Joint retrieval method of multi-lag autocorrelation spectrum estimation and meteorological parameters for mini dual-polarization weather radar

Abstract

This invention relates to the field of radar analysis technology, and more specifically, to a method for multi-hysteresis autocorrelation spectrum estimation and joint inversion of meteorological parameters for a miniature dual-polarization weather radar. The method includes: Step 1, a solid-state transmitter transmits a composite pulse consisting of the superposition of the first phase-coded waveform of the horizontal polarization channel and the second phase-coded waveform of the vertical polarization channel; the two polarization echoes are separated by matched filtering and simultaneous transmission and reception isolation is achieved; then, range oversampling is performed on the two echoes; Step 2, the whitening recombination coefficient is determined based on the range oversampling correlation structure, achieving sample multiplication while maintaining the difference components for each path; Step 3, multi-hysteresis autocorrelation spectrum estimation is performed on the multiple whitened sample sequences, and meteorological parameters are jointly inverted and output under the constraints of the same radial velocity and the same spectral width. This invention improves detection capability and parameter estimation accuracy under low peak power of the solid-state transmitter.

Description

Technical Field

[0001] This invention belongs to the field of radar analysis technology, specifically relating to a method for estimating the multi-hysteresis autocorrelation spectrum and jointly inverting meteorological parameters of a micro-miniature dual-polarization weather radar. Background Technology

[0002] Weather radar transmits electromagnetic waves and receives the backscattered echoes of precipitation particles, inverting the intensity, motion, and microphysical characteristics of precipitation. It is an important tool for nowcasting and monitoring severe convection. Dual-polarization weather radar transmits and receives on two channels, horizontally and vertically polarized. In addition to echo power and radial velocity, it can also provide polarization parameters such as differential reflectivity, differential propagation phase, and correlation coefficient, which are used for quantitative precipitation estimation and water condensate phase identification. To reduce size and power consumption, miniature weather radars often use solid-state transmitters and use pulse compression to achieve range resolution and echo energy comparable to short pulses at low peak power. To reduce estimation variance within a limited dwell time, existing research has oversampled the echoes in the range direction and then used whitening transformation to reconstruct the relevant oversampled samples into more effective observations.

[0003] However, the aforementioned methods still have shortcomings in micro-scale dual-polarization scenarios. Solid-state transmitters have low peak power, limiting sensitivity to weak echoes at long distances; to ensure the simultaneity of the two polarizations, the two polarization echoes need to be separated within the same pulse, otherwise cross-polarization crosstalk will be introduced; when the whitening transform is applied separately to the horizontal and vertical polarization channels, the reconstruction methods obtained by the two channels are not consistent, which will destroy the differential reflectivity, differential propagation phase, and correlation coefficient, etc.; in addition, the spectral moment estimation accuracy of a single hysteresis is limited, and the unambiguous velocity is narrow. Therefore, how to balance detection sensitivity and range resolution at low peak power, maintain differential components while achieving sample doubling, and robustly invert multiple meteorological parameters remains an unsolved problem. Summary of the Invention

[0004] The main objective of this invention is to provide a method for estimating the multi-hysteresis autocorrelation spectrum and jointly inverting meteorological parameters for a micro-miniature dual-polarization weather radar. This method balances detection sensitivity and range resolution under the condition of low peak power of a solid-state transmitter, and achieves sample doubling while maintaining the difference between the horizontal and vertical polarization channels, under the premise of unchanged dwell time and transmission power. This allows for robust inversion and output of multiple meteorological parameters.

[0005] To solve the above problems, the technical solution of the present invention is implemented as follows: A method for joint inversion of meteorological parameters with multi-hysteresis autocorrelation spectrum estimation from a miniature dual-polarization weather radar includes the following steps: Step 1: The solid-state transmitter transmits a composite pulse in each pulse repetition period, consisting of the superposition of the first phase-coded waveform loaded on the horizontal polarization channel and the second phase-coded waveform loaded on the vertical polarization channel, forming an intra-frame orthogonal polarization waveform encoding. The first phase-coded waveform and the second phase-coded waveform are orthogonal to each other. The receiver performs matched filtering on the echoes from the horizontal polarization channel and the vertical polarization channel with the first phase-coded waveform and the second phase-coded waveform, respectively, to obtain the horizontal polarization echo and the vertical polarization echo, achieving simultaneous transmission and reception isolation. Range oversampling is performed on the horizontal polarization echo and the vertical polarization echo, resulting in a number of horizontal polarization oversampled subsamples and vertical polarization oversampled subsamples, each with an oversampling factor greater than 1, within each meteorological resolution volume. Step 2: Determine the whitening recombination coefficient based on the distance oversampling correlation structure. For each meteorological resolution volume, linearly combine the horizontally polarized oversampling subsamples and the vertically polarized oversampling subsamples with the same whitening recombination coefficient to obtain multiple horizontally polarized whitening sample sequences and multiple vertically polarized whitening sample sequences, which constitute whitening transformation and achieve sample multiplication. Each path of the horizontally polarized whitening sample sequence and the corresponding path of the vertically polarized whitening sample sequence maintain the same differential reflectance, differential propagation phase and correlation coefficient. Step 3: Perform multi-hysteresis autocorrelation spectrum estimation on the multi-path horizontally polarized whitened sample sequences and the multi-path vertically polarized whitened sample sequences to obtain the horizontally polarized multi-hysteresis autocorrelation sequence, the vertically polarized multi-hysteresis autocorrelation sequence, and the multi-hysteresis cross-correlation sequence. Under the constraints of the same radial velocity and the same spectral width, perform joint inversion of meteorological parameters to obtain and output the horizontally polarized echo power, vertically polarized echo power, radial velocity, spectral width, differential reflectivity, differential propagation phase, and correlation coefficient.

[0006] Furthermore, the first phase-coded waveform and the second phase-coded waveform are each composed of multiple phase modulated sub-pulses sequentially spliced ​​together; the autocorrelation of the first phase-coded waveform exhibits a main peak at 0 range delay, and the autocorrelation of the second phase-coded waveform also exhibits a main peak at 0 range delay. The cross-correlation between the first and second phase-coded waveforms at each range delay is lower than the main peak value of the autocorrelation of the first phase-coded waveform at 0 range delay. Using the first phase-coded waveform for matched filtering, pulse compression gain along the range direction is obtained while obtaining the horizontally polarized echo, thus improving the detection capability of the miniature dual-polarization weather radar under low peak power conditions of the solid-state transmitter. When the first phase-coded waveform is used for matched filtering, the vertically polarized channel transmission component is suppressed in the horizontally polarized echo, and when the second phase-coded waveform is used for matched filtering, the horizontally polarized channel transmission component is suppressed in the vertically polarized echo.

[0007] Furthermore, the receiver arranges the horizontal polarization channel and the vertical polarization channel in parallel, and simultaneously receives the echoes of the horizontal polarization channel and the vertical polarization channel within the same pulse repetition period; the sampling interval of the distance oversampling is obtained by dividing the width of the matched filter resolution unit by the oversampling factor, the horizontal polarization oversampling sub-samples are arranged adjacent to each other along the distance direction, the vertical polarization oversampling sub-samples are arranged adjacent to each other along the distance direction, each oversampling sub-sample carries its own receiver thermal noise, and the horizontal polarization oversampling sub-samples and the vertical polarization oversampling sub-samples correspond one-to-one at the same distance direction position.

