed value of the beat frequency fb _k obtained by the radar 1, performs correlation determination between the observed value of the beat frequency fb _k and the target wake candidate, Whether or not the target is present in the observation region based on the presence or absence of a wake candidate in which a correlation with the observation value of fb _k is recognized and a correlation with the observation value of the PRI distance is recognized by the intra-PRI distance correlation determination unit 21 A process for determining whether or not.
Further, the wake extraction determination unit 22 outputs the determination result indicating the presence / absence of the target to the initial value setting unit 12, and displays the determination result on a display (not shown), for example, to determine the presence / absence of the target. Perform a process to inform the user.
The intra-PRI distance correlation determination unit 21 and the wake extraction determination unit 22 constitute a target presence / absence determination unit.

In the example of FIG. 6, each of the intra-PRI distance correlation determination unit 21, the wake extraction determination unit 22, the initial value setting unit 12, and the motion specification estimation unit 13, which are components of the target tracking device, has dedicated hardware (for example, Although it is assumed that a semiconductor integrated circuit mounted with a CPU or a one-chip microcomputer is used, the target tracking device may be configured with a computer.
When the target tracking device is configured by a computer, a program describing the processing contents of the intra-PRI distance correlation determination unit 21, the wake extraction determination unit 22, the initial value setting unit 12, and the motion specification estimation unit 13 is stored in the computer. What is necessary is just to make it memorize | store in memory and to run the program stored in the said CPU of the said computer.
FIG. 7 is a flowchart showing the processing contents of the target tracking device according to Embodiment 2 of the present invention.

Next, the operation will be described.
The state variables, state transition model, and observation model of the Kalman filter used by the target tracking device 2 are as follows.
As shown in the following equation (42), the state variable includes a beat frequency fb _k , an azimuth angle Az _k , an elevation angle El _k, and a rate of change thereof.

ただし、Φ_ｋは状態遷移行列であり、下記の式（４４）で定義される。

また、ｗ_ｋは運動に加わる外乱であり、下記の共分散を持つガウス分布に従うものとする。

ただし、Ｑ_ｋは事前に設定されるパラメータである。 The state transition model is as shown in the following equation (43).

However, (PHI) _k is a state transition matrix and is defined by the following formula | equation (44).

W _k is a disturbance applied to the motion, and follows a Gaussian distribution having the following covariance.

However, Q _k is a parameter set in advance.

観測値ｚ_ｋは、下記の式（４７）に示すように、ビート周波数の観測値ｚｆｂ_ｋ、方位角の観測値ｚＡｚ_ｋ及び仰角の観測値ｚＥｌ_ｋで構成される。

また、Ｈ_{ｆｂＡｚＥｌ}は観測行列であり、下記の式（４８）で定義される。

The observation model is as shown in the following formula (46).

Observations _{z k,} as shown in the following equation (47), the observed value Zfb _k beat frequency, and a observations Zel _k observations ZAZ _k and elevation of azimuth.

H _fbAzEl is an observation matrix and is defined by the following equation (48).

このｅ_{ｆｂＡｚＥｌ}の共分散Ｒ_{ｆｂＡｚＥｌ}は、下記の式（５０）で示され、パラメータとして事前に与えられる。

Further, e _fbAzEl is a vector composed of observation error standard deviations of beat frequency fb _k , azimuth angle Az _k , and elevation angle El _k .

Covariance _{R FbAzEl} This _{e FbAzEl} is represented by the following formula (50) is given in advance as parameters.

ただし、ｘ_ｋ（−）ハットは航跡候補の予測値であり、下記の式（５２）で算出される。

また、Ｓ_ｋは残差共分散行列であり、下記の式（５３）で算出される。

ただし、Ｐ_ｋ（−）は予測誤差共分散行列であり、下記の式（５４）で算出される。

Hereinafter, processing for one sampling time will be described in detail.
First, track extraction determination unit 11 as a "gate outside judgment", the step of the correlation determination performed (FIG. 7 of the track candidate observations and the target beat frequency fb _k as shown in the following equation (51) ST11).

However, x _k (−) hat is a predicted value of a wake candidate, and is calculated by the following equation (52).

S _k is a residual covariance matrix and is calculated by the following equation (53).

