JP5699404B2 - Radar received signal processing apparatus and method - Google Patents

Description

  Embodiments of the present invention relate to a radar reception signal processing apparatus and method for accurately detecting only a target signal from radar reception signals in which target signals and unnecessary signals are mixed in a radar.

  As is well known, a weather radar observes precipitation by receiving an echo of a weather target and analyzing the received power. The wind speed is also observed by analyzing the Doppler frequency of the radar reception signal using the Doppler effect of electromagnetic waves. Similarly, the detection radar detects the flying object by processing the reception signal of the echo of the flying object or the like.

  However, the radar reception signal includes not only the target signal but also an unnecessary signal composed of echoes of the earth, mountains, and the sea surface. Since unnecessary signals obstruct observation, a moving target indicator (MTI) is used in the received signal processing device of the radar to remove the unnecessary signals.

  However, the MTI removes unnecessary signals with a low-frequency cutoff filter in which a cutoff frequency is set in advance using the difference in frequency change between the target signal and the unnecessary signal. Therefore, components below the set cut-off frequency are removed without distinguishing between the target signal and the unnecessary signal.

  For example, in a weather radar, if the weather echo and the unnecessary signal have the same frequency change, it is not possible to accurately remove only the unnecessary signal, so that it is not possible to correctly observe precipitation and wind speed.

Masahito Ishihara, Principle and Basics of Doppler Weather Radar, Meteorological Research Note No.200, Japan Meteorological Association, pp.1-38, 2001

  As described above, in the conventional radar received signal processing apparatus, when the target signal and the unnecessary signal have the same frequency change, the two cannot be accurately distinguished, and the target signal is removed. was there.

According to the embodiment, a radar radar reception signal of a weather radar including a weather echo and a terrain echo, which is repeatedly obtained at a constant period, is converted into a frequency domain to obtain a frequency spectrum, and the radar reception signal acquired at the constant period is obtained. The frequency spectrum represents the spectrum shape of the weather echo, and represents the spectrum shape of the first density function by the von Mises distribution having the power value, the Doppler frequency, and the spectrum width as parameters and the topographic echo, the power value, the Doppler frequency. A process of sequentially modeling with a mixed density function that is a sum of second density functions by a normal distribution with a spectral width as a parameter, an echo mixture ratio of the mixed density function, the first density function, and a second density function Each parameter is repeatedly executed as a variable, and the frequency spectrum is matched. That applies Mari degree of mixing density function sequentially estimated as the echo mixing ratio and the optimum value of the parameter of each of the first and second density function when a maximum, based on the von Mises distribution, the estimated The reception value, average Doppler frequency, and spectrum width of the meteorological echo included in the radar reception signal from the optimum values of the power value, Doppler frequency, and spectrum width, which are parameters of the first density function sequentially estimated by the means, are meteological echoes. In the estimation of the parameter, the second density function is determined from the data of terrain echoes observed in advance, and the parameter of the determined second density function is used as a variable from the statistical properties. A prior distribution followed by the second density function is determined, and the likelihood function obtained by observing the determined prior distribution and the radar reception signal is determined; The posterior distribution is calculated from the parameters, and the parameter of the mixed density function when the posterior distribution is maximized is estimated as an optimum value, and the maximization of the posterior distribution is performed by calculating the mixture density function with respect to the frequency spectrum. Evaluate the fit with a penalty-likelihood function and calculate each parameter of the mixed density function when maximizing the expected value of the penalty-likelihood function until the value of the parameter converges The penalty-likelihood function determines the prior distribution that each parameter of the mixed density function follows from the statistical properties of the average Doppler frequency, spectrum width, and received power of the echo group, and the prior distribution is The penalty is determined by adding to the likelihood function .

The block diagram which shows the structure of the weather radar signal processing apparatus with which the radar received signal processing apparatus of embodiment is applied. 5 is a flowchart illustrating a flow of processing for calculating an average Doppler frequency, a spectrum width, and reception power of a target signal from a radar reception signal in the radar reception signal processing device of the embodiment. In the said embodiment, it is a wave form diagram which shows a mode that the frequency spectrum of a radar received signal is modeled with a mixed density function. In the said embodiment, it is a flowchart which shows the flow of a process of the parameter estimation method of the optimal mixing density function using prior knowledge. In the said embodiment, it is a flowchart which shows the flow of a process of the parameter estimation method of the optimal mixing density function. In the said embodiment, it is a flowchart which shows the example of the flow of a process which calculates precipitation and a wind speed from a radar received signal.

