JPS6111681A - Tracking filter - Google Patents

Abstract

PURPOSE:To perform the optimum estimation of a forecasting position by using an optimum estimation gain based upon residual variance between a forecasting position before sampling time and a new observation position by a radar, etc. CONSTITUTION:The tracking filter which estimates or forecasts the observation data, target position, and speed of the radar, etc., supplies an estimation gain controller 2 with the residual variance that a variance estimating device 1 estimates from the residual nut between the new observation position Zt by the radar, etc., and the forecasting position before the sampling time. Then, the controller 2 performs arithmetic minimizing the estimated error variance to calculate the optimum estimation gain K1 for determining whether the contribution of the observation data is large or not when the current position of a moving target is estimated, an optimum estimating device 3 estimates and outputs the current position of the target according to the gain K1, and a target motion simulator calculates and outputs the target position in next sampling. This optimum gain is used to estimate whether the contribution of the observation is large or not, and consequently even when the target has variation in motion characteristic, tracking corresponding to the variation is carried out.

Description

DETAILED DESCRIPTION OF THE INVENTION [Technical Field of the Invention] The present invention relates to a tracking filter that estimates or predicts the position and velocity of a flying object or the like from observation data obtained by radar or the like.

[Prior art]

Conventionally, with this type of tracking filter, when estimating the current position from the position predicted before the sampling time and the position newly observed by radar etc., an estimation method is used to determine the ratio of the contribution of the two positions. Since the gain was processed by internal calculation based on the assumption of the target motion characteristics, the results of estimation or prediction were not fed back. According to such a tracking filter, as the number of observations increases, the observed data is gradually ignored, and its contribution to estimation gradually becomes smaller. However, if one target changes its motion characteristics due to a sharp turn or the like, the contribution of the latest observation data should be made larger again than the predicted value based on the previous motion characteristics. Conventional tracking filters cannot handle this kind of response, so if the motion characteristics of the target change and the original assumptions no longer hold, large errors will occur in estimation and prediction, and the target may sometimes be lost. There were some drawbacks.

[Summary of the invention]

This invention was made with the aim of improving the drawbacks of the conventional methods as described above. By using an estimation gain that always optimizes the magnitude of the contribution of observation data to position estimation, the current target position is optimally estimated, and the target position can be estimated even when the motion characteristics of the target change. Alternatively, the present invention provides a tracking filter that does not cause large errors in prediction.

[Embodiments of the invention]

Normally, the target moves in three-dimensional space, but here the tracking filter of the present invention will be described as moving in one direction, without any loss of generality in practice.

Now, the tracking filter is a digital system that operates at sampling time τ5. The position of the moving target at every sampling time τ8 is taken as a time series (yt). Therefore, the observation error vt is always added to the radar observation value 21 at the position yt in this time series (yt).

Zt=y1+vt, ・・・・・・・・・・・・
(1) Here, the suffix t indicates the value at time t. It is assumed that this observation error Vi is a regular white noise sequence with an average of zero and a variance Rt. That is, if B(・) is the averaging operator, E(vl)=0 ・・・・・・・・・・・・
・・・・・・・・・・・・・・・(2)

The role of the tracking filter is to estimate or predict the true position from the observed value to which the observation error N/i is added.

At time t, the estimated value of the position △ at this time t is written as yBt, and the predicted value of the position after the sampling time τS at this time t is 9t.
Let's write it as ++ l t. Moreover, if these error variances are respectively Pflip Pt+11t, Pt1t = E((ytlt - yt)") P t+1
1t = E ((yt+tlt-yt+t)2).

Embodiments of the present invention will be described below with reference to the drawings.

The figure is a block configuration diagram showing a tracking filter that is an embodiment of the present invention. First, take the difference between the observed position Zt newly obtained by the radar and the current predicted position 11t-s predicted before the sampling time τ5, and calculate this residual as Pt
Then, Pt "Zl 3'tlt-s °=°゛-°
°“°゛°°°゛°゛° (4) The time series (Pt) of this residual νt is called the innovation process. In the figure, 1 represents the variance of the residual between the observed position and the predicted position. This variance estimator 1 inputs an innovation νt, estimates its variance online, and outputs it. The estimated variance of this innovation νt is set to et. 2 is a variance estimator for position estimation. This is an estimated gain control device that determines the contribution of observed data, and this estimated gain control device 2 receives the estimated variance St as input, and when estimating the current position of the moving target, it determines the magnitude of the contribution of observed data. The estimated gain KL to be determined is optimally divided and output.3
is an optimal estimator that estimates the target position with an estimated gain of 1, and this optimal estimator 3 inputs the estimated gain Kt, innovation νt, and prediction ()Ill△ position Yt 1t-s, and calculates the current optimal estimation. The target Δ position yt1t is calculated and output. Reference numeral 4 denotes a target motion simulator 1/- which predicts the target position after a period of time τ8 from the estimated position from the past to the present. The target position after sampling time τ5 is predicted and output from the motion characteristics of the target modeled in an unsteady time series. This Δ predicted target position is assumed to be yt-1-+4t. Reference numeral 5 denotes a delay element that delays the time by the sampling time τ5, and this delay element 5 delays the time by the sampling time τ5. Therefore, the predicted target position yt+tlt predicted after sampling time △ τS from the current time is the predicted target position △ predicted at the present time before sampling time τS.
to Yt l t-s. this predicted position)'tlt-t
is calculated as a new observed value 21 and used again to create the innovation νt.

