JPH0797134B2 - Tracking filter - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION [Industrial field of application] The present invention inputs target position information including observation noise and a target distance change rate from a target observing device to obtain various target motions such as a true value and velocity of a target position. This paper proposes a method for improving the accuracy of tracking filters that estimate elements.

[Conventional technology]

Figure 4 shows, for example, IEEE TRANSACTIONS ON AEROSPACE AND E
LECTRONIC SYSTEMS VOL AES-13 NO.3, MAY 1977, P310〜
P317 「MANEUVERING TARGET TRACKING USING ADAPTIVE S
It is a block diagram of the conventional tracking filter in the case of having a plurality of motion models indicated by "TATE ESTIMATION". In the figure, (1) is a target observation device for measuring a target position and a target distance change rate including observation noise. , (2) is a position observation error evaluator for each movement model for evaluating the target position observation error for each of the movement models, and (3) is for calculating the reliability of each movement model. Reliability calculator for each motion model of (4), the first delay circuit,
(5) is a gain matrix calculator for calculating the Kalman gain matrix used to calculate the smooth value of the desired motion parameter, (6) is a smoother for calculating the smooth value of the target parameter, and (7) is a plurality. For each of the exercise models, a predictive value calculator for each exercise model that calculates the expected values of the desired exercise parameters after one sampling from the present time, (8) a third delay circuit, and (9) a plurality of exercise models A smoothing error evaluator for each motion model that evaluates the smoothing error, which is the difference between the smoothed value and the true value,
(10) is a prediction error evaluator for each motion model that evaluates the prediction error that is the difference between the prediction value and the true value of each of the plurality of motion models, (11) is the second delay circuit, and (12) is the fourth Delay circuit.

The conventional tracking filter having a plurality of motion models is configured as described above, and uses, for example, fixed Cartesian coordinates and a plurality of different models in which a constant acceleration vector is added to the constant velocity linear motion model and does not depend on the sampling time. The case of having each acceleration level is used as a plurality of motion models. The target observing device (1) converts target position information including observation noise in polar coordinates into Cartesian coordinates. In the position observation error evaluator (2) for each motion model,
From the current time obtained by the prediction error evaluator (10) for each motion model, the target position prediction vector calculated one sampling before the current time obtained by the prediction value calculator (7) for each motion model is used as the average vector of the target positions. Obtain the covariance matrix of the difference between the target position observation vector and the target position prediction vector from the prediction error covariance matrix calculated one sampling before and the observation noise covariance matrix obtained from the preset observation model, and observe the target position Assuming that the vector follows a three-dimensional normal distribution, the error of the target observation position input from the target observation device with respect to the target predicted position is evaluated for each of a plurality of motion models. In the reliability calculator (3) of each motion model, the reliability of each motion model calculated one sampling before the current time, and Markov property in the motion model transition are assumed, and the motion model preset is changed. The reliability of each of the plurality of motion models is calculated from the probability and the target position observation error evaluation value of each of the motion models input from the position observation error evaluator (2) of each motion model. In the gain matrix calculator (5), the observation noise covariance matrix obtained from the preset observation model and the motion model calculated by the prediction error evaluator (10) for each motion model one sampling before the present time The gain matrix is calculated from the Kalman filter theory from the prediction error covariance matrix for each. In the smoother (6), the smoothed value calculated one sampling before the present time, the target observation position value input from the target observation device (1), the gain matrix input from the gain matrix calculator (5), and Smoothing the target position and target velocity by summing the constant acceleration vectors that make up a plurality of motion models weighted by the reliability of each motion model obtained by the reliability calculator (3) of each motion model Calculate the value. The predicted value calculator (7) for each motion model uses the target position and target speed calculated by the smoother (6) and the constant acceleration vector for each motion model to calculate the target position and target speed one sampling after the current time. Calculate the predicted value. In the smoothing error evaluator (9) for each motion model, the covariance matrix of the difference between the smoothed value and the true value of the target position and the target velocity is calculated by the gain matrix calculator (5) and one sampling before the present time. It is calculated by the prediction error covariance matrix calculated by the prediction error evaluator (10) for each motion model. In the prediction error evaluator (10) for each motion model, the smoothing error covariance matrix input by the smoothing error evaluator (9) for each motion model and the driving noise covariance matrix obtained from the preset motion model are used. The covariance matrix of the difference between the predicted value and the true value after one sampling from the present time is calculated.

