JP7645834B2 - Tracking device, tracking method, and tracking program - Google Patents

Description

This disclosure relates to a tracking device, a tracking method, and a tracking program.

The tracking device estimates the target's motion parameters based on sensor information, updates the motion parameters for each observation time, and performs processing to estimate the target's position or path. The motion parameters include position, speed, acceleration, etc. The sensor information also includes observed values related to the target's motion parameters and the observation time at which the target was observed. In the prior art, as shown in Patent Document 1, an interacting multiple model (IMM) filter or a multi-interacting multiple model (M-IMM) filter is used as a filter that estimates motion parameters using multiple models.

In the IMM method, the future position of the target trajectory is predicted by incorporating multiple motion models in a single smooth calculation, and in order to improve the prediction accuracy, it is necessary to add more motion models. In addition, since it is necessary to ensure linearity for each motion model, it is difficult to incorporate multiple models with different parameters, such as incorporating a periodic model for meandering motion and an acceleration model for turning motion.
On the other hand, the M-IMM method is a parallelized version of the IMM method, and is capable of processing multiple nonlinear motion models in parallel.

JP 2020-144092 A

In the IMM filter, a motion model corresponding to each of all combinations for all patterns of parameters to be considered is created. Therefore, the more complex the target motion is, and the finer the pattern step size is, the more parallel calculations are required, resulting in a higher processing load.
Here, if the number of motion models is limited, the processing load is suppressed, but if the number of motion models is simply limited, the target motion will be approximated to a simple motion such as an acceleration model, etc. Therefore, if the number of motion models in the IMM filter is simply limited, the prediction accuracy of the target path will decrease, that is, the target tracking accuracy will decrease.

In addition, a variable structure IMM (VS-IMM: Variable Structure-Interacting Multiple Model) filter has been proposed as a derivative of the IMM filter. In the variable structure IMM method, the motion model used when estimating the motion parameters of a target is dynamically switched based on environmental constraints. As a result, relatively high tracking accuracy is achieved for motion accompanied by acceleration changes. However, in the variable structure IMM method, although the motion model is appropriately switched based on foresight information or expected values, the smooth error covariance and expected values of the motion model added by switching the motion model are reset. As a result, there is a concern that convergence may deteriorate after switching the motion model.

The present disclosure aims to provide a tracking device with relatively high target tracking accuracy and suppress switching of motion models even when the number of motion models in a filter having multiple motion models is limited.

The tracking device according to the present disclosure comprises:
A tracking device that estimates at least one of a position and a path of a moving target, comprising:
When each parameter of each motion model of a filter having a plurality of motion models is set as a target parameter, when predicting at least one of a position and a path of the target at a next target time using an observation value of the target at a current target time,
a model selection unit that determines whether or not the target parameter is to be a selected parameter based on a difference between a current value, which is a value corresponding to an observation value of the target at the current target time and corresponds to the target parameter, and a previous value, which is a value corresponding to a result of predicting at least one of a position and a path of the target at the previous target time and corresponds to the target parameter;
A smoothing unit sets the target parameter as a parameter of a motion model corresponding to the target parameter when the target parameter is set as the selected parameter, and sets the current value as a state quantity estimated by the filter when the target parameter is not set as the selected parameter.

According to the present disclosure, a value corresponding to an observed value is used for a parameter of a motion model based on the difference between the current value and the previous value. Therefore, although the number of motion models is limited, the decrease in target tracking accuracy is minor, and switching of motion models is suppressed. Therefore, according to the present disclosure, even if the number of motion models in a filter having multiple motion models is limited in a tracking device, it is possible to relatively increase the target tracking accuracy and suppress switching of motion models.

FIG. 1 is a diagram showing an example of the configuration of a tracking device 10 according to a first embodiment. FIG. 2 is a diagram showing an example of the hardware configuration of the tracking device 10 according to the first embodiment. FIG. 2 is a diagram for explaining a tracking system 9 according to the first embodiment. FIG. 2 is a diagram for explaining a tracking system 9 according to the first embodiment. FIG. 13 is a diagram for explaining the number of models in a conventional method. FIG. 4 is a diagram for explaining the number of models in the method according to the first embodiment. FIG. 4 is a diagram showing an example of a hardware configuration of a tracking device 10 according to a modified example of the first embodiment.

