CN113010991B - Spectral radiometer system simulation and performance evaluation method - Google Patents
Spectral radiometer system simulation and performance evaluation method Download PDFInfo
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Abstract
The invention belongs to the technical field of microwave remote sensing instruments and signal processing, and particularly relates to a simulation method based on a spectrum radiometer system, which comprises the following steps: respectively simulating and generating a cold calibration source input signal, a hot calibration source input signal and an input signal of a scene target source according to a pre-established thermal radiation noise model; the cold calibration source input signal, the hot calibration source input signal and the input signal of the scene target source are respectively input into a spectrum radiometer system, a cold output power spectrum, a hot calibration source output power spectrum and a scene target source output power spectrum are correspondingly output, and the output radiation spectrum of the scene target source is determined through calibration according to the cold output power spectrum, the hot calibration source output power spectrum and the scene target source output power spectrum; calculating performance indexes of a spectrum radiometer simulation system according to the output radiation spectrum of the scene target source; and adjusting the design index of the spectrum radiometer system until the performance index meets the requirement.
Description
Technical Field
The invention belongs to the technical field of microwave remote sensing instruments and signal processing, and particularly relates to a spectrum radiometer system simulation and performance evaluation method.
Background
High-precision earth atmosphere observation is the basis of numerical weather forecast and climate change research. Satellites can provide global atmospheric monitoring in a short period of time. Instruments such as nadir microwave probes and infrared detectors have been used to measure atmospheric temperature and humidity, but have poor vertical resolution and height ranges.
Terahertz critical edge detection is a particularly important technology in stratosphere and middle layer temperature and chemical detection, and has great potential in global wind measurement of middle and high-level atmosphere. At present, the terahertz edge detector adopts a spectrum radiometer, so that not only can the better vertical resolution be provided, but also the chemical component information can be acquired in a wider height range, and the influence of day and night circulation is avoided.
The existing spectrum radiometer has a simple structure, can detect the radiation spectrum of a target, and is widely applied to edge detection. At present, the system design process of the spectrum radiometer is simple and rough, and the number of channels of the system is determined only through a known spectrum resolution formula, but the formula is not combined with the radiation characteristic of the target, so that the design index is not fine enough. In addition, the conventional method based on the spectrum radiometer system has no difficulty in considering errors caused by side band unbalance, quantization errors and window function selection, which brings great limitation to quantitative remote sensing.
Disclosure of Invention
The invention aims to solve the defects in the prior art, and provides a spectrum radiometer system simulation and performance evaluation method, which establishes a parameterized model and a simulation framework of a spectrum radiometer from the perspective of signal processing, evaluates simulation results, and when performance indexes meet preset expectations, the corresponding performance indexes are reasonable performance index values; and if the corresponding performance index does not meet the preset expected, adjusting the performance index until the adjusted performance index meets the preset expected, and finishing.
In order to achieve the above object, the present invention provides a method for simulating a spectrum radiometer system, which specifically includes:
respectively simulating and generating a cold calibration source input signal, a hot calibration source input signal and an input signal of a scene target source according to a pre-established thermal radiation noise model;
the cold calibration source input signal, the hot calibration source input signal and the input signal of the scene target source are respectively input into a spectrum radiometer system to correspondingly output a cold output power spectrum, a hot calibration source output power spectrum and a scene target source output power spectrum,
determining an output radiation spectrum of a scene target source through calibration according to the cold output power spectrum, the hot calibration source output power spectrum and the scene target source output power spectrum;
calculating performance indexes of a spectrum radiometer simulation system according to the output radiation spectrum of the scene target source;
and adjusting the design index of the spectrum radiometer system until the performance index meets the requirement.
As one of the improvements of the technical scheme, according to a pre-established thermal radiation noise model, respectively generating a cold calibration source input signal, a thermal calibration source input signal and an input signal of a scene target source in a simulation mode; the method comprises the following steps:
when the radiation spectrum of the observation target is a cold calibration source, the cold calibration source is a constant, and the thermal radiation noise is Gaussian white noise with band limitation; wherein, gaussian white noise is generated by pseudo random numbers, and the average value is 0; cold standard deviation sigma of white gaussian noise 1 Determined by equation (1):
wherein sigma 1 Cold standard deviation of gaussian white noise; k is boltzmann constant; t (T) C The bright temperature of the cold calibration source, namely the bright temperature of the thermal radiation noise;
a group of bright temperatures T can be generated by using the formula (2) C Is a time series of (a):
s C [i]～N(μ,σ 1 2 ) (2)
wherein s is C [i]Inputting a signal for a cold calibration source; i is the number of signal points; n (mu, sigma) 1 2 ) Representing a normal distribution; mu is the average value of normal distribution; sigma (sigma) 1 2 Standard deviation of normal distribution;
when the radiation spectrum of the observation target is a thermal calibration source, the thermal calibration source is a constant, and the thermal radiation noise is Gaussian white noise with band limitation; wherein Gaussian white noise passes through pseudo-randomGenerating the number of machines, wherein the average value is 0; thermal standard deviation sigma of Gaussian white noise 2 Determined by equation (3):
wherein sigma 2 Is the thermal standard deviation of Gaussian white noise; k is boltzmann constant; t (T) H The bright temperature of the thermal calibration source, namely the bright temperature of thermal radiation noise;
a set of bright temperatures T can be generated by using the formula (4) H Is a time series of (a):
s H [i]～N(μ,σ 2 2 ) (4)
wherein s is H [i]Inputting a signal for a thermal calibration source; i is the number of signal points: n (mu, sigma) 2 2 ) Representing a normal distribution; mu is the average value of normal distribution; sigma (sigma) 2 Is the standard deviation of the normal distribution.
