JPH0264480A - Tracking apparatus - Google Patents

Abstract

PURPOSE:To perform stable tracking with respect to a target moving at a low speed with high accuracy by estimating only the position of the target two-dimensionally supposing that the target is stationary and subsequently changing over said estimation to four-dimensional estimation supposing that the target performs linear motion with constant velocity to perform tracking. CONSTITUTION:At the initial stage of tracking, observation data is inputted to a two-dimensional filter 1 from an input terminal 4 and the difference with an estimated observation value is taken by an adder 12 to generate an error signal. This error signal is multiplied by an estimation gain by a multiplier 13 and the sum with the estimated value of the position of a target is taken by an adder 14 to output an estimated value from an output terminal 20. Subsequently, after a proper time, a switch 19 is changed over to a four-dimensional filter 2 and the difference between observation data and the estimated observation value is taken by an adder 5 to generate an error signal. The error signal is multiplied by an estimated gain by a multiplier 6 and the sum of the estimated value position of the target and that of the speed of the target is taken by an adder 7 to output an estimated value from the output terminal 20. By this method, stable tracking can be performed with high accuracy.

Description

DETAILED DESCRIPTION OF THE INVENTION [Field of Industrial Application] The present invention relates to a tracking device, and more particularly to a passive target tracking device that tracks a moving target using only azimuth observation data.

[Conventional technology]

As a method for tracking a moving target only from azimuth observation data, there is a method shown in FIG. 3 that has been used in the past. This is, for example, the document "IEEE Transaxilan Aerospace and Electronic Systems" (IEEE Tan 5. Aero
space and electronic system
ems.

Vol, AES-15, Nal, Jan, 1979
．． V.J. Aidala's paper “Kalman filter behavior in bearings only” published in pp. 29-39).
Tracking Applications J (Kalman
filter behavior in beari
ngs-only tracking applica
This is a block diagram representation of the tracking method shown in ``Actions'').This tracking method assumes that the moving target is in uniform linear motion, and applies an extended Kalman filter to the observed data of relative orientation. By doing so, the position and velocity of the target are estimated.When the moving target performs uniform linear motion, the equation of motion is expressed as follows.

Here, it is expressed as X (k)-AX (k-1). Here, ...(1) and w (k) is white Gaussian noise of fraction σ2.

When the extended Kalman filter is applied to the model expressed by equations (1) and (2), the equations for updating the estimated values of position and velocity become as follows.

X(k) =X(k) +L(k)(θ(k)−h(k,v(k)))
...(3) where T is the observation time interval and k is the observation time.

The observation data is the relative orientation of the target, θ(k)=h (k, r (k))+w (k)...
・(2), and the predicted value is X (k) from the estimated value one step ago
=AX (k −1) ・<4). Further, L (k) is the estimated gain of the <4X1) matrix, and is determined using the following series of equations.

M (k)-AP (k-],)A? ...
(5) Ω (k) −1((k) M(k) H'
(k) +σ2 ... (7) L (k)
=M(k) H” (,k) Ω-1(k)
...(8)P (k) = (1-L(k
)H(k))M(k)...(9)In this, M(k) and P(k) are (4X 4) matrices, H
(k) is an (I x 4) matrix, and Ω(k) is a scalar.

In Figure 3, each time observation data is input (3)
The configuration is such that the estimated value is updated by calculating equation (9). In the figure, 4 is an input terminal, 5 is an adder, 6 is a multiplier, 7 is an adder, 8 is a delay device, 9 is a multiplier, and 10 is L
The calculation section 1) calculates h (k, r
(k) ), and 20 is an output end of the h calculation section.

Next, the operation will be explained. When observed data θ(k) is input from input terminal 4, adder 5 adds predicted observed value h
(k, ?(k)) is taken and the error signal θ(k)
-h (k, 'ii' (k)) occurs.

This error signal is multiplied by an estimated gain L(k) in a multiplier 6, and the sum of the predicted value X(k) of the target position and velocity is calculated in an adder 7. k) is output. Note that the L calculation unit 10 calculates the equation (5)-0 to obtain L (k).