In the description of the embodiments and the drawings, the same elements and corresponding elements are given the same reference numerals. Descriptions of elements given the same reference numerals are omitted or simplified as appropriate. Arrows in the drawings primarily indicate data flow or processing flow. In addition, "part" may be interpreted as "circuit," "step," "procedure," "processing," or "circuitry" as appropriate.

Embodiment 1.
Hereinafter, the present embodiment will be described in detail with reference to the drawings.

***Configuration Description***
1 shows an example of the configuration of a tracking device 10 according to a first embodiment. The tracking device 10 includes a mixer 11, a smoother 12, an integrator 13, a model switching unit 14, and a model selector 15. The tracking device 10 estimates at least one of the position and the path of a moving target 60, and divides the parameters of the model using a technique that is a derivative of an IMM filter. The model is typically a motion model.

In the following description, the meanings of symbols and notations are as follows:
μ: model probability k: index representing sampling time t _k k-1: index representing previous sampling time t _k-1 π _ij : transition probability from model i to model j i, j: index for identifying model (i): calculation result in model i (j): calculation result in model j j|i: value of j calculated based on i x: target state quantity (position, speed, etc.)
P: Error covariance matrix Σ _j : Sum by index j ^: Predicted value ￣: Smoothed value (mixed processing result)
~ (tilde above the letter): Residual vector ': Transpose Q: System noise matrix H: Observation matrix R: Observation noise matrix F: State transition matrix S: Residual covariance matrix K: Kalman gain matrix L: Model likelihood N(z,a,A): Probability density function at z of a trivariate normal distribution with mean a and covariance matrix A
_km|kn : value at time km calculated based on data up to time kn dx: amount of change in state quantity th: threshold value specified by user

The mixer 11 receives an input from the smoother 12, and calculates a predicted value of each model probability and various values after mixing using the received input.
Specifically, the mixing unit 11 calculates the predicted value of the model probability shown in [Equation 1], the mixed model probability shown in [Equation 2], the mixed smoothed value shown in [Equation 3], and the mixed smoothed error covariance matrix shown in [Equation 4].

The smoothing unit 12 receives sensor information as an input, estimates a state quantity of the target at the next time and thereafter using a model and a filter, and outputs information indicating the estimated state quantity to each of the mixer 11 and the integrator 13. In this case, when each parameter of each motion model of a filter having a plurality of motion models is set as a target parameter, when predicting at least one of the position and the path of the target 60 at the next target time using the observation value of the target 60 at the current target time, the smoothing unit 12 sets the target parameter as a parameter of the motion model corresponding to the target parameter when the target parameter is set as a selected parameter, and sets the current value as a state quantity estimated by the filter when the target parameter is not set as a selected parameter. A specific example of the filter having a plurality of motion models is an interacting multiple model filter. The interacting multiple model filter includes a filter of a method of deriving an interacting multiple model. Specific examples of the method of deriving the interacting multiple model include M-IMM (Multi-Interacting Multiple Model) and VS-IMM (Variable Structure-IMM). A specific example of the current target time is the current sampling time. A specific example of the next target time is the next sampling time. Whether or not the target parameter is a selected parameter is determined by the model selection unit 15. The observed value is a value observed by the sensor device 70. The current value is a value corresponding to the observed value of the target 60 at the current target time, and is a value corresponding to the target parameter. The value corresponding to the observed value may be the observed value itself, or may be a value calculated based on the observed value.
Specifically, the smoothing unit 12 uses a model and a filter to predict the state quantity of the target as shown in [Equation 5], and calculates each of the prediction error covariance matrix shown in [Equation 6], the error vector of the observation vector shown in [Equation 7], the residual covariance matrix shown in [Equation 8], the Kalman gain matrix shown in [Equation 9], the smoothed value of the state quantity of the target as shown in [Equation 10], and the smoothed error covariance matrix of the state quantity of the target as shown in [Equation 11].

In addition, as an update process, the smoothing unit 12 calculates the model likelihood shown in [Equation 12] and the model probability shown in [Equation 13]. The calculation results of the update process are fed back to the mixing unit 11 by the delay process of the smoothing unit 12.