[0008] Furthermore, determining the whitening recombination coefficient includes: selecting multiple adjacent meteorological resolution volumes within the same distance range of the same meteorological resolution volume; using horizontally polarized oversampled subsamples and vertically polarized oversampled subsamples at each distance position of the multiple adjacent meteorological resolution volumes as statistical objects; statistically analyzing the correlation between the oversampled subsample values ​​of any two distance positions; and summarizing the correlation between each pair of distance positions to obtain a set of correlation quantities characterizing the distance oversampling correlation structure; and determining the whitening recombination coefficient based on this set of correlation quantities. The distance oversampling correlation structure is introduced by a composite pulse and a matched filter between adjacent oversampled positions in the distance direction, and remains consistent among meteorological resolution volumes within the same distance range, with each meteorological resolution volume within the same distance range sharing the same whitening recombination coefficient.

[0009] Furthermore, the whitening recombination coefficient matches the distance oversampling correlation structure, and the whitening transformation is a linear preconditioning of covariance matching; the whitening transformation reduces the pairwise correlation between multiple horizontally polarized whitened sample sequences and reduces the pairwise correlation between multiple vertically polarized whitened sample sequences, forming an oversampling equivalent observation space; the number of paths of both horizontally polarized and vertically polarized whitened sample sequences is equal to the oversampling factor, and the number of sample sequences that can be used for meteorological parameter estimation within a single pulse repetition period increases to several times the oversampling factor.

[0010] Furthermore, within the same meteorological resolution volume, the differential reflectance and differential propagation phase between the horizontal and vertical polarization channels are common to all range positions. The whitening transformation applies the same whitening recombination coefficient to the oversampled subsamples of the horizontal and vertical polarization channels at the same range position and then adds them together, so that each path of the horizontal polarization whitening sample sequence and the corresponding path of the vertical polarization whitening sample sequence maintain the same differential reflectance, differential propagation phase, and correlation coefficient as at each range position. The multiple horizontal polarization whitening sample sequences and the multiple vertical polarization whitening sample sequences carry differential reflectance, differential propagation phase, and correlation coefficient information in pairs.

[0011] Furthermore, autocorrelation is calculated along the pulse dimension at lags of 1, 2, and 3 for each horizontally polarized whitening sample sequence; autocorrelation at the same lag is calculated along the pulse dimension for each vertically polarized whitening sample sequence; and cross-correlation at the same lag is calculated between each horizontally polarized whitening sample sequence and its corresponding vertically polarized whitening sample sequence along the pulse dimension. The autocorrelation values ​​at the same lag for multiple horizontally polarized whitening sample sequences are summed and averaged to obtain a horizontally polarized multi-lag autocorrelation sequence. Similarly, the autocorrelation values ​​at the same lag for multiple vertically polarized whitening sample sequences are summed and averaged to obtain a vertically polarized multi-lag autocorrelation sequence. The cross-correlation values ​​at the same lag for multiple horizontally polarized whitening sample sequences are then calculated. The average of the corresponding values ​​at the same lag is used to obtain a multi-lag cross-correlation sequence. The distance oversampling correlation structure reduces the statistical efficiency of meteorological parameter estimation obtained by directly averaging the oversampling subsamples. Under the linear preconditioning effect of covariance matching, the average of the multi-lag moment estimation of the multi-path horizontally polarized whitened sample sequence and the multi-path vertically polarized whitened sample sequence approximates the linear estimate with the minimum variance under the distance oversampling correlation observation condition, compensating for the reduction in statistical efficiency caused by the distance oversampling correlation structure, and reducing the estimated variance of horizontally polarized echo power, vertically polarized echo power, radial velocity, spectral width, differential reflectivity, differential propagation phase and correlation coefficient.

[0012] Furthermore, the horizontal and vertical polarization channels observed the same batch of hydrocondensate within the same meteorological resolution volume within the same pulse repetition period. The horizontal and vertical polarization echoes had the same radial velocity and the same spectral width. The Doppler spectrum of the meteorological echoes was described using a Gaussian spectrum, and the autocorrelation corresponding to the Gaussian spectrum was a Gaussian autocorrelation. A Gaussian autocorrelation model was fitted based on the horizontal polarization multi-hysteresis autocorrelation sequence, so that the values ​​of the Gaussian autocorrelation model at hysteresis 1, hysteresis 2, and hysteresis 3 matched the values ​​of the horizontal polarization multi-hysteresis autocorrelation sequence at the same hysteresis, thus obtaining the horizontal polarization echo power, radial velocity, and spectral width. A Gaussian autocorrelation model was fitted based on the vertical polarization multi-hysteresis autocorrelation sequence under the constraint of the same radial velocity and the same spectral width, thus obtaining the vertical polarization echo power. The differential reflectivity was obtained from the horizontal and vertical polarization echo power.

[0013] Furthermore, the phases of the multi-hysteresis cross-correlation sequence at hysteresis 1, hysteresis 2, and hysteresis 3 include the phase caused by the radial velocity and the differential propagation phase between the horizontally polarized channel and the vertically polarized channel. Using the radial velocity obtained from the horizontally polarized multi-hysteresis autocorrelation sequence as a known quantity, the phase caused by the radial velocity is separated from the phases of the multi-hysteresis cross-correlation sequence at each hysteresis to obtain the differential propagation phase. Using the spectral width obtained from the horizontally polarized multi-hysteresis autocorrelation sequence as a known quantity, the amplitude of the multi-hysteresis cross-correlation sequence at each hysteresis is normalized by the spectral width to obtain the correlation coefficient. The differential phase is obtained from the rate of change of the differential propagation phase along the range direction.

[0014] Furthermore, the differential propagation phase monotonically increases along the range direction from near to far. The differential propagation phase at each range direction position is used to attenuate and correct the horizontal polarization echo power, vertical polarization echo power, and differential reflectivity at the same range direction position along the range direction. The horizontal polarization echo power, vertical polarization echo power, radial velocity, spectral width, differential reflectivity, differential propagation phase, differential phase ratio, and correlation coefficient are solved simultaneously under the constraints of the same radial velocity and the same spectral width to achieve joint inversion of meteorological parameters. The horizontal polarization echo power, vertical polarization echo power, radial velocity, spectral width, differential reflectivity, differential propagation phase, differential phase ratio, and correlation coefficient for each meteorological resolution volume are output. These parameters are then used for precipitation estimation and water condensate phase identification.