[Problems to be Solved by the Invention]

In the conventional tracking filter as described above, the tracking filter is configured only by the target position information even when the target distance change rate is observed by the target observation device (1) like the pulse Doppler radar, so that the observation is performed at the time of the target turning. The rapid change in the target distance change rate is not reflected in the reliability of each of the multiple motion models obtained by the reliability calculator (3) of each motion model, and the target position calculated by the smoother (6) Despite the smoothness of the target velocity and the value reflecting the reliability for each of the multiple motion models obtained by the reliability calculator (3) for each motion model, the predicted values of the target position and target speed are During one sampling, the target was calculated as performing a uniform uniform linear motion. For this reason, the tracking accuracy with respect to the turning target must be degraded.

The present invention has been made to solve such a problem, and an object thereof is to obtain a tracking filter capable of accurately tracking even a turning target.

[Means for Solving the Problems]

The tracking filter of the present invention uses the target distance change rate to calculate the reliability of each of the plurality of motion models, and uses the reliability of each of the plurality of motion models to calculate the predicted value of the target motion specifications. It is a thing.

[Work]

In the present invention, the probability density of the difference between the observed value of the target distance change rate and the predicted value of the distance change rate of each of the plurality of motion models (that is, the target distance change rate observation error evaluation value) is set to the plurality of motion models. Prediction value of each motion model, prediction error which is the difference between prediction value and true value of each motion model. Prediction error covariance matrix for each motion model and calculation by target distance change rate observation noise, Using the target position observation error evaluation value for each of the multiple motion models calculated from the target position information as a weighting factor for calculating the reliability of each of the multiple motion models, the matching degree of the multiple motion models for the turning target The reliability for each of the plurality of motion models is calculated more appropriately than in the case where only the target position information is calculated, and the reliability is calculated in this way. Using the reliability for each of the multiple motion models and the constant acceleration vector that composes the multiple motion models, the term of influence of acceleration in the prediction is calculated, and the effect of each of the current multiple motion models is calculated in this term. Calculate the predicted value obtained by integrating the influence of each motion model by adding the predicted value after one sampling calculated by the uniform velocity linear motion prediction based on the smoothed value obtained by integrating I am trying to do it.

〔Example〕

FIG. 1 is a block diagram showing an embodiment of the present invention,
(1) to (12) are exactly the same as the above conventional device. (13) is the predicted value calculator, and (14) is the distance change rate observation error evaluator for each motion model.

The motion model when the number of the plurality is N is x _k = Φ _k-1 x _k-1 + Γ _k-1 W _k-1 + Γ ′ _k-1 u _k-1.
(1)

Where: x _k is a state vector that represents the true value of the target motion specifications at the sampling time t _k , and is the target position vector in Cartesian coordinates. The target velocity vector in Cartesian coordinates When Is.

Φ _k-1 is a transition matrix of the state vector x _k from the sampling time t _k-1 to t _k , and it is assumed that the target makes a uniform linear motion. Is.

· W _k is driving noise vector gamma _k at the sampling time t _k for example a transformation matrix driving noise vector at sampling time t _k, the truncation error term due to the assumed constant velocity linear motion target motion model [rho _{k- If we consider 1} W _k-1 , W _k is equivalent to the acceleration vector. Is.

-U _k is a constant acceleration vector forming N motion models at the sampling time t _k , and u _k = α ₁ or u _k = α ₂ or ... or u _k = α _N ... (2) and Γ ' _k is the conversion matrix of the constant acceleration vector at the sampling time t _k Is.

Fig. 3 is a diagram for explaining the constant acceleration vector in the plane parallel to the horizontal plane. In the figure, 0 is the origin of coordinates 0-xy with the target observation device as the origin, and X is the east direction and the x-axis is positive. X-axis of coordinates 0-xy, Y is the y-axis of coordinates 0-xy with the north direction as the positive y-axis, A1 is a constant acceleration vector in the positive direction of the y-axis, and A2 is a constant in the positive direction of the x-axis. An acceleration vector, A3 is a constant acceleration vector in the negative direction of the y-axis, and A4 is a constant acceleration vector in the negative direction of the x-axis. In the case of a motion model in which the magnitude of the constant acceleration vector in Fig. 3 is 10g (g is the gravitational acceleration) and the constant acceleration vector with zero acceleration is considered, N = 5 (3) (2) is And can be written regardless of the sampling time t _k .

Next, at the sampling time t _k , the hypothesis that u _k-1 = α _a (a = 1,2 ..., N) (5) is true Write.

