WO2021059331A1 - Smoothing filter device and smoothing method - Google Patents

Abstract

This smoothing filter device (1) calculates, using a tracking index, a driving noise standard deviation at each observation time so that smoothing error standard deviations that respectively correspond to a plurality of observation methods reach the same value, and performs, using the calculated driving noise standard deviation, a smoothing process on time-series data of observed values.

Description

Smoothing filter device and smoothing method

The present invention relates to a smoothing filter device and a smoothing method for smoothing time-series data of observed values.

Conventionally, the smoothing filter has been used to smooth the time-series data of the observed values for the purpose of suppressing the variation in the time-series data of the observed values observed by the sensor. For example, Non-Patent Document 1 describes a Kalman filter, which is one of smoothing filters. For the smoothing process, the information of the observation error covariance matrix and the drive noise covariance matrix set in the smoothing filter is used.

The observation error covariance matrix is a covariance matrix of the error from the true value of the observed value, and is derived using the observation error standard deviation. Observation error The standard deviation is a parameter that indicates the observation accuracy of the observation method for obtaining the observed value. For example, when smoothing time-series data in which observation values obtained by observation methods having different observation accuracy are mixed, an observation error covariance matrix for each observation method is set in the smoothing filter.

The drive noise covariance matrix is a covariance matrix of the drive noise vector representing the ambiguity of the motion of the observation target, and is derived using the drive noise standard deviation. The drive noise covariance matrix is a filter setting parameter that represents the magnitude of ambiguity in the motion model to be observed. The smoothing performance of the smoothing filter depends on the setting value of the observation error standard deviation for deriving the observation error covariance matrix and the setting value of the drive noise standard deviation for deriving the drive noise covariance matrix.

The conventional smoothing filter device is driven according to the difference in the observation method when smoothing the time series data in which the observation values in which the common observation target is observed by multiple observation methods having different observation accuracy and observation timing are mixed. No adjustment of the noise co-dispersion matrix is performed. Therefore, there is a problem that the smoothing performance of the smoothing filter differs depending on the observation method and uniform smoothing may not be possible.

The present invention solves the above-mentioned problems, and is used in a plurality of observation methods in smoothing processing of time-series data in which observation values in which a common observation target is observed by a plurality of observation methods having different observation accuracy and observation timing are mixed. It is an object of the present invention to obtain a smoothing filter device and a smoothing method capable of matching the smoothing performance corresponding to each of the above.

The smoothing filter device according to the present invention inputs time-series data in which observation values in which a common observation target is observed by a plurality of observation methods having different observation accuracy and observation timing are input, and the time interval of the observation time of the observation values is input. Using the first calculation unit that calculates the standard deviation of the observation error, the standard deviation of the driving noise, and the tracking index expressed as a function of the time interval of the observation time, the smoothness error standard deviation corresponding to each of the multiple observation methods can be obtained. The second calculation unit that calculates the drive noise standard deviation at each observation time, the time interval of the observation time calculated by the first calculation unit, and the second calculation unit calculated so that the values are the same. Using the drive noise standard deviation at each observation time and the smoothing vector and smoothing error covariance matrix of the state of the observation target, the prediction unit that calculates the prediction vector and prediction error covariance matrix of the state of the observation target, and each observation A smoothing unit for calculating a smoothing vector and a smoothing error covariance matrix using the observation error standard deviation at time and the prediction vector and the prediction error covariance matrix calculated by the prediction unit is provided.

According to the present invention, the driving noise standard deviation at each observation time is calculated by using the tracking index so that the smoothing error standard deviation corresponding to each of the plurality of observation methods has the same value, and the calculated driving noise standard is calculated. The deviation is used to smooth the time-series data of the observed values. In the smoothing process of time-series data in which observation values in which common observation targets are observed by multiple observation methods with different observation accuracy and observation timing are mixed, it is possible to match the smoothing performance corresponding to each of the multiple observation methods. ..

It is a block diagram which shows the structure of the smoothing filter apparatus which concerns on Embodiment 1. FIG. It is an image diagram which shows the smoothing process by the smoothing filter apparatus which concerns on Embodiment 1. FIG. It is an image figure which shows the smoothing process for random noise. It is a flowchart which shows the setting process of the initial value of a tracking index. It is a flowchart which shows the smoothing method which concerns on Embodiment 1. FIG. 6A is a block diagram showing a hardware configuration that realizes the function of the smoothing filter device according to the first embodiment, and FIG. 6B is a block diagram that executes software that realizes the function of the smoothing filter device according to the first embodiment. It is a block diagram which shows the hardware configuration. It is an image diagram which shows the outline of the positioning of an aircraft in an aviation surveillance system. It is an image diagram which shows the outline of the time management of a receiving station in an aviation surveillance system. It is a graph which shows the relationship between the observation time of a clock offset and the smoothing error absolute value of an observed value. It is a graph which shows the result of the Monte Carlo trial of the smoothing processing of the observed value of the clock offset.