[Problem to be solved by the invention]

As mentioned above, conventional tracking devices are constructed on the assumption that the moving target performs uniform linear motion, so as pointed out in the paper by V., J., and Aidala, the series of observation positions is There was a problem that if it was not taken properly, it would not be observable and the specified value would diverge.

This will be explained using FIGS. 4 and 5.

In FIG. 4, 21 to 23 indicate several routes of moving targets, and 24 indicates a route of an observer, all of which are assumed to be in uniform linear motion. Each point on the path 24 ``.

FIG. 5 shows the relative orientation of the target observed from (1), ra(2), . . . In this case, the relative orientations of all targets will be the same, and even if there is no observation noise, the position of the target cannot be uniquely determined.

That is, as long as the observer moves in a uniform straight line, the target is unobservable, and the position of the target cannot be specified in principle.

Therefore, in order to make the target observable, the observer needs to perform some kind of acceleration motion, but even in that case, the filter remains unstable until a sufficient amount of time has passed, and sometimes the estimated value diverges. There was a problem with this.

This problem occurred regardless of the speed of the moving target, and caused similar difficulties when the target was moving at very low speeds, such as when tracking a ship's position from an aircraft.

This invention was made to solve the above-mentioned problems, and in particular, by limiting the target to low-speed moving targets as in the above example, it does not impose severe restrictions on the movement of the observer. (The purpose is to obtain a tracking device that can perform stable tracking.

[Means to solve the problem]

The tracking device according to the present invention assumes that the target is stationary and estimates only its position using a two-dimensional filter at an initial time, and then switches to a four-dimensional filter after an appropriate time to track the target including its speed. In addition, the timing of the switching can also be determined from the estimated data.

[Effect]

In this invention, with the above configuration, the target becomes unobservable at an initial time only when the observer moves on a straight line connecting the target and the observer.
Except for such special cases, the filter will operate stably, and the problem of divergence of specified values will be solved.

〔Example〕

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

Before entering into a description of specific embodiments of the present invention, the principle of the present invention will first be explained.

First, when the target is considered to be stationary, the equation of state is r (k) = r (k-1) . . . instead of equation (1).
The αω observed value is the same as equation (2), θ(k)=h (k, r (k))+w (k)...
・αD However, in this model, the target position cannot be uniquely determined from the observed values only when the observer moves on a straight line connecting the target and the observer. Applying a two-dimensional extended Kalman filter to this model results in the following.

7(k)−♀(k−1) ・・・(2
)Q (k)=7 (k) +L+ (k) (θ (k)−h (k, 7 (
k))...[131 M, (k)=PI (k-1) ・
・・α0ΩI(k) −81(k)Ml(k)Hl”
(k) +σ2 ...αQL+(k) =M
I(k)Hl ” (k)Ωs(k) ...09
PI(k)=(I −Ll(k)Hl(k))M
l(k) -Ql Among these, Ll (k) is the estimated gain and is a (2X1) matrix, Ml(k) and PI (k)
is a (2×2) matrix.

Hl (k) is an (IX2) matrix, and Ql (k) is a scalar.

If the speed of the target is small, it is better from the viewpoint of stability and accuracy to specify only the target position using a two-dimensional filter (Equations (2) 2 to (2)) at the initial time. desirable.

However, with only a two-dimensional filter, modeling errors due to the assumption that the target is stationary will increase over time, so it is necessary to switch to a four-dimensional filter that performs tracking including speed. .

The timing of this switching is based on the speed distribution (v1 ≦
V? 1. □uniform distribution) variance (-1/2vT+l1l
It is sufficient to set the point at which the value falls below llll+).

In order to make Pvv proximal, a four-dimensional filter ((3)
The following algorithm is used, which extracts only the part for determining the covariance matrix P (k) from Equations (9) to (9).

M(k)-AP(k-1)A"-(J'
4Ω (k) −H(k)M(k)H? (k)
+σ2...(21)L(k) =M(k
)H" (k) Ω-' (k) ・・・(
22) p (k) = (I −L(k)H(
k)) M(k) (23) This is a covariance matrix of speed estimation errors obtained only from the (4×4) matrix data thus obtained. Note that r (k) = (x(
k), y (k)) are two-dimensional filters (□□□2~aΦ
Use the predicted position obtained by formula).

