JPH0362229B2 - - Google Patents

Description

[Detailed Description of the Invention] [Field of Industrial Application] The present invention relates to a tracking filter that predicts the state (position and velocity) of a target such as a flying object from radar observation data, and particularly relates to a tracking filter that predicts the state (position and velocity) of a target such as a flying object from radar observation data. In order to improve the efficiency of antenna beams when tracking multiple targets, we continue to predict without performing observations while the prediction accuracy is high, and when the accuracy is likely to deteriorate, we select an appropriate time to perform observations. This relates to a tracking filter that continues.

[Conventional technology]

Figure 6 shows the tracking filters that have been commonly used in the past, especially those that allow external users to predict the future by inputting observation data.
If you receive a command to predict the future time,
A configuration diagram of a tracking filter that continues tracking by outputting a predicted state one time in the future and its error variance,
In the figure, 1 is a filtering indicator, 2a,
2b is a current time information switch; 3a and 3b are conversion paths from a polar coordinate system to a rectangular coordinate system; 4 is an estimation gain calculator; 5 is a state estimator; 6 is an estimation error variance calculator; 7 is a state predictor; 8 is a prediction error variance calculator,
9a and 9b are converters from an orthogonal coordinate system to a polar coordinate system, and 10a and 10b are delay elements.

Next, in order to explain the operation of this conventional tracking filter, the tracking operation will be modeled and various symbols will be defined.

First, a motion model of the tracking target is determined as shown in Equation 1.

x ^(C) _K+1 = Φx ^(C) _K + ΓW ^(C) _K ...(1) Here, the superscript (C) means orthogonal coordinate system,
The subscript K indicates that these are values at time K. Furthermore, x ^(C) _K is the target state, and when this is expressed together with the polar coordinates, the second and third equations are obtained, respectively.

x ^(C) _K = Target position (X direction) 〃 Velocity 〃 〃 Acceleration 〃 〃 Position (Y direction) 〃 Velocity 〃 〃 Acceleration 〃 〃 Position (Z direction) 〃 Velocity 〃 〃 Acceleration 〃 〓 ｜ ｜ ｜ ｜ ｜ ｜ ^|| _{_} Velocity 〃 〃 Acceleration 〃 〓 ｜ ｜ ｜ ｜ ｜ ｜ ｜ ｜ ｜ ｜ ｜ ｜ 〓K
...(3). However, the superscript (P) means a polar coordinate system, and the method of determining the coordinates is shown in FIG.

Further, Φ and Γ are called a transition matrix and an input matrix, respectively, and are given by the fourth equation and the fifth equation, respectively.

Γ=T3/6 T2/2 T 0 0 0 0 0 0 0 0 0 T3/6 T2/2 T 0 0 0 0 0 0 0 0 0 T3/6 T2/2 T...(5) However, here T is the basic step width of the discrete time system.

Further, W ^(C) _K is a cubic vector representing the rate of change in acceleration in each of the X, Y, and Z directions. Each element is normal white noise with zero mean, and its variance is Q
(3×3 matrix). This is the 6th
As shown in the formula.

E{W ^(C) _K }=O, E{W ^(C) _K W ^(C) _lT } =Qδ _K,l ...(6) Here, T on the right shoulder is transposed, and E{・} is the average , and δ means Kronetzker's delta, respectively.

On the other hand, the observation equation is given by Equation 7.

Z ^(P) _K = Cx ^(P) _K +V ^(P) _K ……(7) Here, it must be noted that the observed values are given in the polar coordinate system. In other words, the observed value is defined by Equation 8 as a third-order vector whose elements are positions detected by the radar.

Z ^(P) _K = target observation position (range) 〃 (azimuth) 〃 (elevation)〓 | | | | | | | | | Defined by Eq.

C=100000000 000100000 000000100 ...(9) And V ^(P) is a cubic vector whose elements are observation noise at each position of range, azimuth, and elevation, and each element is a zero-average vector. It is normal white noise and its variance is R ^(P) (3×
3). This is shown in Equation 10.

E{V ^(P) _K }O, E{V ^(P) _K V ^(P) _lT }=R ^(P) _K δ _K,l ……(1
0) The tracking filter of the converter works as follows for the target motion modeled above and its observation.