Embodiment 1.
FIG. 1 is a block diagram showing a configuration of a smoothing filter device 1 according to the first embodiment. The smoothing filter device 1 is, for example, a Kalman filter that smoothes time-series data of observed values using a motion model and an observation model. The motion model to be observed includes a constant velocity linear motion model, and the constant velocity linear motion model is defined by using the following equations (1) to (6). In the following _{formula, t k (k = 0,1,2,} ···) is an observation target of observation time (sampling time). x _k is the state vector representing the state of the observed object (the position and velocity of the observation target) at time t _k. Φ _k is a transition matrix of the state vector x _k from the time t _k to the time t _{k + 1.} T _k is the difference between the previous time t _k-1 and the time t _k. That is, T _k is the time interval of the observation time. w _k is a driving noise vector and indicates the ambiguity of the motion of the observed object. That is, the drive noise vector w _k represents an error when the observation target deviates from the constant velocity linear motion. s _k is the true value of the object of observation state, s _k dot is the time rate of change of the true value s _k. [A] ^T is a transposed vector of the vector A. Q _k is a drive noise covariance matrix, and is a covariance matrix of the drive noise vector w _k . The drive noise covariance matrix Q _k represents the magnitude of the ambiguity of the motion model to be observed. E is the symbol representing the average, q _k is the power spectral density of the drive noise at time t _k. σ _{w and k} are the driving noise standard deviations at _{time t k.}

The observation model of the sensor that observes the observation target can be represented by, for example, the following equations (7) to (9). In the following formulas, z _k is the observed value at time t _k, is the observation vector state of the observation target at time t _k. H is a known observation matrix for extracting only the position vector from the state vector x _k. v _k is the observation noise of the observed value at time t _k (also referred to as the observation error). R _k is the observation error covariance matrix at time t _k, represented by a scalar value. σ _{v, k} ² is the observation error variance at _{time t k , and σ v, k} is the observation error standard deviation at _{time t k.}

As shown in FIG. 1, the smoothing filter device 1 includes an initial value setting unit 10, a first calculation unit 11, a second calculation unit 12, a prediction unit 13, and a smoothing unit 14. Prediction unit 13 uses the driving noise standard deviation sigma _{w, k} at time interval _{T k} and the time _{t k} of the observation time, the equation (2) and (4), the time _{t k} in the driving noise covariance matrix Q Calculate _k and the transition matrix Φ _k. Furthermore, the prediction unit 13 uses a [Phi _k driving noise covariance matrix Q _k and the transition matrix at time t _k, the observation target at time t _k and a smoothing vector x _k hat and smoothing the error covariance matrix P _k hat , The prediction vector x _{k + 1} bar of the observation target and the prediction error covariance matrix P _{k + 1} bar at _{the next time t k + 1} are calculated according to the following equation (10). Note that Φ _k ^T is a transposed matrix of the transition matrix Φ _k.

Smoothing unit 14, the above equation (9) using the observation error standard deviation σ _{v, k + 1} at the next time _{t k + 1,} and calculates the observation error covariance matrix _{R k + 1} at the next time _{t k + 1.} Smoothing unit 14, the next time _t observation error covariance matrix in _{k + 1 R k + 1,} and the observation matrix at the next time _{t k + 1,} to be observed at the next time _{t k + 1} prediction vector _{x k + 1} bar and the prediction error both at the next time _{t k + 1} Using the variance matrix P _{k + 1} bar, the smoothing vector x _{k + 1} hat of the observation target and the smoothing error covariance matrix P _{k + 1} hat at _{the next time t k + 1} are calculated according to the following equation (11). H _{k + 1} ^T is a transposed matrix of the observation matrix H _{k + 1 at} the next time t _{k + 1.}

The smoothing process by the smoothing filter device 1 requires a drive noise covariance matrix Q _k and an observation error covariance matrix R _k as shown in the above equations (10) and (11). That is, the smoothing process requires information on _{the drive noise standard deviation σ w, k} and the observation error standard deviation σ _{v, k for deriving them.} The smoothing performance in the smoothing filter device 1 depends on the set values of _{the drive noise standard deviation σ w, k} and the observation error standard deviation σ _{v, k.}

Further, it can be said that the Kalman filter is an α-β filter whose _{gain is determined from the prediction error covariance matrix P k + 1} bar and the observation error standard deviation σ _{v, k.} Therefore, there is a relationship shown in the following equations (12) and (13) between the steady-state gain K in the Kalman filter and the filter setting parameters initially set in the Kalman filter. In the following equation, α is the gain of position in the α-β filter, and β is the gain of velocity. T is the time interval (sampling interval) of the observation time.

