JPH0769417B2 - Tracking filter - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION [Industrial application] The present invention inputs target position information including observation noise from a target observation device, and estimates a true value of a target position and target motion parameters such as velocity and acceleration. It relates to the tracking filter.

[Conventional technology]

Figure 4 shows, for example, IEEE TRANSACTIONS ON AEROSPACE AND E
LECTRONIC SYSTEMS VOL AES-13 No.3 MAY1977, P310〜P
317 `` MANEUVERING TRAGET TRACKING USING ADAPTIVE ST
FIG. 2 is a configuration diagram of a conventional tracking filter having a plurality of motion models indicated by “ATE ESTIMATION”, in which (1) is a target observation device that measures a target position including observation noise, and (2) is An observation error evaluator for each motion model for evaluating the observation error for each of the plurality of motion models, (3) is a reliability calculation of each motion model for calculating the reliability of each of the plurality of motion models , (4) is the first delay circuit, (5) is a gain matrix calculator for calculating the Kalman gain matrix used for calculating the smoothed value of the target motion data, and (6) is the smoothed value of the target motion data. Is a smoothing device for calculating, a (7) is a predictive value calculator for each motion model that calculates a predicted value of target motion data after one sampling from each of the plurality of motion models, and (8) is a third delay Circuit, multiple (9) A smooth error evaluator for each motion model that evaluates the smooth error that is the difference between the smooth value and the true value of each motion model. (10) shows the prediction error that is the difference between the predicted value and the true value of each of the motion models. Prediction error evaluator for each motion model to be evaluated, (11) is the second delay circuit,
(12) is a fourth delay circuit.

A conventional tracking filter having a plurality of motion models is configured as described above, and, for example, using fixed Cartesian coordinates, a model in which a constant acceleration vector independent of the sampling time is added to a constant velocity linear motion model is used. 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 observation error evaluator (2) for each motion model, the target position prediction vector calculated one sampling before the current time obtained from the prediction value calculator (7) for each motion model is set as the average vector of the target positions, and each motion model is calculated. Target position observation vector and target position prediction from the prediction error covariance matrix obtained from the prediction error evaluator (10) calculated 1 time before the present time and the observation noise covariance matrix obtained from the preset observation model The covariance matrix of the vector difference is obtained, and 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 assuming that the target position observation vector follows a three-dimensional normal distribution. In the reliability calculator (3) of each motion model, the reliability of each of the motion models calculated one sampling before the current time, and the transition probability of the motion model preset assuming Markov property in the motion model transition And observation error evaluator for each motion model (2)
The reliability of each of the multiple motion models is calculated from the observation error evaluation value input for each of the multiple motion models. 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 current time, the target observation device (1)
Target observation position and gain matrix calculator input from (5)
Based on the sum of constant acceleration vectors that make up a plurality of motion models weighted by the gain matrix and the reliability of each motion model (3) The smoothed value of the target position and the target speed is calculated. 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 from 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. In addition, target observation device (1)
Then, the predicted value of the target position after one sampling from the present time is calculated in Cartesian coordinates based on the smoothed values of the target position and the target speed input from the smoother (6), assuming that the target performs constant velocity linear motion, and the distance is calculated.・ Convert to polar coordinates of high angle and azimuth,
The target observation device (1) is oriented in the direction of the predicted value of the target position after one sampling from the present time.

[Problems to be solved by the invention]

In the conventional tracking filter as described above, the smoothed values of the target position and the target velocity calculated by the smoother (6) are the reliability for each of the plurality of motion models obtained by the reliability calculator (3) of each motion model. Although there is only a method for calculating the predicted value of the target position and target speed for each motion model, the target is a constant velocity straight line for one sampling from the present The predicted value was calculated as exercising. For this reason, the reliability of each motion model is not reflected in the prediction calculation.
Prediction value calculation accuracy deteriorates, for example, when the target observation device is a radar, there is no target in the beam even if the target observation device points in the direction of the prediction value of the target position, or there is no target in the range gate. There was a problem that the target position information could not be observed, and tracking was eventually lost.

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 problems]

The tracking filter of the present invention is configured to calculate the predicted values of target motion parameters by using the reliability of each constant acceleration vector forming a plurality of motion models.

[Action]

In the present invention, the reliability for each of the plurality of motion models and the constant acceleration vector forming the plurality of motion models are used to calculate the term of influence of acceleration in the prediction, and based on this term, the smoothed value at the present time is used. The predicted value is calculated by adding the predicted value after one sampling calculated by the constant velocity linear motion prediction to.

