JP2002181926A - Method and apparatus for tracking of target - Google Patents

Abstract

PROBLEM TO BE SOLVED: To obtain a method in which a target is tracked with high accuracy by a radar or the like and to obtain its apparatus. SOLUTION: A target judgment part 14, to which an observed value is inputted, gives an observation residual to an adaptive Kalman filter 5 and a parameter estimation part 6. The filter 5 finds the covariance of a preliminarily estimated value and the observation residual from the observed value, and the covariance is given to the part 4. The part 6 estimates a parameter (the standard deviation of a target speed and a correlation time constant) on the basis of the observation residual from the part 4 and on the basis of the covariance of the observation residual from the filter 5, and the parameter is given to the filter 5. The filter 5 uses the parameter received from the part 6, and it self-adjusts a transition matrix and a system noise. Thereby, the target is converged to an optimum filter, and the target is tracked with satisfactory accuracy.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method and a device for tracking a target with high accuracy using a radar or the like.

[0002]

2. Description of the Related Art A Kalman filter (hereinafter, simply referred to as a "filter") has been often used as a method of tracking a target with a radar or the like. In a target tracking method using a filter, a system equation representing a target motion is described by a discrete-time Langevin equation by modeling the target motion in a Markov process. 160831, Reference 2: RJFI
TZGERALD; Simple Tracking Filter: Steady-State Fil
tering and Smoothing Performance, IEEE Trans. Aero
sp. Electron. Sys. Vol. AES-16 No. 6 1980).

[0003] The filter is composed of this system equation and an observation equation representing an observation value by a radar or the like, and optimally estimates the position and speed of the moving target and tracks the target.

In this case, since the movement of the target is unknown,
Since the standard deviation of the autocorrelation function and the correlation time constant characterizing the Markov process are assumed, the transition matrix of the system equation and the system noise generally differ from the actual one. With such a filter in which the transition matrix and the system noise are different from the actual one, the target cannot be accurately tracked.

[0005] In order to accurately track a target, a filter (hereinafter referred to as an "adaptive filter") which self-adjusts system noise different from the actual one using system noise estimated from observation values and converges the filter to an optimum filter. (See Reference 3: FRCASTELLA; An Adaptive Tow-Dimensional Ka)
lman Tracking Filter, IEEE Trans Aerosp.Electron.S
ys.Vol.AES-16 No.61980, Reference 4: P.GUTMAN,
M.VERGERT; Tracking Targets Using Adaptive Kalman
Filtering, IEEE Trans. Aerosp. Electron. Sys. Vo
l. AES-26 No. 51990).

[0006]

However, in the tracking method using the conventional adaptive filter, the system noise is self-adjusted, but the transition matrix is not self-adjusted. Therefore, the adaptive filter does not always converge to the optimum filter. The target cannot be tracked accurately.

SUMMARY OF THE INVENTION It is an object of the present invention to provide a target tracking method and a target tracking apparatus capable of tracking a target with high accuracy by making both the transition matrix and the system noise self-adjusted.

[0008]

SUMMARY OF THE INVENTION The present invention relates to a method for detecting a relative position of a target.
Position observation z_kInto the adaptive Kalman filter
Estimate the relative position and speed of the target from the
And the observed value z_kAnd the observation residue, which is the difference between
Difference Δz_kAnd the covariance R of the observed residuals_akFrom said adaptive cal
Estimate the parameters of the Mann filter and add
From the transition matrix A_kAnd system noise covariance V _k
Self-adjust.

Thus, the adaptive filter self-adjusts the transition matrix and system noise at each update cycle using the estimated parameters, converges the filter on the optimal filter, and tracks the target with high accuracy.

[0010] The present invention further provides an input of an observation value of a relative position of a target measured by a radar apparatus, and the observation value is tracked using a covariance of a prior estimation value and an observation residual input from the adaptive Kalman filter. Determine whether or not from the target in the middle, if it is from the target being tracked, while providing an observation residual to the parameter estimator, comprising a target determination unit to provide an observation value to the adaptive Kalman filter, When the observation value is not input, the adaptive Kalman filter estimates the relative position and velocity of the target using a propagation equation. This prevents tracking a wrong target.