When the brightness temperature T of the thermal radiation noise is respectively the brightness temperature T of the thermal calibration source H Or the bright temperature T of a cold calibration source C When in use; respectively generating a cold scaling source input signal and a hot scaling source input signal s by simulation according to formulas (2) and (4) C [i]Sum s H [i]And generates heat source spectrum S of heat radiation noise through FFT operation H [i]Or cold source spectrum S C [i]；
When the radiation spectrum of the observation target is a scene target source, a bright temperature reference T is assumed ref A lower noise signal; performing i-point Fourier transform on the signal to obtain the noise signal s ref [i]:
s ref [i]～N(μ,σ 2 /π 2 ) (5)
Wherein s is ref [i]The lighting temperature of each frequency point is T ref The method comprises the steps of carrying out a first treatment on the surface of the Sigma is the thermal standard deviation of gaussian white noise or the cold standard deviation of gaussian white noise;
from the gaussian distribution, an input noise signal with a radiation spectrum T (f), i.e. a scene target source input signal, is obtained:
wherein s is T(f) [i]Inputting signals for a scene target source; t (f) is the radiation spectrum; t (T) ref Is S ref [i]The lighting temperature of each frequency point;
when the bright temperature T of the thermal noise is the bright temperature T of the scene target source S (f) When in use; generating a scene target source input signal s in a simulation manner according to equation (6) T(f) [i]And generates scene target source spectrum S of thermal radiation noise through FFT operation S [i]。
As one of the improvements of the above technical solutions, the spectrum radiometer system includes a radio frequency front-end signal model and a digital back-end signal model;
the establishment of the radio frequency front end signal model specifically comprises the following steps:
according to formula (7), a radio frequency front end signal model is established, and the signal spectrum after passing through the radio frequency front end can be expressed as:
S fe [i]＝(S u [i]·SRF u [i]+flip(S l [i]·SRF l [i])) (7)
wherein flip () represents the array inverse; s is S fe [i]The frequency spectrum of the output signal output by the radio frequency front end signal model; s is S u [i]And S is l [i]The frequency spectrum of the input noise signal of the upper sideband and the lower sideband respectively; wherein the frequency spectrum of the input noise signal is the heat source frequency spectrum S of radiation noise H [i]Spectrum S of cold source C [i]Or scene target source spectrum S of thermal radiation noise S [i]The method comprises the steps of carrying out a first treatment on the surface of the The frequency spectrum of the output signal is S H [i]Frequency spectrum of corresponding output signal, S C [i]Frequency spectrum or S of corresponding output signal S [i]The frequency spectrum of the corresponding output signal; SRF (SRF) u [i]And SRF (SRF) l [i]Channel response functions of the upper sideband and the lower sideband respectively;
channel response function SRF through upper and lower sidebands u [i]And SRF (SRF) l [i]For S fe [i]IFFT is carried out to obtain the output signal s of the radio frequency front end fe [i]Completing the establishment of a radio frequency front end signal model; wherein, shootSignal s output from the frequency front end fe [i]The method comprises the steps of outputting a signal for a cold calibration source, outputting a signal for a hot calibration source or outputting a signal for a scene target source;
the digital back-end signal model is established specifically as follows:
the spectrum radiometer system is used as a discrete system to finish sampling the radio frequency front end output signal output by the radio frequency front end signal model;
radio frequency front end output signal s output to radio frequency front end signal model fe [i]Quantization is carried out to obtain quantized signals
Wherein Q is n []Representing the RF front end output signal s output to the RF front end signal model fe [i]Performing n bit quantization operation;
for quantized signalsFirstly, performing i-point FFT operation, and then squaring a modulus to obtain an output power spectrum S output by a digital back-end signal model be [i]：
Completing the establishment of a digital back-end signal model; wherein, the output power spectrum S output by the digital back-end signal model be [i]The method is an output power spectrum corresponding to the cold calibration source output signal, an output power spectrum corresponding to the hot calibration source output signal or an output power spectrum corresponding to the scene target source output signal.
As one of the improvements of the technical scheme, the cold calibration source input signal, the hot calibration source input signal and the input signal of the scene target source are respectively input into a spectrum radiometer system to correspondingly output a cold output power spectrum, a hot calibration source output power spectrum and a scene target source output power spectrum; the method comprises the following steps:
respectively inputting the cold calibration source input signal, the hot calibration source input signal and the input signal of the scene target source into a radio frequency front end signal model, and obtaining a cold calibration source output signal, a hot calibration source output signal and a scene target source output signal according to a formula (7);
and then the obtained cold calibration source output signal, the hot calibration source output signal and the scene target source output signal are respectively input into a digital back-end signal model, and a cold output power spectrum, a hot calibration source output power spectrum and a scene target source output power spectrum are obtained according to formulas (8) and (9), namely, an output power spectrum corresponding to the cold calibration source output signal, an output power spectrum corresponding to the hot calibration source output signal or an output power spectrum corresponding to the scene target source output signal.
As one of the improvements of the technical scheme, the output radiation spectrum of the scene target source is determined through calibration according to the cold output power spectrum, the thermal calibration source output power spectrum and the scene target source output power spectrum; the method comprises the following steps:
and according to the obtained cold output power spectrum, the obtained heat calibration source output power spectrum and the obtained scene target source output power spectrum, performing two-point calibration on the scene target output power spectrum of each frequency point through the cold calibration source and the heat calibration source with known bright temperatures, and determining the output radiation spectrum of the scene target.
As one of the improvements of the above technical solutions, the performance indexes of the spectrum radiometer simulation system include: scaling accuracy and spectral resolution.