However, P _k (−) is a prediction error covariance matrix, and is calculated by the following equation (54).

ただし、ｒｐｒｉ_ｋは候補中最短の距離であり、既知である。ΔＲｐｒｉはパルス間隔によって定まる折り返し幅であり、既知である。
これに対して、折り返し回数ｎは未知である。１サンプリング時刻前のＰＲＩ内距離についても同様に表現することができる。

The intra-PRI distance correlation determining unit 21 performs correlation determination between the observed value of the PRI inner distance, which is the distance from the radar 1 to the target, and the target track candidate (step ST12).
Specifically, it is as follows.
A candidate of distance information obtained from the observed value of the distance within the PRI is expressed as the following equation (55).

However, rpri _k is the shortest distance among candidates and is known. ΔRpri is a folding width determined by the pulse interval and is known.
On the other hand, the number of times n is unknown. The distance in the PRI before one sampling time can be expressed in the same manner.

Assuming that the distance change rate is constant, the expected value of the beat frequency at the two sampling times can be calculated as follows.

ただし、σ² _ｆｂはビート周波数の観測値の観測誤差標準偏差、σ² _ＲｐｒｉはＰＲＩ内距離の観測値の観測誤差標準偏差である。また、ｄ_ｆｂｓは事前に設定されるパラメータである。 Whether or not the PRI intra-distance is correlated is determined by the success or failure of the following expression.

However, σ ² _fb is the observation error standard deviation of the observation value of the beat frequency, and σ ² _Rpri is the observation error standard deviation of the observation value of the distance in the PRI. D _fbs is a parameter set in advance.

The wake extraction determination unit 22 performs correlation determination between the observed value of the beat frequency fb _k and the target wake candidate, and the PRI intra-distance correlation determination unit 21 determines correlation between the observed value of the PRI intra-distance and the target wake candidate. Is performed, the observation value in the gate is selected as “determination of wake candidate correlation” (step ST13).
As a method for selecting an observation value, a method of selecting an observation value with the smallest value on the left side of Equation (51) and assigning it to a wake candidate under the condition that Equation (59) is satisfied, A method of generating a plurality of wake candidates to which each is assigned can be considered.

ただし、Δｔはサンプリング間隔である。
２つのビート周波数の観測値ｚｆｂ_０，ｚｆｂ_１の線形結合であるため、以降のカルマンフィルタに基づく処理で必要となる推定誤差共分散行列の初期値Ｐ_１（＋）の各成分は、ビート周波数の観測誤差標準偏差より算出することができる。 When selecting the observation value in the gate, the wake extraction determination unit 22 updates the state estimation value of the Kalman filter with the observation value assigned to the wake candidate as “update state in filter” (step ST14).
For example, when the current process is the second sampling time for the wake candidate, the state estimated value is the observed values zfb ₀ and zfb ₁ of the beat frequency for two sampling times as shown in the following equation (63). Can be calculated.

However, Δt is a sampling interval.
Since each of the observed values zfb ₀ and zfb ₁ of the two beat frequencies is a linear combination, each component of the initial value P ₁ (+) of the estimated error covariance matrix required in the subsequent processing based on the Kalman filter is It can be calculated from the observation error standard deviation.

ただし、Ｉは単位行列、Ｋ_ｋはカルマンゲインであり、下記の式（６６）で算出される。

When the current process is the third or later sampling time for the wake candidate, the state estimated value can be calculated from the observed value zfb _k of the beat frequency as shown in the following equation (64).

However, I is a unit matrix, _Kk is a Kalman gain, and is calculated by the following equation (66).

ただし、γ_ｋ−１は１サンプリング時刻前の当該航跡候補の尤度であり、尤度の初期値γ_１は事前に設定されるパラメータである。 The wake extraction determination unit 22 updates the likelihood γ _{k of the} wake candidate when the state estimation value of the Kalman filter is updated (step ST15).
The likelihood γ _{k of the} wake candidate is calculated by the following equation (67) when updated using a certain observation value.

However, γ _k−1 is the likelihood of the wake candidate one sampling time before, and the initial value γ _{1 of the} likelihood is a parameter set in advance.