[0011]

FIG. 1 is a block diagram showing a configuration of a target tracking device according to an embodiment of the present invention. here,
The radar device 1 transmits and receives radio waves from the own ship in a predetermined azimuth, and observes a relative position of the target to the own ship based on the echo signals. Own ship speed sensor 2 measures the moving speed of own ship. The main body 3 of the target tracking device includes a target determination unit 4,
It comprises an adaptive Kalman filter 5 and a parameter estimator 6. The target determination unit 4 inputs the observation value (the relative position of the target) and the own ship speed from the radar device 1, and inputs the pre-estimated value and the covariance of the observation residual from the adaptive Kalman filter 5,
The observation value is given to the adaptive Kalman filter 5, and the observation residual is given to the parameter estimating unit 6, respectively. The adaptive Kalman filter 5 obtains a covariance of a pre-estimated value and an observation residual from the observed value and the own ship speed, and supplies the obtained covariance to the target determination unit 4. Also,
The parameter estimating unit 6 receives the observation residual from the target determination unit 4, inputs the covariance of the observation residual from the adaptive Kalman filter 5, and calculates the assumed parameter from the observation residual and its covariance.
(The standard deviation of the target speed and the correlation time constant) are estimated and given to the adaptive Kalman filter 5. The adaptive Kalman filter 5 gives the covariance of the observation residual to the parameter estimating unit 6 and receives the parameter estimation value from the parameter estimating unit 6. Then, the transition matrix and the system noise are self-adjusted for each update cycle using these parameters, thereby converging to the optimum filter, and accurately tracking the target.
The optimum estimated value of the relative position and speed of the target being tracked with respect to the own ship is output to an external device.

Using the covariance of the pre-estimated value and the observation residual input from the adaptive Kalman filter 5, the target judgment unit 4 judges whether or not the observed value is from the target being tracked. If it is from the target, the observation value and the own ship speed are inputted to the adaptive Kalman filter 5, and the observation residual is inputted to the parameter estimating unit 6, respectively.

The adaptive Kalman filter 5 estimates the relative position and speed of the target from the observation value and the own ship speed when the observation value is input, and uses the propagation equation when the observation value is not input. The target is tracked by estimating the relative position and speed of the target.

Next, a system equation will be described. [1] System Equation If the motion of the target is modeled by a Markov process, the autocorrelation function of the speed of the target is expressed by equation (1).

[0015]

(Equation 1)

Therefore, the system equation representing the motion of the target is as shown in equation (2). Where T _S is the update cycle,
k indicates time (kT _S ), and T indicates transposition.

[0017]

(Equation 2)

Here, E is an average operation of a random variable, and V _k is a root mean square (covariance of system noise) of system noise.

Although u _k is the original system noise, B _k u _k will be treated as system noise in the following for the sake of simplicity. Since the standard deviation of the target velocity and the correlation time constant are unknown in the system equation of Equation (2), the initial values of the parameters σ _{1k = 0} , τ _{1k = 0} and σ _{2k = 0} ,
τ _{2k = 0} is an assumed value. Therefore, the transition matrix and
The initial values A _{k = 0} and V _{k = 0} of the covariance of the system noise are different from the actual values.

[2] Observation equation If the observed value is the distance between the ship and the target in the x and y directions, the observation equation can be expressed by equation (3).

[0021]

(Equation 3)

The white observation noise of formula (3) is, for example, and the standard deviation Shigumashita the angle measurement error of the radar, slant range (three-dimensional direct distance) to the target and a _{R k w 1k = w 2k =} σθ
R _k may be used.

[3] Adaptive Filter The adaptive filter for estimating the relative position and velocity is composed of the system equation of equation (2) and the observation equation of equation (3).
, (5).

<Propagation formula>

[0025]

(Equation 4)

<Update type>

[0027]

(Equation 5)

Here, Z _k -Cx _{k / k-1} is an observation residual. In the text of the specification, it means an estimated value ^
A symbol with a (hat) is represented by two characters arranged to the right of a character to be added.

The adaptive filters of Equations (4) and (5) estimate the relative position and speed of the target using the observation value input from the target determination unit and the own ship speed, accurately track the target, and and outputs to the device, the covariance _{R ak = CP k / k-} 1 C T + W k of the observation residuals obtained during calculations of the filter parameter estimator, the target determines the covariance of pre estimate and the observed residual Output to the section. Further, a transition matrix A _k different from the actual one and a covariance V _k of the system noise are converted into estimated values σ _{1k + 1} , τ _{1k + 1} , σ _{2k +1} , τ of the parameters input from the parameter estimating unit.
Self-adjust using _{2k + 1} .

Although the standard deviation and the correlation time constant are unknown in the present adaptive filter, the present invention can be applied to a case where a state of a phenomenon that can be described by a Markov process is estimated.

