JP5560154B2 - Model parameter estimation apparatus and program thereof - Google Patents

Description

  The present invention relates to a model parameter estimation apparatus and its program for estimating model parameters by a sequential Monte Carlo method.

Conventionally, in a certain observation model, there is a sequential Monte Carlo method (particle filter, particle filter) as a method for estimating a current state from a past state. This sequential Monte Carlo method is a method in which past observation information is sequentially input, and a current state (model parameter) adapted to the observation model is sequentially calculated. That is, the sequential Monte Carlo method (particle filter, particle filter) sets a plurality of hypotheses (particles, particles) that are candidates for parameter solutions from observation information, and uses these hypotheses to calculate the probability distribution function of model parameters. Is estimated by Monte Carlo approximation (see Non-Patent Document 1).
On the other hand, the applicant of the present application has proposed a method of executing the sequential Monte Carlo method in an autonomous distributed environment (see Patent Document 1). In this method, each of a plurality of distributed agents (state estimation apparatuses) shares different observations and integrates state estimation via communication.

JP 2007-72709 A

A Doucet, N de Freitas and N Gordon: "Sequential Monte Carlo Methods in Practice," Springer, 2001. ISBN 978-0387951461.

However, in the sequential Monte Carlo method described in Non-Patent Document 1, when the model parameters are high-dimensional, or when the probability distribution of the model parameters is widely distributed in the parameter space, the number and dimension are sufficiently large. If this hypothesis is not used, the approximation accuracy of the Monte Carlo approximation will be insufficient.
As described above, the conventional sequential Monte Carlo method has a problem that if the approximation accuracy of the Monte Carlo approximation is insufficient, it falls into a local solution (local solution) and a global optimum solution cannot be obtained. In addition, if the number of hypotheses is increased in order to increase the approximation accuracy of the Monte Carlo approximation, there is a problem that the calculation load increases correspondingly and state estimation cannot be performed at high speed.

  On the other hand, the method of executing the sequential Monte Carlo method described in Patent Document 1 in an autonomous distributed environment enables parallel operation by distributing and integrating estimations of individual observations, and can estimate the state at high speed. Excellent in terms. However, as described above, even when there are many hypotheses, further contrivances are required for performing state estimation at high speed in each state estimation apparatus.

  The present invention has been made in view of the above problems, and it is an object of the present invention to provide a model parameter estimation apparatus and its program for performing state estimation at high speed and high accuracy by a sequential Monte Carlo method. .

  The present invention has been made to solve the above-mentioned problems. First, the model parameter estimation apparatus according to claim 1 is a model parameter estimation apparatus that estimates model parameters by a sequential Monte Carlo method. And a plurality of hypothesis processing means, control means, and representative value calculation means.

In such a configuration, the model parameter estimation apparatus generates new hypothesis data by sampling hypothesis data based on a proposed Monte Carlo method distribution that is a predetermined parameter distribution by a plurality of hypothesis processing means. The hypothesis data stored in the hypothesis storage means is updated together with the generation time of the hypothesis data . The proposed distribution of the sequential Monte Carlo method is a distribution whose distribution is already known. For example, a probability density function can be used as the proposed distribution. In this way, the hypothesis processing means generates hypothesis data whose distribution approximates the proposed distribution by sampling certain hypothesis data based on the proposed distribution.

At this time, the model parameter estimation device retains the state of whether or not the hypothesis processing means is in the process of updating the hypothesis data by the control means, and the hypothesis processing means that is not performing the update operation Based on the generation time of hypothesis data stored in the storage means, hypothesis data that has not been updated since the last update time is distributed, and a plurality of hypothesis processing means are operated. As a result, the plurality of hypothesis processing means are activated in parallel, generate new hypothesis data individually for each hypothesis data, and update the hypothesis data stored in the hypothesis storage means.
In this way, the model parameter estimation apparatus can sequentially assign unupdated hypothesis data to the hypothesis processing means that has finished updating hypothesis data early by the control means. Whether or not the hypothesis processing means is in the process of updating the hypothesis data may be determined by a general determination method such as setting a flag for the hypothesis processing means being processed.

Then, the model parameter estimation apparatus, the control means, hypothesis data that is stored in the hypothesis storage means, at a stage that is updated every hypothesis data since the last update time, the update time for the next update time update To do . As a result, the hypothesis data is updated at a certain point in time.

  Then, the model parameter estimation device calculates the statistical representative value of the plurality of hypothesis data stored in the hypothesis storage means as the estimated value of the parameter solution by the representative value calculation means. The timing for calculating the representative value may be any timing. For example, the representative value calculation means may be operated at a constant time interval or by an instruction signal from the outside.

Also, the model parameter estimation apparatus according to claim 2, in the model parameter estimation apparatus according to claim 1, in the hypothesis storage means in association with the hypothesis data store weight indicating the importance of the hypothesis data The hypothesis processing means includes a Monte Carlo sampling means, an observation simulation means, a likelihood evaluation means, and a weight update means.

  In this configuration, the model parameter estimation device samples and generates hypothesis data that is a candidate for a parameter solution based on the proposed distribution by the Monte Carlo sampling unit of the hypothesis processing unit. Then, the model parameter estimation device generates a simulated observation value, which is an observation value updated by a predetermined observation model, from the hypothesis data generated by the Monte Carlo sampling means by the observation simulation means of the hypothesis processing means.

  Then, the model parameter estimation device inputs the observation value from the outside by the likelihood evaluation means of the hypothesis processing means, the input observation value that is the observation value input at the present time, the simulated observation value generated by the observation simulation means, The likelihood indicating the degree of approximation is calculated. As for the degree of approximation between the input observation value and the simulated observation value, for example, if the observation value is a vector, it can be said that the closer the distance between vectors, the greater the degree of approximation. In this way, if the input observation value and the simulated observation value are approximated, it can be said that the hypothesis data that generated the simulated observation value is a more likely hypothesis.