〔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 a predictive value calculator that predicts a value of the target motion data one sampling after the present time.

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 the target position vector in Cartesian coordinates is The target velocity vector in Cartesian coordinates And 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 at transformation matrix driving noise vector at sampling time t _k, for example, a truncation error term due to the assumed constant velocity linear motion target motion model gamma _{k -1} W _k-1 , W _k is equivalent to the acceleration vector, Is.

· U _k is a constant acceleration vectors constituting the N number of motion models at sampling time t _k, a _u k = alpha ₁ or u _k = alpha ₂ or ... or _{u k = α N (2)} , Γ k ' Is the transformation matrix of constant acceleration vector at sampling time t _k , Is.

Fig. 2 is a diagram for explaining the constant acceleration vector in the plane parallel to the horizontal plane. In the figure, O is the origin of the coordinate O-xy with the target observation device as the origin, and X is the east direction with the positive x-axis. X-axis of coordinate O-xy, Y is the y-axis of coordinate O-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. If the magnitude of the constant acceleration vector in Fig. 3 is 10g (g is the gravitational acceleration), and in addition to this, in the case of a motion model considering the constant acceleration vector, N = 5 ... (3), Equation (2) is And can be written regardless of the sampling time t _k .

Next, the hypothesis that u _k−1 = α _a (a = 1,2, ..., N) (5) is true at the sampling time t _k is given by Ψ _{k, a} (a = 1,2, …, N) Write (6).

E is a symbol representing the mean, and W _k is a three-dimensional normally distributed white noise with mean 0. E [ W _k ] = 0 (7) E [ W _k W ₁ ^T ] = Q _k (when k = 1 ), OI (when k ≠ 1)
… (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 observation model is z _k = H _k x _k + v _k (9).

Here, · z _k 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 = the observation matrix at sampling time t _k (I OI).

・V _k is an observation noise vector at the sampling time t _k , and is a three-dimensional normally distributed white noise with an average of 0 E [ v _k ] = 0 E [ v _k v ₁ ^T ] = R _k (when k = 1) , OI (when k ≠ 1)
… (10).

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

Also, the entire observation vector from sampling time t ₁ to t _k is written as Z _k , that is, Z _k = [ z ₁ , z ₂ , ..., Z _k ] ... (11).

From the above, according to the usual theory of Kalman filter, ^a _k▼ (-) = Φ_{k-1 k-1}(+) + Γ ′_k-1α_a ......
(12) ▲ P^a _k▼ (-) = Φ_k-1P_k-1(+) ▲ Φ^T _k-1▼ + Γ_k-1Q
_k-1▲ Γ^T _k-1▼ …… (13) ▲ ^a _k▼ (＋) ＝ ▲ ^a _k▼ (-) + K_k(z _k−H_k▲ ^a _k
▼ ()) …… (14) K_k= ▲ P^a _k▼ (-) ▲ H^T _k▼ (H_k▲ P^a _k▼ (-) ▲ H^T _k
▼ + R_k)^-1 …… (15) ▲ P^a _k▼ (+) = ▲ P^a _k▼ (-)-K_kH_k▲ P^a _k▼ (-)
(16) (a = 1,2, ..., N)

Where: ▲ ^a _k▼ (-) is hypothesis Ψ_{k, a}Observation vector under
z ₁,z ₂, ...,z _k-1Than x_kConditional with prediction vector of
If you write it as an average vector, it is based on the theory of Kalman filter ▲ ^a _k▼ (-) = E [x _k| Ψ_{k, a}, Z^k-1]… (17)

・ _k(+) Is the observation vectorz ₁,z _Two…z _kThanx _k
With the smooth vector of _k (+) = E [x _k| Z^k] …… (18)

・ ▲ ^a _k▼ (+) is hypothesis Ψ_{k, a}Observation vector under
z ₁,z ₂, ...,z _kThanx _kWith the smooth vector of ▲ ^a _k▼ (+) = E [x _k| Ψ_{k, a}, Z^k] …… (19).

・ P_k(+) Is sampling time t_kCovariance of the smooth error at
It is a dispersion matrix, and from the theory of Kalman filter P_k(+) = E [(x _k− _k(+)) (x _k−
_k(+)) T | Z^k] ... (20).