The integration unit 13 receives an input from the smoothing unit 12, and calculates an integrated smoothed value by integrating the smoothed values of each model based on the reliability corresponding to each model using the received input, calculates an integrated smoothed value by integrating the covariance matrices of each model based on the reliability corresponding to each model, and outputs information indicating each of the calculated integrated smoothed value and integrated smoothed covariance matrix to the model switching unit 14. At this time, the integration unit 13 calculates an integrated smoothed value by integrating the smoothed values corresponding to each motion model calculated when estimating at least one of the position and the path of the target 60 at the previous target time based on the reliability corresponding to each motion model. Here, the reliability is a value normalized by the observation error covariance for the difference between the matrix of the observed value, the observed value at one time before, and the matrix of the estimated value (predicted value) predicted using the motion model. The reliability is determined for each motion model. The integration unit 13 also calculates an integrated smoothed error covariance matrix by integrating the smoothed error covariance matrices corresponding to each motion model calculated when estimating at least one of the position and the path of the target 60 at the previous target time based on the reliability corresponding to each motion model. The previous target time is specifically the previous sampling time.
Specifically, the integrator 13 calculates an integrated smoothed value shown in [Equation 14] and an integrated smoothed error covariance matrix shown in [Equation 15].

The model switching unit 14 receives an input from the integration unit 13, calculates model selection information using the received input, and outputs information indicating each of the calculated model selection information to the model selection unit 15. Specific examples of the model selection information include observed values such as altitude and the direction of acceleration change. At this time, the model switching unit 14 selects a motion model of a filter used to predict at least one of the position and the path of the target 60 at the next target time based on the calculated integrated smoothed value and the calculated integrated smoothed error covariance matrix. The model switching unit 14 is also called a motion model switching unit.
Specifically, the integrated smoothed value and the integrated smoothed error covariance matrix are input to the model switching unit 14, and the model switching unit 14 calculates model selection information based on the input integrated smoothed value and integrated smoothed error covariance matrix.

The model selection unit 15 calculates the amount of variation based on the input from the model switching unit 14 and the sensor information, and determines the model and parameters to be used based on the calculated amount of variation. At this time, the model selection unit 15 determines whether or not to select the target parameter as a selected parameter based on the difference between the current value and the previous value. The previous value is a value corresponding to the result of predicting at least one of the position and the path of the target 60 at the current target time at the previous target time, and is a value corresponding to the target parameter. The model selection unit 15 is also called a motion model selection unit.
The model selection unit 15 sets the value corresponding to the observed value corresponding to a relatively large amount of fluctuation as the state quantity to be estimated by the filter, thereby making it possible to omit the model switching process that occurs due to value range constraints when estimating a state quantity using a model.
There are two methods for the model selection unit 15 to switch parameters:

(First switching method: switching based on threshold value)
The model selection unit 15 predetermines a threshold value for each parameter of the model, and compares the determined threshold value with the variation corresponding to the parameter at the target time. [Equation 16] shows the variation. As shown in [Equation 17], when the variation amount is less than the threshold value, the model selection unit 15 sets the parameter corresponding to the variation amount as the parameter of the model, and when the variation amount is equal to or greater than the threshold value, sets the value corresponding to the observation value corresponding to the parameter corresponding to the variation amount as the state amount estimated by the filter. That is, when the distance between the current value corresponding to the target parameter and the previous value corresponding to the target parameter is less than the threshold value, the model selection unit 15 determines that the target parameter is the selected parameter. As a specific example, the distance is the absolute value of the difference between the current value and the previous value.

(Second switching method: switching based on the number of state quantities)
The model selection unit 15 calculates the fluctuation rate per unit time at the target time for the value corresponding to each parameter, and compares each parameter based on the calculated fluctuation rate. The model selection unit 15 predetermines the number of parameters to be treated as the state quantity to be estimated by the filter, extracts a determined number of parameters corresponding to the fluctuation rates in descending order of the fluctuation rate, and sets the value corresponding to the observation value corresponding to the extracted parameter as the state quantity to be estimated by the filter. That is, the model selection unit 15 determines to select the target parameter as the selected parameter when the ranking of the magnitude of the fluctuation rate corresponding to the current value corresponding to the target parameter and the previous value corresponding to the target parameter is lower than a threshold value among the magnitudes of the fluctuation rates corresponding to each of all parameters of the motion model corresponding to the target parameter.

Figure 2 shows an example of the hardware configuration of the tracking device 10 according to this embodiment. The tracking device 10 is composed of a computer. The tracking device 10 may be composed of multiple computers.

As shown in the figure, the tracking device 10 is a computer equipped with hardware such as a processor 21, a memory 22, an auxiliary storage device 23, an input/output IF (Interface) 24, and a communication device 25. These pieces of hardware are appropriately connected via signal lines 29.