E is a symbol representing the average, and W _k is a three-dimensional normally distributed white noise with an average of 0. E [ W _k ] = 0 (7) E [ W _k ▲ W ^T _l ▼] = Q _k (k = 1 , And 0I (when k ≠ l) (8).

Here, 0 is a zero vector, Q _k is a driving noise covariance matrix at sampling time t _k , and a ^T represents a transposed vector of vector a.

The target position observation model and _{Z k = H k x k +} v k ...... (9).

Here, · Z _k is the target position observation vector · H _k by configured orthogonal coordinate than the observed value of the target position information at sampling time t _k is H _k = (I 0I) in the observation matrix at sampling time t _k .

V _k is a target position observation noise vector at the sampling time t _k, which is a three-dimensional normally distributed white noise with an average of 0 E [ v _k ] = 0 E [ v _k ▲ v ^T _l ▼ = R _k (k = 1 , 0I (when k ≠ l) ... (10).

Note that R _k is the target position observation noise covariance matrix at the sampling time t _k and is a value that does not depend on the motion model.

Target distance change rate observation model_o (K) = (k) + v _(k) …… (11)

Here, · _{o (k)} is the observed value of the target range rate at the sampling time t _k · (k) is the true value of the target range rate at the sampling time t _k Is the target distance change rate observation noise at the sampling time t _k , which is a one-dimensional normally distributed white noise with an average of 0. Is.

In addition, Is the variance of the target distance change rate at the sampling time t _k and is a value that does not depend on the motion model.

In addition, the target distance is R (k) Then, by differentiating both sides of equation (14), Is.

The entire target position observation vector from sampling time t _k to t _k is z ^k , and the entire observed value of the target distance change rate is ▲ Z.
^k _D ▼, that is, Write.

From the above, from the theory of ordinary Kalman filter Is.

here In the prediction vector of x _k for the sampling time t _k of the original, than the Kalman filter theory to write in the conditional mean vector Is.

・ _k(+) Is sampling time t_kAgainstx _kSmoothness of
In vectorIs.

With a smooth vector of x _k for sampling time t _k under Is.

・ P _k (+) is the smooth error covariance matrix at the sampling time t _k , which is derived from the Kalman filter theory. Is.

_{^{· ▲ P a k ▼ (-}} ) hypothesis at the sampling time t _k The prediction error covariance matrix under Is.

_{^{· ▲ P a k ▼ (+}} ) hypothesis at the sampling time t _k With the smooth error covariance matrix under Is.

・ K _k is the gain matrix at the sampling time t _k .

Note that ^AT represents the transposed matrix of matrix A.

Also, in the same way as when applying the Kalman filter normally.
Initial value _{0 (+)}, P₀(+) Is determined separately
It

From the equation _{^{(19) ▲ P a k ▼}} (-) hypothesis Since it is a value that does not depend on, K _k from equation (21) and ▲ from equation (22)
P ^a _k ▼ (+) similarly hypothesis It does not depend on the value.

Hypothesis based on observation information up to sampling time t _k The reliability β _{k, a} of Write.

Markov property is assumed for the transition of the motion model. Ie the motion model Is independent of the motion model up to sampling time t _K-2 . At this time, the transition probability Pab of the motion model is Write.

hypothesis Evaluation of target position observation error under the condition fa _(K) (a = 1,2, ..., N). Is.

Here, g ( Z _K , a _K , A _K ) is the probability density at Z _K of the three-dimensional normal distribution of the mean vector a _K and the covariance matrix A _K.

As can be seen from equation (33), the observation vector of the target positionZ
_kIs the target position prediction vector H_K▲ ^a _K▼ Close to (-)
Th fa_(K)The value of becomes large and the goal is hypothesizedIt is highly evaluated that the user has exercised under Fig. 4
Is the evaluation value fa of the target position observation error_(K)In one dimension
In the figure, G is a horizontal line indicating the target position.
Axis, F is vertical axis showing probability density, Z is observation vectorZ _Kof
Target position, PA is hypothesisTarget predicted position, FA is probability density fa_(K), N is the average H_K▲
^a _K▼ (-) dispersion H_K▲ P^a _K▼ (-) ▲ H^T _K▼ + R_KBy
Is a normal distribution curve determined by

hypothesis The predicted value of the target distance change rate for the sampling time t _K under ▲ ^a _p ▼ _(K) , that is, If you write, from formula (15) Is.

here Is.

From equation (14) Is.

Moreover, if the first-order approximation is performed from the property of total differentiation, Is.

Where h_K(▲ ^a _K▼ (-) isofx _K= ▲ ^a _K▼ (-) is the valueIs.