As one of the improvements of the above technical solution, the calculating the performance index of the spectrum radiometer system according to the output radiation spectrum of the scene target source specifically includes:
obtaining a calibration accuracy delta R; the method comprises the following steps:
ΔR＝mean(R out (i)-R in (i))| i＝1:m (10)
wherein R is out (i) An output radiation spectrum representing a scene object; r is R in (i) An input radiation spectrum representing a scene object; i represents a spectrumAn ith channel of the radiometer; m represents the number of channels;
spectral resolution DeltaR f The method is obtained by adopting a standard deviation analysis method, and specifically comprises the following steps:
ΔR f ＝STD(R out (i)-R in (i))| i＝1:m (11)
wherein R is out (i) An output radiation spectrum representing a scene object; r is R in (i) An input radiation spectrum representing a scene object; i denotes the ith channel of the spectral radiometer; m represents the number of channels.
As one of the improvements of the above technical solutions, the design indexes of the spectrum radiometer system include: scaling mode, sideband imbalance, channel number and quantization bit number:
as one of the improvements of the technical scheme, the design index of the spectrum radiometer is adjusted until the performance index meets the requirement; the method specifically comprises the following steps:
judging whether the performance indexes of the spectrum radiometer simulation system meet the corresponding preset expected values or not;
if the performance indexes of the spectrum radiometer simulation system are smaller than the preset expected values, the performance indexes of the spectrum radiometer simulation system meet the corresponding preset expected values, and the process is finished;
if the performance index of the spectrum radiometer simulation system does not meet the corresponding preset expected value, redesigning the design index of the spectrum radiometer simulation system until the performance index of the spectrum radiometer simulation system is smaller than the preset expected value, and ending.
Compared with the prior art, the invention has the beneficial effects that:
by constructing a thermal radiation noise source model and a spectrum radiometer system, a radiation noise source and a spectrum radiometer in an actual observation target scene are accurately described, and model support is provided for evaluation of various performance indexes; in the simulation process, performance indexes of calibration accuracy and spectrum resolution are introduced, the accuracy of the simulation result evaluation is improved, meanwhile, the error between the true value and the theoretical value of the calibration accuracy can be controlled within 5%, and the error between the true value and the theoretical value of the spectrum resolution can be controlled within 10%, so that the simulation accuracy is higher, and the accuracy and the effectiveness of the method provided by the invention are ensured. By enabling each performance index to meet design expectations, key design indexes such as a calibration mode, side band unbalance degree, channel number, quantization degradation ratio and the like are determined.
Drawings
FIG. 1 is a flow chart of a method of simulating a spectral radiometer system of the present invention;
FIG. 2 (a) is a schematic diagram of simulation results of a spectrum of thermal radiation noise of a cold and hot calibration source in a simulation example of a simulation method of a spectrum radiometer system of the present invention;
FIG. 2 (b) is a schematic diagram of simulation results of the spectrum of thermal radiation noise of a scene target source in a simulation example of a simulation method of a spectrum radiometer system of the present invention;
FIG. 3 (a) is a schematic diagram of simulation results of the spectrum of the cold and hot calibration source signal passing through the front end in a simulation example of a simulation method of a spectrum radiometer system of the present invention;
FIG. 3 (b) is a schematic diagram of simulation results of the spectrum of the front end of the source signal of field Jing Mubiao in a simulation example of a simulation method of a spectral radiometer system of the present invention;
FIG. 4 (a) is a schematic diagram of simulation results of signals of a cold-heat calibration source and a scene target source signal after the rear end 3bit quantization in a simulation example of a simulation method of a spectrum radiometer system of the present invention;
FIG. 4 (b) is a schematic diagram of a simulation result of a signal power spectrum of a heat calibration source and a scene target source signal after the signal is quantized by a back end 3 bits in a simulation example of a simulation method of a spectrum radiometer system of the present invention;
FIG. 5 (a) is the bright temperature of a scene target source after calibration at a sideband imbalance of 0.9 in a simulation example of a spectral radiometer system simulation method of the present invention;
FIG. 5 (b) is a schematic diagram of the brightness temperature error after calibration of the scene target source when the sideband imbalance is 0.9 in a simulation example of a simulation method of a spectrum radiometer system of the present invention;
FIG. 6 (a) is the bright temperature of a scene target source after calibration at a spectral resolution of 1MHz in a simulation example of a spectral radiometer system simulation method of the present invention;
FIG. 6 (b) is the bright temperature of the scene target source after calibration at a spectral resolution of 2MHz in a simulation example of a spectral radiometer system simulation method of the present invention;
FIG. 6 (c) is the bright temperature of the scene target source after calibration at a spectral resolution of 4MHz in a simulation example of a spectral radiometer system simulation method of the present invention;
FIG. 7 is a graph of signals from the digital back ends of a cold and hot calibration source and a scene target source using a Blackman window function in a simulation example of a simulation method of a spectral radiometer system of the present invention;
FIG. 8 (a) is a graph of the digital back end signals of a cold and hot calibration source and a scene target source after 8bit quantization using Blackman window function in a simulation example of a spectral radiometer system simulation method of the present invention;
FIG. 8 (b) is a schematic representation of the spectral resolution of a scene target source using the Blackman window function and after 8bit quantization in a simulation example of a spectral radiometer system simulation method of the present invention;
Detailed Description
The invention will now be further described with reference to the accompanying drawings.