By the above algorithm (Qg1 formula to (23) formula), P
Find vv(k), trace (P vv (k) )≦1/2 V ”
When r, -, .= (24), the two-dimensional filter is switched to the four-dimensional filter. As the four-dimensional filter, the same ones as in formulas (3) to (9) of the conventional example are used.

A block diagram of a device that executes the above-mentioned tracking method is shown in FIG. 1. In FIG. Input terminal, 5 is an adder, 6 is a multiplier, 7 is an adder, 8 is a delay device, 9 is a multiplier, 10 is L (
The calculation part 1) calculates h (k, 7'(k
)), 12 is an adder, 13 is a multiplier, 14 is an adder, 15 is a delay device, 16 is a calculation unit that calculates L+(k), 17 is h (k, γ( 18 is a Pvv calculation section that calculates Pv and (k), 19 is a switch for switching the filter, and 20 is an output end.

Next, the operation will be explained. Two-dimensional filter 1 calculates @formula to formula, and four-dimensional filter 2 calculates (3)2 to (9)
), and the means 3 for determining the timing of filter switching calculates the equations Ql2 to (23).

The switch 19 is initially set to the two-dimensional filter 1 side. Observed data θ(k) from input terminal 4 at the initial time
is input, the adder 12 inputs the predicted observed value h (k,
+r (k) ) is taken and the error signal θ(
k)-h (k,?(k)) occurs.

This error signal is multiplied by the estimated gain Ll (k) in the multiplier 13, and the predicted value of the target position in the adder 14? (k), and the estimated value ♀(k) is output from the output terminal 20. The switch 19 switches to the four-dimensional filter 2 side when the determination condition of equation (24) is satisfied. The operation from that point on is the same as that of the conventional example.

Although the above embodiment describes the case where observation data is input at equal time intervals, the present invention can also be applied to cases where observation data is input at non-equal time intervals. In this case, the same effects as in the above embodiment can be obtained.

That is, when observation data is input at unequal time intervals, the time is tl, ! +'ff+..., then the equation of motion of the target becomes X (k)-A (k)X (k-1) instead of equation (1) in the four-dimensional filter.

That is, the (4×4) matrix A in equation (1) replaces A(k), and the two-dimensional filter is the same as in the case of equally spaced data.

FIG. 2 is a block diagram of a device that executes this tracking method. The function of each block is the same as that of the corresponding block in FIG. 1, and the corresponding blocks are given the same number.

〔Effect of the invention〕

As described above, according to the tracking device of the present invention, passive target binary stars are detected using a stable two-dimensional filter in the initial period, and then switched to a highly accurate four-dimensional filter after a certain period of time. Since the configuration is configured to perform this, there is an effect that stable and highly accurate tracking can be performed throughout.

[Brief explanation of the drawing]

Fig. 1 is a block diagram for explaining a tracking device according to an embodiment of the present invention, Fig. 2 is a block diagram for explaining another embodiment of the invention, and Fig. 3 is a block diagram of a conventional tracking system. 4 and 5 are diagrams for explaining the operation of the conventional tracking method shown in FIG. 3. In the figure, 1 is a two-dimensional filter, 2 is a four-dimensional filter, 3 is a means for determining the timing of filter switching, 4 is an input terminal, 5, 7, 12.14 are adders, 6, 9.13 are multipliers , 8.15 is a delay element, 10 is an L calculation unit, 1).
17 is an h calculation unit, 16 is a beam calculation unit, 18 is a p vv calculation unit, 19 is a switch, 20 is an output end, 21.22.2
3 is the path of the moving target, and 24 is the path of the observer. Note that the same reference numerals in the figures indicate the same or equivalent parts.

Claims (1)

[Claims] (1) In a tracking device that estimates the position of the target in real time from azimuth observation data of the target moving at a low speed, means for estimating the two-dimensional state of only the position by regarding the target as a stationary target; A means for estimating the four-dimensional state including speed by assuming the target as a uniform linear motion, a means for determining the timing of switching between the two state estimating means from the estimation data, and estimating the two-dimensional state at the initial stage of tracking. A tracking device comprising: means for selecting the four-dimensional state estimating means after the switching instruction is given by the switching timing determining means.