[0015] The method for multi-hysteresis autocorrelation spectrum estimation and joint inversion of meteorological parameters of a miniature dual-polarization weather radar of the present invention has the following beneficial effects: This invention employs a solid-state transmitter in conjunction with intra-frame orthogonal polarization waveform encoding to transmit two orthogonal coded waveforms. Matched filtering separates the two polarization echoes within the same pulse, achieving pulse compression gain. This improves the detection sensitivity of weak echoes at long distances under low peak power while maintaining detailed range resolution. Simultaneously, the echoes from both polarization channels are taken from the same pulse and at the same time, ensuring the necessary simultaneity for differential measurements and suppressing cross-polarization crosstalk. Based on the range oversampling correlation structure, this invention determines the whitening recombination coefficient and applies the same whitening recombination coefficient to both the horizontal and vertical polarization channels. This recombines related oversampled subsamples into uncorrelated multiple whitening sample sequences, achieving sample multiplication without changing the dwell time and transmit power. Since the two polarizations share the same whitening recombination coefficient, each whitening sample sequence maintains the same differential reflectivity, differential propagation phase, and correlation coefficient in pairs, ensuring that sample multiplication does not sacrifice the fidelity of differential measurements. This invention further performs multi-hysteresis autocorrelation spectrum estimation and cross-path averaging on multiple whitened sample sequences, and performs joint inversion under the constraints of the same radial velocity and the same spectral width, which reduces the estimation variance of each meteorological parameter and improves the accuracy and self-consistency of meteorological parameter inversion. Attached Figure Description

[0016] Figure 1 A schematic diagram of the phase code patterns of the first phase-coded waveform and the second phase-coded waveform in intra-frame orthogonal polarization waveform coding provided in an embodiment of the present invention; Figure 2 This is a schematic diagram showing the comparison of the correlation between oversampled subsamples before and after whitening transformation as a function of sample number interval, provided in an embodiment of the present invention. Figure 3 This is a schematic diagram comparing the retention of differential propagation phase and correlation coefficient during whitening of horizontal and vertical polarization channels sharing the same whitening recombination coefficient, as well as during independent whitening, according to an embodiment of the present invention. Figure 4 A schematic diagram illustrating the inversion of echo power, spectral width, and radial velocity based on a Gaussian autocorrelation model using a multi-hysteresis autocorrelation sequence, as provided in an embodiment of the present invention. Figure 5 This is a comparative diagram showing how the standard deviation of meteorological parameter estimation decreases with the number of sample routes involved in the averaging after sample doubling, as provided in an embodiment of the present invention. Detailed Implementation

[0017] A method for joint inversion of meteorological parameters with multi-hysteresis autocorrelation spectrum estimation from a miniature dual-polarization weather radar includes the following steps: Step 1: The solid-state transmitter transmits a composite pulse in each pulse repetition period, consisting of the superposition of the first phase-coded waveform loaded on the horizontal polarization channel and the second phase-coded waveform loaded on the vertical polarization channel, forming an intra-frame orthogonal polarization waveform encoding. The first phase-coded waveform and the second phase-coded waveform are orthogonal to each other. The receiver performs matched filtering on the echoes from the horizontal polarization channel and the vertical polarization channel with the first phase-coded waveform and the second phase-coded waveform, respectively, to obtain the horizontal polarization echo and the vertical polarization echo, achieving simultaneous transmission and reception isolation. Range oversampling is performed on the horizontal polarization echo and the vertical polarization echo, resulting in a number of horizontal polarization oversampled subsamples and vertical polarization oversampled subsamples, each with an oversampling factor greater than 1, within each meteorological resolution volume. Step 2: Determine the whitening recombination coefficient based on the distance oversampling correlation structure. For each meteorological resolution volume, linearly combine the horizontally polarized oversampling subsamples and the vertically polarized oversampling subsamples with the same whitening recombination coefficient to obtain multiple horizontally polarized whitening sample sequences and multiple vertically polarized whitening sample sequences, which constitute whitening transformation and achieve sample multiplication. Each path of the horizontally polarized whitening sample sequence and the corresponding path of the vertically polarized whitening sample sequence maintain the same differential reflectance, differential propagation phase and correlation coefficient. Step 3: Perform multi-hysteresis autocorrelation spectrum estimation on the multi-path horizontally polarized whitened sample sequences and the multi-path vertically polarized whitened sample sequences to obtain the horizontally polarized multi-hysteresis autocorrelation sequence, the vertically polarized multi-hysteresis autocorrelation sequence, and the multi-hysteresis cross-correlation sequence. Under the constraints of the same radial velocity and the same spectral width, perform joint inversion of meteorological parameters to obtain and output the horizontally polarized echo power, vertically polarized echo power, radial velocity, spectral width, differential reflectivity, differential propagation phase, and correlation coefficient.

[0018] The following provides a specific implementation of the solid-state emission, intra-frame orthogonal polarization waveform coding, matched filtering to separate the two polarizations, and distance oversampling involved in step 1.

[0019] Solid-state transmitters, limited by their components, typically deliver only tens to hundreds of watts of transmission power, far lower than vacuum tube transmitters like klystrons and magnetrons. Simply adopting a short-pulse system would result in insufficient peak power to accumulate enough energy for weak weather echoes over long distances, leading to inadequate sensitivity. This method addresses this by having the solid-state transmitter emit a time-widened, internally phase-modulated long pulse within each pulse repetition cycle, which is then recompressed in time at the receiver using matched filtering. After pulse widening, the energy carried by a single pulse increases linearly with the pulse width; the internal phase modulation broadens the signal bandwidth, and the matched filter converts this bandwidth into a narrow main lobe equivalent to the inverse of the bandwidth. Thus, the range resolution is no longer limited by the long pulse width but determined by the modulation bandwidth. Consequently, a small solid-state transmitter that does not require a high-voltage modulator achieves the necessary transmission energy for long distances while maintaining fine range resolution. For example, the carrier frequency is 9.4 GHz in the X-band, corresponding to a wavelength of approximately 0.0319 meters; the pulse width... The pulse repetition period is set to 20 microseconds; the peak transmit power of each polarization channel is set to 100 watts; the pulse repetition period is set to 1 millisecond, corresponding to a maximum unambiguous distance of approximately 150 kilometers; a dwell time typically transmits 64 pulses for subsequent slow-time processing.

[0020] The miniature dual-polarization weather radar has two transceiver channels: horizontal and vertical. These channels are connected to the horizontal and vertical polarization ports of the antenna respectively via orthogonal mode couplers, arranged in parallel and operating within the same pulse repetition period. The horizontal polarization channel transmits the first phase-coded waveform, and the vertical polarization channel transmits the second phase-coded waveform. Both waveforms occupy the same pulse time and frequency band, but are assigned orthogonal phase codes and radiated simultaneously, forming a composite pulse. Because the codes for both polarizations are given within the same frame, i.e., the same pulse repetition period, this arrangement is called intra-frame orthogonal polarization waveform coding. The two waveforms can be written as... , , In the formula For time; The code length for phase encoding is the number of sub-pulses (chips) contained in a waveform; The width of a single sub-pulse; The envelope of a single sub-pulse can be a rectangle or a raised cosine with slightly smoothed edges; and These are the first phase encoded waveform and the second phase encoded waveform, respectively. Complex weighting of sub-pulses, and It is the phase assigned to the corresponding sub-pulse. This is the imaginary unit. Following the above value, determine the code length. Then the sub-pulse width microseconds, waveform bandwidth Megahertz. The phase can be determined by taking only the 0 and 0 of the two phases. It is possible to take 0 from the four phases. , , Alternatively, multiple phases can be used continuously; this implementation uses four phases, which is a compromise between the freedom of code design and the simplicity of hardware implementation.

[0021] See Figure 1 , Figure 1 The diagram illustrates the phase codes of the first and second phase-coded waveforms in this embodiment, with the horizontal axis representing the sub-pulse number and the vertical axis representing the phase assigned to each sub-pulse. Figure 1 It can be seen that the first phase-coded waveform used in the horizontal polarization channel and the second phase-coded waveform used in the vertical polarization channel occupy the same pulse time and the same frequency band. They are modulated by different phase sequences and are orthogonal to each other, so they radiate simultaneously in the same frame and can be separated from each other by matched filtering at the receiving end.

