JP2015049143A - Detection performance calculation device, method of the same, and program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To calculate, in short time, at least one of detection performance and detection items of a signal processing part for performing integration during scanning without using a large scale detection performance calculation device for performing Monte Carlo simulation.SOLUTION: A detection performance calculation device comprises a detection performance calculating part for calculating at least one of detection performance and detection items of a signal processing part for performing integration during scanning on the basis of a probability density function of a cumulative distribution function of Gamma distribution or Erlang distribution.

Description

  The present invention relates to a detection performance calculation apparatus, a method, and a program for calculating at least one of detection performance and detection specifications of a signal processing unit that performs integration between scans in a radar apparatus, a sonar apparatus, and the like.

  In developing a signal processing unit that performs integration between scans, it is necessary to calculate the detection performance. In order to calculate the detection performance, a detection performance calculation device that performs many Monte Carlo simulations using a signal processing unit or a simulation means (simulator) of the signal processing unit, statistically processes the result, and calculates the detection performance. is there. Here, the inter-scan integration is also referred to as scan integration or inter-frame integration (or frame integration), and is particularly often implemented by being incorporated in a TBD (Track Before Detect) algorithm for a target having a low signal-to-noise ratio. .

  An example of a conventional detection performance calculation apparatus is shown in FIG. FIG. 1 is a block diagram showing an example of the configuration of a conventional detection performance calculation apparatus. The detection performance calculation apparatus includes a simulation signal generation unit 101, a signal processing unit (or signal processing simulation unit) 102, a recording unit 103, a statistical processing unit 104, and an operation / display unit 105.

  The simulation signal generation unit 101 generates a simulation signal for Monte Carlo simulation and outputs the simulation signal to the signal processing unit (or signal processing simulation unit) 102. The signal processing unit (or signal processing simulation unit) 102 receives the simulation signal from the simulation signal generation unit 101, performs signal processing including integration between scans, and outputs the signal processing result to the recording unit 103. The recording unit 103 records the signal processing result from the signal processing unit (or signal processing simulation unit) 102. The statistical processing unit 104 records the signal recorded in the recording unit 103 for each specification of the simulation signal generated by the simulation signal generation unit 101 and each specification of the signal processing performed by the signal processing unit (or signal processing simulation unit) 102. The detection results are calculated by statistically processing the processing results. The operation / display unit 105 displays the detection performance calculated by the statistical processing unit 104.

Scan between the detection performance of the signal processing unit performs integration to calculate the (detection probability P _D is the detection performance for the false alarm probability P _FA and the target is a detection performance against _noise) is for performing a Monte Carlo simulation It was necessary to configure a large-scale detection performance calculation device. Similarly, in order to calculate (back-calculate) the detection specifications (threshold value T, integral number K between scans, and expected value a of the signal amplitude) satisfying the detection performance, a large-scale detection performance calculation apparatus as described above is used. There was a need to configure. In addition, when calculating detection performance and detection specifications with few errors, it is necessary to perform many Monte Carlo simulations, and it takes time to calculate detection performance and detection specifications.

JP 2003-107149 A JP 2010-276475 A

S.M. Tonissen, et al. “Performance of Dynamic Programming Techniques for Track-Before-Detect”, IEEE Trans. AES, Vol.32, No.4, pp.1440-1451, Oct. 1996.

  As described above, in order to calculate the detection performance and detection specifications of a signal processing unit that performs integration between scans, there is a problem that a large-scale detection performance calculation device for performing a Monte Carlo simulation is required. It was. In addition, when calculating detection performance and detection specifications with small errors, it is necessary to perform many Monte Carlo simulations, and there is a problem that it takes time to calculate detection performance and detection specifications.

  The present embodiment has been made in view of the above problems, and without using a large-scale detection performance calculation device for performing Monte Carlo simulation, at least the detection performance and detection specifications of the signal processing unit that performs inter-scan integration. It is an object of the present invention to provide a detection performance calculation apparatus, method and program capable of calculating one in a short time.

  The detection performance calculation apparatus according to the present embodiment is a detection that calculates at least one of detection performance and detection specifications of a signal processing unit that performs integration between scans based on a probability density function or cumulative distribution function of gamma distribution or Erlang distribution. A performance calculating unit is provided.

  In addition, the detection performance calculation method according to the present embodiment calculates at least one of the detection performance and detection specifications of the signal processing unit that performs inter-scan integration based on the probability density function or cumulative distribution function of the gamma distribution or Erlang distribution. And a detection performance calculating step.