As shown in fig. 1, the present invention provides a spectral radiometer system simulation method, the method comprising:
respectively simulating and generating a cold calibration source input signal, a hot calibration source input signal and an input signal of a scene target source according to a pre-established thermal radiation noise model;
specifically, when the radiation spectrum of the observation target is a cold calibration source, the cold calibration source is a constant, and the thermal radiation noise is Gaussian white noise with band limitation; wherein, gaussian white noise is generated by pseudo random numbers, and the average value is 0; cold standard deviation sigma of white gaussian noise 1 Determined by equation (1):
wherein sigma 1 Cold standard deviation of gaussian white noise; k is BoltzA Mannich constant; t (T) C The bright temperature of the cold calibration source, namely the bright temperature of the thermal radiation noise;
a group of bright temperatures T can be generated by using the formula (2) C Is a time series of (a):
s C [i]～N(μ,σ 1 2 ) (2)
wherein s is C [i]Inputting a signal for a cold calibration source; i is the number of signal points; n (mu, sigma) 1 2 ) Representing a normal distribution; mu is the average value of normal distribution; sigma (sigma) 1 2 Standard deviation of normal distribution;
when the radiation spectrum of the observation target is a thermal calibration source, the thermal calibration source is a constant, and the thermal radiation noise is Gaussian white noise with band limitation; wherein, gaussian white noise is generated by pseudo random numbers, and the average value is 0; thermal standard deviation sigma of Gaussian white noise 2 Determined by equation (3):
wherein sigma 2 Is the thermal standard deviation of Gaussian white noise; k is boltzmann constant; t (T) H The bright temperature of the thermal calibration source, namely the bright temperature of thermal radiation noise;
a set of bright temperatures T can be generated by using the formula (4) H Is a time series of (a):
s H [i]～N(μ,σ 2 2 ) (4)
wherein s is H [i]Inputting a signal for a thermal calibration source; i is the number of signal points: n (mu, sigma) 2 2 ) Representing a normal distribution; mu is the average value of normal distribution; sigma (sigma) 2 Is the standard deviation of the normal distribution.
When the brightness temperature T of the thermal radiation noise is respectively the brightness temperature T of the thermal calibration source H Or the bright temperature T of a cold calibration source C When in use; respectively generating a cold scaling source input signal and a hot scaling source input signal s by simulation according to formulas (2) and (4) C [i]Sum s H [i]And generates heat source spectrum S of heat radiation noise through FFT operation H [i]Or cold source spectrum S C [i]；
When the radiation spectrum of the observation target is a scene target source, a bright temperature reference T is assumed ref A lower noise signal; performing i-point Fourier transform on the signal to obtain the noise signal s ref [i]:
s ref [i]～N(μ,σ 2 /π 2 ) (5)
Wherein s is ref [i]The lighting temperature of each frequency point is T ref The method comprises the steps of carrying out a first treatment on the surface of the Sigma is the thermal standard deviation of gaussian white noise or the cold standard deviation of gaussian white noise;
from the gaussian distribution, an input noise signal with a radiation spectrum T (f), i.e. a scene target source input signal, is obtained:
wherein s is T(f) [i]Inputting signals for a scene target source; t (f) is the radiation spectrum; t (T) ref Is S ref [i]The lighting temperature of each frequency point;
when the bright temperature T of the thermal noise is the bright temperature T of the scene target source S (f) When in use; generating a scene target source input signal s in a simulation manner according to equation (6) T(f) [i]And generates scene target source spectrum S of thermal radiation noise through FFT operation S [i]。
Wherein, as shown in FIG. 1, the bright temperature T of the scene target source is obtained by utilizing an Arts radiation transmission model according to the atmospheric profile and auxiliary data S (f) The method comprises the steps of carrying out a first treatment on the surface of the The auxiliary data shown include: HITRAN database and instrument frequencies.
Fig. 2 (a) shows the thermal noise signal of the cold or hot calibration source generated by simulation, and fig. 2 (b) shows the thermal noise signal of the scene calibration source generated by simulation. The frequency of the spectrum radiometer is 240GHz, the intermediate frequency bandwidth is 2GHz, and the scene target source is a radiation spectrum at a cut-off height of 30 Km.
The cold calibration source input signal, the hot calibration source input signal and the scene target source input signal are respectively input into a spectrum radiometer simulation system, a cold output power spectrum, a hot calibration source output power spectrum and a scene target source output power spectrum are correspondingly output, and the performance index of the spectrum radiometer simulation system is calculated;
wherein the spectral radiometer system comprises a radio frequency front-end signal model and a digital back-end signal model;
the establishment of the radio frequency front end signal model specifically comprises the following steps:
according to formula (7), a radio frequency front end signal model is established, and the signal spectrum after passing through the radio frequency front end can be expressed as:
S fe [i]＝(S u [i]·SRF u [i]+flip(S l [i]·SRF l [i])) (7)
wherein flip () represents the array inverse; s is S fe [i]The frequency spectrum of the output signal output by the radio frequency front end signal model; s is S u [i]And S is l [i]The frequency spectrum of the input noise signal of the upper sideband and the lower sideband respectively; wherein the frequency spectrum of the input noise signal is the heat source frequency spectrum S of radiation noise H [i]Spectrum S of cold source C [i]Or scene target source spectrum S of thermal radiation noise S [i]The method comprises the steps of carrying out a first treatment on the surface of the The frequency spectrum of the output signal is S H [i]Frequency spectrum of corresponding output signal, S C [i]Frequency spectrum or S of corresponding output signal S [i]The frequency spectrum of the corresponding output signal; SRF (SRF) u [i]And SRF (SRF) l [i]Channel response functions of the upper sideband and the lower sideband respectively;
channel response function SRF through upper and lower sidebands u [i]And SRF (SRF) l [i]For S fe [i]IFFT is carried out to obtain the output signal s of the radio frequency front end fe [i]Completing the establishment of a radio frequency front end signal model; wherein, the signal s output by the radio frequency front end fe [i]The method comprises the steps of outputting a signal for a cold calibration source, outputting a signal for a hot calibration source or outputting a signal for a scene target source; because the receiver system of the spectrum radiometer is generally double-sideband, the SRF of the upper sideband and the SRF of the lower sideband are needed to model the frequency band of the radio frequency front end.
Fig. 3 (a) shows the spectrum of the thermal noise signal of the cold or hot calibration source after passing through the rf front end of the spectrum radiometer, and fig. 3 (b) shows the spectrum of the thermal noise signal of the scene target source after passing through the rf front end of the spectrum radiometer. Wherein the in-band flatness of the single sideband SRF is 3dB and the upper sideband is symmetrical with the lower sideband.