  Hereinafter, embodiments will be described with reference to the drawings.

  FIG. 1 is a block diagram illustrating a configuration of a weather radar signal processing device to which a radar reception signal processing device according to an embodiment is applied. In FIG. 1, the radar pulse signal generated by the pulse signal generator 11 is frequency-converted by the transmission device 12, power amplified, and radiated from the antenna 14 toward the space via the circulator 13.

  The reflected signal of the radar wave received by the antenna 14 is sent to the receiving device 15 via the circulator 13. The receiving device 15 amplifies the signal received by the antenna 14 and converts the frequency to baseband, and the output is sent to the radar received signal processing device 16.

  The radar reception signal processing device 16 converts the input radar reception signal into digital data by the A / D converter 161, converts it into IQ data in a complex format by the IQ detector 162, and converts the terrain echo by the observation processor 163. The observation data by weather echo is obtained by removing the components.

  FIG. 2 is a flowchart showing a flow of processing for calculating the average Doppler frequency, spectrum width, and received power of the target signal (meteorological echo component) from the radar received signal (IQ data) in the observation processor 163.

  First, a frequency spectrum is obtained by converting the radar received signal into the frequency domain (step S11). Next, the obtained frequency spectrum is modeled with a mixed density function (step S12). Subsequently, the optimum value of the parameter of the mixed density function is estimated by learning (step S13), and the average Doppler frequency, spectrum width, and received power of the target signal are calculated from the estimated parameter and output as the observation result (step S14). .

  FIG. 3 is a waveform diagram for explaining the process of modeling the frequency spectrum with the mixed density function in step S12, wherein A represents the frequency spectrum and B represents the mixed density function. In FIG. 3, the horizontal axis X represents the Doppler velocity [m / s], and the vertical axis Y represents the amplitude [dB]. First, a mixed density function for modeling the frequency spectrum is given. The mixed density function is represented by the sum of the density functions of a plurality of echoes, and the parameter is a value related to the mixing ratio and spectral shape of each echo.

  The use of prior knowledge can be considered for estimating the optimum parameter of the mixing density function corresponding to the frequency spectrum. FIG. 4 shows the flow of processing when estimating the parameters of the optimal mixing density function using prior knowledge.

  In FIG. 4, first, prior distribution is determined from statistical properties using parameters of density function of each of a plurality of echoes as variables from prior knowledge (step S21). The posterior distribution is calculated from the determined prior distribution and the likelihood by observation, and the optimal mixture density function parameter is obtained by maximizing the posterior distribution (step S22).

  FIG. 5 is a flowchart showing a method for estimating the optimum parameter of the mixed density function by maximizing the posterior distribution. First, a likelihood function with a penalty is determined using the frequency spectrum and prior knowledge (step S31). Next, an expected value of the logarithmic likelihood function with a penalty is calculated from the determined likelihood function with a penalty (step S32). Subsequently, a parameter that maximizes the expected value of the log-likelihood function with a penalty is calculated (step 33). Here, it is determined whether or not the parameter value has converged (step S34). If the parameter value has not converged, the process returns to step S32. That is, the procedure from the expected value calculation of the logarithmic likelihood function with a penalty is performed again using the parameter that maximizes the expected value, and is repeated until the parameter value converges. The value of the converged parameter is set as a parameter of a mixing density function that is optimal for modeling the frequency spectrum of the radar reception signal.

Example 1
FIG. 6 is a specific example when the above embodiment is applied to a weather radar signal processing apparatus (referred to as Example 1), and is a flowchart showing the flow of processing when calculating precipitation and wind speed from a radar received signal. .