First, as an input from the outside, a signal is given to the filtering indicator 1 such as "Predict the future one time by inputting observation data" or "Predict the future one time without observation data." If this signal is the former, the observed value Z ^(P) _K and its error variance R ^(P) _K are input with the current time information switchers 2a and 2b both connected to the a side. These values are converted into respective values Z ^(C) _K and R ^(C) _K in the orthogonal coordinate system via coordinate converters 3a and 3b. These are shown in the state estimator equations 11 and 12.

Z ^(C) _K = Target observation position (corresponding to the X direction) 〃 (Y direction 〃 ) 〃 (Z direction 〃 )〓 | | | | | | | | | | 〓K……(11) R ^(C) _K ]E {(Z ^(C) _K −Cx ^(C) _K ) (Z ^(C) _K −Cx ^(C) _K ) ^T } ...(12) Now, here, the estimated state x^ in the orthogonal coordinate system
^(C) _K and predicted state x〓 ^(C) _K and their error variance P^

^(C) _K , P〓 ^(C) Equations 13 and 14 for _K , respectively,
Define it in the 15th and 16th equations.

x^ ^(C) _K = Estimated target position (X direction) 〃 Velocity 〃 〃 Acceleration 〃 〃 Position (Y direction) 〃 Velocity 〃 〃 Acceleration 〃 〃 Position (Z direction) 〃 Velocity 〃 〃 Acceleration 〃 〓 ｜ ｜ ｜ ｜ ｜ ｜ ｜ ｜ ｜ ｜ ｜ ｜ ｜ 〓K
...(13) x〓 ^(C) _K = Target predicted position (X direction) 〃 Velocity 〃 〃 Acceleration 〃 〃 Position (Y direction) 〃 Velocity 〃 〃 Acceleration 〃 〃 Position (Z direction) 〃 Velocity 〃 〃 Acceleration 〃 K
...(14) P^ ^(C) _K = E {(x^ ^(C) _K −x^ ^(C) _K ) (x^ ^(C) _K −x ^(C) _K ) ^T }...9×9 matrix ...(15) P〓 ^(C) _K = E {(x〓 ^(C) _K −x〓 ^(C) _K ) (x〓 ^(C) _K −x ^(C) _K ) ^T }...9×9 matrix ...(16) The following operation is an application of the Kalman filter theory, which estimates and predicts the state of a dynamic system so that the mean square error is minimized. This Kalman filter is described in detail, for example, in Takashi Arimoto's "Kalman Filter" (1971, Sangyo Tosho).

From the observation error variance R ^(C) _K converted to the orthogonal coordinate system and the prediction error variance P〓 ^(C) _K at the current time, the estimated gain calculator 4 calculates the estimated gain K ^(C) _K as shown in Equation 17. Calculate as follows.

K ^(C) _K = P〓 ^(C) _K C ^T [CP〓 ^(C) _K C ^T +R ^(C) _K ] ^-1 ...9x3 matrix ... (17) This gain K ^(C) _K The state estimator 5 calculates the estimated state x^ ^(C) _K using Equation 18.

x^ ^(C) _K =x〓 ^(C) _K +K ^(C) _K [Z ^(C) _K −Cx〓 ^(C) _K ]...
(18) The error variance of this estimation is calculated using the estimated error variance calculator 6.
is calculated as shown in Equation 19 from the estimated gain K ^(C) _K and the prediction error variance P〓 ^(C) _K at the current time.

P^ ^(C) _K =P〓 ^(C) _K −K ^(C) _K CP〓 ^(C) _K ……(19) Estimated state x^ ^(C) _K obtained in this way and estimated error variance P ^ ^(C) _K is the current time information switch 2
Since a and 2b are both connected to the a side, they are delivered to the state predictor 7 and the prediction error variance state estimator 8, respectively. The state predictor 7 calculates the predicted state x 〓 ^(C) _K+1 one time in the future from the received information according to Equation 20.

x〓 ^(C) _K+1 = Φx^ ^(C) _K ......(20) Also, the prediction error variance calculator 8 calculates the prediction error variance P〓 ^(C) _K+ for one time in the future from the received information. ₁ to 21st
Calculate according to the formula.