The digital back-end signal model is established specifically as follows:
the digital back end of the spectrum radiometer adopts an FFT type spectrometer for calculating the signal spectrum S output by the radio frequency front end fe [k]Is a power spectrum of (2); since power is linear with light temperature, the light temperature spectrum can be represented by the output power. The digital back-end signal model simulates the working process of the FFT type spectrometer, and specifically comprises the steps of sampling, quantizing, windowing, FFT operation and integral operation of a radio frequency front-end output signal output by the radio frequency front-end signal model.
Among them, it is necessary to clarify: the relation between sampling rate, bandwidth, FFT point number and channel resolution. First, the sampling rate of the spectral radiometer system is 2 times the baseband bandwidth, and the channel resolution Δf is equal to the sampling rate divided by the FFT point number (i.e., the number of channels). When the number of FFT points is determined, the number of the time domain signals for carrying out FFT operation is required to be equal to the number of FFT points, so that the limited integration time and the resources of the FPGA can be utilized to the greatest extent.
The spectrum radiometer system is used as a discrete system to finish sampling the radio frequency front end output signal output by the radio frequency front end signal model;
radio frequency front end output signal s output to radio frequency front end signal model fe [i]Quantization is carried out to obtain quantized signals
Wherein Q is n []Representing the RF front end output signal s output to the RF front end signal model fe [i]Performing n bit quantization operation;
for quantized signalsFirstly, performing i-point FFT operation, and then squaring a modulus to obtain an output power spectrum S output by a digital back-end signal model be [i]：
Completing the establishment of a digital back-end signal model; wherein, the output power spectrum S output by the digital back-end signal model be [i]The method is an output power spectrum corresponding to the cold calibration source output signal, an output power spectrum corresponding to the hot calibration source output signal or an output power spectrum corresponding to the scene target source output signal.
Since the SRF of the rf front-end is not a rectangular function, the output power spectrum S output by the digital back-end signal model be [i]The influence of SRF is superimposed, and the radiation spectrum of the scene target can be determined only through scaling.
Fig. 4 shows the output signal of the hot and cold calibration source and scene target source thermal noise signals after passing through the digital back end. Fig. 4 (a) shows a signal after 3bit quantization at the digital back end, and fig. 4 (b) shows output power spectrums of SRF as non-ideal transfer functions, respectively.
The specific process for establishing the spectrum radiometer system is as follows:
step 1) generating a radiation spectrum of a scene target source through Arts;
step 2) modeling a thermal noise signal of the cold calibration source through a formula (2), modeling a thermal noise signal of the thermal calibration source through a formula (4), and modeling a thermal noise signal of the scene target source through a formula (6); the scene target radiation spectrum is obtained by the step 1);
step 3) respectively generating a cold calibration source input signal, a hot calibration source input signal and an input signal of a scene target source through simulation of a formula (5), and respectively inputting the cold calibration source input signal, the hot calibration source input signal and the input signal of the scene target source into a pre-established radio frequency front end signal model to obtain corresponding front end output signals, namely a cold calibration source output signal spectrum, a hot calibration source output signal spectrum and an output signal spectrum of the scene target source;
and 4) respectively inputting the output signal spectrum of the cold calibration source, the output signal spectrum of the hot calibration source and the output signal spectrum of the scene target source into a pre-established digital back-end signal model, carrying out back-end quantization and power spectrum calculation through a formula (8) and a formula (9), obtaining a plurality of groups of power spectrums, and carrying out averaging to obtain a power spectrum result under expected integration time.
The cold calibration source input signal, the hot calibration source input signal and the input signal of the scene target source are respectively input into a spectrum radiometer system to correspondingly output a cold output power spectrum, a hot calibration source output power spectrum and a scene target source output power spectrum;
specifically, the cold calibration source input signal, the hot calibration source input signal and the input signal of the scene target source are respectively input into a radio frequency front end signal model, and a cold calibration source output signal, a hot calibration source output signal and a scene target source output signal are obtained according to a formula (7);
and then the obtained cold calibration source output signal, the hot calibration source output signal and the scene target source output signal are respectively input into a digital back-end signal model, and a cold output power spectrum, a hot calibration source output power spectrum and a scene target source output power spectrum are obtained according to formulas (8) and (9), namely, an output power spectrum corresponding to the cold calibration source output signal, an output power spectrum corresponding to the hot calibration source output signal or an output power spectrum corresponding to the scene target source output signal.
Determining an output radiation spectrum of a scene target source through calibration according to the cold output power spectrum, the hot calibration source output power spectrum and the scene target source output power spectrum;
specifically, according to the obtained cold output power spectrum, the obtained heat calibration source output power spectrum and the obtained scene target source output power spectrum, and then through the cold calibration source and the heat calibration source with known bright temperatures, the scene target output power spectrum of each frequency point is subjected to two-point calibration, so that the output radiation spectrum of the scene target is determined.
Calculating performance indexes of a spectrum radiometer simulation system according to the output radiation spectrum of the scene target source;
specifically, the performance indicators of the spectral radiometer simulation system include: scaling accuracy and spectral resolution.
The process for acquiring the scaling accuracy and the spectrum resolution is specifically as follows:
obtaining a calibration accuracy delta R; the method comprises the following steps:
ΔR＝mean(R out (i)-R in (i))| i＝1:m (10)
wherein R is out (i) An output radiation spectrum representing a scene object; r is R in (i) An input radiation spectrum representing a scene object; i denotes the ith channel of the spectral radiometer; m represents the number of channels;
spectral resolution DeltaR f The method is obtained by adopting a standard deviation analysis method, and specifically comprises the following steps:
ΔR f ＝STD(R out (i)-R in (i))| i＝1:m (11)
wherein R is out (i) An output radiation spectrum representing a scene object; r is R in (i) An input radiation spectrum representing a scene object; i denotes the ith channel of the spectral radiometer; m represents the number of channels.