The processor 21 is an integrated circuit (IC) that performs arithmetic processing and controls the hardware of the computer. Specific examples of the processor 21 include a central processing unit (CPU), a digital signal processor (DSP), and a graphics processing unit (GPU).
The tracking device 10 may include a plurality of processors that replace the processor 21. The plurality of processors share the role of the processor 21.

The memory 22 is typically a volatile storage device, and a specific example is RAM (Random Access Memory). The memory 22 is also called a primary storage device or main memory. Data stored in the memory 22 is saved in the auxiliary storage device 23 as necessary.

The auxiliary storage device 23 is typically a non-volatile storage device, and specific examples thereof include a read only memory (ROM), a hard disk drive (HDD), or a flash memory. Data stored in the auxiliary storage device 23 is loaded into the memory 22 as necessary.
The memory 22 and the auxiliary storage device 23 may be integrated into one unit.

The input/output IF 24 is a port to which an input device and an output device are connected. As a specific example, the input/output IF 24 is a USB (Universal Serial Bus) terminal. As a specific example, the input device is a keyboard and a mouse. As a specific example, the output device is a display.

The communication device 25 is a receiver and a transmitter. A specific example of the communication device 25 is a communication chip or a NIC (Network Interface Card).

Each part of the tracking device 10 may use the input/output IF 24 and the communication device 25 as appropriate when communicating with other devices, etc.

The auxiliary storage device 23 stores a tracking program. The tracking program is a program that causes a computer to realize the functions of each part of the tracking device 10. The tracking program is loaded into the memory 22 and executed by the processor 21. The functions of each part of the tracking device 10 are realized by software.

Data used when executing the tracking program and data obtained by executing the tracking program are appropriately stored in the storage device. Each part of the tracking device 10 appropriately uses the storage device. As a specific example, the storage device is composed of at least one of the memory 22, the auxiliary storage device 23, a register in the processor 21, and a cache memory in the processor 21. Note that data and information may have the same meaning. The storage device may be independent of the computer.
The functions of the memory 22 and the auxiliary storage device 23 may be realized by other storage devices.

The tracking program may be recorded in a computer-readable non-volatile recording medium. Specific examples of the non-volatile recording medium include an optical disk and a flash memory. The tracking program may be provided as a program product.
The hardware configuration of the other devices according to this embodiment may be similar to the hardware configuration of the tracking device 10.

*** Operation Description ***
The operation procedure of the tracking device 10 corresponds to a tracking method, and the program that realizes the operation of the tracking device 10 corresponds to a tracking program.

3 shows a conceptual diagram of the tracking system 9. The tracking system 9 is composed of a target 60, a sensor device 70, a fire control device 80, a launcher 90, and a flying object 100, as shown in FIG.
The target 60 is a moving object that is to be tracked by the tracking device 10 .
The sensor device 70 has a function of detecting the position, speed, etc. of the target 60, and outputs information indicating the detection results to the fire control device 80. The sensor device 70 may also have a function of detecting the position, speed, etc. of the flying object 100.
The fire control device 80 outputs information for guiding the flying object 100 to the flying object 100 based on the sensor information acquired by the sensor device 70.
The launching device 90 is a device that launches the flying object 100 .
The projectile 100 is launched by a launcher 90 and flies based on the output from the fire control system 80 .

FIG. 4 shows a functional conceptual diagram of the tracking system 9.
The sensor device 70 captures the target 60, tracks the target 60, and outputs information indicating observed values such as the position and velocity of the target 60 detected at a certain time t to the tracking device 10.
The tracking device 10 predicts the position and velocity of the target 60 based on information indicative of the observations received from the sensor device 70 .
The fire control system 80 consists of a tracking device 10 and an interception guidance calculation unit 81.
The interception guidance calculation unit 81 calculates the guidance specifications of the flying object 100 using the output of the tracking device 10 and the output of the flying object sensor 103, and outputs information indicating the calculated guidance specifications to the guidance control unit 101.
The flying object 100 has a guidance control unit 101 , a flying unit 102 , and a flying object sensor 103 .
The guidance control unit 101 calculates a rotation command for flying the flying object 100 based on the information indicating the guidance specifications output by the interception guidance calculation unit 81, and outputs the calculation result to the flying unit 102.
The flying unit 102 generates physical acceleration for the flying object 100 based on information indicating the turning command output by the guidance control unit 101.
The missile sensor 103 outputs estimated values of the position and speed of the missile 100 to the interception guidance calculation unit 81.