From equation (11) and equation (37) Is.

Expression (39), Expression (23), Expression (12) and v _(K)Is white noise
From the assumptionTherefore, from equation (33)Is.

Formula (39), Formula (41), Formula (27), Formula (13) and From the assumption of white noise Is.

Hypothesis from equation (41) and equation (42) Of target distance change rate observation error under Is approximated by a one-dimensional normal distribution Is.

Here, g ₂ (l; m, n) is the probability density at 1 of the one-dimensional normal distribution with mean m and variance n.

Hypothesis at the time when observation information Z _K and _{o (K) at} sampling time t _K cannot be obtained The reliability P [ψ _{k, a} | Z ^K-1 ,, Z ^K-1 _D ▼] of the Is each hypothesis before sampling Because it can be obtained by changing more, From β _K-1 , b in equation (29), which is the reliability of, and Pab in equation (30), which is the transition probability Is obtained as.

Observed value of target position observation vector Z _K and target distance change rate
Hypothesis at the time when _{O (K)} was obtained Β _{K, a} is the reliability of the hypothesis when the observation vector Z _K cannot be obtained. Hypothesis Evaluation value fa _(K) based on the target position observation vector Z _K and evaluation value ▲ f ^a ₂ ▼ _(K) based on the target distance change rate observed value _{O (K)}
Value multiplied by, that is, equation (45), equation (31) and equation (4
From 3) It can be considered to be proportional to.

From the nature of probability Therefore, normalize equation (46) Is.

From equation (29) and Bayes' theorem Is.

From formula (24), formula (25) and formula (49) So Is.

From formula (50) and formula (20), formula (18), and formula (47) _K (+) = Φ_{K-1 K-1}(+) + Γ '_{K-1 K-1} ＋ K_K〔Z _K−H_K(Ф_{K-1 K-1 (+)}+ Γ '_{K-1 K-1})] ...
… (51).

here Using Bayes' theoremIs. _K (-) Is the sampling time t_KAgainstx _KThe prediction of
Khutor, ieThen, from equation (53) and equation (23)SoIs.

From the nature of probability Therefore, substituting equation (18) into equation (55) To get

From equation (45) and equation (57) Is.

As mentioned earlier, the hypothesis Error covariance matrix ▲ P ^a _K ▼ (+) is hypothesis Is a value that is determined regardless of And

Next, the operation of the tracking filter of the present invention will be described with reference to FIG.

It is assumed that the initial value is set in advance as in the case where the Kalman filter is normally applied to the tracking filter.