・ ▲ P^a _k▼ (-) is sampling time t_kHypothesis Ψ at
_{k, a}Prediction error covariance matrix under^a _k▼ (-) = E [(x _k-▲ ^a _k▼ (-)) (x _k
-▲ ^a _k▼ (−)) T | Ψ_{k, a}, Z^k-1}… (21).

・ ▲ P^a _k▼ (+) is sampling time t_kHypothesis Ψ at
_{k, a}Is the smooth error covariance matrix under^a _k▼ (+) = E [(x _k-▲ ^a _k▼ (+)) (x _k
-▲ ^a _k▼ (+)) T | Ψ_{k, a}, Z^k}… (22).

・ 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
To do.

Equation (13) from ▲ P ^a _k ▼ (-) since the value that does not depend on the hypothesis Ψ _{k, a, K k} from equation (15), equation (16) from ▲ P ^a _k ▼ (+)
Also becomes a value that does not depend on the hypothesis Ψ _{k, a} .

Hypothesis Ψ when the observation vectors z ₁ , z ₂ , ..., z _k are obtained
_k, by the reliability β _{k, a} conditional probability density function of _{a β k, a} = P [Ψ _{^k, a} | Z _k] ...... (23) (a = 1,2 , ... N) to write.

Markov property is assumed for the transition of the motion model. That is, the motion model Ψ _{k, a} is determined from the motion model at the sampling time t _k-1 and does not depend on the motion model up to the sampling time t _k-2 . At this time, the transition probability P _a b of the motion model is P _a b = P [Ψ _{k, a} │Ψ _{k−1, b} ] ... (24) (a = 1,2, ..., N; b = 1,2 ,…, N) is written.

Hypothesis Ψ_{k, a}Evaluation of observation error under_a(K) (a = 1,2, ..., N) …… (25) is approximated by a three-dimensional normal distribution, the theory of Kalman filter
Than f_a(K) = g (z _k; H_k▲ ^a _k▼ (-), H_Kp^a _k(-) ▲
H^T _k▼ + R_k … (26).

Where g ( z _k ; a _k , A _k ) is the mean vector a _k , the covariance matrix
It is the probability density in z _k of the three-dimensional normal distribution of A _k .

As can be seen from equation (26), the observation vector of the target positionz
_kIs the target position prediction vector H_k▲ ^a _k▼ Close to (-)
Th f_aThe value of (k) becomes large and the goal is hypothesis Ψ._{k, a}Under
The reliability of having exercised is highly evaluated. Figure 3 shows incorrect observation
Difference evaluation value f_aIt is a figure explaining (k) in one dimension.
In the figure, G is the horizontal axis representing the target position, and F is the probability density.
Degree of vertical axis, Z is the observation vectorz _kThe goal shown by
Where PA is the hypothesis Ψ_{k, a}Target predicted position under
Degree f_a(K), N is the average H_k▲ ^a _k▼ (-) dispersion H_k▲ P^a _k▼
(-) ▲ H^T _k▼ + R_kIs a normal distribution curve determined by
It Observation vector z_kHypothesis Ψ at the time when is not obtained
_{k, a}Reliability P {Ψ of_{k, a}| Z^k-1} Is tentative from the Markov property.
Theory Ψ_{k, a}Is each hypothesis Ψ before one sampling_{k-1, b}(B = 1,
2,…, N)_{k-1, b}Reliability of
Β in equation (23) that is_{k-1, b}And the transition probability equation (2
4) P_afrom bIs obtained as.

Reliability beta _{k, a} hypothesis [psi _{k, a} at the time of the observation vector z _k is obtained, the observation vector z _k is hypothesized Never point obtained [psi _{k, a} reliability P [[psi _{k, a} | [z ^k-1 ] is multiplied by the evaluation value f _a (k) of the hypothesis Ψ _{k, a based on} the observation vector z _k , that is, from equations (27) and (25), It can be considered to be proportional to.

From the nature of probability Therefore, normalize equation (28) Is.

From equation (23) and Bayes' theorem Is.

From equation (18), equation (19) and equation (31) So Is.

From equation (32) and equation (14), equation (12), and equation (29) _k (+) = Φ_{k-1 k-1}(+) + Γ ′_{k-1 k-1}＋ K_k〔z
_k−H_k(Φ_{k-1 k-1}(+) + Γ ′_{k-1 k-1})] …… (3
3)

here, Is.

Using Bayes' theoremIs. _k (-) Is the observation vectorz ₁,z ₂, ...,z _k-1Thanx
_kThe prediction vector of, ie _k (-) = E [x _k| Z^k-1] (36) From equations (35) and (17),Is.