The parameters estimated by the tracking device 10 include parameters indicating position, velocity, acceleration, jerk, aerodynamic coefficient, etc. According to conventional technology, a model corresponding to each combination of all combinations of patterns of these parameters is created as a model of the filter. Therefore, the number of models is the product of the number of patterns of each parameter. Here, the number of models corresponds to the number of parallel calculations in the IMM.

As a specific example, assuming that a model has five parameters and each parameter has five patterns, the number of models in the IMM method is ⁵⁵ , as shown in FIG.
On the other hand, as a specific example, consider a case where the model selection unit 15 uses the second switching method to estimate values corresponding to three parameters with relatively large fluctuation rates as state quantities. In this case, the number of parameters that the model has is two, and the number of models in this method is ⁵² , as shown in FIG.
The processing load is expressed by a function of the number of models. Therefore, the processing load according to the above-mentioned specific example is 5 ⁵ × (M3 filter) in the conventional IMM method, and 5 ² × (M3 filter) in the second switching method. Here, M3 is an abbreviation of Multiple Maneuver Model. In addition, model switching is suppressed by setting a value corresponding to a parameter corresponding to a relatively large amount of fluctuation as a state quantity estimated by the filter.

***Description of Effect of First Embodiment***
As described above, according to this embodiment, the parameters to be estimated based on the amount of variation are divided and processed separately into models and filters, thereby reducing the number of models to be processed simultaneously. Therefore, according to this embodiment, the calculation load can be reduced while ensuring tracking accuracy. Furthermore, according to this embodiment, since more parameters can be handled without approximating the movement of the target 60 to a simple movement, the movement of the target 60 can be expressed more precisely, and the movement of the target 60 can be estimated more precisely. Furthermore, according to this embodiment, the number of parallel processes can be reduced by reducing the number of models, thereby reducing the processing load.
Furthermore, in the conventional IMM filter, the range of values that each motion model can take is determined for the parameters that each motion model handles. Therefore, when the amount of variation in the parameter value is large, it is necessary to switch the motion model. Therefore, the conventional IMM filter is inferior in tracking the target 60. On the other hand, according to this embodiment, the value corresponding to the observation value corresponding to the parameter corresponding to a relatively large amount of variation is set as the state quantity to be estimated by the filter, so that the parameter is not restricted by the value range. Therefore, since the filter processing can be performed without switching the model according to the value range restriction, according to this embodiment, the tracking ability of the target 60 is relatively high.
This embodiment can be applied to IMM, M-IMM, and VS-IMM.

***Other configurations***
<Modification 1>
FIG. 7 shows an example of the hardware configuration of the tracking device 10 according to this modified example.
The tracking device 10 includes a processing circuit 28 in place of the processor 21 , the processor 21 and the memory 22 , the processor 21 and the auxiliary storage device 23 , or the processor 21 , the memory 22 , and the auxiliary storage device 23 .
The processing circuit 28 is hardware that realizes at least a portion of each unit of the tracking device 10.
The processing circuitry 28 may be dedicated hardware, or may be a processor that executes programs stored in the memory 22 .

When processing circuitry 28 is dedicated hardware, processing circuitry 28 may be, for example, a single circuit, a multiple circuit, a programmed processor, a parallel programmed processor, an ASIC (Application Specific Integrated Circuit), an FPGA (Field Programmable Gate Array), or a combination thereof.
The tracking device 10 may include a plurality of processing circuits that replace the processing circuit 28. The plurality of processing circuits share the role of the processing circuit 28.

In the tracking device 10, some functions may be realized by dedicated hardware, and the remaining functions may be realized by software or firmware.

Processing circuitry 28 is illustratively implemented in hardware, software, firmware, or a combination thereof.
The processor 21, the memory 22, the auxiliary storage device 23, and the processing circuit 28 are collectively referred to as the “processing circuitry.” In other words, the functions of the functional components of the tracking device 10 are realized by the processing circuitry.

***Other embodiments***
Although the first embodiment has been described, it is possible to combine a plurality of parts of the present embodiment. Alternatively, it is possible to partially implement the present embodiment. In addition, the present embodiment may be modified in various ways as necessary, and may be implemented in any combination, either as a whole or in part.
The above-described embodiment is essentially a preferred example, and is not intended to limit the scope of the present disclosure, its applications, and uses. The described procedure may be modified as appropriate.