Therefore, the model parameter estimation device uses the weight updating unit of the hypothesis processing unit to assign a weight based on the likelihood calculated by the likelihood evaluating unit so that the value becomes larger as the input observation value and the simulated observation value are closer to each other. Update.
Then, the model parameter estimation device calculates a representative value by performing a weighted average of the plurality of hypothesis data stored in the hypothesis storage unit based on the weight corresponding to the hypothesis data by the representative value calculation unit.

The model parameter estimation device according to claim 3 is the model parameter estimation device according to claim 1 or 2 , further comprising a resampling means.

  In such a configuration, the model parameter estimation device resamples the plurality of hypothesis data stored in the hypothesis storage unit by the resampling unit using a predetermined probability density distribution. In this way, by re-sampling with the probability density distribution, the hypothesis data is reorganized with a distribution close to the probability density distribution, and uneven distribution data can be eliminated.

The model parameter estimation device according to claim 4 is the model parameter estimation device according to claim 3 , wherein the control unit is configured to use a plurality of hypothesis data stored in the hypothesis storage unit as parameters. The resampling means is operated when it is unevenly distributed over a predetermined condition in the space.

  In such a configuration, the model parameter estimating device operates the resampling unit when the hypothetical data is distributed at a certain time interval or when a plurality of hypothetical data is unevenly distributed in the parameter space. As a result, the hypothesis data that is unevenly distributed can be eliminated.

Furthermore , the model parameter estimation device according to claim 5 is the model parameter estimation device according to claim 2 , further comprising a resampling means, wherein the control means stores a plurality of hypothesis data stored in the hypothesis storage means. The re-sampling means is operated when hypothesis data having a weight smaller than a predetermined minimum value exceeds a predetermined number.

  In such a configuration, when the hypothesis data with a small weight increases, the model parameter estimation device causes the control means to operate the resampling means, so that the hypothesis data is reorganized with a distribution close to the probability density distribution. Thus, hypothesis data having a small weight can be excluded.

The model parameter estimation program according to claim 6 is configured to cause a computer to function as a plurality of hypothesis processing means, control means, and representative value calculation means in order to estimate model parameters by a sequential Monte Carlo method. .

In such a configuration, the model parameter estimation program generates new hypothesis data by sampling hypothesis data based on a proposed Monte Carlo method distribution that is a predetermined parameter distribution by a plurality of hypothesis processing means. The hypothesis data stored in the hypothesis storage means is updated together with the generation time of the hypothesis data .
At this time, the model parameter estimation program retains the state of whether or not the hypothesis processing means is in the process of updating the hypothesis data by the control means, and applies the hypothesis to the hypothesis processing means not performing the update operation. Based on the generation time of hypothesis data stored in the storage means, hypothesis data that has not been updated since the last update time is distributed, and a plurality of hypothesis processing means are operated. As a result, the plurality of hypothesis processing means are activated in parallel, generate new hypothesis data individually for each hypothesis data, and update the hypothesis data stored in the hypothesis storage means.

Then, the model parameter estimation program, by the control means, hypothesis data that have been stored in the hypothesis storage means, at the stage that has been updated all the hypothesis data since the last update time, the update time in the next update time update To do .
Then, the model parameter estimation program calculates the statistical representative value of the plurality of hypothesis data stored in the hypothesis storage means as the estimated value of the parameter solution by the representative value calculation means.

The present invention has the following excellent effects.
According to the first and sixth aspects of the present invention, a plurality of hypothesis data by the sequential Monte Carlo method can be processed by each hypothesis processing means for each hypothesis data, and parallel processing can be realized. it can. As a result, according to the present invention, each hypothesis processing means can be operated by a parallel computer, a computer equipped with a multi-core CPU, etc., and even a large amount of hypothesis data can be calculated at high speed. It is possible to estimate parameters well.

Further , according to the first and sixth aspects of the present invention, it is possible to eliminate an empty state in which the hypothesis processing means is not operating, and it is possible to efficiently operate a plurality of hypothesis processing means. As a result, according to the present invention, the load is distributed to the hypothesis processing means capable of operating at higher speed according to the load state of each hypothesis processing means, so that the parameter can be estimated at high speed.

According to the second aspect of the present invention, since the weight can be added to the hypothesis data according to the observed value, the effectiveness of the hypothesis data can be added to the parameter estimation. Thus, according to the present invention, accurate parameter estimation is possible even when hypothesis data is small, and parameter estimation can be performed at higher speed.

According to the invention described in claims 3 to 5 , the hypothesis data can be reorganized with a distribution close to the probability density distribution. Thereby, the present invention prevents hypothesis data from being unevenly distributed in the parameter space, and can estimate an accurate parameter with less hypothesis data.

It is a block block diagram which shows the whole structure of the model parameter estimation apparatus which concerns on embodiment of this invention. It is a block block diagram which shows the structure of the hypothesis processing means of the model parameter estimation apparatus which concerns on embodiment of this invention. It is a figure which shows the content of the state management table of the hypothesis processing means which the control means of the model parameter estimation apparatus which concerns on embodiment of this invention manages. It is a figure which shows the memory content of the hypothesis memory | storage means of the model parameter estimation apparatus which concerns on embodiment of this invention. It is a flowchart which shows the whole operation | movement of the model parameter estimation apparatus which concerns on embodiment of this invention. It is a flowchart which shows hypothesis parallel processing operation | movement of the model parameter estimation apparatus which concerns on embodiment of this invention.

Embodiments of the present invention will be described below with reference to the drawings.
[Configuration of model parameter estimation device]
First, the configuration of the model parameter estimation apparatus according to the embodiment of the present invention will be described with reference to FIG. The model parameter estimation apparatus 1 sequentially estimates a parameter (model parameter) that matches a predetermined model based on an observation value of an observation target input from the outside.