[0022] Whether two waveforms are orthogonal depends on their correlation characteristics. The correlation between the first phase-coded waveform and itself at different distance shifts is denoted as... , The correlation between the first phase-coded waveform and the second phase-coded waveform is denoted as... , in For integer distance shifts in units of sub-pulses, the superscript... Represents complex conjugation. The ideal code type should allow... exist A tall and narrow main peak should be erected, while the other displaced side lobes should be kept as low as possible, while also allowing... The values ​​are close to zero on all shifts. The former ensures that the echo after matched filtering is compressed into a sharp main lobe without being disturbed by its own sidelobes, while the latter ensures that the two polarizations do not crosstalk each other at the receiver. This implementation performs a numerical search on the four-phase sequence (e.g., iteratively using simulated annealing) to select a pair of codes under the two objectives of reducing autocorrelation sidelobes and reducing cross-correlation. This results in the peak sidelobe level of the autocorrelation being about 30 dB lower than the main peak after mismatch weighted filtering, and the maximum value of the cross-correlation being about 30 dB lower than the main peak of the autocorrelation. This level corresponding to the cross-correlation directly determines the isolation between the two polarization channels. The lower it is, the cleaner the horizontally polarized echo and vertically polarized echo will be.

[0023] The reason for designing orthogonal coding instead of having both polarizations transmit the same waveform is that dual polarization is truly concerned with the differences between the horizontal and vertical echoes, namely the power ratio, phase difference, and correlation between them. Imagine that both transmissions are the same waveform: in the echo received by the horizontal receiver, the component scattered horizontally back horizontally by the target and the component cross-scattered horizontally by the target vertically use the same waveform. After matched filtering, they are superimposed and cannot be separated. The cross-scattering component from the vertical transmission is mixed into the otherwise pure horizontally polarized echo, polluting the subsequently calculated difference component. With orthogonal coding, although the horizontal receiver still receives both components simultaneously, they carry different coding markers: the matched filter only matches the first-phase coded waveform used in the horizontal transmission, thus suppressing the portion using the first-phase coded waveform as the main peak, while the cross-scattering component using the second-phase coded waveform only yields a low cross-correlation response and is suppressed. Another common approach is to have the two polarizations transmit alternately, i.e., one pulse is horizontal and the next is vertical. Although this can separate them, the horizontal and vertical signals are sent to different pulses and at different times. The decorrelation caused by the random fluctuations of the target directly impairs the accuracy of differential components such as the correlation degree. Intra-frame orthogonal polarization waveform coding avoids both of these problems: the two echoes are taken from the same pulse and at the same time, and they are isolated from each other by coding. This maintains the simultaneity required for differential measurements and avoids crosstalk from cross-polarization.

[0024] During reception, both the horizontally polarized and vertically polarized channels down-convert the echo to baseband, and then perform matched filtering with their respective phase-coded waveforms. Taking the horizontally polarized channel as an example, the baseband echo at a certain distance can be written as... , In the formula The time delay of the echo relative to the transmission corresponds one-to-one with the target distance; The scattering coefficient that scatters horizontally emitted light back to horizontally received light is the target. The scattering coefficients are both complex numbers that cross-scatter the vertically emitted signal to the horizontally received signal. Receiver thermal noise introduced to the horizontally polarized receiving channel. The first phase-coded waveform is used for... When performing matched filtering, the output at the target delay is approximately: , in The cross-correlation between the second-phase encoded waveform and the first-phase encoded waveform, with magnitudes of... The values ​​are relatively low, hence the lower values. It can be seen that carrying... That item falls on the autocorrelation main peak The upper part is coherently accumulated and significantly elevated, carrying cross-components. The term is suppressed by the low cross-correlation, leaving almost only horizontally transmitted and received components in the matched filter output, i.e., the required horizontally polarized echo. The vertically polarized channel undergoes the same processing using the second phase-coded waveform to obtain the vertically transmitted and vertically received vertically polarized echoes. The two paths are separated within the same pulse, achieving simultaneous transmit and receive isolation. While separating the two polarizations, the matched filter also compresses the broadened pulse in terms of range, resulting in a range resolution of [value missing]. , In the formula For the speed of light, take meters per second; The bandwidth of the aforementioned waveform. Substitute... megahertz Meters. The signal-to-noise ratio improvement factor brought about by matched filtering is equal to the time-bandwidth product of the waveform. , Substitution microseconds megahertz Approximately 20 decibels, numerically related to the code length. Essentially, the energy of 100 sub-pulses is coherently superimposed onto a single main lobe, which is why low-peak-power solid-state transmitters can achieve long-range detection. To prevent the range sidelobes of the strong precipitation unit from drowning out adjacent weak echoes, matched filtering can employ mismatched least-squares weighting, or a Taylor window or Hamming window can be added in the frequency domain to further suppress the sidelobes at the cost of slightly widening the main lobe.

[0025] Phase coding is somewhat sensitive to the Doppler shift of the echo, so it's necessary to verify whether compression still holds true within the velocity range of the meteorological target. Taking a wavelength of 0.0319 meters and a radial velocity of 30 meters per second as an example, the corresponding Doppler shift is approximately 1881 Hz (equal to twice the radial velocity divided by the wavelength). The accumulated phase shift within a 20-microsecond pulse is less than 0.04 cycles, approximately 13.5 degrees, which is negligible relative to the 5 MHz bandwidth. Compression within a single pulse is essentially unaffected. The real velocity information is the phase change between pulses (slow time), which is left for subsequent processing. If operating at higher frequencies or facing greater radial velocities where Doppler shift can no longer be ignored, a code type more adaptable to Doppler shifts can be used, such as P4 polyphase coding, or a linear frequency modulation pair (one path up-modulated, the other down-modulated) can be employed to maintain the stability of the compressed main lobe across the entire velocity range.

[0026] After obtaining the horizontally polarized and vertically polarized echoes, they are oversampled in the range direction, meaning the interval between adjacent range samples is less than the width of a resolution cell. The output of the matched filter is bandwidth-limited; sampling denser along the range direction than a resolution cell does not add extra detail to the signal itself. However, each additional sample adds a separate thermal noise sample to the receiver. These samples, closely spaced within a resolution cell, exhibit a correlation structure in both signal and noise components, determined by the transmitted waveform and the matched filter. This increased number of correlated samples provides a basis for the next stage of whitening to reassemble correlated samples into a statistically more effective observation, thereby reducing the estimation variance without extending the dwell time. Let the oversampling factor be... , If the integer is greater than 1, then the distance interval between adjacent oversampled subsamples is... , In the formula For the aforementioned distance resolution, This is the oversampling factor. (Take...) , Meters, then the subsample interval Rice, in terms of time, is... The sampling interval is microseconds, corresponding to a sampling rate of approximately 20 MHz. Therefore, within a 30-meter range corresponding to each meteorological resolution volume, the horizontally polarized echo provides four horizontally polarized oversampled subsamples arranged adjacently along the range direction, and the vertically polarized echo also provides four vertically polarized oversampled subsamples. Since the two polarizations share the same set of range sampling times at the receiver, the horizontally polarized oversampled subsamples and the vertically polarized oversampled subsamples correspond one-to-one at each range direction position. Oversampling factor Generally, values ​​between 2 and 8 are used: the larger the value, the more samples can be used in a single resolution unit, but the stronger the signal correlation between adjacent samples and the higher the risk of noise amplification. It is necessary to weigh the benefits that whitening can bring. In this implementation, a value of 4 is a more prudent choice.