The tracking index Γ is a parameter representing the behavior of the observation error and the drive noise, and is a function of the observation error standard deviation σ _v , the drive noise standard deviation σ _w, and the time interval T of the observation time, as shown in the following equation (14). It is expressed as. Further, the tracking index Γ has the relationship shown in the following equation (14) using α and β. However, q is the power spectrum density of the driving noise. From the above equation (13) and the following equation (14), it can be seen that if the tracking index Γ is determined, α and β are uniquely determined.

FIG. 2 is an image diagram showing a smoothing process by the smoothing filter device 1. The observation error standard deviation σ _{v, k} is a parameter corresponding to the observation accuracy of the observation method. Also, the observation timing interval (sampling interval) of the observation time is T _k. For example, the observation error standard deviation in the observation method (1) is σ _{v, k} (1), and the sampling interval is T (1). The observation error standard deviation in the observation method (2) is σ _{v, k} (2), and the sampling interval is T (2). σ _{v, k} (1) and σ _{v, k} (2) are different from each other, and T (1) and T (2) are different from each other. Further, in FIG. 2, it is assumed that the observation method (1) has higher observation accuracy than the observation method (2).

When time-series data in which observation values in which common observation targets are observed by the observation method (1) and the observation method (2) are mixed is input to the smoothing filter device 1, it is shown on the left side of FIG. As described above, since the observation method (1) has higher observation accuracy than the observation method (2), the observed values shown by the circled plots are close to the true values. On the other hand, the observed values (indicated by the plot of square marks) observed by the observation method (2) having low observation accuracy have a large degree of deviation from the true values. Since the observation timings of the observation method (1) and the observation method (2) are different, the time interval between the observed values is also different from moment to moment.

When smoothing time-series data in which the observed values observed by the observation method (1) and the observation method (2) are mixed, the conventional smoothing filter has an observation error standard deviation (for the observation accuracy of the observation method). (Equivalent) is set for each observation method, but the drive noise standard deviation associated with the motion model to be observed is set regardless of the observation method. For this reason, in the conventional smoothing filter, when smoothing time-series data in which observation values in which common observation targets are observed by the observation method (1) and the observation method (2) are mixed, the observation method is different. The drive noise co-dispersion matrix Qk was not adjusted accordingly, and there was a possibility that the smoothing performance would differ depending on the observation method and the observed values could not be smoothed uniformly.

FIG. 3 is an image diagram showing smoothing processing for random noise. In FIG. 3, N1 is random noise before smoothing, and N2 is random noise after smoothing by the smoothing filter device 1. As an index of the smoothing performance of the smoothing filter that smoothes the random noise N1 to the random noise N2 as shown in FIG. 3, there is a noise suppression ratio S (α, β) of the smoothing value in the steady state. The noise suppression ratio S (α, β) can be calculated from the following equation (15).

As shown in the above equation (15), the noise suppression ratio S (α, β) is a function of only α and β. Therefore, if the tracking index Γ is determined, the noise suppression ratio S (α, β) is uniquely determined. Further, when the noise suppression ratio S (α, β) is determined, the smoothing error standard deviation σ _{smoothing error} can be calculated from the following equation (16) using the square root of the noise suppression ratio S (α, β). it can. Here, σ _v is the observation error standard deviation.

_{The initial value setting unit 10 sets the initial values Γ 1,0} and Γ _2,0 for _{the tracking index Γ so that the smoothing error standard deviation σ smoothing error} is the same in the observation method (1) and the observation method (2). The calculated initial values Γ _1,0 and Γ _2,0 are set in the second calculation unit 12. Γ _1,0 is the initial value of the tracking index in the observation method (1), and Γ ₂ , 0 is the initial value of the tracking index in the observation method (2). The initial value setting unit 10 can be a component provided in an external device provided separately from the smoothing filter device 1. In this case, the second calculation unit 12 included in the smoothing filter device 1 sets the initial value of the tracking index from the initial value setting unit 10 included in the external device.

First computing unit 11, the observation method (1) and observation methods observations of common observation target is observed by (2) inputs the time-series data are mixed, the time interval T _k of observation time of observations Is calculated. The second calculation unit 12 uses the tracking index gamma, as smooth error standard deviation σ _{smoothing errors} of observation methods (1) and observation method (2) of the same value, the driving noise standard deviation at time t _k Calculate σ _{w and k.}

The second calculation unit 12 calculates the drive noise standard deviation σ _{w, k} at _{time t k} so that the tracking index Γ _{k at time t k} and the initial value Γ _{1, 0} or Γ _{2, 0 match.} The smoothing filter device 1 uses the drive noise standard deviations σ _{w and k} calculated by the second calculation unit 12, and observes that a common observation target is observed by the observation method (1) and the observation method (2). In the smoothing process of time-series data in which values are mixed, the smoothing performance for the observed value by the observation method (1) and the smoothing performance for the observed value by the observation method (2) can be matched.