Here, the observation target is a thing accompanied by a change in a state such as movement or fluctuation, or an event, and a person, a vehicle, etc. accompanied by a movement, a stock price accompanied by a fluctuation, or the like can be the target. For example, the model parameter estimation apparatus 1 can estimate a person's three-dimensional position, speed, and the like as model parameters by using a person as an observation target and using the position of the person in an image captured by a camera as an observation value. .
Here, the model parameter estimation device 1 estimates the model parameter x _t at a certain time t (for example, t is an integer). This time t is a physical time having a time dimension. It is also possible to use an index that simply represents a processing step. Hereinafter, for the sake of convenience, the expression “time” is used.

  Here, the model is a process capable of approximating a state (model parameter) estimated from an observation value of an observation target to a probability density distribution. The model parameter is one or more data obtained by internal processing of the model, and its mathematical expression such as a scalar, a vector, a matrix, a tensor, or a function is arbitrary. Here, a vector is used. To express.

Here, the model parameter estimation device 1, become candidates hypotheses data of the solution of the model parameters x _t at time t (hereinafter, referred to as the hypothesis) and K _t pieces (K _t is a natural number) generated, k-th time t ( The model parameter x _t shown in the following equation (1) is obtained by K _t pair of the hypothesis x _t ^{(k) of} k = 0, 1,..., K _t −1) and the weight w _t ^(k) for the hypothesis. Let us operate to approximate the probability density distribution p (x _t ). Note that δ is a Dirac delta function. Since the hypothesis x _t ^(k) is a model parameter candidate, it is data of the same dimension as the model parameter, and is expressed using a vector.

Hereinafter, with reference to FIG. 1, each structure of the model parameter estimation apparatus 1 is demonstrated.
As shown in FIG. 1, here, the model parameter estimation device 1 includes a control unit 10, a hypothesis storage unit 20, and a plurality (N) of hypothesis processing units 30 (30 ₁ , 30 ₂ ,..., 30 _N ). And a re-sampling means 40 and a representative value calculation means 50.

  The control means 10 performs access control of data (hypotheses, weights) to the hypothesis storage means 20, and progress status and end between a plurality of hypothesis processing means 30, resampling means 40 and representative value calculation means 50. Depending on the situation, operation control of each means and data exchange are performed.

Specifically, the control means 10 searches the hypothesis processing means 30 that is not operating (in an empty state) from the _N hypothesis processing means 30 ₁ , 30 ₂ ,. Scheduling is performed to distribute the K _t hypotheses (hypothesis group) stored in the hypothesis processing means 30 in an empty state for each hypothesis. Then, the control means 10 operates the re-sampling means 40 so as to re-sample the hypotheses performed by the hypothesis processing means 30 ₁ , 30 ₂ ,..., 30 _N , or calculates a representative value of the model parameter. In this way, control for operating the representative value calculating means 50 is performed.
Here, the control means 10 includes a hypothesis access control means 11, a hypothesis parallel processing control means 12, a resampling control means 13, and a representative value calculation control means 14.

  The hypothesis access control means 11 controls access (reading and writing) to hypotheses and weights stored in the hypothesis storage means 20. Here, the hypothesis processing means 30, the resampling means 40, the representative value calculation means 50, and each means in the control means 10 are connected to the hypothesis storage means 20 via the hypothesis access control means 11. Reading and writing are performed.

The hypothesis parallel processing control unit 12 searches for the hypothesis processing unit 30 in an empty state, and performs scheduling for allocating (distributing) a plurality of (K _t ) hypotheses stored in the hypothesis storage unit 20 for each hypothesis. is there.
The hypothesis parallel processing control unit 12 updates a hypothesis and weight at a time (t−1) that has not been updated among a plurality of hypotheses stored in the hypothesis storage unit 20 at a certain time t. The hypothesis processing means 30 in the empty state in which the hypothesis update processing is not performed is operated, and an identification number (for example, k-th) for specifying an unupdated hypothesis is notified. As a result, the hypothesis processing means 30 instructed to operate generates the kth hypothesis and weight at the time t from the kth hypothesis and weight at the time (t−1), and writes it to the hypothesis storage means 20. Update hypotheses and weights.

Incidentally, the hypothesis processing means _{30 1,} 30 2, ..., is whether 30 or _N is empty, it can be determined by a flag. For example, the hypothesis parallel processing control means 12 sets a flag corresponding to the hypothesis processing means 30 at the stage of instructing a certain hypothesis processing means 30 to update the hypothesis and weight, and at the stage of obtaining a notification of update completion, Reset the flag. For example, the hypothesis parallel-processing control unit 12, the state management table as shown in FIG. 3, the hypothesis processing means _{30 1,} 30 2, ..., or 30 _N are each operating state (e.g., "1"), the free A state indicating the state (for example, “0”) is associated with the state, and the state is held and managed. This state management table may be set in a memory or the like not shown. As shown in FIG. 3, the hypothesis parallel processing control means 12 sets which hypothesis is being processed as a hypothesis number k in the operating state.

As described above, the hypothesis parallel processing control unit 12 performs parallel processing for each hypothesis by the plurality of hypothesis processing units 30 by causing the hypothesis processing unit 30 in the empty state to sequentially update the hypotheses and weights. be able to.
Then, the hypothesis parallel processing control means 12 updates the time when all the hypotheses stored in the hypothesis storage means 20 are updated to the hypothesis at time t, which is the next time.
Here, the hypothesis parallel processing control means 12 notifies the resampling control means 13 to that effect when all the hypotheses stored in the hypothesis storage means 20 have been updated to the hypotheses at time t, When the hypothesis re-sampling is completed, the representative value calculation control means 14 is notified to that effect.

The resampling control means 13 performs activation control on the resampling means 40 for resampling a plurality of hypotheses (hypotheses group) stored in the hypothesis storage means 20.
This re-sampling control means 13 is in a stage when it is notified from the hypothesis parallel processing control means 12 that all the hypotheses stored in the hypothesis storage means 20 have been updated to the hypotheses at time t, that is, at a constant time interval ( Here, the resampling means 40 is activated at time t).