[4] Parameter Estimating Unit A method of estimating parameters for optimizing the adaptive filters of equations (4) and (5) in the parameter estimating unit will be described. From σ _1k , τ _1k , σ _2k , τ _{2k at} time k to time k
Consider the observation residuals for estimating σ _{1k + 1} , τ _{1k + 1} , σ _{2k + 1} , τ _{2k + 1} at ₊₁ .

The covariance _Rak of the observation residual input from the adaptive filter is given by equation (6).

[0033]

(Equation 6)

Let the covariance of the actual estimation error be Q _{k / k−1} ,
The covariance R _rk of the observation residual corresponding to Q _{k / k−1} can be expressed by equation (7).

[0035]

(Equation 7)

If the difference between the actual system noise covariance and V _k is ΔV _k , equation (7) becomes equation (8).

[0037]

(Equation 8)

By _calculating the difference between R _rk and R _ak , the following equation (9) is obtained.

[0039]

(Equation 9)

Where R _ak is known and R _rk is Q
_{Since k / k-1} is unknown, it cannot be calculated directly, but
Observation residual Δz _k = Z _k −Cx input from the target determination unit
^ _{k / k- 1} is mean-squared and estimated by equation (10).

[0041]

(Equation 10)

[0042] Thus, by using the R ^ _rk instead of R _rk, error [Delta] V _k of the covariance of the system noise by the formula (9) it can be estimated.

The error ΔV _k is _{σ 1k, τ 1k, σ 2k} , error Δσ _1k to the actual value of _{τ 2k, Δτ 1k, Δσ 2k} , Δτ 2k,
Therefore, these errors may be obtained from equation (9). Element ( ₁₁ ) of (1,1) of (R ^ _{rk- Rak} ) of matrix
And the errors Δσ _1k and Δτ _1k are obtained.

[0044] element V _11k of (1,1) of the CV _k C ^T has the formula (11)
It is represented by

[0045]

[Equation 11]

When the relational expression between R _11k and Δσ _1k , Δτ _1k is obtained by using the partial coefficient of V _11k , the following equation (12) is obtained.

[0047]

(Equation 12)

Γ _1k is a design parameter, for example, τ
Ratio of the partial coefficient of V _11k with respect to _1k and σ _1k γ _1k = −2τ
Assuming that _1k / σ _1k , Δσ _1k and Δτ _1k are obtained from the equation (12) by the equations
(13), (14) can be obtained.

[0049]

(Equation 13)

[0050]

[Equation 14]

Similarly, the matrix (R ^ _{rk- Rak} ) of (2,
2) When the errors Δσ _2k and Δτ _2k are obtained from the element R _{22k of}
Equations (15) and (16) are obtained.

[0052]

(Equation 15)

[0053]

(Equation 16)

Parameter σ _{1k + 1 at} time k _{+ 1} , τ
The estimated values of _{1k + 1} , σ _{2k + 1} , and τ _{2k + 1} are calculated using the errors Δσ _1k , Δτ _1k , Δσ _2k , and Δτ _2k found in Equations (13) to (16).
Determined from (20).

[0055]

[Equation 17]

[0056]

(Equation 18)

[0057]

[Equation 19]

[0058]

(Equation 20)

Parameters σ _{1k + 1} , τ _{1k + 1} , σ _{2k + 1} , τ
_{2k + 1} is input to the adaptive filter. The adaptive filter self-adjusts the covariance of the transition matrix and the system noise at time k + 1 using these estimated values, thereby converging on the optimal filter.

As shown in equation (10), by using a moving averaged observation residual for parameter estimation, even when an abnormal observation value is input to the filter, the parameter can be stably estimated. The target can be tracked stably.

[5] Target Judgment Unit The target judgment unit _calculates the covariance matrix _Rak = _{CPk / k-1} of the observation residual.
Using C ^T + W _k−1 , it is determined whether or not the observation value of the radar is an observation value from the target being tracked.

The normalized quadratic form t _k of the observation residual Δz _k = z _k −Cx ^ _{k / k−1} can be expressed by equation (21).

[0063]

(Equation 21)

It is known that the distribution of t _k is a χ (chi) square distribution with two degrees of freedom, and its density function is given by equation (22).

[0065]

(Equation 22)

[0066] When the small consisting of a threshold Th there is a t _k, when the observed value is assumed to be the observed value from the target of being tracked, the threshold T
The relationship between h and the probability P _{fa of} determining that the observation value is not an observation value from the target despite being an observation value from the target is given by Equation (22).
Is obtained from Equation (23).