9 Tracking system, 10 Tracking device, 11 Blending section, 12 Smoothing section, 13 Integration section, 14 Model switching section, 15 Model selection section, 21 Processor, 22 Memory, 23 Auxiliary storage device, 24 Input/output IF, 25 Communication device, 28 Processing circuit, 29 Signal line, 60 Target, 70 Sensor device, 80 Fire control device, 81 Intercept guidance calculation section, 90 Launching device, 100 Missile, 101 Guidance control section, 102 Missile section, 103 Missile sensor.

Claims (7)

A tracking device that estimates at least one of a position and a path of a moving target, comprising:
When each parameter of each motion model of a filter having a plurality of motion models is set as a target parameter, when predicting at least one of a position and a path of the target at a next target time using an observation value of the target at a current target time,
a model selection unit that determines whether or not the target parameter is to be a selected parameter based on a difference between a current value, which is a value corresponding to an observation value of the target at the current target time and corresponds to the target parameter, and a previous value, which is a value corresponding to a result of predicting at least one of a position and a path of the target at the previous target time and corresponds to the target parameter;
a smoothing unit that sets the target parameter as a parameter of a motion model corresponding to the target parameter when the target parameter is set as the selected parameter, and sets the current value as a state quantity estimated by the filter when the target parameter is not set as the selected parameter. The tracking device according to claim 1, wherein the model selection unit determines that the target parameter is to be the selected parameter when the distance between the current value corresponding to the target parameter and the previous value corresponding to the target parameter is less than a threshold value. The tracking device according to claim 1, wherein the model selection unit determines to select the target parameter as the selected parameter when the rank of the magnitude of the fluctuation rate corresponding to the current value corresponding to the target parameter and the previous value corresponding to the target parameter is lower than a threshold value among the magnitudes of the fluctuation rates corresponding to all parameters of the motion model corresponding to the target parameter. The tracking device further comprises:
an integration unit that calculates an integrated smoothed value by integrating smoothed values corresponding to each motion model calculated when at least one of the target position and the path was estimated at the previous target time based on a reliability corresponding to each motion model, and calculates an integrated smoothed error covariance matrix by integrating smoothed error covariance matrices corresponding to each motion model calculated when at least one of the target position and the path was estimated at the previous target time based on a reliability corresponding to each motion model;
The tracking device according to any one of claims 1 to 3, further comprising a model switching unit that selects a motion model of a filter used when predicting at least one of the position and the path of the target at the next target time based on the calculated integrated smoothed value and the calculated integrated smoothed error covariance matrix. The tracking device according to any one of claims 1 to 4, wherein the filter is an interacting multiple model filter. A tracking method in which a computer estimates at least one of a position and a path of a moving target, the method comprising the steps of: when each parameter of each motion model of a filter having a plurality of motion models is set as a target parameter, predicting at least one of a position and a path of the target at a next target time using an observation value of the target at a current target time,
the computer determines whether or not to set the target parameter as a selected parameter based on a difference between a current value, which is a value corresponding to an observation value of the target at the current target time and which corresponds to the target parameter, and a previous value, which is a value corresponding to a result of predicting at least one of a position and a path of the target at the previous target time and which corresponds to the target parameter,
The computer sets the target parameter as a parameter of a motion model corresponding to the target parameter when the target parameter is set as the selected parameter, and sets the current value as a state quantity estimated by the filter when the target parameter is not set as the selected parameter. A tracking program executed by a tracking device which is a computer that estimates at least one of a position and a path of a moving target, the tracking program comprising: a filter having a plurality of motion models, each of which has a parameter of the motion model; and a filter having the motion models, the filter having the plurality of motion models, the filter having the parameter of the moving target, the filter having the parameter of the motion model of the target, the filter having the parameter ...
a model selection process for determining whether or not the target parameter is to be a selected parameter based on a difference between a current value, which is a value corresponding to an observation value of the target at the current target time and corresponds to the target parameter, and a previous value, which is a value corresponding to a result of predicting at least one of a position and a path of the target at the previous target time and corresponds to the target parameter, at the previous target time;
a smoothing process for setting the target parameter as a parameter of a motion model corresponding to the target parameter when the target parameter is set as the selected parameter, and setting the current value as a state quantity estimated by the filter when the target parameter is not set as the selected parameter.

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