Note that the resampling means 40 does not necessarily have to be activated periodically. For example, the resampling control means 13 detects the states of a plurality of hypotheses (hypotheses group) stored in the hypothesis storage means 20. It may be activated when the state satisfies a predetermined condition.
For example, as this condition, the resampling control unit 13 activates the resampling unit 40 on the condition that the weight distribution in the hypothesis group stored in the hypothesis storage unit 20 is extremely unevenly distributed. Whether or not the weight distribution is unevenly distributed is determined based on the statistics of the weight value set stored in the hypothesis storage means 20 (for example, the variance of the weight value, the standard deviation of the weight value, the maximum value of the weight value) (E.g. difference between minimum values) and quantity calculated based on intra-class variance and inter-class variance when the weight set is divided into two classes using Otsu's binarization method (for example, inter-class variance and intra-class variance) The degree of separation defined by the ratio) can be determined.
The condition may be that the number of hypotheses having a weight smaller than a predetermined minimum value is greater than a predetermined number.

The representative value calculation control means 14 performs activation control on the representative value calculation means 50 that generates a representative value from a plurality of hypotheses stored in the hypothesis storage means 20.
The representative value calculation control means 14 is in a stage when it is notified from the hypothesis parallel processing control means 12 that the hypothesis stored in the hypothesis storage means 20 has been resampled, that is, at a certain time interval (here, time t ) Activates the representative value calculating means 50.

  The representative value calculation means 50 does not necessarily have to be started periodically. For example, when there is a request from a user who operates the model parameter estimation device 1, that is, through an input means not shown from the outside. It may be activated only when an instruction signal for outputting a representative value (estimated value) is input.

The hypothesis storage means 20 stores a plurality of model parameter hypotheses calculated by the hypothesis processing means 30 and a weight indicating the importance of the hypothesis in association with the time. The hypothesis storage means 20 can be composed of a general storage device such as a hard disk or a semiconductor memory. Here, the total number of hypotheses at time t is K _t (K _t is a natural number), the k th (k = 0, 1,..., K _t −1) hypothesis is x _t ^(k) , and the k th Let w _t ^(k) be the weight of. As shown in FIG. 4, the hypothesis storage means 20 stores a hypothesis, a weight, and a time when the hypothesis is generated in association with each hypothesis number indicating the kth.
In the initial state (time t = 0), it is assumed that K _t hypotheses and weights are stored in advance in the hypothesis storage unit 20.
The hypothesis and weight stored in the hypothesis storage unit 20 are read by the control unit 10 and updated by the control unit 10 when a new hypothesis and weight are generated by the hypothesis processing unit 30.

The hypothesis processing means 30 generates hypotheses and weights at the present time by performing sampling (sampling) based on a proposed distribution of a predetermined sequential Monte Carlo method from past hypotheses or observation values. The hypothesis processing means 30 is provided in a plurality (30 ₁ , 30 ₂ ,..., 30 _N ) and operates in parallel.
Further, each hypothesis processing means 30 ₁ , 30 ₂ ,..., 30 _N receives an identification number (here, the hypothesis x _t-1 ^(k) estimated at time (t−1) from the control means 10. By being notified of the hypothesis number k), the k-th hypothesis x _t ^(k) and the weight w _t ^(k) at time t are generated.

Here, the detailed configuration of the hypothesis processing means 30 will be described with reference to FIG.
As shown in FIG. 2, the hypothesis processing means 30 includes a Monte Carlo sampling means 31, an observation simulation means 32, a likelihood evaluation means 33, and a weight update means 34.

The Monte Carlo sampling unit 31 generates a hypothesis x _t ^(k) at time t from the ^k _- th hypothesis x _t-1 ^{(k) at} time (t−1) notified from the control unit 10. Note that the Monte Carlo sampling unit 31 uses the hypotheses x ₀ ^(k) , x ₁ ^(k) ,..., X _t−1 ^(k) before the time (t−1) notified from the control unit 10 and before the time t. observed value _{y 0,} y 1 in, ..., it is also possible to generate a hypothesis _x ^{t (k)} at time t from one or more of _{y t.}

Here, the Monte Carlo sampling means 31 is, for example, the observation value history (y ₀ , y ₁ ,..., Y _t ) and the hypothesis history (x ₀ ^(k) , x ₁ ^(k) ,..., X _t− ⁾ . ₁ ^(k) ), sampling is performed as shown in Equation (3) from a predetermined proposal distribution π shown in Equation (2) below, and hypothesis x _t ^(k) at time t is ^obtained . Generate.

Here, the proposed distribution is approximated using another distribution function (preferably a distribution function that can be sampled more easily) instead of extracting a sample (sample) directly from the corresponding model. It is a distribution function (Proposal distribution).
Here, sampling means to randomly select a sample from a population (hypothesis or history of observation values) so that the distribution is approximate to the proposed distribution π.
Here, the Monte Carlo sampling means 31 uses a probability density function p (prior transition probability) as shown in the following equation (4) as an example of the proposed distribution π.

For example, when generating a hypothesis x _t ^(k) at time t, the state transitions by a random walk of the variance-covariance matrix Σ _{v in which} the hypothesis x _t ^(k) is determined randomly (randomly). In this case, the Monte Carlo sampling unit 31 can use the probability density function p (x _t | x _t−1 ) of the following expression (5) as the probability density function p of the expression (4).

Here, the "dim" indicates the number of dimensions of information of the hypothesis _{x t.}
When this probability density function p is used, the Monte Carlo sampling unit 31 generates a hypothesis x _t ^(k) at time t from the hypothesis x _t-1 ^(k) notified from the control unit 10.

In this way, the Monte Carlo sampling means 31 generates a hypothesis x _t ^(k) at time t by sampling from a predetermined proposal distribution (or probability density function). Then, the Monte Carlo sampling unit 31 writes the generated hypothesis x _t ^(k) at time t to the hypothesis storage unit 20 via the control unit 10 and updates the hypothesis. Here, the Monte Carlo sampling means 31 outputs the generated hypothesis x _t ^(k) at time t to the observation simulation means 32.