Next, the setting process of the initial values Γ _1,0 and Γ _2,0 will be described in detail.
FIG. 4 is a flowchart showing the setting process of the initial values Γ _1,0 and Γ _2,0. In FIG. 4, time-series data in which observation values in which common observation targets are observed by the observation methods (1) and observation methods (2), which have different observation accuracy and timing, are input to the smoothing filter device 1. To. _{The time interval T 0} of the observation time of the observation method (1) and the observation method (2) is 1.0 (seconds), respectively. In this case, in the time-series data observed value is observed object observed by the observation method (1) and observation method (2) are mixed, the time interval of the observation time _{T k (= t k -t k} -1) is , Varies between 0 (seconds) and 2 (seconds).

_{First, the initial value setting unit 10 calculates the initial value Γ 1,0} of the tracking index Γ related to the observation method (1) having higher observation accuracy than the observation method (2) (step ST1). For example, the initial value setting unit 10 has _{a known observation error standard deviation σ v1} corresponding to the observation method (1) for deriving _{a predetermined constant smoothing error standard deviation σ smoothing error} , and an observation method ( A known observation error standard deviation σ _v2 corresponding to 2) is set.

The initial value setting unit 10 determines the _{drive noise standard deviation σ w1} , 0 corresponding to the observation method (1). For example, the initial value setting unit 10 determines _{the initial value σ w1,0} of the drive noise standard deviation from the above equations (15) and (14) by using the smoothing error standard deviation represented by the following equation (17). ..

In addition, by simulating the smoothing process using the observation error standard deviation σ _v1 and the time interval T ₀ = 1.0 (seconds) and evaluating the smoothing error standard deviation, the drive corresponding to the appropriate smoothing error standard deviation is performed. The noise standard deviation σ _w1,0 may be determined. If the smoothing error standard deviation is _{smaller than the observed error standard deviation σ v1} , it can be said that it is an appropriate value that gives a smoothing effect. However, if the smoothing error standard deviation is _{significantly smaller than the observation error standard deviation σ v1} , the tracking performance of the smoothing filter device 1 to the observation target deteriorates. Therefore, it is necessary to determine the smoothing error standard deviation within an acceptable range.

The actual gains α ₁ and β ₁ cannot be obtained analytically. Therefore, in the smoothing filter device 1, the update equation of the Kalman filter shown in the above equations (10) to (11) is repeatedly executed until the value of the steady gain K shown in the above equation (12) converges, and then converges. _{The gains α 1} and β ₁ are determined from the values of the steady gain K obtained.

The initial value setting unit 10 uses the determined initial value σ _{w1 , 0 of} the drive noise standard deviation, the known observation error standard deviation σ _v1, and the time interval T 0 (= 1.0 (seconds)), and uses the following equation. According to (18), the initial value Γ _1,0 is calculated.

Next, the initial value setting unit 10 _{calculates S (α 1} , β ₁ ) σ _v1 ² corresponding to the observation method (1) (step ST2). In order for the smoothing error standard deviations corresponding to the observation method (1) and the observation method (2) to have the same value, the following equation (19) must be established.

The initial value setting unit 10 calculates the _{drive noise standard deviation σ w2} , 0 by solving the optimization problems shown in the following equations (20) and (21). Since the following optimization problem cannot be solved analytically, the search range _{from the minimum value σ w2,0, min} to the maximum value σ _{w2,0, max} is searched for each _{step Δσ w2,0 of a constant value.} By doing so, the drive noise standard deviation σ _w2 , 0 corresponding to the observation method (2) is determined.

First, the initial value setting unit 10 sets the minimum value σ _{w2,0, min to the drive noise standard error σ w2,0} (step ST3). Subsequently, the initial value setting unit 10, gain alpha ₁ and beta ₁ when the same procedure was determined from the value of the steady gain K of the gain alpha ₂ and beta _2, gain alpha ₂ and beta ₂ and known observation using the error standard deviation sigma _v2, according to the above formula (15) and _{(17), S (α 2} , β 2) corresponding to the observation method ^₍₂₎ σ v2,0 2 is calculated (step ST4). Next, the initial value setting unit 10 confirms whether or not the calculated value satisfies the above equation (21) (step ST5).

If not satisfying the above formula (19) (step ST5; NO), the initial value setting unit 10, a value obtained by adding the step .DELTA..sigma _W2,0 to the current sigma _W2,0, next drive noise standard deviation sigma _{w2, Set to 0} (step ST6). The process from step ST4 is executed using the drive noise standard deviation σ _{w2, 0 set at this time.} These processes are repeated within the above search range.