  In addition, the program in the present embodiment calculates at least one of detection performance and detection specifications of a signal processing unit that performs integration between scans based on a probability density function or cumulative distribution function of gamma distribution or Erlang distribution. It is characterized by functioning as detection performance calculation means.

It is a block diagram which shows the structure of the detection performance calculation apparatus in 1st Embodiment. It is a flowchart which shows the specific example of the flow of the process which the detection performance calculation part in 1st Embodiment performs. It is a block diagram which shows the structure of the signal processing apparatus in 2nd Embodiment. It is a block diagram which shows an example of a structure of the conventional detection performance calculation apparatus.

Hereinafter, embodiments will be described with reference to the drawings.
(First embodiment)
FIG. 1 is a block diagram illustrating a configuration of a detection performance calculation apparatus according to the first embodiment. This detection performance calculation apparatus includes a detection performance calculation unit 1 and an operation / display unit 2.

The detection performance calculation unit 1 inputs the specifications of the inter-scan integration from the operation / display unit 2 and calculates the detection performance of the inter-scan integration. The operation / display unit 2 displays the detection performance calculated by the detection performance calculation unit 1.
The background theory will be described before showing a specific example of the flow of processing.

Assuming that the signal amplitude of the observation cell is z and the state vector of the k-th integration between scans is x _k , the cumulative cell I (x _k ) of the integration between scans is expressed by the following equation. Here, q represents the cumulative cell search number, and max [·] represents the maximum value calculation.

In the present embodiment, by setting the cumulative cell search number q to 1, a simplified expression that does not include the maximum value calculation is used as follows. Of the detection performance obtained by the following equation, the detection performance for noise (false alarm probability P _FA ) indicates a theoretical lower limit value, and the detection performance for the target (detection probability P _D ) is theoretically Indicates the upper limit value of.

In the present embodiment, square detection is assumed as the detection method of the signal processing unit for calculating the detection performance. As a result, the distribution of the signal amplitude z of the observation cell with no noise and no target follows an exponential distribution in which the probability density function f ₀ (z; a) is expressed by the following equation. Here, a represents an expected value of the signal amplitude. Furthermore, the distribution of the signal amplitude z of the observation cell in which the swirling classification 1 variation target exists also follows the exponential distribution.

The distribution of the k sums (z ₁ + z ₂ +... + Z _k ) of the random variable Z according to the exponential distribution follows a gamma distribution in which the probability density function f ₁ (z; k, a) is expressed by the following equation. Here, Γ (·) represents a gamma function.

Further, the cumulative distribution function F ₁ (z; k, a) of the gamma distribution is expressed by the following expression. Here, γ (·) represents an incomplete gamma function.

  In the present embodiment, at least one of detection performance for noise and detection performance for a target is calculated based on a probability density function or cumulative distribution function of a gamma distribution.

FIG. 2 is a flowchart illustrating a specific example of the flow of processing performed by the detection performance calculation unit according to the first embodiment. First, a specific example of calculating the relationship between detection performance and false is alarm probability P _FA and the threshold value T to noise.

The detection performance calculation unit 1 inputs specifications from the operation / display unit 2 (step S11). Here, the specifications from the operation / display unit 2 include an inter-scan integration number K = 10, an expected value of noise signal amplitude a _n = 1, an expected value of target signal amplitude a _t = 0, and a plurality of threshold values T. values [0, 1, 40] is applied at, as specifications for calculating the detection performance, scanning between integral number K = 10, the expected value _{a = a n + a t =} 1 the signal amplitude, A threshold T = 0 (first value among a plurality of values) is set (step S12).

  When the specifications are set in step S12, the detection performance of the set specifications is calculated based on the probability density function or cumulative distribution function of the gamma distribution (step S13), and the calculated detection performance is displayed on the operation / display unit. 2 (step S14).

  In the case where the specifications input from the operation / display unit 2 are a plurality of values such as the threshold value T, the steps until the detection performance for the last value (the threshold value T = 40 in the above example) is calculated. The steps from S12 to step S14 are repeated.

Next, a specific example of calculating the relationship between the detection probability P _D and the threshold value T is a detection performance with respect to the target. Except that the expectation value a _t of the signal amplitude of the target exceeds 0, the flow of processing detection performance calculating unit performs are the same. As a specific example, in the case of an expected value a _n = 1 of a noise signal amplitude and an expected value a _t = 2 of a target signal amplitude (signal-to-noise ratio 3 dB), detection with respect to a target is performed with an expected signal amplitude value a = 3. it is possible to calculate the relationship between the detection probability P _D and the threshold value T is the performance.