The design indexes of the spectrum radiometer system comprise: scaling mode, sideband imbalance, channel number and quantization bit number.
Wherein, the calibration process of the spectrum radiometer simulation system is as follows:
conventional full power radiometers use a two-point calibration to determine the amount of radiation at the target. The calibration principle of a spectral radiometer is similar, except that it requires two-point calibration of each channel to obtain the amount of radiation for that channel. The radiation spectrum can be obtained by connecting the radiation amounts of all channels.
The output of the FFT spectrometer is the power values of discrete frequency points, which can still be equivalent to channels. Therefore, the FFT spectrometer is similar to the traditional full-power radiometer in calibration mode, namely, the power of each frequency point is subjected to two-point calibration through a heat source and a cold source with known bright temperatures.
Wherein R is i Representing the amount of radiation input to the spectral radiometer, C i Is the count value of the power spectrum output by the digital back end. The scaling equation for each channel needs to be determined, and can be expressed as:
C i ＝a i ·R i +b i (12)
wherein a is i And b i The first and constant terms of the scaling equation for the ith channel can be obtained from the following equation:
in the simulation process, cold air which is kept at 3K in the whole bandwidth and a calibration source of 200K are respectively adopted as cold and hot targets. And simulating the bright temperature spectrum of the scene target source by adopting the Arts. The calibration process assumes that the instrument remains stable for one calibration period.
For spectral radiometers, spectral resolution is the most important indicator. Spectral resolution is defined as the minimum resolvable input light temperature of the frequency domain of the receiver. The spectral resolution of the bright temperature in the frequency domain is calculated by adopting the same method. The spectral resolution in this band can be obtained by standard deviation analysis. Standard deviation analysis can be expressed as:
ΔR f ＝STD(R out (i)-R in (i))| i＝1:m (11)
wherein R is out Output radiation spectrum representing scene object, R in Representing the input radiation spectrum of the scene object.
The spectrum resolution of the frequency band can be obtained by solving the root mean square of the result.
The two-point calibration is carried out through the spectrum radiometer simulation model, the spectrum resolution is calculated, and after the two-point calibration, the influence of SRF is eliminated.
Table 1 gives the spectral resolution at different integration times, with a simulation value of 1.25K for the spectral resolution at 100ms integration time.
TABLE 1 spectral resolution at different integration times
The process of determining the sideband unbalance by the spectrum radiometer simulation system comprises the following steps:
equation (14) and equation (15) represent theoretical values of the input light temperature and the output light temperature of the spectral radiometer of the double-sideband system,
where i represents the ith channel.
As can be seen from the formula, when the SRFs of the upper and lower sidebands of a certain channel are inconsistent, the output brightness temperature of the channel can be caused to deviate. The relationship between the sideband imbalance and the bright temperature deviation was evaluated on the SRF by the spectral radiometer simulation model, and the results are shown in fig. 5 (a) and 5 (b). It can be seen that the error at 0.4GHz and 0.52GHz is greatest due to the coincidence of the ozone absorption peaks of the upper and lower sidebands. The maximum bright temperature error was 8K at a sideband imbalance of 0.9. The sideband imbalance needs to be greater than 0.9.
The process of determining the number of channels by the spectrum radiometer simulation system is as follows:
when the bandwidth of the spectral radiometer is determined, the number of channels determines the frequency resolution. After the double-sideband system is determined, the number of channels needs to be determined, so that the spectrum resolution and the frequency resolution of the spectrometer can meet the requirements at the same time. By setting different channel numbers, the spectrum resolution and the frequency resolution output by the spectrum radiometer simulation model are calculated, whether the spectrum line detection requirement is met is judged according to the result, and the optimal channel number is determined. Simulation results using different channel numbers are shown in fig. 6 (a), 6 (b), and 6 (c). It can be seen that although the spectral resolution is optimal at 512 channels, some narrower absorption lines have been missed due to the barrier effect. When the number of channels is 2048, the frequency resolution is about 1MHz, and most spectral lines can be basically satisfied, however, at this time, the spectral resolution is the worst, which results in that we cannot distinguish some absorption peaks with lower amplitude. It can be seen that the absorption peak at 1.12GHz has been submerged in noise. When the number of channels is 1024, the combination of the frequency resolution and the spectrum resolution is just good so that we can distinguish the absorption peak of 1.12GHz, and the requirements are basically satisfied. It is therefore optimal to set the number of channels to 1024.
Furthermore, the spectral leakage caused by the direct application of the FFT algorithm to the noise signal must be considered. The three window functions and the same frequency resolution are respectively used by a spectrum radiometer simulation model to judge the merits of the spectrum resolution, thereby determining the window function adopted. Fig. 7 shows simulation results using Blackman windows, respectively. By analysis, the spectral resolution calculated using the three window functions is at one level.
In contrast, the spectral resolution of the rectangular window is 1.274K, slightly worse than the Hanning window and the Blackman window. In radio astronomical applications, the Blackman window has good spectral leakage attenuation and amplitude preserving capability for random noise input signals. Thus, the Blackman window function is selected.
Wherein, the process of the spectrum radiometer simulation system for determining the quantitative degradation ratio is as follows:
quantization is the process of analog-to-digital conversion of the output voltage at the front end of the spectrum radiometer. Radiometers require uniform and continuous sampling of the in-channel signal, and thus employ a uniform sampling pattern.
The quantization process necessarily brings about a decrease in measurement accuracy. The quantization degradation ratio is defined as:
wherein, (NEDT) Q Representing the quantized spectral resolution, NEDT represents the unquantized spectral resolution.
In the spectrum radiometer simulation model, the quantization bit number at the digital rear end is set to be different, and the quantization bit number which can meet the design expectations is selected by comparing the degradation ratio of the quantized spectrum resolution. Fig. 8 (a), 8 (b) show simulation results of 8bit quantization.