When the above equation (19) is satisfied (step ST5; YES), the initial value setting unit 10 adopts _{the drive noise standard deviation σ w2, 0 at this time.} With this drive noise standard deviation σ _w2 , 0, the above equation (19) holds, so from the above equation (21), J (σ _w2,0 ) becomes almost zero.

The initial value setting unit 10 uses the determined initial value σ _{w2 , 0 of} the drive noise standard deviation, the observation error standard deviation σ _v2, and the time interval T 0 = 1.0 (seconds), and uses the following equation (22). According to this, the initial value Γ _2.0 is calculated (step ST7). Since the above equation (19) holds for the initial value Γ _1,0 and the initial value Γ _2,0 , the smoothing error standard deviation is the same value in the observation method (1) and the observation method (2). The initial value setting unit 10 sets the initial value Γ _1,0 and the initial value Γ _2,0 in the second calculation unit 12.

Next, the smoothing method according to the first embodiment will be described.
FIG. 5 is a flowchart showing a smoothing method according to the first embodiment. In FIG. 5, time-series data in which observation values in which common observation targets are observed by the observation method (1) and the observation method (2) are mixed is input to the smoothing filter device 1, and a second calculation unit is used. _{The initial value Γ 1,0} and the initial value Γ _2,0 calculated by the initial value setting unit 10 are set in 12.

First computing unit 11, the time series data observed value common observation target is observed by the observation method (1) and observation method (2) are mixed is input, the time interval T _k of observation time Calculate sequentially (step ST1a). The time interval _{T k (= t k -t k} -1) , the time _{t k} and the time _{t k-1} and the observation methods may be different.

The second calculation unit 12 updates the drive noise standard deviations σ _{w and k at time t k} (step ST2a). The second calculation unit 12, the driving noise standard deviation sigma _{w, k} at time _{t k,} is calculated according to the following equation (23) or the following formula (24). The following equation (23), as an observation error standard deviation sigma _{v, k} at time _{t k,} the known sigma _v1 is set, the following equation (24), the observation at time _{t k} error standard deviation sigma _{v, k} As a known σ _v2 is set.

The relationship of the following equation (25) is derived using _{the drive noise standard deviation σ w, k} calculated by the second calculation unit 12 according to the following equation (23) and the above equation (14). In Formula (25), the tracking index gamma _{1, k} is at time _{t k,} a tracking index corresponding to the observation method (1). As shown by the following equation (25), the drive noise standard deviation σ _{w, k at time t k} is calculated so that the tracking index Γ _{1, k} and the initial value Γ _{1, 0 match.} Further, the relationship of the following equation (26) is derived by the same procedure as the following equation (25). In formula (26), Tracking Index gamma _{2, k} is at time _{t k,} a tracking index corresponding to the observation method (2). Thus, the smoothing filter device 1, the smoothing error standard deviation at each time t _k is kept constant.

The prediction unit 13 performs prediction processing (step ST3a). For example, the prediction unit 13 calculates the prediction vector x _{k + 1} bar of the observation target and the prediction error covariance matrix P _{k + 1} bar at _{the next time t k + 1 according to the above equation (10).} Subsequently, the smoothing portion 14 performs a smoothing process (step ST4a). For example, the smoothing unit 14 calculates the smoothing vector x _{k + 1} hat of the observation target and the smoothing error covariance matrix P _{k + 1} hat at _{the next time t k + 1} according to the above equation (11). The smoothing unit 14 outputs the smoothing vector x _{k + 1} hat and the smoothing error covariance matrix P _{k + 1} hat as the smoothing result of the observed value, and feeds it back to the prediction unit 13.

Next, the hardware configuration that realizes the function of the smoothing filter device 1 will be described.
Each function of the initial value setting unit 10, the first calculation unit 11, the second calculation unit 12, the prediction unit 13, and the smoothing unit 14 in the smoothing filter device 1 is realized by the processing circuit. That is, the smoothing filter device 1 includes a processing circuit for executing the processing from step ST1a to step ST4a shown in FIG. The processing circuit may be dedicated hardware, or may be a CPU (Central Processing Unit) that executes a program stored in the memory.

FIG. 6A is a block diagram showing a hardware configuration that realizes the function of the smoothing filter device 1, and FIG. 6B is a block diagram showing a hardware configuration that executes software that realizes the function of the smoothing filter device 1. In FIGS. 6A and 6B, the input interface 100 is an interface that relays time-series data of observed values input from the sensor to the smoothing filter device 1. The output interface 101 is an interface that relays information on the smoothing result output from the smoothing filter device 1 to the outside.