In the target observing device (1), the target distance change rate and polar coordinates
Observe gauge position information and convert target position information to Cartesian coordinates
Then, the observed value of the target distance change rate in equation (11)_OK)And expression
Target position observation vector of (9)Z _KIs output. Exercise mode
The position observation error evaluator (2) for each Dell
From the present value obtained from the predicted value calculator (7) for each
Of each motion model of equation (18) calculated before sampling
Measurement vector ▲ ^a _K▼ (-) is passed through the fourth delay circuit (12).
And input the target position prediction vector H_K▲ ^a _K▼ (-) is calculated
Obtained from the prediction error evaluator (10) for each motion model
Of the formula (19) calculated one sampling before the current time
Prediction error covariance matrix for each motion model ▲ P^a _K▼ (-)
Input through the second delay circuit (11)
Positional error covariance matrix H_K▲ P^a _K▼ (-) ▲ H^T _KCalculate ▼
Obtained from the observation model and the preset observation model
Target position observation noise covariance matrix R of equation (10)_KMore observation
vectorZ _KAnd target position prediction vector for each motion model
H_K▲ ^a _K▼ (−) difference covariance matrix H_K▲ P^a _K▼ (-) ▲
H^T _K▼ + R_KIs calculated and input from the target observing device (1)
Target position observation vectorZ _KMultiple motion models
With the evaluation value of the target position observation error, which is the degree of agreement with each other
Fa in a formula (31)_(K)Is calculated according to the equation (32). motion
The distance change rate observation error evaluator (14) for each model
Current time obtained from the predictive value calculator (7) for each dynamic model
Equation (18) motion model calculated one sampling before
Prediction vector for each ^a _K▼ (-) is the fourth delay circuit
Input through (12) and target distance according to equation (34) and equation (35)
Predicted rate of separation change ▲^a _p▼_(K)(38),
The transformation matrix h in equations (35) and (36)_K(▲ ^a _K▼ (-))
From the prediction error evaluator (10) for each motion model
The formula (1
9) Prediction error covariance matrix for each motion model ▲ P^a _K▼
Input (-) through the second delay circuit (11)
In equation (13) obtained from the observation model that has been set
Target distance change rate Observation noiseObserved value of target distance change rate_OK)And the predicted value_{p (K)}Difference
Of the formula (42), which is the variance ofAnd the target distance input from the target observing device (1)
Observed rate of change_OK)Each of multiple motion models
It is the evaluation value of the target distance change rate observation error
▲ f of certain formula (43)^a ₂▼_(K)Is calculated according to equation (44)
It In the reliability calculator (3) for each motion model,
Multiple motion models calculated one sampling before
Β in equation (29), which is the reliability for each_{K-1, a}The first
Input it through the delay circuit (4) and set it in advance.
The target observation information from the transition probability Pab of equation (30)Z _KOver
And_OK)Is the reliability of the motion model at the time when
Calculate the value of equation (45), and observe the target position with the value of equation (45).
vectorZ _KMotion, which is the degree of agreement with each motion model of
Input from the position observation error evaluator (2) for each model
Fa in formula (31)_(K)And target distance change rate_OK)Each exercise mode
Distance change rate for each motion model, which is the degree of agreement with Dell
▲ f of the equation (43) input from the observation error evaluator (14)^a ₂
▼_(K)The target position observation vector is weighted according to Eq. (48).
CuttleZ _KAnd target distance change rate_OK)At the time
Equation (29), which is the reliability of each of the multiple motion models of
Β of_{K, a}To calculate. Gain matrix calculator
In (5), it is obtained from the preset observation model.
Target position observation noise covariance matrix R of equation (10)_KAnd 1 service
Prediction error for each motion model calculated before sampling
Input from the difference evaluator (10) through the second delay circuit (11)
Error covariance matrix for each motion model ▲ P^a _K▼
(-) And smooth vector according to equation (21) _K(+)
Gain matrix K used for calculation_KTo calculate. Smoother (6)
Then, the smoothing of Eq. (24) calculated before 1 sampling
vector _K-1Insert (+) through the third delay circuit (8)
Φ by force constant velocity linear motion prediction_{K-1 K-1}Calculate (+)
Then, the reliability β of each motion model_{K, a}And preset
Constants that make up the multiple motion models of equation (5)
Speed vectorα _aThe target acceleration according to equation (52)
_K-1And estimate _K-1Is the term Γ ′ that affects the prediction_{K-1 K-1}Calculate
Formulas obtained from these and the target observation device (1)
Target position observation vector of (9)Z _KOn the other hand, smooth vector
Le _KObservation vector at (+)Z _KDegree of contribution
Gain obtained from the gain matrix calculator (5) that determines
Matrix K_KIs applied according to equation (51) and the smooth vector _K(+)
To calculate. Prediction value calculator (7) for each motion model
Is a smooth vector obtained from the smoother (6) _K(+)
More uniform linear motion prediction Φ_{K K}(+) Is calculated,
A set of preset motion models.
Number acceleration vectorα _aIs the term Γ ′ that affects the prediction_K α _aTo
Calculated and sampled one sampling after the current time
Tick t_{K + 1}Prediction vector for multiple motion models for
▲ ^a _{K + 1}▼ (-) is calculated according to equation (18). Exercise model
The smoothing error evaluator (9) for each
The prediction error for each motion model of equation (27)
Covariance matrix ▲ P^a _K▼ (-) is the prediction error evaluation for each motion model
Input from the price device (10) through the second delay circuit (11),
Matrix K obtained from gain matrix calculator (5)_KAnd by the formula
Smooth vector for each motion model in (25) ▲ ^a _K▼ (+)
The smoothing error evaluation value of
Sliding error covariance matrix ▲ P^a _K▼ (+) is calculated according to formula (22)
To do. Prediction error evaluator (10) for each motion model
Equation (2) obtained from the smoothing error evaluator (9) for each model
8) Smoothing error covariance matrix for each motion model ▲ P^a _K▼
(+) Is the smooth error covariance matrix of equation (26) according to equation (59)
P_KIt is regarded as (+) and it is a preset motion model
(8) driving noise covariance matrix Q_KAnd by the formula
According to (19), one sample after the current sampling
Time t_{K + 1}Prediction vector for each motion model for
Tor ▲ ^a _{K + 1}▼ Prediction error, which is the evaluation of (-) prediction error
Covariance matrix ▲ P^a _{K + 1}▼ (-) is calculated.