P〓 ^(C) _K+1 = ΦP^ ^(C) _K Φ ^T + ΓQΓ ^T ... (21) Finally, these values are converted to the polar coordinate system value x〓 via the Cartesian coordinate system - polar coordinate system converter 9. ^(P) _K+1 ,P〓 ^(P) _K+1
are output as respectively. These are defined in the 22nd and 23rd equations.

x〓 ^(P) _K = Target predicted position (range direction) 〃 Velocity 〃 〃 Acceleration 〃 〃 Position (azimuth angle) 〃 Velocity 〃 〃 Acceleration 〃 〃 Position (elevation angle) 〃 Velocity 〃 〃 Acceleration 〃 〓 ｜ ｜ ｜ _｜ ｜ ｜ ｜ _{｜ ｜} ｜ ｜ ｜ ｜ 〓K ……(22 ⁾ P〓 ^{(P ) K} ₌ ^{E P)} _K
) ^T }
...(23) On the other hand, if the signal received by the current time information switch 1 is "Predict one hour in the future without observation data", the current time information switch 1 switches between the information switches 2a and 2b. Switch both contact pieces to the b side. Therefore, the predicted state x〓 ^(C) _K and its error variance P〓 ^(C) _K at the current time are input to the state predictor 7 and the prediction error variance calculator 8, respectively, and the prediction for one time in the future is These will be updated. That is, instead of the 20th and 21st equations, the 24th and 25th equations are calculated.

x〓 ^(C) _K+1 ＝Φx〓 ^(C) _K ……(24) P〓 ^(C) _K+1 ＝ΦP〓 ^(C) _K Φ ^T ＋ΓQΓ ^T ……(25) Finally, these values are outputted as x〓 ^(P) _K+1 and P〓 ^(P) _K+1 through the converters 9a and 9b to the orthogonal coordinates-polar coordinate system, as in the case described above.

Note that the delay elements 10a and 10b are used to calculate the predicted state x〓 ^(C) _K+1 and its error variance P〓 ^(C) _K+1 at the next step, and their values at the current time x〓 ^(C) _K , P〓 ^(C
) _K
It means to be used as.

[Problem that the invention seeks to solve]

However, in the conventional tracking filter described above, even if it is of a type that can continue tracking regardless of the presence or absence of observation data, the judgment of when observation data should be input must be completely dependent on an external device. Must be. However, in multi-target tracking and tracking/search simultaneous processing (Track While Scan), in order to efficiently direct the antenna beam to track and search multiple targets, it is necessary to judgment is necessary. Therefore, it has been desired that the tracking filter itself has the ability to determine when the next observation should be made and in which direction the antenna beam should be directed at that time.

This invention was made to solve these problems, and it uses a tracking filter that determines the next observation time and direction by itself based on the tracking prediction accuracy and the relationship between the antenna and the target and continues tracking. The purpose is to obtain.

[Means for solving problems]

The tracking filter according to the present invention is provided with a next observation instruction device comprising an antenna direction calculator, an incident angle calculator, an expected existence area calculator, a capture possibility determiner, and a next observation determiner.

[Effect]

According to the tracking filter according to the present invention, as long as the prediction is accurate without performing new observations, the prediction is updated without observation data, and when the prediction accuracy is about to deteriorate, the predicted position of the target is updated. By selecting an observable time point based on the antenna direction and issuing instructions for the next observation, tracking can be performed while maintaining prediction accuracy while effectively using the antenna beam for observation.

〔Example〕

FIG. 1 is a block diagram showing one embodiment of a tracking filter according to the present invention, and the same parts as in FIG. 6 are denoted by the same symbols, and detailed explanation thereof is omitted. In the figure, 11 is a newly installed next observation instruction device, which includes an antenna direction calculator 12, an incident angle calculator 13, an expected existence area calculator 14, a capture availability determiner 15, and a next observation determiner. 16. 3c is a converter that converts the orthogonal coordinate system to a polar coordinate system by inputting the predicted state x 〓 ^(C) _K+l to be generated from the next observation judger 16, and 10c is the polar coordinates converted by the converter 3c. A delay element 10d supplies the state estimator 5 with "1
This is a delay element that delays the signal "Predict the future time" and supplies it to the filtering indicator 1. However, the signal "Predict one hour in the future without observation data" output from the next observation judger 16 is directly supplied to the filtering indicator 1. 10e is the next observation judger 1
6, a delay element that delays the error variance P〓 ^(P) _K+l , 3d converts the output signal of the delay element 10e from the rectangular coordinate system to the polar coordinate system, and converts the output signal of the delay element 10e to the estimated gain calculator 4 and the estimation The converter 10f that supplies the error variance calculator is a delay element that delays the error variance P〓 ^(P) _K+l output from the next observation judger 16 and supplies it to the converter 3b. In addition, 26 is an estimation device, 27
indicates a prediction device.