[0027] Here are some alternative approaches. Regarding code patterns, in addition to the four-phase search code mentioned earlier, a pair of low cross-correlation complementary sequences or a pair of sequences derived from the Hadamard matrix can be used, as long as the autocorrelation peak is sharp and the cross-correlation is low across the full shift. To further combat secondary echoes and clutter from range folding, each pulse can use a different orthogonal code pair, causing the folded echoes to be dispersed after matched filtering and no longer coherently accumulate. In terms of frequency bands, in addition to 9.4 GHz, the C-band and Ka-band are also applicable; simply recalculate the pulse width, bandwidth, and pulse repetition period according to the range, resolution, and maximum measurable velocity. Regarding waveform parameters, pulse width, bandwidth, and code length are interrelated: pulse width determines energy, bandwidth determines resolution, and code length is approximately equal to the time-bandwidth product, which is also approximately equal to the compression gain, and can be adjusted in conjunction with detection requirements. For sidelobe suppression, in addition to mismatch weighting and window functions, iterative sidelobe cancellation can also be used to further improve the range response at the adjacent points of strong and weak echoes. These substitutions do not change the essence of this step: two orthogonal codes are simultaneously emitted using solid-state transmission and intra-frame orthogonal polarization waveform encoding. After matched filtering, the horizontal polarization echo and the vertical polarization echo are separated in the same pulse and the pulse compression gain is obtained. Then, oversampling is performed in the range direction to prepare an oversampled subsample for each meteorological resolution volume, with the number of oversampled subsamples equal to the oversampling multiple and corresponding to each position of the two polarizations.

[0028] Following step 1, both the horizontally polarized echo and the vertically polarized echo have been oversampled in the range direction: within the range span corresponding to each meteorological resolution volume, the horizontally polarized echo provides... A horizontally polarized oversampled subsample, with the vertically polarized echo given. One vertically polarized oversampled subsample, That is, the oversampling factor in step 1, for example, 4. This applies to the same meteorological resolution volume and the same pulse... The horizontally polarized oversampled subsamples are arranged in a column according to their distance order, denoted as [a_n]. In the formula For pulse sequence number (slow time), , The number of pulses within a dwell period (64, following step 1). For the first One horizontally polarized oversampled subsample ( ), superscript This indicates transpose; similarly, it represents transpose. A vertically polarized oversampled subsample is arranged into .this The subsamples are not independent of each other; they fall within the same resolution unit and are only a few meters apart. Matched filtering converts the bandwidth of the transmitted waveform into a finite-width distance response, causing the values ​​at adjacent positions to be linked together by the same waveform segment and the same set of filters. This linkage exists both in terms of signal components and in terms of residual receiver thermal noise after matched filtering. The correlation between each pair of oversampled subsamples, i.e., the distance oversampled correlation structure; step 2 first estimates it, and then calculates a set of whitening recombination coefficients shared between the two polarization channels.

[0029] To estimate this structure, it's necessary to understand its origin: it's determined by the transmitted waveform and the matched filter, both of which are fixed within a certain range and are largely independent of whether the rain falling in a specific resolution cell is heavy or light. Therefore, several adjacent meteorological resolution volumes within the same range, despite varying echo strengths, share almost identical range oversampling correlation structures. Utilizing this, range oversampling can be performed near the resolution cell to be processed. Each adjacent meteorological resolution volume (16 in this example) is used to aggregate the oversampled subsamples of each pulse to estimate a... The covariance of the two polarization channels is calculated, and subsamples from both polarization channels are included. This is because the first and second phase-coded waveforms are designed with equal bandwidth and matching main lobe shapes. The distance weighting of the horizontal and vertical polarization channels has the same shape, and they share the same distance oversampling correlation structure. Merging the estimates increases the number of samples and naturally yields a result applicable to both polarizations. Specifically,

[0030] In the formula For the estimated covariance , The first Adjacent meteorological resolution volumes in pulse The horizontally polarized oversampled subsample vector and the vertically polarized oversampled subsample vector are shown below, with superscripts indicating their relative positions. Indicates conjugate transpose, coefficient This is the total number of samples that participate in the average. (Continued) , Two polarizations, with a total of 2048 outer products involved in the averaging, far exceed the degrees of freedom of a 4th-order matrix, resulting in a fairly stable estimate. Normalizing it along the diagonal yields a normalized matrix characterizing the distance oversampling correlation structure.

[0031] in This represents the trace of a matrix (the sum of its diagonal elements), after normalization. The average of the diagonal elements is 1, and only the shape information of how deep the adjacent positions are related is retained, while the total power, which is irrelevant to the shape, is discarded. It typically presents as a band: the diagonal is 1, the adjacent second diagonal is significant (highly correlated with adjacent oversampling positions), and the value decreases with distance from the diagonal. For example, a representative value is... The eigenvalues ​​are 0.85 for adjacent samples, 0.55 for samples separated by one position, and 0.25 for samples separated by two positions. Their eigenvalues ​​are approximately 2.7, 0.9, 0.3, and 0.1 (the sum of the four is 4). The smallest eigenvalue is much less than 1, indicating that only one or two of these four oversampled subsamples carry truly independent information in each direction, while the other directions are highly redundant.

[0032] Yes This allows us to calculate the whitening recombination coefficient, which reassembles related oversampled subsamples into uncorrelated sequences. What we are seeking is a... linear transformation matrix ,make

[0033] for The meaning of this condition is: using an identity matrix of order 1 / 2. After performing a linear combination on the oversampled subsamples, the pairwise correlations between the resulting sequences are compressed to zero, and their respective variances are normalized to one. Perform eigenvalue decomposition ,in Each column is a feature vector. A diagonal matrix formed by eigenvalues ​​( For the first (each eigenvalue) can be taken

[0034] Substitute it back into the previous equation, This perfectly meets the requirements. Matrix Each row represents a set of albino recombination coefficients: Let the first row be the albino recombination coefficient. row vector It gives the first Whitened sample sequence pairs The weighting method for each oversampled subsample. Here Each feature direction is amplified inversely proportional to the square root of its eigenvalue; that is, redundant directions (large eigenvalues) are compressed, and scarce directions (small eigenvalues) are increased, thereby distributing the information originally concentrated in one or two directions to more diverse areas. On the way. It's worth noting that the magnification corresponding to the smallest eigenvalue of 0.1 is approximately... The signal itself is weak in this direction, and amplification also amplifies the thermal noise in this direction. This needs to be constrained when the signal-to-noise ratio is low, and the constraint method is described later.