In the predicted value calculator (13), the smoother (6)
Smooth vector _KEnter (+) to predict constant velocity linear motion.
Φ_{K K}(+) Is calculated to calculate the reliability of each motion model
Reliability of each motion model of equation (48) obtained from device (3) β
_{K, a}From the transition probability Pab of equation (30) set in advance
Target position observation vectorZ _{K + 1}And target distance change rate
_{O (K + 1)}Of each motion model of equation (45) when
Degree of reliability Is calculated and this and a plurality of preset motion modes are calculated.
Constant acceleration vector of formula (5) that composes Dellα _a
ThanZ _{K + 1}as well as_{O (K + 1)}Target acceleration at the time when
DegreeAnd the term that this acceleration affects the prediction.By calculating
Predicted vector after pulling _{K + 1}Calculate (-).

〔The invention's effect〕

As described above, according to the present invention, it is possible to improve the accuracy of target motion parameter calculation at low cost without attaching a special additional device to the normal target automatic tracking device.

In the above, the case of a model in which a constant acceleration vector is added to the constant velocity linear motion model has been described. However, tracking that calculates the target motion parameters from the information of the target observation device with multiple motion models other than this Can be applied to filters.

[Brief description of drawings]

FIG. 1 is a diagram for explaining the configuration of an embodiment of the present invention, and FIG.
FIG. 4 is a diagram illustrating a conventional tracking filter, FIG. 3 is a diagram illustrating a constant acceleration vector, and FIG. 4 is a diagram illustrating a target position observation error evaluation value. In the figure, (1) is a target observation device, (2) is a position observation error evaluator for each motion model, (3) is a reliability calculator for each motion model, (4) is a first delay circuit, and (5) ) Is a gain matrix calculator, (6) is a smoother, (7) is a prediction value calculator for each motion model, (8) is a third delay circuit, (9) is a smoothing error evaluator for each motion model, (10) is the prediction error evaluator for each motion model, (11) is the second delay circuit, (1
2) is the fourth delay circuit, (13) is the predicted value calculator, (14)
Is a distance change rate observation error evaluator for each motion model. In the drawings, the same or corresponding parts are designated by the same reference numerals.

Claims (1)

[Claims] 1. A target observing device for observing target position information and a target distance change rate, a plurality of different motion models each composed of a plurality of constant vectors of the same dimension, and the target observing device. Match between the position observation error evaluator for each motion model that calculates the target position observation error evaluation value that is the degree of matching with the target position information, and each of the motion models and the target distance change rate input from the target observation device. Target distance change rate, which is the degree of observation error, The target position observation error for each of the above motion models calculated by the distance change rate observation error evaluator for each motion model and the position observation error evaluator for each motion model Evaluation value and distance change rate observation error for each movement model Evaluation target distance change rate observation error for each movement model calculated by the evaluator To calculate the reliability of each of the above exercise models, the reliability calculator of each of the exercise models, the gain matrix calculator of calculating the same gain matrix in each of the exercise models, and the reliability of each of the exercise models It is obtained by inputting the reliability of each of the above-mentioned motion models calculated by the calculator, the gain matrix calculated by the gain matrix calculator, and the target position information observed by the target observation device, and integrating the influence of each of the motion models. The smoothing device for calculating the smoothed value of the target motion data such as the target position and speed, and the smoothing value of the target motion data calculated by the smoother are input to input the position observation error evaluator for each motion model and the motion. Distance change rate for each model Calculation of predicted value for each motion model to calculate predicted value after one sampling of target motion specifications for each of the above motion models used in the evaluation error evaluator And, the reliability of each of the above-mentioned motion models calculated by the reliability calculator of each of the above-mentioned motion models and the smooth value of the target motion parameters calculated by the above-mentioned smoother are input to integrate the influence of each of the above-mentioned motion models. A predicted value calculator that calculates a predicted value after one sampling of the obtained target motion specifications and the gain matrix calculated by the gain matrix calculator are input and the error of the smoothed value of the target motion specifications for each of the above motion models is input. The smoothing error evaluator for each motion model to be evaluated and the smoothing error evaluation value for each of the above motion models calculated by the above smoothing error estimator for each motion model are input, and the distance change rate for each motion model is input through a delay circuit. Each of the motion models used by the observation error evaluator, the position observation error evaluator for each motion model, the gain matrix calculator, and the smoothing error evaluator for each motion model. A tracking filter, comprising: a prediction error evaluator for each motion model that evaluates an error in a target motion specification prediction value for each Dell.