If the likelihood γ _{k of the} wake candidate does not exceed the preset threshold th (step ST16), the processing for one sampling time is terminated at this point.
On the other hand, when the likelihood γ _{k of the} wake candidate exceeds a preset threshold value th (step ST16), the process proceeds to the “motion parameter estimation initial value generation” process of step ST17.
That is, when the likelihood γ _{k of the} wake candidate exceeds a preset threshold th, the wake extraction determination unit 22 determines that the target exists in the observation region, and the “motion parameter estimation” in step ST17 is performed. The process proceeds to “initial value generation”.

When the target by track extraction determining unit 22 is determined to be present in the observation area, in step ST17, ST18 to be described later, during the past, when the observed value of the beat frequency fb _k stored in the track candidate Using the sequence, the position and velocity of the target in the three-dimensional space are estimated. The motion parameters to be estimated are the following position and velocity in the three-dimensional space at the current sampling time n.

The initial value setting unit 12 is used when estimating the motion parameters of the target according to the prior information indicating the observation condition of the radar 1 when the wake extraction determining unit 22 determines that the target is present in the observation region. An initial value x _{n — 1} hat for motion condition state search is set (step ST17).
That is, as shown in FIG. 3, the initial value setting unit 12 determines the maximum search distance of the radar 1, the direction in which the beam of the radar 1 is directed, and the observed value of the beat frequency at the initial search time (the beat frequency at the first sampling time). Is used to set an initial value x _{n — 1} hat for the state search of the motion specification using the observed value zfb ₀ ).
As shown in FIG. 3, when the distance _R0 to the target is the maximum search distance of the radar 1 and the elevation angle and azimuth are the beam center, the three-dimensional position of the target is determined.
Further, the target distance change rate R ₀ dot is calculated from the distance R ₀ to the target and the observed value zfb ₀ of the beat frequency at the first sampling time of this wake candidate as shown in the following equation (69). be able to.

The traversal component of the target speed is set to 0, and the motion specifications at the first search time are determined. From the motion parameters at the first search time, extrapolation is made to the latest time n assuming a constant-velocity linear motion, and used as the initial value of the search.
When the elevation angle cannot be obtained from the radar 1, it is difficult to set the initial value as described above. In this case, assuming that the target altitude is 0, as shown in FIG. 4, the initial value is calculated from the boundary of the observable region calculated from the roundness of the earth.
That is, the initial value x _{n — 1} hat for the state search of the motion specification is set using the observation values of the line-of-sight angle, the azimuth angle, and the beat frequency at the initial search time obtained from the installation altitude of the radar 1.

When the initial value setting unit 12 sets the initial value x _{n — 1} hat for the motion _item state search, the motion _item estimation unit 13 sets the initial value x _{n — 1} hat as the initial point for the motion _item state search, The target motion parameters are estimated by performing a motion parameter state search using the time series of the observed values of the beat frequency fb _k accumulated in the wake candidates so far (step ST18). .
As a result, an accurate motion specification is estimated. Hereinafter, the principle of improving the estimation accuracy will be described.

Assuming constant-velocity linear motion as the target motion, if the target motion specification at the latest time n is determined, the motion specification at the previous sampling time k is uniquely determined as shown in the following equation (70). In the target detection, a beat frequency sequence is extracted as in the following formula (71).

上記の予測観測値と実際の観測値の差異が最も小さくなる推定値は、非線形最小自乗法により算出される。

ここで、最小とする関数は、下記の式（７４）で定義される。

ただし、σ_ｆｂはビート周波数の観測値の観測誤差標準偏差、σ_ａｚは方位角の観測値の観測誤差標準偏差、σ_ｅｌは仰角の観測値の観測誤差標準偏差、σ_ＲｐｒｉはＰＲＩ内距離の観測値の観測誤差標準偏差である。 From the estimated value at the latest time n, the observed value can be predicted as shown in the following formula (72).

The estimated value that minimizes the difference between the predicted observed value and the actual observed value is calculated by the nonlinear least square method.

Here, the function to be minimized is defined by the following equation (74).

Where σ _fb is the observation error standard deviation of the observation value of the beat frequency, σ _az is the observation error standard deviation of the observation value of the azimuth angle, σ _el is the observation error standard deviation of the observation value of the elevation angle, and σ _Rpri is the distance within the PRI The observation error standard deviation of the observed value.