In FIG. 6, first, the radar reception signal is converted into the frequency domain, and the amplitude component y _i of the frequency spectrum is obtained (step S41). Next, a mixed density function for modeling the obtained frequency spectrum is given (step 42). Here, a normal distribution f ₁ (x | θ ₁ ) expressed by the following equation (1) is used as a distribution for modeling an unnecessary signal (echo component of ground clutter). In equation (1), x represents the Doppler velocity. Θ = (τ ₁ , τ ₂ , θ ₁₁ , θ ₁₂ , θ ₂₁ , θ ₂₂ ) is a parameter of the mixing density function, and the initial value is arbitrarily set.
f ₁ (x | θ ₁ ) = (2πθ ₁₂ ) ^-1/2 exp {-(x-θ ₁₁ ) ² / (2θ ₁₂ )}… (1)
Further, the von Mises distribution f ₂ (x | θ ₂ ) expressed by the following equation (2) is used as a distribution for modeling the weather echo.
f ₂ (x | θ ₂ ) = exp {θ ₂₂ cos (x-θ ₂₁ )} / {2πI ₀ (θ ₂₂ )}… (2)
I ₀ represents a zero-order modified Bessel function.

From these equations (1) and (2), the mixed density function f (x | θ) for modeling the frequency spectrum is expressed by the following equation (3).
f (x | θ) = τ ₁ f ₁ (x | θ ₁ ) + τ ₂ f ₂ (x | θ ₂ )… (3)
Subsequently, the mixing ratios T _{1, i} and T _{2, i} are calculated by the following equations (4) and (5) from the given mixing density function (step S43).
T _{1, i} = τ ₁ f ₁ (x _i | θ ₁ ) / {f (x | θ)}… (4)
T _{2, i} = τ ₂ f ₂ (x _i | θ ₂ ) / {f (x | θ)}… (5)
Next, a prior distribution is determined from previously observed data (step S44). First, it is assumed that the parameter relating to the power value of the unnecessary signal follows the beta distribution p ₁ (τ ₁ ) expressed by the following equation (6).
p ₁ (τ ₁ ) = {τ ₁ ^α-1 (1-τ ₁ ) ^β-1 } / B (α, β)… (6)
Here, B (α, β) represents a beta function.

The parameter relating to the Doppler frequency of the unnecessary signal is assumed to follow a normal distribution p ₂ (θ ₁₁ ) expressed by the following equation (7).
p ₂ (θ ₁₁ ) = (2πφ ₂ ) ^-1/2 exp {-(θ ₁₁ -φ ₁ ) ² / (2φ ₂ )}… (7)
Further, it is assumed that the parameter relating to the spectrum width of the unnecessary signal follows the gamma distribution p ₃ (θ ₁₂ ) expressed by the following equation (8).
p ₃ (θ ₁₂ ) = b ^-a θ ₁₂ ^a-1 exp (-θ ₁₂ / b) / Γ (a)… (8)
Here, Γ (a) represents a gamma function. These prior distribution parameters α, β, φ ₁ , φ ₂ , a and b are determined from data of unnecessary signals observed in advance.

Next, each parameter Q (θ | θ ^(t) ) is maximized by partially differentiating the expected value of the log-likelihood function with penalty shown in Equation (9) with each parameter (step S45).
Q (θ | θ ^(t) ) = Σ ⁿ _{i = 1} [y _i T _{1, i} {logτ ₁ f ₁ (θ ₁ | x _i )} + y _i T _{2, i} {logτ ₂ f ₂ (θ ₂ | x _i )}]
+ S ₁ log {p ₁ (τ ₁ )} + S ₂ log {p ₂ (θ ₁₁ )} + S ₃ log {p ₃ (θ ₁₂ )}… (9)
Here, n represents the number of sample points of the Fourier transform. Further, (t) represents the number of repetitions of steps S43 and S45. The update formula for each parameter is shown below.