When the processing circuit is the processing circuit 102 of the dedicated hardware shown in FIG. 6A, the processing circuit 102 may be, for example, a single circuit, a composite circuit, a programmed processor, a parallel programmed processor, or an ASIC (Application Specific Integrated Circuit). ), FPGA (Field-Programmable Gate Array), or a combination of these. The functions of the initial value setting unit 10, the first calculation unit 11, the second calculation unit 12, the prediction unit 13, and the smoothing unit 14 in the smoothing filter device 1 may be realized by separate processing circuits, and these functions may be realized. May be realized in one processing circuit collectively.

When the processing circuit is the processor 103 shown in FIG. 6B, the functions of the initial value setting unit 10, the first calculation unit 11, the second calculation unit 12, the prediction unit 13, and the smoothing unit 14 in the smoothing filter device 1 are software. , Firmware or a combination of software and firmware. The software or firmware is described as a program and stored in the memory 104.

By reading and executing the program stored in the memory 104, the processor 103 reads and executes the initial value setting unit 10, the first calculation unit 11, the second calculation unit 12, the prediction unit 13, and the smoothing unit in the smoothing filter device 1. It realizes 14 functions. For example, the smoothing filter device 1 includes a memory 104 for storing a program in which the processes from steps ST1a to ST4a in the flowchart shown in FIG. 5 are executed as a result when executed by the processor 103. These programs cause the computer to execute the procedure or method of the initial value setting unit 10, the first calculation unit 11, the second calculation unit 12, the prediction unit 13, and the smoothing unit 14. The memory 104 is a computer-readable storage medium in which a program for making a computer function as an initial value setting unit 10, a first calculation unit 11, a second calculation unit 12, a prediction unit 13, and a smoothing unit 14 is stored. You may.

The memory 104 is, for example, a RAM (Random Access Memory), a ROM (Read Only Memory), a flash memory, an EPROM (Erasable Programmable Read Only Memory), an EEPROM (Electrically-volatile) semiconductor, an EPROM (Electrically-volatile), or the like. This includes discs, flexible discs, optical discs, compact discs, mini discs, DVDs, and the like.

Some of the functions of the initial value setting unit 10, the first calculation unit 11, the second calculation unit 12, the prediction unit 13, and the smoothing unit 14 in the smoothing filter device 1 are realized by dedicated hardware, and some of them are software. Alternatively, it may be realized by firmware. For example, the initial value setting unit 10 realizes the function by the processing circuit 102 which is the dedicated hardware, and the processor 103 sets the first calculation unit 11, the second calculation unit 12, the prediction unit 13, and the smoothing unit 14. The function is realized by reading and executing the program stored in the memory 104. As described above, the processing circuit can realize the above-mentioned functions by hardware, software, firmware or a combination thereof.

Next, the smoothing filter device 1 applied to the aviation surveillance system (MLAT) will be described. The MLAT synchronously receives signals transmitted from the aircraft by a plurality of sensors installed on the airport surface, and based on the arrival time difference (Time Difference Of Arrival; TDOA) between the signals received by the multiple sensors, the airport surface. Position the aircraft that exist in. However, since there is a time synchronization error (hereinafter referred to as clock offset) between the actual sensors, it is necessary to observe and estimate the value of the clock offset in advance. The clock offset observation method includes a reference station method and a GPS (Global Positioning System) method.

In the reference station method, signals transmitted from reference stations with known positions are received by a plurality of receiving stations (corresponding to sensors) with known positions, which are distributed on the airport surface, and the reception times are relative to each other. This is a method of observing the target deviation as a clock offset. In the GPS method, GPS pulse signals are received from GPS satellites by each of a plurality of receiving stations (corresponding to sensors), and GPS between receiving stations is based on the GPS time obtained for each 1PPS (Pulse Per Second). This is a method of observing the relative time lag as a clock offset.

FIG. 7 is an image diagram showing an outline of positioning of the aircraft 30 in MLAT. The receiving stations 21 to 24 installed on the airport surface 20 synchronously receive the signals transmitted from the aircraft 30, and solve the following equation (27) using the time difference in the reception timing between the receiving stations to solve the aircraft 30. Positioning is performed. The positions of the receiving stations 21 to 24 on the airport surface 20 are known. In the following equation (27), TDOA _ij is the arrival time difference between the signal arriving at the i-th receiving station and the signal arriving at the j-th receiving station. x is a position vector of the aircraft 30 to be positioned. p _i is the position vector of the i-th receiving station is a known value. For example, when performing three-dimensional positioning, at least three TDOAs are required, so four or more receiving stations are required.

For TDOA observation, the clock value of each receiving station at the time when the signal is received by each receiving station is referred to. However, since the clocks of the receiving station are not actually synchronized, it is necessary to estimate the asynchronous component by some method and compensate the TDOA by using the estimated asynchronous component.