The motion specification estimation unit 13 uses the initial value set by the initial value setting unit 12 (the distance is the maximum search distance, the speed is a typical value, and the speed when traveling straight in the sensor direction) as a starting point. The optimum state is searched according to the Newton method.
That is, as shown in FIG. 5, the motion specification estimation unit 13 starts from the initial point x _{n — 1} hat of the state search, and the objective function values F (z ₁ ,..., Z _n , x _{n — 1} hat at the initial point. ) And the inclination of the tangent plane, the next search point x _{n — 2} hat is determined.
For the next search point _{x n_3} hat it is also determined in the same manner as the search point _{x n_2} hat (the search point _{x n_3} hat, a a starting search point _{x n_2} hat instead of the initial point _{x n_1} hat).
By repeatedly determining the search point, the point x _{n_opt} hat at which the objective function is minimized is determined, and the point x _{n_opt} hat is output as an estimated value of the target motion specification.

As is apparent from the above, according to the second embodiment, the wake extraction determining unit 22 performs correlation determination between the observed value of the beat frequency fb _k obtained by the radar 1 and the target wake candidate, and the beat frequency Whether or not the target is present in the observation region based on the presence or absence of a wake candidate in which a correlation with the observation value of fb _k is recognized and a correlation with the observation value of the PRI distance is recognized by the intra-PRI distance correlation determination unit 21 Therefore, the target detection accuracy can be improved as compared with the first embodiment.
In other words, the target wake can be extracted early with only the observed value of the beat frequency fb _k , even if the cross correlation occurs and the extraction of the target wake is delayed.
In addition, in the search for estimating the motion specification, in addition to the observed value of the beat frequency, the observed value of the azimuth angle, the elevation angle, and the PRI internal distance is used, so that there is an effect that a more accurate solution can be obtained.

  In the present invention, within the scope of the invention, any combination of the embodiments, or any modification of any component in each embodiment, or omission of any component in each embodiment is possible. .

  DESCRIPTION OF SYMBOLS 1 Radar, 2 Target tracking apparatus, 11 Track extraction determination part (target presence determination means), 12 Initial value setting part (initial value setting means), 13 Motion specification estimation part (motion specification estimation means), 21 PRI internal distance Correlation determination unit (target presence / absence determination means), 22 Track extraction determination unit (target presence / absence determination means).

Claims (5)

The correlation between the observed beat frequency value obtained by the frequency modulation type radar and the target track candidate is determined, and whether or not the target exists in the observation area is determined based on the presence or absence of the track candidate with a correlation. A target presence / absence judging means;
When the target presence / absence determining means determines that the target is present in the observation area, the state search of the motion specification used when estimating the motion specification of the target according to the prior information indicating the observation condition of the radar is performed. An initial value setting means for setting an initial value;
By setting the initial value set by the initial value setting means to the initial point of the state search of the movement specifications, using the time series of the observed values of the beat frequency, by carrying out the state search of the movement specifications, A target tracking device comprising: a motion specification estimating means for estimating a motion specification of a target.   The initial value setting means sets the initial value of the state search of the motion parameters using the maximum search distance of the radar, the direction in which the radar beam is directed, and the observed value of the beat frequency at the initial search time. The target tracking device according to claim 1.   The initial value setting means sets the initial value of the state search of the motion specification using the observation angle obtained from the radar installation altitude, the azimuth angle of the radar and the beat frequency observed at the initial search time. The target tracking device according to claim 1.   2. The target tracking device according to claim 1, wherein the motion specification estimation means reduces the number of motion specifications to be estimated when the sampling number of beat frequencies observed by the radar is less than a predetermined number.   The target presence / absence determining means performs a correlation determination between the observed value of the beat frequency obtained by the radar and the target track candidate, and between the observed value of the distance in the PRI, which is the distance from the radar to the target, and the target track candidate. Whether or not the target exists in the observation area is determined based on the presence or absence of a wake candidate in which a correlation with the observed value of the beat frequency is recognized and a correlation with the observed value of the PRI distance is recognized. The target tracking device according to any one of claims 1 to 4, wherein the target tracking device is determined.

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