τ ₁ = {Σ ⁿ _{i = 1} y _i T _{1, i} + S ₁ (α-1)} / {Σ ⁿ _{i = 1} y _i + S ₁ (α + β-2)}… (10)
τ ₂ = 1-τ ₁ (11)
θ ₁₁ = {Σ ⁿ _{i = 1} y _i T _{1, i} x _i + S ₂ (φ ₁ θ ₁₂ / φ ₂ )} / {Σ ⁿ _{i = 1} y _i T _{1, i} + S ₂ (θ ₁₂ / φ ₂ )}
… (12)
θ ₁₂ = (1-S ₃ ) {Σ ⁿ _{i = 1} y _i T _{1, i} (x _i -θ ₁₁ ) ² / Σ ⁿ _{i = 1} y _i T _{1, i} }
+ S ₃ {-Σ ⁿ _{i = 1} y _i T _{1, i} +2 (a-1) + [{Σ ⁿ _{i = 1} y _i T _{1, i} -2 (a-1)} ² + 8 / bΣ ⁿ _{i = 1} y _i T _{1, i} (x _i -θ ₁₁ ) ² ] ^1/2 } / {4 / b}
…(13)
θ ₂₁ = tan ^-1 {(Σ ⁿ _{i = 1} y _i T _{2, i} sinx _i ) / (Σ ⁿ _{i = 1} y _i T _{2, i} cosx _i )}… (14)
I ₁ (θ ₂₂ ) / I ₀ (θ ₂₂ ) = Σ ⁿ _{i = 1} y _i T _{2, i} cos (x _i − θ ₂₁ ) / Σ ⁿ _{i = 1} y _i T _{2, i} (15)
As described above, θ ₂₂ is obtained by solving the equation (15). S ₁ , S ₂ , and S ₃ take 1 or 0, and S ₁ = 1 if prior knowledge about the power value of unnecessary signals is used, and S ₁ = 0 if not. Further, S ₂ = 1 is used when prior knowledge about the Doppler frequency of the unnecessary signal is used, and S ₂ = 0 when not used. Further, S ₃ = 1 is used when prior knowledge about the spectrum width of the unnecessary signal is used, and S ₃ = 0 when not used.

  Next, it is determined whether or not the parameters calculated according to the above formula have converged (step S46). In this determination process, when the difference between the parameter at the time of calculating the mixture ratio and the updated parameter is 1/1000 or less, it is determined that the parameter has converged. If the difference is larger than that, the processes in steps S43 and S45 are performed again using the calculated parameters.

  If it is determined that the parameters have converged, the average Doppler frequency, spectrum width, and received power of the weather echo are calculated as estimated values from the estimated von Mises distribution parameters (step S47). Subsequently, precipitation and wind speed are calculated from the estimated average Doppler frequency of the weather echo, spectrum width, and received power (step S48).

  By performing the above processing, it is possible to estimate the components of the weather echo and the terrain echo with high accuracy even if the terrain echo by the ground clutter overlaps with the weather echo as an unnecessary signal. Precipitation and wind speed can be reliably estimated from data with mixed echoes.

(Example 2)
In the first embodiment, the case where the frequency spectrum of the received signal is modeled by the sum of two density functions assuming a weather echo and a terrain echo (ground clutter) has been described. According to such processing, a certain degree of effect can be expected, but the actual reception signal includes unnecessary components such as noise (hereinafter referred to as unnecessary echo) in addition to the weather echo and the terrain echo. It is assumed that modeling the frequency spectrum of such a received signal as the sum of two density functions assuming a weather echo and a terrain echo will cause an error in weather echo estimation.

  Therefore, as a second embodiment, a case where modeling is performed using the sum of three density functions including unnecessary echoes such as noise will be described with reference to FIG. 6 again.

In FIG. 6, first, the radar reception signal is converted into the frequency domain, and the amplitude component y _i of the frequency spectrum is obtained (step S41). Next, a mixed density function for modeling the obtained frequency spectrum is given (step 42). Here, a normal distribution f ₁ (x | θ ₁ ) expressed by the following equation (16) is used as a distribution for modeling unnecessary signals (terrain echoes and unnecessary echoes). Where x represents the Doppler velocity. θ = (τ ₁ , τ ₂ , τ ₃ , θ ₁₁ , θ ₁₂ , θ ₂₁ , θ ₂₂ ) is a parameter of the mixed density function, and the initial value is arbitrarily set.
f ₁ (x | θ ₁ ) = (2πθ ₁₂ ) ^-1/2 exp {-(x-θ ₁₁ ) ² / (2θ ₁₂ )}… (16)
Further, the von Mises distribution f ₂ (x | θ ₂ ) expressed by the following equation (17) is used as a distribution for modeling weather echoes.
f ₂ (x | θ ₂ ) = exp {θ ₂₂ cos (x-θ ₂₁ )} / {2πI ₀ (θ ₂₂ )}… (17)
I ₀ represents a zero-order modified Bessel function.