FIG. 8 is an image diagram showing an outline of time management of the receiving station in MLAT. For example, in the reference station method, the receiving stations 26 to 28 receive the same signal (radio wave) transmitted from the reference station 25. When the clocks of the receiving stations 26 to 28 are not synchronized, as shown in the following formula (28), the arrival time difference of the above signal measured by using the clock provided by the receiving station and each receiving station from the reference station 25 There is a difference Δ with the arrival time difference of the radio wave estimated from the distance to. The reference station method is a method of observing this difference Δ as a clock offset. In the following formulas, delta _{ij, reference station} is an observation target in a reference station method, and the i-th receiving station is a clock offset observations between the j-th receiving station, T _{i, the reference station,} the i It is the reception time of the above signal measured by the clock provided in the second receiving station.

In the GPS method, as shown in the following equation (29), the difference Δ between the GPS time measured by the GPS pulse signal for each 1PPS and the time measured by the clock provided in the receiving station is observed as a clock offset. .. In the following formulas, delta _{ij, GPS} is a observation target in the GPS method is a clock offset observations between the i-th receiving station and the j th receiving _{station, T i, GPS} is the i It is the reception time of the above signal measured by the clock provided in the second receiving station.

_{Δij, reference} station and _{Δij, GPS} are observation values observed by the reference station method and the GPS method, which have different observation accuracy and observation timing. Time-series data in which these observed values are mixed is input to the smoothing filter device 1. Smoothing filter device 1 uses the tracking index gamma, as a smoothing error standard deviation corresponding to the smoothing error standard deviation and GPS method corresponding to the reference station method is the same value, the driving noise standard deviation at time t _k sigma Calculate _{w and k.} The smoothing filter device 1 uses the calculated drive noise standard deviation σ _{w, k at the time t k} , and observes by the reference station method in the smoothing process of the time series data in which the observed values _{Δij, the reference} station and _{Δij, and GPS are mixed.} It is possible to match the smoothing performance with respect to the value and the smoothing performance with respect to the observed value by the GPS method.

FIG. 9 is a graph showing the relationship between the observation time of the clock offset and the smoothing error absolute value of the observed value. The relationship shown in FIG. 9 is obtained by simulating clock offset observations by the reference station method and the GPS method, and smoothing time-series data in which the observed values obtained by these simulations are mixed. The smoothing process is performed by the smoothing filter device 1 and a conventional smoothing filter. In the simulation of clock offset observation, the observation accuracy in the reference station method, that is, the observation error standard deviation σ _{v1 is set} to 1 (nanosecond), and the observation error standard deviation σ _v2 in the GPS method is set to 15 (nanosecond). The accuracy is inferior to the reference station method.

In FIG. 9, the relationship A showing the absolute smoothing error value by the square plot is the result of the smoothing process by the conventional smoothing filter device. Relationship B, which shows the absolute value of smoothing error by a round plot, is the result of smoothing processing by the smoothing filter device 1. In the conventional smoothing filter, the processing for matching the smoothing performance between the reference station method and the GPS method is not performed. Therefore, the smoothing process of the conventional smoothing filter has a larger smoothing error than the smoothing process of the smoothing filter device 1.

Further, FIG. 10 is a graph showing the results of Monte Carlo trials of smoothing the observed values of the clock offset, and the Monte Carlo simulation was performed 100 times for the smoothing processing of the observed values obtained by the simulation of the clock offset observation shown in FIG. It shows the mean squared error (RMSE) in each trial when it was tried. In FIG. 10, the relationship C showing the RMSE by the square plot is the result of the smoothing process by the conventional smoothing filter device. Relationship D, which indicates RMSE by a round plot, is the result of smoothing by the smoothing filter device 1. As shown in FIG. 10, it can be said that the smoothing process of the smoothing filter device 1 has a smaller RMSE than the smoothing process of the conventional smoothing filter.

Next, a case where the smoothing filter device 1 is applied to the bistatic radar system will be described. The bistatic radar system is a system in which the transmitter and receiver of radar waves are placed apart from each other and connected by communication, and the communication between the transmitter and receiver is highly synchronized. It is required to be. In a bistatic radar system, in order to synchronize communication between a transmitter and a receiver, accuracy control of absolute time using an atomic clock (for example, a rubidium clock) is generally performed. The time measurement in the atomic clock has lower measurement accuracy than the time measurement in GPS, and the time measured by the atomic clock may gradually drift and deviate from the true value. Therefore, the time measured by the atomic clock needs to be corrected using the GPS time.

_{In the bistatic radar system, the smoothing filter device 1 uses the tracking index to drive the smoothing error standard deviation σ w, k} so that the smoothing error standard deviation becomes the same value between the time measurement by the atomic clock and the time measurement by GPS. Is calculated, and smoothing is performed using the calculated drive noise standard deviations σ _{w and k.} As a result, in the smoothing process of time series data in which the time value measured by the atomic clock and the time value measured by GPS are mixed, the smoothing performance with respect to the time measured by the atomic clock and the time measured by GPS It is possible to match the smoothing performance with respect to.