FIG. 2 shows the antenna direction calculator 1 shown in FIG.
2 calculates the direction 19 of the antenna in the future by a time lT (l is a positive integer), and from the relationship with the target azimuth position 20 predicted at that time, the incident angle calculator 13 calculates the direction 19 of the antenna at that time. Calculate the angle of incidence in the azimuth direction ′ _K+l 21 with respect to the target antenna. That is, 19 is the direction of the antenna in the future by time lT, 20 is the target position predicted in the future by time lT obtained through the converter 9a that converts the output of the state predictor 7 from the rectangular coordinate system to the polar coordinate system. 2
1 is the time calculated by the incident angle calculator 13
The angle of incidence when looking at the target predicted in the future by lT,
22 indicates the rotation direction of the antenna.

FIG. 3 shows how to take the coordinates shown in FIG. 2 as well as the definition of the expected existence area. Let K be the time when a new observed value is obtained. After that, the prediction is updated one time at a time without any observed values, and the predicted state x = ^(P) K+l at time K ₊ l (l is a positive integer)
Suppose we obtain the error variance P〓 ^(P) _K+l . in this case,
Since prediction continues without obtaining new observation information, the prediction accuracy deteriorates as l increases. This is expressed quantitatively by P〓 ^(P) _K+l , where the 1 and 1 elements are the prediction error variance in the range direction, and the 4 and 4 elements and the 7 and 7 elements are the azimuth angle and the 7 and 7 elements, respectively. Those are the elevation angles. Take the square roots of these and get σ〓,
If σ, σ〓, these are range, azimuth,
This is the standard deviation of the prediction error for each elevation.

Now, the predicted state at that time x〓 ^(P) _± Fσ〓3±Fσ,
Take the area of ±Fσ〓. However, F is an appropriate coefficient (positive real number). At this time, this area is at time K
+l is a region where the existence of a target is predicted with a certain probability or more. This area is defined as the "existence expected area" 18.

The size of this expected existence area is calculated by the expected existence area calculator 14 shown in FIG. The size of this expected region will gradually expand if there are no new observations. However, if this becomes too large, it becomes larger than the beam width, making it difficult to capture or making it impossible to distinguish it from another target. Therefore, thresholds are set for each of the three directions, and when the time when even one of Fσ〓, Fσ, Fσ〓 is predicted to be exceeded, "capture possible" is set until then.
We will install a capture availability determiner 15 which will now output a "capturing not possible" signal instead of the "capturing not possible" signal.

The explanation so far has clarified the operation of each part, and next, the operation of the next observation determination device 16 will be explained. This sends a signal to the filtering indicator 1 to control what corresponds to a conventional tracking filter.

FIG. 4 is a flowchart showing the operation of the next observation determination unit 16, and FIG. 5 is a prediction information table for writing and reading data in this operation. The operation of the next observation determination unit 16 will be explained along these lines. First, in step _S1 , the current time is set to K. It is assumed that observation is performed on the target at this time. It is assumed that the input of this time to the filtering indicator 1 was "input observation data and predict the future by one hour". Therefore, at this time, the next observation judgment unit 16 first determines the predicted state x〓 ^(P) _K+1 based on the predicted data and observed data at the current time.
, and its error variance P〓 ^(P) _K+1 will be input.
Write these into the prediction information table. Next step S ₂
In step _S3 , the incident angle ' _K+1 of the target one time in the future is inputted from the incident angle calculator 13 and written in the table. Furthermore, in step _S4 , a signal is input from the capture availability determiner 15, and if this signal is "observable" in step _S5 , l=l+1 is set in step _S6 , and the process proceeds to step _S7 . At this point, a signal is sent to the filtering indicator to ``update the forecast by one hour without observation data.'' Then, in step _S8 , the updated predictions x〓 ^(P) _K+l and P〓 ^(P) _K+l are input and written in the table. As in the previous case, input the target incident angle 'K+l at time _K+l , write it in the table, and input the acquisition possibility determination signal. Repeat the above as long as it is "captureable". When this signal becomes "uncaptureable", this loop is exited and the process moves to step _S9 . Next, in step _S7 ,
Read out the expected angle of incidence ′ _K+l at that time from the table. Next, in step _S10 , the time when this angle of incidence was within a certain range around the antenna direction is searched backwards. Here, this range is defined as −π/3≦′ _K+l ≦π/3. If a time when the incident angle ′ _K+l is within the specified range is found, that time is set as the next observation time. If, by searching for this time through the processing in steps S ₁₁ and S ₁₂ , you have climbed backwards to time K+1, step K+1 is
By moving from step _S12 to step _S13 , the next observation time is forced. Once the next observation time is determined, in step _S14 , set this time to K+L and calculate the predicted state x from time K+1 to K+L ^(P) _K+l
and its error variance P〓 ^(P) _K+l (l=1, 2, . . . , L) from the prediction information table shown in FIG. Here, 2
3 is a prediction information table that is written or read out by the next observation judger 16, 24 is a part that is actually written or read out, and 25 is a table up to the point in time when the capture possibility judger 15 determines that "capturing is not possible". Each section shows the part to be written.