Further, a uniform distribution f ₃ (x | θ ₃ ) expressed by the following equation (18) is used as a distribution for modeling unnecessary echoes other than the above.

f ₃ (x | θ ₃ ) = 1 / (2V _nyq )… (18)
Here, V _nyq represents the Nyquist speed.

From these equations (16), (17), and (18), the mixed density function f (x | θ) for modeling the frequency spectrum is expressed by the following equation (19).
f (x | θ) = τ ₁ f ₁ (x | θ ₁ ) + τ ₂ f ₂ (x | θ ₂ ) + τ ₃ f ₃ (x | θ ₃ )… (19)
Subsequently, the mixing ratios T _{1, i} , T _{2, i} , T _{3, i} are calculated from the given mixing density function by the following equations (20), (21), (22), respectively (step S43).
T _{1, i} = τ ₁ f ₁ (x _i | θ ₁ ) / {f (x _i | θ)}… (20)
T _{2, i} = τ ₂ f ₂ (x _i | θ ₂ ) / {f (x _i | θ)}… (21)
T _{3, i} = τ ₃ f ₃ (x _i | θ ₃ ) / {f (x _i | θ)}… (22)
Next, a prior distribution is determined from previously observed data (step S44). First, it is assumed that the parameter relating to the power value of the unnecessary signal follows the beta distribution p ₁ (τ ₁ ) expressed by the following equation.
p ₁ (τ ₁ ) = {τ ₁ ^α-1 (1-τ ₁ ) ^β-1 } / B (α, β)… (23)
Here, B (α, β) represents a beta function.

It is assumed that the parameter relating to the Doppler frequency of the unnecessary signal follows a normal distribution p ₂ (θ ₁₁ ) expressed by the following equation.
p ₂ (θ ₁₁ ) = (2πφ ₂ ) ^-1/2 exp {-(θ ₁₁ -φ ₁ ) ² / (2φ ₂ )}… (24)
Further, it is assumed that a parameter relating to the spectrum width of the unnecessary signal follows a gamma distribution p ₃ (θ ₁₂ ) expressed by the following equation.
p ₃ (θ ₁₂ ) = b ^-a θ ₁₂ ^a-1 exp (-θ ₁₂ / b) / Γ (a)… (25)
Here, Γ (a) represents a gamma function. These prior distribution parameters α, β, φ ₁ , φ ₂ , a and b are determined from data of unnecessary signals observed in advance.

Next, each parameter Q (θ | θ ^(t) ) is maximized by partially differentiating the expected value of the log-likelihood function with penalty shown in Expression (26) with each parameter (step S45).
Q (θ | θ ^(t) ) = Σ ⁿ _{i = 1} [y _i T _{1, i} {logτ ₁ f ₁ (θ ₁ | x _i )} + y _i T _{2, i} {logτ ₂ f ₂ (θ ₂ | x _i )}
+ y _i T _{3, i} {logτ ₃ f ₃ (θ ₃ | x _i )}]
+ S ₁ log {p ₁ (τ ₁ )} + S ₂ log {p ₂ (θ ₁₁ )} + S ₃ log {p ₃ (θ ₁₂ )}… (26)
Here, n represents the number of sample points of the Fourier transform. Further, (t) represents the number of repetitions of steps S43 and S45.