So far, we have described time-series data in which observation values observed by two observation methods with different observation accuracy and timing are mixed, but the smoothing filter device 1 has observed values observed by three or more observation methods. Time-series data in which is mixed can be smoothed. That is, the smoothing filter device 1 is set with the initial value of the tracking index Γ calculated so that the smoothing error standard deviations corresponding to each of the three or more observation methods have the same value. The smoothing filter device 1 can match the smoothing performance corresponding to three or more observation methods by using this initial value.

As described above, in the smoothing filter device 1 according to the first embodiment, the driving noise standard at each observation time is used so that the smoothing error standard deviation corresponding to each of the plurality of observation methods becomes the same value by using the tracking index. The deviation is calculated, and the calculated drive noise standard deviation is used to smooth the time-series data of the observed values. In the smoothing process of time-series data in which observation values in which common observation targets are observed by multiple observation methods with different observation accuracy and observation timing are mixed, it is possible to match the smoothing performance corresponding to each of the multiple observation methods. ..

The present invention is not limited to the above-described embodiment, and within the scope of the present invention, it is possible to modify any component of the embodiment or omit any component of the embodiment.

The smoothing filter device according to the present invention can be used for, for example, MLAT.

1 smoothing filter device, 10 initial value setting unit, 11 first calculation unit, 12 second calculation unit, 13 prediction unit, 14 smoothing unit, 20 airport surface, 21 receiving station, 22, 23, 24, 26, 27 , 28 receiving station, 25 reference station, 30 aircraft, 100 input interface, 101 output interface, 102 processing circuit, 103 processor, 104 memory.

Claims (4)

1. A first calculation unit that inputs time-series data in which observation values in which common observation targets are observed by multiple observation methods with different observation accuracy and observation timing are input and calculates the time interval of the observation time of the observation values. When,
   Using the tracking index, which is expressed as a function of the observation error standard deviation, the drive noise standard deviation, and the time interval of the observation time, each observation has the same smoothing error standard deviation corresponding to each of the plurality of observation methods. A second calculation unit that calculates the drive noise standard deviation at time, and
   Both the time interval of the observation time calculated by the first calculation unit, the driving noise standard deviation at each observation time calculated by the second calculation unit, and the smoothing vector and smoothing error of the state of the observation target. A prediction unit that calculates the prediction vector of the state of the observation target and the prediction error covariance matrix using the variance matrix, and
   Using the observation error standard deviation at each observation time, the prediction vector calculated by the prediction unit, and the prediction error covariance matrix, a smoothing unit that calculates the smoothing vector and the smoothing error covariance matrix, and a smoothing unit that calculates the smoothing error covariance matrix.
   A smoothing filter device characterized by being equipped with.
2. An initial value of the tracking index set so that the smoothing error standard deviations corresponding to the plurality of observation methods have the same value is calculated, and the initial value of the tracking index is set in the second calculation unit. Equipped with a value setting unit
   The second calculation unit calculates the drive noise standard deviation by using the initial value of the tracking index, the observation error standard deviation, and the time interval of the observation time calculated by the first calculation unit. The smoothing filter device according to claim 1, wherein the smoothing filter device is characterized.
3. The initial value setting unit calculates the smoothing error standard deviation, which is the product of the square root of the noise suppression ratio and the observed error standard deviation, and the smoothing error standard deviation corresponding to each of the plurality of the observation methods has the same value. The smoothing filter device according to claim 2, wherein the initial value of the tracking index is calculated for each of the observation methods.
4. The first calculation unit inputs time-series data in which observation values in which common observation targets are observed by a plurality of observation methods having different observation accuracy and observation timing are input, and the time interval of the observation time of the observation values is set. Steps to calculate and
   The second calculation unit uses a tracking index expressed as a function of the observation error standard deviation, the driving noise standard deviation, and the time interval of the observation time, and the smoothing error standard deviation corresponding to each of the plurality of observation methods is the same value. The step of calculating the drive noise standard deviation at each observation time and
   The prediction unit has the time interval of the observation time calculated by the first calculation unit, the drive noise standard deviation at each observation time calculated by the second calculation unit, and the smoothing vector of the state of the observation target. And the step of calculating the prediction vector and the prediction error covariance matrix of the state of the observed object using the smoothing error covariance matrix and
   The smoothing unit calculates the smoothing vector and the smoothing error covariance matrix by using the observation error standard deviation at each observation time, the prediction vector calculated by the prediction unit, and the prediction error covariance matrix. Steps and
   A smoothing method characterized by being provided with.

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