Here, the processing content of step S13 which calculates the detection performance of the set item based on the probability density function or cumulative distribution function of the gamma distribution will be specifically described. Detection probability P _D is the detection performance for false alarm probability P _FA and the target is a detection performance against noise because it can be calculated by the same steps as shown above for convenience, false alarm probability P _FA and detection probability If P _D is expressed as a probability P without being divided, the probability P can be calculated by the following equation.

  As described above, the detection performance calculation unit 1 of the detection performance calculation apparatus according to the first embodiment calculates the detection performance of the signal processing unit that performs inter-scan integration based on the probability density function or cumulative distribution function of the gamma distribution. can do.

In addition, by using the equation (6) as an inverse function, it is possible to calculate (reverse calculation) the detection specifications (threshold value T, integral number K between scans, and expected value a of the signal amplitude) that satisfy the detection performance. As a specific example, if the false alarm probability P _FA , which is detection performance against noise, the inter-scan integration number K, and the expected value a of the signal amplitude are known, a threshold value T that is an unknown number can be calculated (back-calculated).

(Second Embodiment)
FIG. 3 is a block diagram illustrating a configuration of the signal processing apparatus according to the second embodiment. This signal processing apparatus includes a detection performance calculation unit 3 and a signal processing unit 4.

  The detection performance calculation unit 3 inputs the specification of the inter-scan integration from the signal processing unit 4 and calculates the detection specification of the inter-scan integration. The signal processing unit 4 performs inter-scan integration based on the detection specifications calculated by the detection performance calculation unit 3.

  The detection performance calculation unit 3 according to the second embodiment uses a probability density of gamma distribution in order to calculate the detection performance and detection specifications of the signal processing unit in which the detection performance calculation unit 1 according to the first embodiment performs integration between scans. Whereas the function or cumulative distribution function is used, the probability density function or cumulative distribution function of the Erlang distribution is used.

In the first embodiment, it has been shown that the distribution of the k sums (z ₁ + z ₂ +... + Z _k ) of the random variable Z that follows the exponential distribution follows the gamma distribution. Here, when the argument k of the gamma function Γ (k) of the gamma distribution is a natural number, the gamma function Γ (k) is the factorial (k−1)! It can be expressed in the form of That is, the distribution (z ₁ + z ₂ +... + Z _k ) of k random variables Z (k is a natural number) according to the exponential distribution has a probability density function f ₂ (z; k, a) represented by the following equation: According to the Erlang distribution represented by

The cumulative distribution function F ₂ (z; k, a) of the Erlang distribution is expressed by the following equation.

For convenience, when expressed as a probability P without distinguishing false alarm probability P _FA and detection probability P _D, probability P can be calculated by the following equation.

The detection performance calculation unit 3 according to the second embodiment uses the equation (9) as an inverse function to detect detection parameters that satisfy the detection performance (threshold value T, integral number K between scans, and expected value a of the signal amplitude). Can be calculated (reverse calculation). The false alarm probability P _FA that is the detection performance against noise, the inter-scan integration number K and the expected value a of the signal amplitude are input from the signal processing unit 4 as the inter-scan integration, and the inter-scan integration is detected as A specific example of calculating the threshold T will be shown.

  The flowchart showing the processing flow of the second embodiment is the same as that of the first embodiment shown in FIG. 2, and therefore the processing of each step will be described with a focus on the differences from the first embodiment.

The detection performance calculation unit 3 inputs specifications from the signal processing unit 4 (step S11). Here, as specifications from the signal processing unit 4, a false alarm probability P _FA = 10 ⁻⁵ which is a detection performance against noise, and a plurality of values [1, 2,... When the expected value a _n = 1 of the noise signal amplitude and the expected value a _t = 0 of the target signal amplitude are input, the false alarm probability P _FA = 10 ⁻⁵ as the specification for calculating the detection specification. scan between integral number K = 1 (first value among the plurality of values), sets an expected value _{a = a n + a t =} 1 the signal amplitude (step S12).

  When the specification is set in step S12, a threshold T as a detection specification for the set specification is calculated based on the probability density function of the Erlang distribution or the inverse function of the cumulative distribution function (step S13). The detected specifications are output to the signal processing unit 4 (step S14).