From the nature of probability Therefore, substituting equation (12) into equation (37) To get

From equation (27) and equation (39) Is.

Note that error covariance matrix under the assumption as mentioned above ^{_{Ψ k, a ▲ P a k}} ▼ (+) Since values determined independent of the hypothesis _{Ψ k, a P k (+} ) = ▲ P ^a _k ▼ and (+) (41).

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 previously determined in the same manner as when the Kalman filter is normally applied to the tracking filter.

The target observation device (1) observes the target position information in polar coordinates.
Then, the result is converted into target position information in Cartesian coordinates,
Observation vector Z of (9)_kIs output. For each exercise model
The observation error evaluator (2) calculates the predicted value for each motion model.
One sampling before the current time obtained from the output device (7)
Predicted vector for each calculated motion model of equation (12) ▲
^a _k▼ (-) is input through the fourth delay circuit (12) and the target
Position prediction vector H_k▲ ^a _k▼ (-) is calculated and the motion model
From the present time obtained from the prediction error evaluator (10) for each
For each motion model of equation (13) calculated before 1 sampling
Prediction error covariance matrix ▲ P^a _k▼ (-) is the second delay circuit
(11) and input the predicted position error for each motion model.
Covariance matrix H_k▲ P^a _k▼ (-) ▲ H^T _k▼ is calculated and this
In equation (10) obtained from the observation model that has been set
Observation noise covariance matrix R_kMore observation vectorz _kAnd exercise model
Target position prediction vector H for each_k▲ ^a _k▼ (-) difference
The covariance matrix is calculated and input from the target observing device (1).
Observation vectorz _kFor each of the multiple motion models of
F in Eq. (25) that is the evaluation value of the observation error_a
(K) is calculated according to the equation (26). Trust of each movement model
In the degree calculator (3), sampling time t_k-1Calculated by
An expression that is the reliability for each of a plurality of motion models
Β in (23)_{k-1, a}Input through the first delay circuit (4)
And the transition probability of this and the preset equation (24)
P_aobservation vector from bz _kExercise at the time when
Calculate the value of equation (27), which is the reliability of the model, and
Observation vector to the value ofz _kDegree of agreement with each motion model of
Input from observation error evaluator (2) for each motion model
F in Equation (25)_a(K) is weighted according to equation (30).
Observation vectorz _kMultiple motion modes at the time
Β in equation (23), which is the reliability of each Dell_{k, a}Calculate
It In the gain matrix calculator (5), preset
(10) observed noise covariance line obtained from the observed model
For each row and exercise model calculated one sample before
Of the second delay circuit (11) from the prediction error evaluator (10) of
Prediction error covariance matrix for each motion model input as
P^a _k▼ (-) and smooth vector according to equation (15) _k
(+) Gain matrix K used for calculation_kTo calculate. In addition,
From equation (13), the prediction error covariance matrix for each motion model ▲ P
^a _k▼ (-) is a value that does not depend on the motion model.
Gain matrix K from (15)_kAlso depends on the luck model
It In the smoother (6), calculate it before 1 sampling
Equation (18) smooth vector _k-1(+) Is the third delay time
Input through the road (18) and predict Φ by constant velocity linear motion prediction_k-1
k-1(+) Is calculated and the reliability calculator of each motion model
The reliability β of each motion model of Expression (30) obtained from (3)
_{k, a}And a plurality of motion modes of equation (5) set in advance.
Constant acceleration vector that composes Dellα _aThe expression (3
4) Target acceleration according to _k-1And estimate _k-1Is in the forecast
Resonating Γ ′_{k-1 k-1}And the target observation device
Observation vector of equation (9) obtained from (1)z _kAgainst
Smooth vector _kObservation vector in (+) calculation
z _kGain matrix calculator (5) for determining the degree of contribution of
Gain matrix K obtained by_kIs applied according to equation (33) and smoothed
vector _kCalculate (+). Prediction for each motion model
The value calculator (7) uses the smooth vector obtained from the smoother (6).
Cuttle _kΦ from (+) based on constant velocity linear motion prediction_{k k}
(+) Is calculated, and multiple preset motion modes are calculated.
Constant acceleration vector that composes Dellα _aInfluences prediction
Term Γ ′_k α _aIs calculated and after one sampling from the current time
Sampling time t_{k + 1}Multiple motion models for
Prediction vector with ^a _{k + 1}▼ (-) is calculated according to formula (12)
Put out. In the smoothing error evaluator (9) for each motion model, 1
The motion model of equation (21) calculated before sampling
Prediction error covariance matrix for each ▲ P^a _k▼ (-) is a motion model
Prediction error evaluator (10) for each second delay circuit (11)
Input from the gain matrix calculator (5)
Gain matrix K_kBy and, the flatness for each motion model in Eq.
Smooth vector ▲ ^a _k▼ (+) is the evaluation value of the smoothing error.
Smooth error covariance matrix for several motion models ▲ P^a _k▼
(+) Is calculated according to equation (16). Equation (13), equation
From (15) and (16), the smooth error covariance for each motion model
Matrix ▲ P^a _k▼ (+) is a value that does not depend on the motion model.