Table 2 gives the degradation ratio and spectral resolution using 3bit,5bit and 8bit quantization, respectively. The result showed that the quantization degradation ratio was 1.039 and the spectral resolution was 1.251K at 8bit quantization.
TABLE 2 quantization degradation ratio and spectral resolution at different quantization bits
And adjusting the design index of the spectrum radiometer system until the performance index meets the requirement.
Specifically, judging whether performance indexes of the spectrum radiometer simulation system all meet corresponding preset expected values or not;
if the performance indexes of the spectrum radiometer simulation system are smaller than the preset expected values, the performance indexes of the spectrum radiometer simulation system meet the corresponding preset expected values, and the process is finished;
if the performance index of the spectrum radiometer simulation system does not meet the corresponding preset expected value, redesigning the design index of the spectrum radiometer simulation system until the performance index of the spectrum radiometer simulation system is smaller than the preset expected value, and ending.
That is, determining whether the calibration accuracy and the spectral resolution of the spectral radiometer simulation system both meet corresponding preset expected values;
if the calibration accuracy and the spectrum resolution of the simulation are smaller than the preset expected value, the calibration accuracy and the spectrum resolution of the simulation system meet the preset expected value, and the simulation is finished;
otherwise, if the simulated calibration accuracy and the simulated spectrum resolution do not meet the corresponding preset expected values, repeating the signal processing method, and redesigning the design index of the simulation system until the simulated calibration accuracy and the simulated spectrum resolution meet the corresponding preset expected values, and ending.
Finally, it should be noted that the above embodiments are only for illustrating the technical solution of the present invention and are not limiting. Although the present invention has been described in detail with reference to the embodiments, it should be understood by those skilled in the art that modifications and equivalents may be made thereto without departing from the spirit and scope of the present invention, which is intended to be covered by the appended claims.
Claims (4)
1. A method of simulating a spectral radiometer based system, the method comprising:
respectively simulating and generating a cold calibration source input signal, a hot calibration source input signal and an input signal of a scene target source according to a pre-established thermal radiation noise model;
the cold calibration source input signal, the hot calibration source input signal and the input signal of the scene target source are respectively input into a spectrum radiometer system to correspondingly output a cold output power spectrum, a hot calibration source output power spectrum and a scene target source output power spectrum,
determining an output radiation spectrum of a scene target source through calibration according to the cold output power spectrum, the hot calibration source output power spectrum and the scene target source output power spectrum;
calculating performance indexes of a spectrum radiometer simulation system according to the output radiation spectrum of the scene target source;
adjusting design indexes of the spectrum radiometer system until the performance indexes meet the requirements;
according to a pre-established thermal radiation noise model, respectively simulating and generating a cold calibration source input signal, a thermal calibration source input signal and an input signal of a scene target source; the method comprises the following steps:
when the radiation spectrum of the observation target is a cold calibration source, the cold calibration source is a constant, and the thermal radiation noise is Gaussian white noise with band limitation; wherein, gaussian white noise is generated by pseudo random numbers, and the average value is 0; cold standard deviation sigma of white gaussian noise 1 Determined by equation (1):
wherein sigma 1 Cold standard deviation of gaussian white noise; k is boltzmann constant; t (T) C Bright temperature for cold calibration sourceI.e. the bright temperature of the thermal radiation noise;
a group of bright temperatures T can be generated by using the formula (2) C Is a time series of (a):
s C [i]～N(μ,s 1 2 ) (2)
wherein s is C [i]Inputting a signal for a cold calibration source; i is the number of signal points; n (mu, s) 1 2 ) Representing a normal distribution; mu is the average value of normal distribution; s is(s) 1 2 Standard deviation of normal distribution;
when the radiation spectrum of the observation target is a thermal calibration source, the thermal calibration source is a constant, and the thermal radiation noise is Gaussian white noise with band limitation; wherein, gaussian white noise is generated by pseudo random numbers, and the average value is 0; thermal standard deviation sigma of Gaussian white noise 2 Determined by equation (3):
wherein sigma 2 Is the thermal standard deviation of Gaussian white noise; k is boltzmann constant; t (T) H The bright temperature of the thermal calibration source, namely the bright temperature of thermal radiation noise;
a set of bright temperatures T can be generated by using the formula (4) H Is a time series of (a):
s H [i]～N(μ,s 2 2 ) (4)
wherein s is H [i]Inputting a signal for a thermal calibration source; i is the number of signal points: n (mu, s) 2 2 ) Representing a normal distribution; mu is the average value of normal distribution; sigma (sigma) 2 Standard deviation of normal distribution;
when the brightness temperature T of the thermal radiation noise is respectively the brightness temperature T of the thermal calibration source H Or the bright temperature T of a cold calibration source C When in use; respectively generating a cold scaling source input signal and a hot scaling source input signal s by simulation according to formulas (2) and (4) C [i]Sum s H [i]And generates heat source spectrum S of heat radiation noise through FFT operation H [i]Or cold source spectrum S C [i]；
When the radiation spectrum of the observation target is a scene target source, setting a bright temperature reference T ref A lower noise signal; performing i-point Fourier transform on the signal to obtain the noise signal s ref [i]:
s ref [i]～N(μ,s 2 /p 2 ) (5)
Wherein s is ref [i]The lighting temperature of each frequency point is T ref The method comprises the steps of carrying out a first treatment on the surface of the Sigma is the thermal standard deviation of gaussian white noise or the cold standard deviation of gaussian white noise;
from the gaussian distribution, an input noise signal with a radiation spectrum T (f), i.e. a scene target source input signal, is obtained:
wherein s is T(f) [i]Inputting signals for a scene target source; t (f) is the radiation spectrum; t (T) ref Is S ref [i]The lighting temperature of each frequency point;
when the bright temperature T of the thermal noise is the bright temperature T of the scene target source S (f) When in use; generating a scene target source input signal s in a simulation manner according to equation (6) T(f) [i]And generates scene target source spectrum S of thermal radiation noise through FFT operation S [i]；