The observation simulation unit 32 simulates (calculates) what observation value the hypothesis sampled and generated by the Monte Carlo sampling unit 31 is observed by the observation model modeled in advance.
Here, the observation simulation means 32 uses the observation model p (y _t | x _t ) as a model parameter (hypothesis x _t ^(k) ) at time t sampled and generated by the Monte Carlo sampling means 31. As shown in Equation (6), the k-th observation value y _t ^(k) is generated as a simulation result (simulation observation value).

More specifically, the observation model p, as shown in the following equation (7), defined as a model which simulated observations y _t is generated as a result of the calculated model parameter x _t by a function h _t May be.

For example, when the observation model is a constant acceleration motion model or a constant velocity motion model, this function h _t is a function for calculating the position at time t from the position at time (t−1) by the constant acceleration and constant velocity. is there. That is, the function h _t, depending on the observation model, it is sufficient to define the predetermined function.

In this way, the observation simulation unit 32 generates the simulated observation value y _t ^(k) by simulating the hypothesis sampled and generated by the Monte Carlo sampling unit 31 using the observation model. Then, the observation simulation means 32 outputs an observation value (simulation observation value y _t ^(k) ) as a result of simulation (calculation) to the likelihood evaluation means 33.

Likelihood evaluation means 33 is based on the observation value (input observation value) input from the outside, how much the simulation result (simulation observation value) generated by observation simulation means 32 is a likely result (how much) The likelihood indicating whether or not it is an approximate value is calculated.
Here, the likelihood evaluation unit 33, and the simulated observations y _{t ^(k)} at time t is generated simulated results observed simulator means 32, and an input observation value y _t at time t input from the outside The likelihood L _t ^(k) is calculated by comparison. The likelihood L _t ^(k) preferably takes a larger value as the simulated observation value y _t ^(k) and the input observation value y _t are closer.

For example, the likelihood evaluation means 33 can define the likelihood L _t ^(k) by a Gaussian function based on the Mahalanobis distance shown in the following equation (8).

Here, Σ _y is a variance covariance matrix for defining the Mahalanobis distance by normalizing the observation space, and T indicates transposition. As a result, the likelihood L _t ^(k) increases as the simulated observation value y _t ^(k) and the input observation value y _t are closer.

Further, for example, the likelihood evaluating means 33 may define the likelihood L _t ^(k) by an exponential function based on the Mahalanobis distance as shown in the following equation (9).

  In this way, the likelihood evaluation means 33 calculates the likelihood of the simulated observation value generated by the observation simulation means 32 from the input observation value. Then, the likelihood evaluation unit 33 outputs the calculated likelihood to the weight update unit 34.

The weight update unit 34 is based on the likelihood L _t ^(k) calculated by the likelihood evaluation unit 33, and the k-th weight w _t−1 ^(k ) at the time (t−1) notified from the control unit 10. ⁾ To generate a weight w _t ^(k) at time t and update the weight.
That is, if the likelihood L _t ^(k) calculated by the likelihood evaluation unit 33 is large, the weight update unit 34 increases the weight for the hypothesis that the hypothesis x _t ^{(k) at} the time t is more likely. If the likelihood L _t ^(k) is small, the weight for the hypothesis is decreased.

For example, if the Monte Carlo sampling means 31 generates a hypothesis x t (k) at time t from the proposed distribution π according to the expression (3), the weight updating means 34 is expressed by the following expression (10). , from the time the weight w t-1 (k) in the (t-1), to produce the weight w t (k) at time t.

Further, for example, if the Monte Carlo sampling means 31 generates the hypothesis x _t ^(k) at time t using the probability density function p as the proposed distribution π according to the above equation (5), the weight update means 34 Generates the weight w _t ^(k) at time t from the weight w _t-1 ^{(k) at} time (t−1) by the following equation (11).

Thus, the weight update unit 34 updates the weight w _t-1 ^(k) at time (t−1) based on the likelihood L _t ^(k) calculated by the likelihood evaluation unit 33, and A weight w _t ^(k) at _t is generated. Then, the weight update unit 34 writes the updated weight w _t ^(k) to the hypothesis storage unit 20 via the control unit 10 and updates the weight.

As described above, the hypothesis processing means 30 stores the hypothesis x _t-1 ^(k) and its weight w _t-1 ^(k) at the k-th time (t−1) notified from the control means 10 as a hypothesis memory. Read from the means 20, generate a new hypothesis x _t ^(k) and its weight w _t ^(k) at time t, and write them to the hypothesis storage means 20 via the control means 10.

The hypothesis processing means 30 is notified of other hypotheses and weights at time (t-1) from the control means 10 until all hypotheses at time (t-1) are processed in the control means 10. There is a case. Therefore, the hypothesis processing means 30, until the hypothesis of new time t is entered, it is assumed to hold the illustrated observations y _t to omit the storage means (memory).
Returning to FIG. 1, the description of the overall configuration of the model parameter estimation apparatus 1 will be continued.

The resampling means 40 reorganizes the hypotheses stored in the hypothesis storage means 20. Here, reorganizing a hypothesis means extracting the hypothesis again so that the hypothesis (model parameter) approximates a predetermined distribution. The re-sampling means 40 is assumed to be activated by the control means 10 at regular time intervals (here, time t).
Here, the resampling means 40 reads the data of K _t−1 pairs of hypotheses and weights at time (t−1) shown in the following equation (12) stored in the hypothesis storage means 20. The data is rearranged into K _t pairs of hypotheses and weights at time t shown in the following equation (13), and written in the hypothesis storage means 20. For example, K _t = K _t−1 = K _t−2 =... = K ₀ = constant [K] may be used.