The prediction error evaluator (10) for each motion model
Of the equation (22) obtained from the smooth error evaluator (9) for each
Smooth error covariance matrix for each motion model ▲ P^a _k▼ (+)
According to equation (41), the smooth error covariance matrix P of equation (20)_k(+)
And obtained from a preset motion model.
Driving noise covariance matrix Q of equation (8)_kAnd by the formula (13)
Therefore, from the present time, the sampling time t after one sampling
_{k + 1}Prediction vector for multiple motion models for
^a _{k + 1}▼ (-) prediction error covariance, which is the evaluation of the prediction error
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 (30) obtained from device (3)
β_{k, a}And the transition probability P of equation (24) set in advance_ab
Observation vectorz _{k + 1}(27) at the time when is not obtained
Reliability of each motion modelIs calculated and this and a plurality of preset motion modes are calculated.
Constant acceleration vector of formula (5) that composes Dellα _a
More observation vectorz _{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 (-). Na
In the target observation device (1), the target position
Predicted value H_{k + 1 k + 1}(−) Is calculated and H_{k + 1 k + 1}(-) To the distance
・ Converted to polar coordinates of high angle and azimuth, and 1
The target observing device (1) points in this direction after sampling.
It

〔The invention's effect〕

As described above, according to the present invention, it is possible to improve the accuracy of target motion specification calculation 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, but the target motion parameters are calculated from the information of the target observation device with multiple motion models other than this. Applicable to tracking 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 for explaining a constant acceleration vector, FIG. 3 is a diagram for explaining an observation error evaluation value, and FIG. 4 is a diagram for showing a conventional tracking filter. In the figure, (1) is a target observation device, (2) is an observation error evaluator for each motion model, (3) is a reliability calculator of each motion model, (4) is a first delay circuit, (5) Is a gain matrix calculator, (6) is a smoother, (7) is a predicted value calculator for each motion model, (8) is a third delay circuit, (9) is a smoothing error evaluator for each motion model, ( 10) is a prediction error evaluator for each motion model, (11) is a second delay circuit, (12) is a fourth delay circuit, and (13) is a prediction value calculator. 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,
An observation error for each motion model that calculates an observation error evaluation value that is the degree of agreement between each of a plurality of different motion models composed of a plurality of constant vectors of the same dimension and the target position information input from the above target observation device Input the observation error evaluation value for each of the above motion models from the evaluator and the observation error evaluator for each of the motion models, and calculate the reliability of each of the motion models, and the reliability of each motion model, and the above. A gain matrix calculator that calculates a common gain matrix for each motion model, the latest target position information input from the target observation device, and the reliability of each motion model calculated by the reliability calculator of each motion model And a target position, velocity, acceleration, etc. obtained by integrating the influence of each motion model using the gain matrix calculated by the gain matrix calculator. Input the smoother for calculating the smoothed value of the motion parameters and the smoothed value of the target motion parameter calculated by the smoother, and calculate the predicted value of the target motion parameter for each of the above motion models after one sampling. , And the predicted value calculator for each motion model that outputs the predicted value to the observation error evaluator for each motion model, and the gain matrix from the gain matrix calculator, and the target motion parameters for each of the motion models The smoothed error evaluator for each motion model that evaluates the error in the smoothed value of the For each motion model, the evaluation value of the prediction error is output to the gain matrix calculator, the smoothing error evaluator for each motion model, and the observation error evaluator for each motion model. The influence of each motion model is integrated using the prediction error evaluator, the reliability of each motion model calculated by the reliability calculator of each motion model, and the smooth value of the target motion parameter calculated by the smoother. A tracking filter, comprising: a prediction value calculator that calculates a prediction value after one sampling of the target motion data obtained by the above.