The update formula for each parameter is shown below.
τ ₁ = {Σ ⁿ _{i = 1} y _i T _{1, i} + S ₁ (α-1)} / {Σ ⁿ _{i = 1} y _i + S ₁ (α + β-2)}… (27)
τ ₂ = {Σ ⁿ _{i = 1} y _i T _{2, i} -S ₁ τ ₁ Σ ⁿ _{i = 1} y _i T _{2, i} } / {Σ ⁿ _{i = 1} y _i (T _{2, i} + S ₁ T _{3, i} )}
… (28)
τ ₃ = 1-τ ₁ -τ ₂ (29)
θ ₁₁ = {Σ ⁿ _{i = 1} y _i T _{1, i} x _i + S ₂ (φ ₁ θ ₁₂ / φ ₂ )} / {Σ ⁿ _{i = 1} y _i T _{1, i} + S ₂ (θ ₁₂ / φ ₂ )}
… (30)
θ ₁₂ = (1-S ₃ ) {Σ ⁿ _{i = 1} y _i T _{1, i} (x _i -θ ₁₁ ) ² / Σ ⁿ _{i = 1} y _i T _{1, i} }
+ S ₃ {-Σ ⁿ _{i = 1} y _i T _{1, i} +2 (a-1) + [{Σ ⁿ _{i = 1} y _i T _{1, i} -2 (a-1)} ²
+ 8 / bΣ ⁿ _{i = 1} y _i T _{1, i} (x _i -θ ₁₁ ) ² ] ^1/2 } / {4 / b}… (31)
θ ₂₁ = tan ^-1 {(Σ ⁿ _{i = 1} y _i T _{2, i} sinx _i ) / (Σ ⁿ _{i = 1} y _i T _{2, i} cosx _i )}… (32)
I ₁ (θ ₂₂ ) / I ₀ (θ ₂₂ ) = Σ ⁿ _{i = 1} y _i T _{2, i} cos (x _i − θ ₂₁ ) / Σ ⁿ _{i = 1} y _i T _{2, i} … (33)
Here, θ ₂₂ can be obtained by solving equation (33). S ₁ , S ₂ , and S ₃ take 1 or 0, and S ₁ = 1 if prior knowledge about the power value of the unnecessary signal is used, and S ₁ = 0 otherwise. Further, S ₂ = 1 is used when prior knowledge about the Doppler frequency of the unnecessary signal is used, and S ₂ = 0 when not used. In addition, S ₃ = 1 when prior knowledge about the spectrum width of unnecessary signals is used, and S ₃ = 0 when not used.

  Next, it is determined whether or not the parameters calculated according to the above formula have converged (step S46). In this determination process, when the difference between the parameter at the time of calculating the mixture ratio and the updated parameter is 1/1000 or less, it is determined that the parameter has converged. If the difference is larger than that, the processes in steps S43 and S45 are performed again using the calculated parameters.

  If it is determined that the parameters have converged, the average Doppler frequency, spectrum width, and received power of the weather echo are calculated as estimated values from the estimated von Mises distribution parameters (step S47). Subsequently, precipitation and wind speed are calculated from the estimated average Doppler frequency of the weather echo, spectrum width, and received power (step S48).

  By performing the above processing, it is possible to accurately estimate the components of weather echoes, terrain echoes, and unwanted echoes even in situations where unwanted echoes such as ground clutter and noise are superimposed on the weather echoes as unwanted signals. Therefore, precipitation and wind speed can be reliably estimated from data in which weather echoes, topographic echoes and unnecessary echoes are mixed.

  Although the above embodiment has been described assuming the case of a weather radar, the present invention can be similarly applied to a normal radar apparatus, that is, a case where a target signal is obtained by removing an unnecessary signal from a radar reception signal. Further, the present invention can be similarly implemented when using a radar apparatus that electronically scans a transmission beam, such as an active phased array radar, or a radar apparatus that forms a plurality of reception beams using digital beam forming technology. Therefore, according to the above embodiment, it is possible to provide a radar reception signal processing device that accurately detects only a target signal from a radar reception signal in which a target signal having a similar frequency change and an unnecessary signal are mixed.

  In addition, the said embodiment is not limited as it is, In the implementation stage, a component can be deform | transformed and embodied in the range which does not deviate from the summary. Moreover, an appropriate combination of a plurality of constituent elements disclosed in the above embodiment may be used. For example, some components may be deleted from all the components shown in the embodiment. Furthermore, constituent elements over different embodiments may be appropriately combined.

  DESCRIPTION OF SYMBOLS 11 ... Pulse signal generation part, 12 ... Transmitter, 13 ... Circulator, 14 ... Antenna, 15 ... Receiver, 16 ... Radar received signal processor, 161 ... A / D converter, 162 ... IQ detector, 163 ... Observation Processor.