[0067]

(Equation 23)

[0068] target determining unit compares the threshold value Th calculated by the equation (23) with respect to the probability P _fa set as t _k calculated in equation (21), the observed values in the case of t _k <Th is it is determined as being from the target to output the observation residuals to the adaptive filter and the parameter estimation unit, in the case of t _k ≧ Th does not output the observation residuals determined that not from the target.

As described above, the threshold value obtained from the probability density function regarding the observation residual is compared with the observation residual, and only when the observation value is from the target, the relative value of the target from the observation value and the own ship speed is obtained. By estimating the position and speed, the probability of tracking an erroneous target is reduced.

Next, an example of the processing procedure of the target tracking device shown in FIG. 1 will be described with reference to FIG. First, in step s1, k = 0, the posterior estimated value x ^ _{k = 0} , the posterior covariance _{Pk = 0} , the transition matrix _{Ak = 1} , the system noise covariance _{Vk = 1} , and the observation noise covariance. Initial setting of W _{k = 1} is performed.

In the next step s2, the time k is advanced. In step s3, the prior estimated value x ^ _{k / k-1} and the prior covariance P ^ _{k / k-1} are calculated by the equation (4).

In the following step s4, the following equations (21) and (23) are used.
t_k, Th, and determine the target. t_k<Th,
Assuming that the observation is from the target being tracked,
In step s5, the posterior estimated value x is calculated by the equation (5)._k^ ,fill
Taggain K_k, Posterior covariance P _kIs calculated, and step s6
Then, the parameter σ is given by the equations (17) to (20)._{1k + 1}, Τ_{1k + 1}, Σ
_{2k + 1}, Τ_{2k + 1}, And in step s7, A
_{k + 1}And V_{k + 1}And the transition matrix A_kAnd system noise
Covariance V_kSelf-adjust. Then, in step s8,
Posterior estimate x ^_{k + 1}Is output.

If t _k ≧ Th in the above target determination, it is considered that the observed value is not the observed value from the target being tracked, and in step s9, the above preliminarily estimated value x ＾ _{k / k−1} is output as it is. Thereafter, the process returns to step s2. In this way,
The same processing is repeated while advancing time k.

The transition matrix A _{k in the} equation (2) changes according to the change in τ _{k + 1} . Also, due to the change of τ _{k + 1} and σ _{k + 1} , (2)
Changes the normal white system noise u _k of the formula, the covariance V _k of the system noise is changed by a change in u _k. This
Equation (4) changes. Thus, the transition matrix and the system noise are self-adjusted, the filter is made to converge to the optimum filter, and the target is accurately tracked.

[0075]

According to the present invention, the self-adjustment of the transition matrix and the system noise allows the adaptive filter to converge to the optimum filter even when the transition matrix and the system noise are different from the actual one. The target can be tracked with high accuracy.

Further, according to the present invention, the threshold value obtained from the probability density function regarding the observation residual is compared with the observation residual, and only when the observation value is from the target, the observation value and the own ship speed are used. By estimating the relative position and speed of the target,
The probability of tracking an erroneous target is reduced.

[Brief description of the drawings]

FIG. 1 is a diagram showing a configuration of a target tracking device according to an embodiment of the present invention.

FIG. 2 is a flowchart showing a processing procedure in the apparatus.

Claims (3)

[Claims] We claim: 1. Enter the observed value z _k of the target relative positions, the process of estimating the target of the relative position and speed by adaptive Kalman filter, the parameter estimation unit, and the observation value z _k, and the estimated value Of the observation residual Δz _k , and the covariance R of the observation residual
_e. estimating parameters of the adaptive Kalman filter from a _k and self-adjusting the transition matrix A _k and the covariance V _k of system noise with the parameters. 2. An adaptive Kalman filter means for inputting an observation value z _k of a relative position of a target and estimating a relative position and a velocity of the target, and an observation residue which is a difference between the observation value z _k and the estimated value. Difference Δ
a parameter estimating means for estimating the parameters of the adaptive Kalman filter from z _k and the covariance R _ak of the observation residual, and self-adjusting the transition matrix A _k and the covariance V _k of the system noise using the parameters. Tracking device. 3. An observation value z _k of a relative position of a target measured by a radar device is input, and the observation value is being tracked by using a covariance of a prior estimation value and an observation residual input from the adaptive Kalman filter. Determine whether or not from the target, if it is from the target being tracked, while providing an observation residual to the parameter estimating unit, further comprising a target determining unit to provide an observation value to the adaptive Kalman filter, the adaptive Kalman filter The target tracking device according to claim 2, wherein when the observation value is not input, the relative position and the speed of the target are estimated using a propagation equation.