At this time, it is preferable that the distribution (probability density distribution) approximated by Equation (13) to be reorganized and the distribution (probability density distribution) approximated by Equation (12) are similar to each other.
For example, the resampling means 40 generates the k-th new hypothesis x _t ^(k) by extracting a sample from the probability density distribution D (x) regarding x shown in the following equation (14).

Further, δ is a Dirac delta function.
Here, a method for extracting a sample from the probability density distribution D (x) will be described.
First, the resampling means 40 normalizes the weight w _t−1 ^(k) (k = 0, 1,..., K _t−1 −1) at time (t−1) and accumulates it with respect to k. The numerical sequence (Equation (15)) is calculated by the following Equation (16).

Next, the re-sampling means 40 uses the k-th (k = 0, 1,..., K _t −1) [K _t is a natural number, eg, K _t = K _t−1 = K _t−2 =. A sample u ^(k) of ₀ = constant [K]] is sampled from a continuous uniform distribution U of 0 or more and less than 1 as shown in the following equation (17).

This sample extraction is performed randomly using pseudo-random numbers, but a sample approximated to the distribution U can be extracted by normalizing the range that the pseudo-random numbers can take to be 0 or more and less than 1.
Then, the resampling means 40 generates the k-th new hypothesis x _t ^(k) by the following equation (18).

Further, the resampling means 40 sets a uniform value as shown in the following equation (19) as the new weight w _t ^(k) .

  As described above, the resampling means 40 resamples the hypotheses stored in the hypothesis storage means 20, so that the hypotheses are extremely unevenly distributed in the parameter space or there are many hypotheses with small weights. Can be prevented.

The representative value calculation means 50 obtains a representative value from the hypothesis stored in the hypothesis storage means 20 and outputs it as an estimated value of the model parameter. The representative value calculation means 50 is started by the control means 10 at a constant time interval (here, time t).
Here, the representative value calculation means 50 reads K _t pairs of hypotheses and weights at time t shown in the following equation (20) stored in the hypothesis storage means 20 and obtains representative values.

Here, the representative value calculating means 50 obtains a weighted average (weighted average) of the hypothesis by using the hypothesis and weight of the equation (20), and calculates the representative value x _rep and To do.

  The representative value calculation means 50 is not limited to the weighted average, and various values can be used as representative values by statistical processing. For example, the representative value calculating means 50 may obtain the representative value by other statistical processing such as using an arithmetic average of all hypotheses as a representative value, or using a hypothesis having the largest weight as a representative value.

By configuring the model parameter estimation device 1 as described above, even when a sufficient hypothesis that approximates the probability distribution is used when estimating model parameters by the sequential Monte Carlo method, a plurality of hypotheses are provided for each hypothesis. Since processing can be performed in parallel by the processing means 30, state estimation can be performed at high speed.
Note that the model parameter estimation device 1 can be operated by a program (model parameter estimation program) that causes a general computer to function as each of the above-described means.

[Operation of model parameter estimation device]
Next, the operation of the model parameter estimation apparatus according to the embodiment of the present invention will be described with reference to FIG.
First, the model parameter estimation device 1 initializes the time t by the hypothesis parallel processing control means 12 of the control means 10 (step S1). For example, the value “0” is set to the variable t as an initial value.

The model parameter estimation apparatus 1 is stored in the hypothesis storage unit 20 with respect to the plurality of hypothesis processing units 30 ₁ , 30 ₂ ,..., 30 _N by the hypothesis parallel processing control unit 12 of the control unit 10. Hypothesis parallel processing is performed in which the hypotheses and weights (hypothesis group) are shared and processed (step S2). In this hypothesis parallel processing, the hypothesis parallel processing control means 12 searches the hypothesis processing means 30 in the empty state, and a plurality of (K _t ) hypotheses stored in the hypothesis storage means 20 are replaced with the hypothesis processing means 30 in the empty state. , 30 _N , a plurality of hypothesis update means 30 ₁ , 30 ₂ ,..., 30 _N perform a plurality of hypothesis update processes in parallel.

Here, referring to FIG. 6 (refer to FIGS. 1 and 2 as appropriate for the configuration), the hypothesis parallel processing in step S2 will be described in detail.
In this step S2, first, the model parameter estimation apparatus 1, by hypothesis parallel-processing control unit 12 of the control means 10, the hypothesis processing means _{30 1,} 30 2, ..., idle state in the 30 _N, not processed It is determined whether or not the hypothesis processing means 30 exists (step S21). Here, the hypothesis processing means _{30 1, 30 2, ...,} 30 N is whether it is idle and be determined by the flag, the hypothesis parallel-processing control unit 12, in advance all hypotheses treated at an early stage Assume that a flag indicating that the means 30 ₁ , 30 ₂ ,..., 30 _N are empty is initialized (for example, “0”).

Here, if it is determined that there is no empty hypothesis processing means 30 (No in step S21), the hypothesis parallel processing control means 12 moves the operation to step S28.
On the other hand, if it is determined that there is an empty hypothesis processing means 30 (Yes in step S21), the hypothesis parallel processing control means 12 causes the hypothesis processing means 30 to execute the following hypothesis update processing.

First, the hypothesis parallel processing control unit 12 activates the hypothesis processing unit 30 in an empty state, and updates the ^kth hypothesis x _t-1 ^(k) and weight w _t-1 ^(k) at time (t−1). Instruct to do so. At this time, the hypothesis parallel processing control means 12 sets the flag corresponding to the hypothesis processing means 30 in the empty state to a value (for example, “1”) indicating that processing is in progress.

Then, the hypothesis processing means 30 reads the ^kth hypothesis x _t-1 ^(k) and the weight w _t-1 ^(k) at the time (t−1) notified from the control means 10 from the hypothesis storage means 20. (Step S22).
Then, the hypothesis processing means 30 determines the time at the time t from the kth hypothesis x _t-1 ^(k) and the weight w _t-1 ^{(k) at} the time (t−1) read from the hypothesis storage means 20 in step S22. A hypothesis updating process for generating the ^kth hypothesis x _t ^(k) and the weight w _t ^(k) is executed.