Next, regarding the variance estimator 1, the variance of the time series (ν1) of the innovation νt is estimated using the forgetting weight I, assuming that the variance of the time series (ν1) of the innovation νt changes slowly. This forgetting weight 9 is 0〈31≦1・・・・・・・・・・・・・・・・・・
・・・・・・・・・・・・(5n△) In other words, the estimated variance St is obtained as follows. When this calculation is performed online, the following algorithm is obtained.

At the initial value (1=0), G,=1.0 ・・・・・・・・・・・・
・・・・・・・・・・・・・・・(7)△ So= νo2 ・・・・・・・・・・・・
・・・・・・・・・・・・・・・・・・(8) When t≧1, Wi:, F−Gj−,・・・・・・・・・(9nGt
=1.0+Wt・・・・・・Self・・・・・・
・・・・Old・−(1'01t<=t+1, above (
9) Repeat from equation.

Also, regarding the optimal estimator 3, the estimated target position yt1t of the movement △ target is calculated from the innovation νt△ and the predicted position ytlt−t from before the sampling time τ8.
△ △ ytlt ”)'tlt-t +Kt yt ”
"" --- (obtained by combining 1. The estimated gain Kt at this time is obtained as the output of the estimated gain control device 2.

Regarding the estimated gain control device 2, the estimated gain Kt is a coefficient that determines the magnitude of the contribution of observation data when estimating the target position, and this is the estimated error variance ptl.
Determine so that t is minimized.

This estimation error variance Pt1t is obtained as shown in the following equation.

Pt1t==(I Kt)"tIt- is 10 KIR1・
(13) Here, Pt1t-1 is the sampling time τ and the prediction error variance from before. The optimal estimation gain Kt that minimizes the estimation error variance Pt1t is as follows.

On the other hand, the variance Sj of innovation νt and the prediction error variance P
1 for t1t-x fJ=Ptlt-r +Rt...
There is a relationship of ・・・・・・・・・・・・09. In place of this variance Sj, using the estimated variance t which is the output of the variance estimator 1, 8, -> France 091
．． 1090061120000. If we rewrite the above formula I as aω, we get the following. In this way, the estimation gain control device 2 inputs the estimation variance i k and estimates the gain Kt? that optimizes the contribution of observed data to the estimation. , calculate from the above formula 00 and output.

Further, regarding the target motion simulator 4, this target motion simulator 4 predicts and outputs the future target position within one sampling time τ3 from the estimated values obtained from the manufacturing method up to the present. . For this prediction, the target motion simulator 4 models the target motion as a motion due to acceleration in a linear regression process.
I'm using this. This is expressed as (1+aZ-')(1-Z-'')yt=Wt-- as a non-stationary time series of positions.
......(is. Here, Z-1 is a delay operator, and Wt is regular white noise with a mean of zero. The above (1,81
The formula is also yt++ = (2-a) yt + (2a
-1) yt-+ayt-2-? Wt+t --
−−・= (19) can also be expressed. For prediction, the above (2)
) is used, but since the normal white noise Wt with an average of zero is unknown, its average value O is used instead, and since the true value of the position is also unknown, it is replaced with an estimated value. That is, △
△ △ yi+x lt = (2-a)VBt + (2a
-1) yt-tlt-t△ aVt-zlt-2・・・・・・・・・・・・・・・(
20) is used. Furthermore, if Δyt-+1t-x (i-0+L 2) is used at adjacent sampling points, the error will come into play, so in reality, every second sampling point, 3
Use point-by-point values or smooth values.

As described above, according to the tracking filter of the present invention, the optimal estimated gain Kt is determined from the variance of the innovation process using the above α9 formula, and thereby the magnitude of the contribution of observed data can always be optimally estimated. Therefore, even if the target changes its motion characteristics, corresponding tracking is possible.

In addition, although the above embodiment describes the tracking of a flying target using observed values by radar, the present invention is not limited to this, and can be applied to underwater tracking, space tracking, removal of observation noise in industrial measurements, etc. can also be used.

〔Effect of the invention〕

As explained above, in the tracking filter of this invention,
By using an estimation gain that always optimizes the magnitude of the contribution of observation data to estimating the target position, from the variance of the residual between the position predicted before the sampling time and the position newly observed by radar etc. Since the current target position is optimally estimated, unlike conventional tracking filters of this type, even if the motion characteristics of the target change, the predicted value based on past observations can be calculated using new observation data. It is particularly effective when applied to radar, etc., because it does not cause large errors in estimation and prediction due to overemphasis, and allows extremely accurate tracking in response to changes in the target's motion characteristics. It is something.

[Brief explanation of drawings]

The figure is a block configuration diagram showing a tracking filter that is an embodiment of the present invention. In the figure, 1...dispersion estimator, 2...estimation gain control device, 3...optimum estimator, 4...target motion simulator, 5...delay element.

Claims (1)

[Claims] In a tracking filter that estimates or predicts the position and speed of a flying object from observation data from radar, etc., examine the variance of the residual between the position predicted before the sampling time and the position newly observed by the radar, etc. A variance estimator, an estimation gain control device that optimizes the magnitude of the contribution of observation data regarding estimation of the target position from the variance estimated by the variance estimator, and an estimation gain of the estimation gain control device to calculate the residual error and An optimal estimator that optimally estimates the current target position from new observation data, and a target motion that predicts the target position after a sampling period from the estimated position from the past to the present based on a non-stationary time series model of only the position. A tracking filter comprising a simulator.