[0035] Next, for each meteorological resolution volume, the same... The effects are applied to the horizontally polarized oversampled subsamples and the vertically polarized oversampled subsamples, respectively:

[0036] , Each for A dimensional vector, whose dimensional vector is the first dimensional vector. Each component , This linear combination is the whitening transform. By stringing together the values ​​of the same path across each pulse along a slow time path, a line of length [length missing] is obtained. sequence, The road was then obtained Bar: Horizontal polarization side is obtained The horizontally polarized whitening sample sequence was obtained from the vertically polarized side. The vertical polarization whitening sample sequence. Previously, if a resolution cell was treated as only one sampling point, each resolution cell had only one slow time series per polarization available for subsequent moment estimation; after oversampling and whitening, it became... The number of uncorrelated slow time series available for estimation increases to [number]. This means doubling the number of samples, as shown in the example. That is, it increases to 4 times.

[0037] See Figure 2 , Figure 2 The graph shows the change in correlation between oversampled subsamples before and after whitening transformation as a function of sample index intervals. The horizontal axis represents the sample index interval, and the vertical axis represents the correlation degree. Figure 2 It can be seen that before the whitening transformation, adjacent oversampled subsamples within the same meteorological resolution volume are highly correlated, and the degree of correlation gradually decreases as the sample number interval increases. After linear combination with the same whitening recombination coefficient, the correlation between each pair of whitened sample sequences drops to close to zero, thus obtaining uncorrelated multiple whitened sample sequences from the correlated oversampled subsamples, achieving sample multiplication.

[0038] This explains why we insist on using the same set of whitening and recombination coefficients for both polarizations, rather than whitening their respective channels. The differential reflectivity, differential propagation phase, and correlation coefficient that dual polarization truly measures characterize the power ratio, phase difference, and correlation degree between the horizontal and vertical echoes. These are properties of the hydrogel within the same resolution cell, shared by several oversampling locations only a few meters apart within that cell. The shape of the distance oversampling correlation structure, as mentioned earlier, is shared for both polarizations. Putting these together, the covariances of the horizontal and vertical oversampling subsamples are respectively written as... , The cross-covariance of the two can be written as In the formula , For horizontally polarized echo power and vertically polarized echo power, The correlation coefficient is... For differential propagation phase, The imaginary unit; that is, the difference components are multiplied only by a common scalar factor in a common shape. Above, power is represented as a real scalar, while differential phase and correlation are represented as complex scalars. Therefore, the first... The two-way power and cross-correlation of the whitened sample sequence are in the expected sense as follows:

[0039]

[0040] in In order to achieve the desired result, the superscript To obtain conjugate, It is only with the first A positive real scalar related to the group whitening and recombination coefficient. Dividing these three equations pairwise reveals that the ratio of the two power paths is... , Cancelled, differential reflectivity Unchanged; the phase of cross-correlation is Its amplitude, after being normalized by taking the square root of the two power sources, is: , Even when canceled out, the differential propagation phase and correlation coefficient remain unchanged. In other words, regardless of... How to recombine the samples The value can be chosen as long as the same value is used for both the horizontal and vertical paths. Each path carries the same differential component as before whitening; each path of the horizontally polarized whitening sample sequence corresponds to the path of the vertically polarized whitening sample sequence, thus carrying the differential reflectivity, differential propagation phase, and correlation coefficient in pairs and unchanged. Conversely, if a different whitening matrix is ​​assigned to each of the two polarizations, the three equations above will show different results. and These factors can no longer be eliminated, introducing a path-dependent amplitude and phase into each path, disrupting the differential reflectivity, differential propagation phase, and correlation coefficient. This is why single-channel whitening is unusable in dual-polarization scenarios. Sharing the whitening recombination coefficients between the two polarizations achieves both sample multiplication and maintains the fidelity of differential measurements, thus achieving both goals simultaneously.

[0041] See Figure 3 , Figure 3 This diagram illustrates the differential propagation phase and correlation coefficient of each whitened sample sequence under two processing methods: sharing the same whitening recombination coefficient between the horizontal and vertical polarization channels, and whitening each polarization channel independently. The horizontal axis represents the whitening path number, and the vertical axes represent the differential propagation phase and correlation coefficient, respectively. Figure 3 It is evident that when the two polarization channels share the same whitening recombination coefficient, the differential propagation phase and correlation coefficient carried by each channel remain consistent with those before whitening. However, when the two polarization channels are whitened independently, the differential propagation phase carried by each channel is disrupted, and the correlation coefficient is suppressed. This demonstrates that sharing the same whitening recombination coefficient between the two polarization channels is a prerequisite for each whitened sample sequence to maintain its differential reflectance, differential propagation phase, and correlation coefficient in pairs.

[0042] The benefits of doing this will be fully realized in step 3, but it will be explained here first: after whitening The road slow time series have been discorrelated. By performing multi-lag autocorrelation and cross-correlation calculations on each series and then averaging across the road, the variance can be reduced to at most the original value. However, without albino treatment, Oversampled subsamples are highly correlated, and direct averaging only yields one or two equivalent independent samples, making variance reduction almost impossible. Whitening removes the relevant... Each sample is converted into a solution-related value. The road is designed to achieve this closeness. The variance reduction gain is several times, and as demonstrated above, this gain does not come at the expense of the accuracy of the difference component. The actual amount that can be obtained depends on the signal-to-noise ratio and the strength of the following constraints: close to 4 times the full value at high signal-to-noise ratios, and discounted at low signal-to-noise ratios due to noise amplification.

[0043] Provide several alternative implementation methods. It is possible to perform eigenvalue decomposition without going through feature decomposition. Cholesky decomposition ( (For a lower triangular matrix), take Similarly satisfied It requires less computation and is suitable for real-time implementation; two types The difference is only one unitary transformation, which has no substantial impact on the subsequent cross-path averaging results. It's not necessary to estimate from data every time. If the transmitted waveform and matched filter are fixed, the theoretical distance-weighted correlation can be directly calculated from them, and the system can be constructed accordingly. This eliminates the need for segment-by-segment estimation. The advantage of estimating from data is its ability to adapt to actual filter mismatch and bandwidth fluctuations. Both methods can be used together: theoretical values ​​can be used as initial values, and data-based estimates can be used for slow correction. For noise amplification under low signal-to-noise ratio conditions, constrained whitening can be used, i.e., the diagonal amplification described above can be replaced with...

[0044] As a constraint constant, it is selected according to the level of noise relative to the signal, so that those characteristic directions smaller than the noise floor are no longer excessively amplified (equivalent to...). (Set a lower limit), examples can be taken Approximately equal to noise power and A ratio of several times represents a trade-off between the thoroughness of the solution and the controllability of the noise; it should be noted that... Since the same transformation is still used for both polarizations, the above conclusion on difference component fidelity remains unaffected. Fidelity only requires the use of the same matrix for both paths, not that the matrix should whiten the samples thoroughly, providing ample freedom for constraints. The number of adjacent meteorological resolution volumes. It can also be adjusted: obtaining more covariance estimates leads to greater stability, but requires sufficiently uniform echo statistics over this distance. Therefore, a trade-off must be struck between estimation robustness and distance uniformity. For locations with large precipitation gradients, [the following can be added]: Take the smallest value and update in segments according to distance. and Oversampling factor Increasing the number of paths available for multiplication results in smaller eigenvalues ​​and more severe noise amplification, requiring a trade-off with the constraint strength. These substitutions do not change the essence of this step: based on the distance oversampling correlation structure estimated from adjacent meteorological resolution volumes, a set of whitening recombination coefficients is obtained. The same set of coefficients is applied to the horizontally polarized oversampling subsamples and the vertically polarized oversampling subsamples to perform a linear combination. This recombines the correlated oversampling subsamples into uncorrelated multi-path horizontally polarized whitening sample sequences and multi-path vertically polarized whitening sample sequences, achieving sample multiplication, while ensuring that each path maintains the same differential reflectance, differential propagation phase, and correlation coefficient in pairs.