In other words, the hypothesis processing means 30 generates a new hypothesis x _t ^(k) at time t by sampling by the Monte Carlo sampling means 31 using a predetermined proposal distribution (or probability density function). (Step S23). For example, the Monte Carlo sampling means 31 generates a hypothesis x _t ^(k) by the probability density function p (x _t | x _t−1 ) shown in the above equation (5).

Then, the hypothesis processing means 30 determines what observation value (simulated observation value) the hypothesis x _t ^(k) sampled and generated in step S22 by the observation simulation means 32 is observed by the observation model. Simulation (calculation) is performed (step S24). For example, the observation simulation unit 32 calculates the simulated observation value y _t ^(k) by the calculation of the function h _t that defines the observation model in advance as shown in the equation (7).

Further, the hypothesis processing means 30 is based on the observation value (input observation value y _t ) input from the outside by the likelihood evaluation means 33 at the time t, and the simulated observation value y _t ^(k) calculated in step S24. Is a plausible result (step S25). For example, the likelihood evaluation means 33 calculates the likelihood L _t ^(k) for evaluating the hypothesis using a Gaussian function based on the Mahalanobis distance shown in the above equation (8).

The hypothesis processing means 30 then calculates a new weight w at time t from the weight w _t-1 ^{(k) at} time (t−1) based on the likelihood calculated at step S25 by the weight update means 34. _t ^(k) is generated (step S26). For example, the weight update unit 34 generates a new weight w _t ^(k) by multiplying w _t−1 ^(k) by the likelihood L _t ^(k) as shown in the equation (11).

Thereafter, the hypothesis processing means 30 stores the new hypothesis x _t ^(k) generated in step S23 and the new weight w _t ^(k) generated in step S26 via the control means 10 as a hypothesis memory. Write to the means 20 (step S27).

By the hypothesis update processing operation from step S22 to step S27, the hypothesis processing unit 30 causes the kth hypothesis x _t-1 ^(k) and the weight w _t− at the time (t−1) notified from the control unit 10. ₁ ^(k) is updated to the k-th hypothesis x _t ^(k) and weight w _t ^(k) at time t. At this time, the hypothesis processing means 30 notifies the control means 10 that the hypothesis processing has been completed. As a result, the hypothesis parallel processing control unit 12 of the control unit 10 sets the flag corresponding to the hypothesis processing unit 30 to a value (for example, “0”) indicating that the hypothesis processing unit 30 is in an empty state.

Then, the hypothesis parallel processing control means 12 refers to the hypothesis storage means 20, and the hypothesis x _t-1 ^(k) and the weight w _t-1 ^{(k) at} time ⁽ _t-1 ⁾ are all hypothesis x at time t. _It is determined whether or not _t ^(k) and weight w _t ^(k) have been updated (step S28).

  If it is determined that all hypotheses and weights have not been updated yet (No in step S28), the hypothesis parallel processing control means 12 returns to step S21 to update k (increment here) and operate. Continue. On the other hand, if it is determined that all hypotheses and weights have been updated (Yes in step S28), the hypothesis parallel processing control means 12 ends the hypothesis parallel processing operation at time t.

Here, after the determination in step S21, the steps S22 to S27 are sequentially operated, and then the procedure for performing the determination in step S28 has been described. However, the operation of the hypothesis processing means 30 from this step S22 to S27 is described individually. The hypothesis processing means 30 ₁ , 30 ₂ ,..., 30 _N may be operated individually in parallel.

  That is, the hypothesis parallel processing control unit 12 activates the hypothesis processing unit 30 in the empty state in step S21 and directs execution of the hypothesis update processing (steps S22 to S27) without waiting for completion of the processing. The process proceeds to step S28. As a result, the hypothesis update process (steps S22 to S27) operates in parallel.

At this time, even if the hypothesis parallel processing control means 12 does not determine in step S28 that all hypotheses and weights have been updated, the hypothesis processing means 30 has already been processed with respect to the K _t hypotheses. When the update process is instructed, the process does not proceed to step S21, but waits until all hypothesis processes are completed, and the operation of the hypothesis parallel process is terminated when the update of all hypotheses and weights is completed.

Through the operation in step S2, the hypotheses and weights stored in the hypothesis storage means 20 are all updated corresponding to the new time.
Returning to FIG. 5, the overall operation of the model parameter estimation apparatus 1 will be described.

  After step S2, the model parameter estimation apparatus 1 activates the resampling means 40 by the resampling control means 13 of the control means 10, and resamples the hypotheses stored in the hypothesis storage means 20 ( Step S3). The activated re-sampling means 40 re-samples the hypothesis by, for example, sampling the hypothesis from the hypothesis and weight stored in the hypothesis storage means 20 according to the probability density distribution shown in the equation (12). And generate new hypotheses and new weights.

  Thereafter, the model parameter estimation device 1 activates the representative value calculation means 50 by the representative value calculation control means 14 of the control means 10, calculates the representative value from the hypothesis stored in the hypothesis storage means 20, and The estimated value of the parameter is output (step S4). The representative value calculation means 50 calculates a representative value from the hypotheses and weights stored in the hypothesis storage means 20, for example, by the weighted average calculation shown in the equation (21).

Then, the model parameter estimation device 1 determines whether or not the process has been completed up to a predetermined final time by the control means 10 (step S5), and ends the operation when the process is completed (Yes in step S5). To do. On the other hand, if the process has not been completed until the predetermined final time (No in step S5), the model parameter estimation device 1 updates (increments) the time t (step S6), returns to step S2, and returns to the hypothesis. Continue the update process.
With the above operation, the model parameter estimation device 1 can perform the calculation for each hypothesis in parallel by the plurality of hypothesis processing means 30, and therefore can perform state estimation at high speed.