  When the specifications input from the signal processing unit 4 are a plurality of values such as the inter-scan integration number K, the detection specification for the last value (inter-scan integration number K = 10 in the above example) is Until the calculation, the steps from step S12 to step S14 are repeated.

  When the detection specifications are calculated by the detection performance calculation unit 3, the signal processing unit 4 performs inter-scan integration based on the detection specifications calculated by the detection performance calculation unit 3.

  As described above, the detection performance calculation unit 3 of the signal processing device according to the second embodiment calculates the detection specifications of the signal processing unit that performs inter-scan integration based on the probability density function or cumulative distribution function of the Erlang distribution. can do. Specifically, by using the equation (9) as an inverse function, it is possible to calculate (back-calculate) detection parameters (threshold value T, inter-scan integration number K and expected value a of the signal amplitude) that satisfy the detection performance. it can.

  The detection performance calculation unit 3 of the second embodiment can also calculate the detection performance of the signal processing unit that performs integration between scans based on the probability density function or cumulative distribution function of the Erlang distribution. Specifically, the detection performance of the signal processing unit that performs inter-scan integration can also be calculated by using equation (9). Further, by using the equation (9), the detection performance can be calculated without using an advanced mathematical function as in the equation (6) of the first embodiment.

  In the above-described embodiment, examples of the expression of the probability density function and cumulative distribution function of the gamma distribution and the probability density function and cumulative distribution function of the Erlang distribution are shown. The expression may be changed.

  A program for realizing the function of the detection performance calculation unit 1 in the above-described embodiment is recorded on a computer-readable recording medium, and the program recorded on the recording medium is read by a computer system and executed. You may make it operate | move as the performance calculation part 1. FIG. Note that the “computer system” here includes an OS (operating system) and hardware such as peripheral devices. The “computer system” includes a WWW system having a homepage providing environment (or display environment). The “computer-readable recording medium” refers to a portable medium such as a flexible disk, a magneto-optical disk, and a CD-ROM, and a recording device such as a hard disk and a ROM built in the computer system. Further, the “computer-readable recording medium” refers to a volatile memory (RAM) in a computer system that becomes a server or a client when a program is transmitted via a network such as the Internet or a communication line such as a telephone line. In this way, it is assumed to include those that hold a program for a certain period of time.

  The program may be transmitted from a computer system storing the program in a storage device or the like to another computer via a transmission medium or by a transmission wave in the transmission medium. Here, the “transmission medium” for transmitting the program refers to a medium having a function of transmitting information, such as a network (communication network) such as the Internet or a communication line (communication path) such as a telephone line. Further, the program may realize a part of the functions described above. Furthermore, what can implement | achieve the function mentioned above in combination with the program already recorded on the computer system, and what is called a difference file (difference program) may be sufficient.

  Although several embodiments have been described, these embodiments have been presented by way of example and are not intended to limit the scope of the invention. These novel embodiments can be implemented in various other forms, and various omissions, replacements, and changes can be made without departing from the scope of the invention. These embodiments and modifications thereof are included in the scope and gist of the invention, and are included in the invention described in the claims and the equivalents thereof.

DESCRIPTION OF SYMBOLS 1 Detection performance calculation part 2 Operation / display part 3 Detection performance calculation part 4 Signal processing part 101 Simulated signal generation part 102 Signal processing part (or signal processing simulation part)
103 Recording unit 104 Statistical processing unit 105 Operation / display unit

Claims (4)

A detection performance calculation unit that calculates at least one of detection performance and detection specifications of a signal processing unit that performs integration between scans based on a probability density function or cumulative distribution function of a gamma distribution or an Erlang distribution is provided. Detection performance calculation device. A detection performance calculation step for calculating at least one of detection performance and detection specifications of a signal processing unit that performs integration between scans based on a probability density function or cumulative distribution function of a gamma distribution or an Erlang distribution. Detection performance calculation method. Computer
A program for functioning as detection performance calculation means for calculating at least one of detection performance and detection specifications of a signal processing unit that performs integration between scans based on a probability density function or cumulative distribution function of gamma distribution or Erlang distribution. Based on a probability density function or cumulative distribution function of gamma distribution or Erlang distribution, a detection performance calculation unit that calculates at least one of detection performance and detection specifications of a signal processing unit that performs inter-scan integration,
A signal processing apparatus comprising: a signal processing unit that performs integration between scans based on the detection specifications calculated by the detection performance calculation unit.

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