[0045] Following step 2, at this point, each meteorological resolution volume has two sets of slow time series prepared: one on the horizontal polarization side and one on the horizontal polarization side. Horizontal polarization whitening sample sequence The vertically polarized side has Vertical polarization whitening sample sequence ,in This is the oversampling factor (4 in the example). The pulse number. , This is the number of pulses within a dwell period (64, as used here). Here we recall the origins of these two sets of sequences: the whitening transformation is along the range direction, within a single resolving cell. The linear combination of oversampling locations does not alter the slow time dimension. Therefore, the fluctuations between pulses in each whitened sample sequence still retain the Doppler information of the hydrogel within that resolution volume, namely the average speed of motion and the width of velocity diffusion; while The paths are now largely uncorrelated due to the correlation obtained in step 2, which is equivalent to performing a solution on the same precipitation area. These are nearly independent observations. Step 3 involves using both of these methods: calculating the correlation at multiple lags along the slow time path on each path, spanning... The average road surface is used to suppress the estimated fluctuations, and then the various meteorological parameters are solved based on this.

[0046] First, let's look at autocorrelation. For the first... Horizontal polarization whitening sample sequence, taking hysteresis The autocorrelation at the location is

[0047] In the formula This method takes an integer lag in units of pulse repetition periods. ; superscript Indicates complex conjugation; denominator This is the number of pulse pairs available under this hysteresis. The vertical polarization side is obtained using the same formula. Then put The results at the same lag point are added together and averaged.

[0048] This string That is, horizontally polarized multi-hysteresis autocorrelation sequences. This refers to vertically polarized multi-hysteresis autocorrelation sequences. Here, there is a convenience already established in step 2: because the whitening recombination coefficient satisfies the condition of transforming the normalized distance oversampling correlation structure into an identity matrix, the power normalization coefficient of each whitening sample sequence is exactly equal to 1. The autocorrelation carried by each path is, in the expected sense, the same weighted meteorological autocorrelation. Cross-path averaging will not introduce scale bias that varies with path, but only reduces the random fluctuations in the estimate. Since the road has been solved, this The estimates are nearly independent, and the variance after averaging can be compressed to at most a single path. Example is approximately The standard deviation is halved. This is equivalent to directly analyzing a single resolving unit without whitening. Averaging highly correlated oversampled subsamples reveals that only one or two samples are truly equivalent and independent, making variance reduction nearly impossible. This is where the benefits of oversampling in step 1 and whitening in step 2 come into play. Instead of fitting parameters for each path separately and then averaging, the complex autocorrelation is first averaged across all paths, directly reducing noise and resulting in a cleaner correlation sequence. If parameters are fitted path by path first, phase wrapping or outliers in individual paths can contaminate the parameters under low signal-to-noise ratio.

[0049] The cross-correlation between the two polarizations is also calculated path by path and then averaged:

[0050] The resulting sequence is the multi-hysteresis cross-correlation sequence. It is taken from the horizontally polarized whitening sample sequence and the corresponding vertically polarized whitening sample sequence, rather than from two unrelated channels. This is because step 2 uses the same set of whitening recombination coefficients to process the two polarizations, and each channel retains the true differential reflectance, differential propagation phase, and correlation coefficient in pairs. The cross-correlation of each channel thus cleanly carries these differential components.

[0051] To extract the power, velocity, spectral width, and difference components from these correlation sequences, a model linking them to meteorological parameters is needed. Meteorological echoes are the superposition of scattering from a large number of condensates within a resolving volume. These particles both translate with the overall airflow and exhibit velocity dispersion due to turbulence and wind shear. The superposition result in a bell-shaped spectrum in the frequency domain, with the center determined by the overall motion and the width by velocity dispersion. Therefore, a Gaussian spectrum is used to describe its Doppler spectrum: the center frequency of the spectrum... spectral bandwidth In the formula Radial velocity, For spectral width (in velocity), The wavelength is 0.0319 meters. The inverse Fourier transform of the Gaussian spectrum remains Gaussian in the autocorrelation domain: the amplitude decreases Gaussianly with lag, and the phase increases linearly with lag. This can be written as...

[0052] in The echo power of this polarization (equal to the autocorrelation value at zero hysteresis), The pulse repetition period (using 0.001 seconds) is used. The imaginary unit, The integer lag is applied. Take as horizontally polarized echo power When this equation is used, it is the model followed by the horizontally polarized multi-hysteresis autocorrelation sequence; taking the vertically polarized echo power as... ,and and When sharing the same set with horizontal polarization, i.e., the model of vertical polarization multi-hysteresis autocorrelation sequences. Another advantage of choosing the Gaussian type is that it only contains... , , There are three quantities, with phase only controlling velocity, amplitude only controlling power and spectral width. The two are decoupled, making it easy to determine robustly with a few hysteresis.

[0053] Given a constant radial velocity, observe the phase. The phase in the above formula... With lag linearity, the slope is proportional to the velocity. (This refers to a horizontally polarized multi-lag autocorrelation sequence.) After phase unwinding at the point, for Perform a straight line fitting through the origin to obtain the slope. (For each radian lag), then

[0054] A velocity can be given using only lag 1, but the unambiguous velocity with a single lag only reaches up to... Substituting the numerical value, the result is approximately 7.975 meters per second, which has a narrow span. Using multiple lags for phase slope fitting reduces the impact of random fluctuations and facilitates unwinding by predicting the phases of adjacent lags. For example, a radial velocity of 5 meters per second corresponds to phases of approximately 1.969, 3.938, and 5.908 radians at lags 1, 2, and 3, respectively, where lag 2 has already exceeded... To achieve the apparent winding, a rough value needs to be estimated from lag 1, and based on this, the true phase of lag 2 and lag 3 needs to be predicted before unwinding. Then, the slope needs to be calculated by combining the three points for fine-tuning.

[0055] For a given spectral width and horizontally polarized echo power, consider the amplitude. The amplitude in the above formula is then calculated by taking the logarithm.

[0056] yes A linear function: slope gives the spectral width, intercept gives the power. The horizontally polarized multi-hysteresis autocorrelation sequence is then... Logarithmic magnitude at point Plot a straight line fit, and denote the slope as... (must be negative), then

[0057] The intercept is the line extrapolated to... The value at the specified position is used. Power is determined by attenuation at lags of 1, 2, and 3, and then extrapolated back to zero lag, instead of directly using the zero-lag autocorrelation as power. This is because the zero-lag autocorrelation includes the power of receiver thermal noise, and white noise only correlates with itself at zero lag; its contribution approaches zero at lags of 1 and above. Therefore, a pure non-zero lag is used for fitting and extrapolation, yielding a signal power without a noise floor, eliminating the step of separately measuring noise and then subtracting, along with its error. Two or more lags are needed because both power (intercept) and spectral width (slope) need to be determined simultaneously. Using a third lag transforms the equation into an overdetermined equation, which is both noise-resistant and allows the residual to detect the degree of Gaussian deviation in the echo. For example, at a spectral width of 2 meters per second... Approximately 0.31 per The amplitude decays to approximately 0.73, 0.29, and 0.06 times the power at lags of 1, 2, and 3, respectively. It can be seen that the wider the spectrum, the faster the decay with high lag. When the spectrum is very wide, lag 3 is close to noise and high lag should be used less. When the spectrum is narrow, high lag is still reliable and can be used more often. Lags of 1 to 3 are a compromise to cover common spectrum widths.