Claims (4)

Obtaining means for obtaining a frequency spectrum by repeatedly converting a radar reception signal of a weather radar including a weather echo and a terrain echo into a frequency domain, which is repeatedly obtained at a constant period;
The first density function by the von Mises distribution representing the spectrum shape of the weather echo and the power value, the Doppler frequency, and the spectrum width as parameters for the frequency spectrum of the radar reception signal acquired at the fixed period and the topographic echo The process of sequentially modeling with a mixed density function that is the sum of a second density function by a normal distribution with the power value, Doppler frequency, and spectral width as parameters is represented by the echo mixture ratio of the mixed density function, The parameters of the first density function and the second density function are repeatedly executed as variables, and the echo mixture ratio and the first and second values when the fit of the mixed density function with respect to the frequency spectrum is maximized are maximized. estimation of sequentially estimating the second density function of each parameter as the optimum value And means,
Reception of weather echoes included in the radar reception signal from the optimum values of the power value, Doppler frequency, and spectrum width, which are parameters of the first density function sequentially estimated by the estimation unit based on the von Mises distribution. Including weather echo information calculating means for calculating power, average Doppler frequency, spectrum width as weather echo information ,
In the estimation means,
Determining the second density function from previously observed terrain echo data, using a parameter of the determined second density function as a variable, determining a prior distribution followed by the second density function from statistical properties; The posterior distribution is calculated from the determined prior distribution and the likelihood function by observation of the radar reception signal, and the parameter of the mixed density function when the posterior distribution is maximized is estimated as an optimum value.
The posterior distribution is maximized by evaluating the degree of fit of the mixed density function with respect to the frequency spectrum using a penalty likelihood function and maximizing the expected value of the penalty likelihood function. The procedure of calculating each parameter of is repeated until the value of the parameter converges,
The penalty-likelihood function determines the prior distribution that each parameter of the mixed density function follows from the statistical properties of the average Doppler frequency, spectrum width, and received power of the echo group, and the prior distribution is considered as the penalty. A radar received signal processing apparatus characterized by being determined by adding to a degree function .   2. The radar received signal according to claim 1, further comprising weather information calculating means for calculating weather information of precipitation and wind speed from the average Doppler frequency, spectrum width and received power calculated as the weather echo information. Processing equipment. It is obtained repeatedly at a fixed period, and the radar signal received by the weather radar including weather echo and topographic echo is converted to the frequency domain to obtain the frequency spectrum,
The first density function by the von Mises distribution representing the spectrum shape of the weather echo and the power value, the Doppler frequency, and the spectrum width as parameters for the frequency spectrum of the radar reception signal acquired at the fixed period and the topographic echo The process of sequentially modeling with a mixed density function that is the sum of a second density function by a normal distribution with the power value, Doppler frequency, and spectral width as parameters is represented by the echo mixture ratio of the mixed density function, The parameters of the first density function and the second density function are repeatedly executed as variables, and the echo mixture ratio and the first and second values when the degree of fit of the mixed density function to the frequency spectrum is maximized. Sequentially estimate the parameters of each density function as optimal values ,
Reception of weather echoes included in the radar reception signal from the optimum values of the power value, Doppler frequency, and spectrum width, which are parameters of the first density function sequentially estimated by the estimation unit based on the von Mises distribution. Power, average Doppler frequency, and spectrum width shall be calculated as weather echo information .
In the estimation of the parameters,
Determining the second density function from previously observed terrain echo data, using a parameter of the determined second density function as a variable, determining a prior distribution followed by the second density function from statistical properties; The posterior distribution is calculated from the determined prior distribution and the likelihood function by observation of the radar reception signal, and the parameter of the mixed density function when the posterior distribution is maximized is estimated as an optimum value.
The posterior distribution is maximized by evaluating the degree of fit of the mixed density function with respect to the frequency spectrum using a penalty likelihood function and maximizing the expected value of the penalty likelihood function. The procedure of calculating each parameter of is repeated until the value of the parameter converges,
The penalty-likelihood function determines the prior distribution that each parameter of the mixed density function follows from the statistical properties of the average Doppler frequency, spectrum width, and received power of the echo group, and the prior distribution is considered as the penalty. A radar received signal processing method characterized by being determined by adding to a degree function . 4. The radar received signal processing method according to claim 3 , further comprising calculating precipitation and wind speed weather information from the average Doppler frequency, spectrum width and received power calculated as the weather echo information.

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