The configuration and operation of the model parameter estimation device 1 according to the embodiment of the present invention have been described above, but the present invention is not limited to this embodiment.
For example, in the model parameter estimation apparatus 1, the function of re-sampling hypotheses avoids the waste of hypotheses with too small weights and increases effective (not small weight) hypotheses. Although it is excellent in that it can reduce the risk of falling into, it is not always essential. When this hypothetical sampling function is omitted, the resampling control means 13 and the resampling means 40 may be omitted from the configuration.

  As described above, the model parameter estimation apparatus 1 according to the present invention can execute the sequential Monte Carlo method at high speed by the parallel calculation by the plurality of hypothesis processing means 30. Thus, by realizing parallel processing by the plurality of hypothesis processing means 30, the model parameter estimation device 1 can also be implemented by parallel hardware. This parallel processing is also suitable for multi-thread processing by computers equipped with multiple CPUs, multi-core, hyper-threading compatible CPUs, and parallel computing processing by cluster computers. Utilizing high-speed arithmetic processing becomes possible.

  In addition, the sequential Monte Carlo method that can be calculated by the model parameter estimation apparatus 1 is versatile, and can be widely applied to estimation of model parameters of physical phenomena such as weather, financial systems, and biological systems, for example. In addition, the model parameter estimation apparatus 1 can apply a sequential Monte Carlo method such as online learning in machine learning, inverse problem solving methods such as video / audio restoration processing, data fusion in measurement systems such as observers and sensor networks in control systems. Can be applied in the field.

DESCRIPTION OF SYMBOLS 1 Model parameter estimation apparatus 10 Control means 11 Hypothesis access control means 12 Hypothesis parallel processing control means 13 Resampling control means 14 Representative value calculation control means 20 Hypothesis storage means 30 Hypothesis processing means 31 Monte Carlo sampling means 32 Observation simulation means 33 Likelihood Degree evaluation means 34 weight update means 40 resampling means 50 representative value calculation means

Claims (6)

In the model parameter estimation device that estimates the parameters of the model by the sequential Monte Carlo method,
Hypothesis storage means for storing a plurality of hypothesis data as candidate solutions of the parameter in association with the generation time of the hypothesis data ;
A new hypothesis data is generated by sampling the hypothesis data based on the proposed Monte Carlo method distribution, which is a predetermined parameter distribution, and the hypothesis stored in the hypothesis storage means together with the generation time A plurality of hypothesis processing means for updating data;
Control means for operating the plurality of hypothesis processing means by distributing a plurality of hypothesis data stored in the hypothesis storage means to the plurality of hypothesis processing means;
Representative value calculation means for calculating representative values of a plurality of hypothesis data stored in the hypothesis storage means as estimated values of the solution of the parameter,
The control means holds the state of whether or not the hypothesis processing means is in the process of updating the hypothesis data, based on the generation time for the hypothesis processing means not performing the update operation, the hypothesis data that have not been updated in the last update time later distributed to the plurality of hypotheses processing means, the hypothesis storage means hypothesis that have been stored in the data has been updated, all the hypotheses data since the last update time A model parameter estimation device, wherein the update time is updated to the next update time in a step. The hypothesis storage means stores a weight indicating the importance of the hypothesis data in association with the hypothesis data,
The hypothesis processing means includes
Monte Carlo sampling means for sampling and generating hypothesis data that is a candidate for the parameter solution by the proposed distribution;
Observation simulation means for generating simulated observation values, which are observation values updated by a predetermined observation model, from hypothesis data generated by this Monte Carlo sampling means,
A likelihood evaluation unit that inputs an observation value from the outside and calculates a likelihood indicating a degree of approximation between the input observation value that is an observation value input at the present time and the simulated observation value generated by the observation simulation unit;
Based on the likelihood calculated by the likelihood evaluation means, the weight update means for updating the weight so that the value becomes larger as the input observation value and the simulated observation value are closer,
The representative value calculating unit calculates the representative value by performing a weighted average of a plurality of hypothesis data stored in the hypothesis storage unit based on a weight corresponding to the hypothesis data. Item 2. The model parameter estimation device according to Item 1 . Model parameters according to claim 1 or claim 2, further comprising a resampling unit for resampling the plurality of hypotheses data stored in the hypothesis storage means by a predetermined probability density distribution Estimating device. The control means operates the re-sampling means when a plurality of hypothesis data stored in the hypothesis storage means are unevenly distributed over a predetermined condition in a parameter space at a certain time interval. The model parameter estimation apparatus according to claim 3 , wherein Re-sampling means for re-sampling a plurality of hypothesis data stored in the hypothesis storage means with a predetermined probability density distribution;
In the plurality of hypothesis data stored in the hypothesis storage means, the control means resamples the hypothesis data when hypothesis data having a weight smaller than a predetermined minimum value exceeds a predetermined number. The model parameter estimation apparatus according to claim 2 , wherein the model parameter estimation apparatus is operated. To estimate the parameters of the model by the sequential Monte Carlo method,
In a hypothesis storage means for storing a plurality of hypothesis data that are candidates for the parameter solution in association with the generation time of the hypothesis data, the hypothesis data based on a proposed distribution of the sequential Monte Carlo method that is a predetermined distribution of the parameters the by sampling, to generate new hypotheses data, a plurality of hypotheses processing means to update the hypotheses data stored in the hypothesis storage means together with the generation time,
Control means for distributing the plurality of hypothesis data stored in the hypothesis storage means to the plurality of hypothesis processing means and operating the plurality of hypothesis processing means;
A representative value calculation means for calculating a representative value of a plurality of hypothesis data stored in the hypothesis storage means as an estimated value of the solution of the parameter;
The control means holds the state of whether or not the hypothesis processing means is in the process of updating the hypothesis data, based on the generation time for the hypothesis processing means not performing the update operation, the hypothesis data that have not been updated in the last update time later distributed to the plurality of hypotheses processing means, the hypothesis storage means hypothesis that have been stored in the data has been updated, all the hypotheses data since the last update time A model parameter estimation program that updates the update time to the next update time in a step.

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