Next, in step _S15 , since the observation error changes depending on the target echo incident angle (azimuth and elevation), the observation error variance is calculated from these predicted values at the observation time.

Next, in step _S16 , the next observation time K+L, the predicted state x〓 ^(P) _K+l and its error variance P〓 ^(P) _K+l (l=1, 2,... , L).
These are the originally desired tracking filtering results, and at the same time, some of them are the next observation time K.
+L and the current target position Cx〓 ^(P) _K+L are also sent to the antenna beam controller and used to obtain the observed value of the target.

Finally, in step _S17 , the signal "Input observation data to predict the future one hour", the predicted state x〓 ^(P) _K+L at the next observation time, and the prediction error variance
P〓 ^(P) _K+L and observation error variance R ^(P) _K+L are output. These values, together with the new observation value Z ^(P) _K+L , are used after L time has elapsed to make a prediction using observation data.

At the next observation time K+L, the same operation as described above is repeated again, and tracking is continued.

By the way, in the above explanation, these inventions are based on observation of only position (range, azimuth, elevation) and estimation and prediction of acceleration in each direction, and filtering is performed using a standard Kalman-type tracking filter. In addition to this case, when range rate is obtained as observation data, and when estimating and predicting speed in each direction, filtering using the LOS (Line of Sight) coordinate system can be used. When adopted, it is also effective to apply it to a tracking filter, such as when the transition matrix Φ and the input matrix Γ are changed.

〔Effect of the invention〕

As explained above, this invention continues tracking without making new observations while the prediction accuracy is high.
If the accuracy deteriorates, observation is performed before the target is missed, so it has the excellent effect of being able to continue tracking while maintaining accuracy while effectively using the antenna beam.

[Brief explanation of drawings]

FIG. 1 is a block diagram showing an embodiment of the tracking filter according to the present invention, FIG. 2 is a diagram explaining the calculation of the angle of incidence, FIG. 3 is a diagram explaining how to take coordinates and the expected existence area, and FIG. 4 is a diagram explaining the calculation of the angle of incidence. 5 is a flowchart showing the operation of the next observation judgment device, FIG. 5 is a diagram showing a prediction information table, and FIG. 6 is a configuration diagram showing a conventional tracking filter. In the figure, 1 is a filtering indicator, 2 is a current time information switch, 11 is a next observation indicator, 12 is an antenna direction calculator, 13 is an incident angle calculator, 14 is an expected existence area calculator, and 15 is an acquisition 16 is a next observation determination device, 26 is an estimation device, and 27 is a prediction device. Note that the same reference numerals in each figure indicate the same or corresponding parts.

Claims (1)

[Claims] 1. A filtering indicator that controls a current time information switch, an estimation device, and a prediction device; a current time information switch that selects input to the prediction device;
In a tracking filter that includes an estimation device that takes in an observed signal and a predicted signal and outputs an estimated signal, and a prediction device that takes in the estimated signal or predicted signal and outputs a new predicted signal, the antenna is oriented at a certain time in the future. an antenna direction calculator that outputs a direction; an incident angle calculator that inputs the output of the antenna direction calculator and a prediction signal output from the tracking filter to calculate an incident angle to the target antenna; and the tracking filter. An expected existence area calculator that takes the predicted signal as input and outputs the size of the expected existence area, and an output of this expected existence area calculator that takes the output of this expected existence area calculator as input and outputs a signal indicating whether the target can be captured at a certain time in the future. The prediction signal output from the above-mentioned tracking filter, the output of the incident angle calculator, and the output of the capture possibility judgment device are input to the signal to the filtering indicator, and the next observation time and the prediction signal up to that point are input. A tracking filter comprising: a next observation determining device that outputs the error variance of the next observation; and a next observation instruction device.