The spectrum radiometer system comprises a radio frequency front end signal model and a digital back end signal model;
the establishment of the radio frequency front end signal model specifically comprises the following steps:
according to formula (7), a radio frequency front end signal model is established, and the signal spectrum after passing through the radio frequency front end is expressed as:
wherein flip () represents the array inverse; s is S fe [i]The frequency spectrum of the output signal output by the radio frequency front end signal model; s is S u [i]And S is l [i]The frequency spectrum of the input noise signal of the upper sideband and the lower sideband respectively; wherein said at least one ofThe frequency spectrum of the input noise signal is the heat source frequency spectrum S of the radiation noise H [i]Spectrum S of cold source C [i]Or scene target source spectrum S of thermal radiation noise S [i]The method comprises the steps of carrying out a first treatment on the surface of the The frequency spectrum of the output signal is S H [i]Frequency spectrum of corresponding output signal, S C [i]Frequency spectrum or S of corresponding output signal S [i]The frequency spectrum of the corresponding output signal; SRF (SRF) u [i]And SRF (SRF) l [i]Channel response functions of the upper sideband and the lower sideband respectively;
channel response function SRF through upper and lower sidebands u [i]And SRF (SRF) l [i]For S fe [i]IFFT is carried out to obtain the output signal s of the radio frequency front end fe [i]Completing the establishment of a radio frequency front end signal model; wherein, the signal s output by the radio frequency front end fe [i]The method comprises the steps of outputting a signal for a cold calibration source, outputting a signal for a hot calibration source or outputting a signal for a scene target source;
the digital back-end signal model is established specifically as follows:
the spectrum radiometer system is used as a discrete system to finish sampling the radio frequency front end output signal output by the radio frequency front end signal model;
radio frequency front end output signal s output to radio frequency front end signal model fe [i]Quantization is carried out to obtain quantized signals
Wherein Q is n []Representing the RF front end output signal s output to the RF front end signal model fe [i]Performing nbit quantization operation;
for quantized signalsFirstly, performing i-point FFT operation, and then squaring a modulus to obtain an output power spectrum S output by a digital back-end signal model be [i]：
Completing the establishment of a digital back-end signal model; wherein, the output power spectrum S output by the digital back-end signal model be [i]The method comprises the steps of obtaining an output power spectrum corresponding to a cold calibration source output signal, an output power spectrum corresponding to a hot calibration source output signal or an output power spectrum corresponding to a scene target source output signal;
the performance indexes of the spectrum radiometer simulation system comprise: scaling accuracy and spectral resolution;
the performance index of the spectrum radiometer system is calculated according to the output radiation spectrum of the scene target source, and the performance index is specifically as follows:
obtaining a calibration accuracy delta R; the method comprises the following steps:
ΔR＝mean(R out (i)-R in (i))| i＝1:m (10)
wherein R is out (i) An output radiation spectrum representing a scene object; r is R in (i) An input radiation spectrum representing a scene object; i denotes the ith channel of the spectral radiometer; m represents the number of channels;
spectral resolution DeltaR f The method is obtained by adopting a standard deviation analysis method, and specifically comprises the following steps:
ΔR f ＝STD(R out (i)-R in (i))| i＝1:m (11)
wherein R is out (i) An output radiation spectrum representing a scene object; r is R in (i) An input radiation spectrum representing a scene object; i denotes the ith channel of the spectral radiometer; m represents the number of channels;
the design indexes of the spectrum radiometer system comprise: scaling mode, sideband imbalance, channel number and quantization bit number.
2. The method according to claim 1, wherein the cold calibration source input signal, the hot calibration source input signal and the scene target source input signal are respectively input into a spectrum radiometer system, and a cold output power spectrum, a hot calibration source output power spectrum and a scene target source output power spectrum are respectively output; the method comprises the following steps:
respectively inputting the cold calibration source input signal, the hot calibration source input signal and the input signal of the scene target source into a radio frequency front end signal model, and obtaining a cold calibration source output signal, a hot calibration source output signal and a scene target source output signal according to a formula (7);
and then the obtained cold calibration source output signal, the hot calibration source output signal and the scene target source output signal are respectively input into a digital back-end signal model, and a cold output power spectrum, a hot calibration source output power spectrum and a scene target source output power spectrum are obtained according to formulas (8) and (9), namely, an output power spectrum corresponding to the cold calibration source output signal, an output power spectrum corresponding to the hot calibration source output signal or an output power spectrum corresponding to the scene target source output signal.
3. The method of claim 1, wherein the determining the output radiation spectrum of the scene target source by scaling is based on the cold output power spectrum, the hot scaled source output power spectrum, and the scene target source output power spectrum; the method comprises the following steps:
and according to the obtained cold output power spectrum, the obtained heat calibration source output power spectrum and the obtained scene target source output power spectrum, performing two-point calibration on the scene target output power spectrum of each frequency point through the cold calibration source and the heat calibration source with known bright temperatures, and determining the output radiation spectrum of the scene target.
4. The method of claim 1, wherein the adjusting the design criteria of the spectral radiometer is performed until the performance criteria meet a requirement; the method specifically comprises the following steps:
judging whether the performance indexes of the spectrum radiometer simulation system meet the corresponding preset expected values or not;
if the performance indexes of the spectrum radiometer simulation system are smaller than the preset expected values, the performance indexes of the spectrum radiometer simulation system meet the corresponding preset expected values, and the process is finished;
if the performance index of the spectrum radiometer simulation system does not meet the corresponding preset expected value, redesigning the design index of the spectrum radiometer simulation system until the performance index of the spectrum radiometer simulation system is smaller than the preset expected value, and ending.
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