[0058] See Figure 4 , Figure 4 The process of retrieving meteorological parameters using a Gaussian autocorrelation model based on multi-lag autocorrelation sequences is shown. Figure 4 In the graph, one plots the autocorrelation logarithmic amplitude against the square of the hysteresis, showing an approximately linear relationship. The slope of this line corresponds to the spectral width, and the intercept, extrapolated to zero hysteresis, corresponds to the echo power. Since receiver thermal noise only contributes power at zero hysteresis, values ​​from non-zero hysteresis are used for fitting and extrapolation to zero hysteresis; the resulting echo power has its noise floor subtracted. The other plot plots the autocorrelation phase against the hysteresis, showing an approximately linear increase; the slope of this line corresponds to the radial velocity. Figure 4 It can be seen that the amplitude and phase of the autocorrelation sequence carry the echo power, spectral width and radial velocity, respectively, and can be robustly inverted from a few values ​​at hysteresis of 1, hysteresis of 2 and hysteresis of 3.

[0059] The method for calculating the vertically polarized echo power reflects the design concept of having the same radial velocity and the same spectral width constraints. The horizontally polarized channel and the vertically polarized channel transmit and receive the same batch of hydrophobic particles within the same meteorological resolution volume during the same pulse repetition period. The overall motion and velocity dispersion of these particles are the same for both polarizations; therefore, the Doppler spectrum of the vertically polarized channel shares the same value as that of the horizontally polarized channel. and the same The only difference is power. Therefore, there's no need to use a vertically polarized sequence, which typically has a lower signal-to-noise ratio, to estimate the velocity and spectral width again, as that would generate more noise and potentially be inconsistent with the results of horizontal polarization; instead, we should... and Locked at a fixed value for horizontal polarization, only the magnitude intercept of the vertically polarized multi-hysteresis autocorrelation sequence is fitted. : Fix the slope of the logarithmic amplitude line above to the value calculated from the horizontal polarization spectral width. ,but With two fewer free parameters, the vertical polarization power estimation is more stable and physically consistent with the horizontal polarization. After obtaining the two power values, the differential reflectivity is...

[0060] In decibels, , As defined above. The horizontal polarization channel is selected to determine the velocity and spectral width and to constrain the others, because for most precipitation, flat raindrops have stronger backscattering in the horizontal direction, the horizontal polarization channel has a higher signal-to-noise ratio, and the determined velocity and spectral width are more reliable; when the signal-to-noise ratio is very high, the autocorrelation of the two power channels can also be used to determine the velocity and spectral width, which has an even higher signal-to-noise ratio, as explained in the optional methods.

[0061] The differential propagation phase and correlation coefficient are taken from the multi-lag cross-correlation sequence. Cross-correlation occurs in the lag... Follow

[0062] In the formula The correlation coefficient is... This represents the differential propagation phase; the other symbols are the same as before. It can be seen that its phase at each lag is a superposition of two segments: one segment is the fixed phase of the differential propagation. The other segment is the Doppler phase, which is caused by the overall motion and increases linearly with lag. Its amplitude is the correlation coefficient multiplied by the square root of the two power sources, and then multiplied by the same Gaussian decay as the autocorrelation (because the two sources correspond to the same Doppler spectrum, and the decay is naturally isomorphic). Separating these two segments yields the difference component. In terms of phase, since... The Doppler phase at each lag point has been determined by the horizontal polarization. Subtracting from the cross-correlation phase, the remainder should equal the value at each lag. To find the average and stabilize across lags,

[0063] (The unwinding method is the same as at the speed). In terms of amplitude, since... Once determined, remove the Gaussian attenuation that deepens with increasing lag, then normalize by taking the square root of the two power sources to obtain the correlation coefficient.

[0064] in The attenuation factor, calculated from the horizontal polarization spectral width, is divided to compensate for the spectral width reduction. This step is spectral width normalization of the cross-correlation amplitude. If normalization is neglected and a non-zero hysteresis cross-correlation amplitude is directly used as the correlation coefficient, the wider the spectrum, the lower the measured correlation coefficient, misclassifying a pure rain region that should be close to 1 as a mixed phase. Spectral width normalization precisely corrects this bias. Using non-zero hysteresis instead of zero hysteresis to obtain these two difference components has two advantages: firstly, it shares the same multi-hysteresis estimation and cross-channel averaging with power, velocity, and spectral width, making it statistically more stable; secondly, in a dual-channel simultaneous transmission system, zero-hysteresis cross-correlation is prone to incorporating transient coupling residues between the two channels, avoiding this is more reliable; of course, when coupling is negligible, the phase of the zero-hysteresis cross-correlation can be directly used as the correlation coefficient. Its amplitude is normalized. A simpler approach is described in the optional methods section.

[0065] Looking at the above steps together, it's a joint inversion anchored by horizontal polarization: the radial velocity is determined in one step from the horizontal polarization multi-hysteresis autocorrelation sequence. Spectral width With horizontally polarized echo power ;Bundle , As a common constraint, the vertical polarization echo power is determined by applying it to the vertical polarization multi-hysteresis autocorrelation sequence. The two are compared to obtain differential reflectance. Then put , Applying this to a multi-hysteresis cross-correlation sequence and subtracting the Doppler phase yields the differential propagation phase. The correlation coefficient is obtained by subtracting spectral width attenuation and normalizing. A meteorological resolution volume ultimately outputs seven quantities: horizontally polarized echo power, vertically polarized echo power, radial velocity, spectral width, differential reflectivity, differential propagation phase, and correlation coefficient. The benefits of shared constraints are clear: if each of the three sequences estimates the velocity and spectral width three times, it not only adds noise but may also give contradictory motions, leading to differential component distortion; locking them into a single set reduces free parameters, achieves mutual consistency, and maintains the accuracy of the differential components; all of this is based on the fact that the two polarizations are taken from the same pulse and target the same batch of hydrogels, and this simultaneity is achieved by intra-frame orthogonal polarization waveform encoding and simultaneous transmission and reception isolation in step 1. Combined with the preceding cross-... By reducing the variance of the path, this step improved the overall estimation accuracy of the seven meteorological parameters without extending the dwell time or increasing the transmission power.

[0066] See Figure 5 , Figure 5This illustrates the impact of cross-path averaging on the standard deviation of meteorological parameter estimates after sample doubling. The horizontal axis represents the number of sample paths participating in the averaging, and the vertical axis represents the normalized standard deviation of the estimates. Figure 5 It is evident that when averaging uncorrelated multi-path whitened sample sequences obtained through whitening, the estimated standard deviation decreases significantly with the increase of the number of paths involved in the averaging. However, when directly averaging highly correlated oversampled subsamples within the same meteorological resolution volume, the estimated standard deviation decreases slowly due to the limited number of equivalent independent samples. Therefore, whitening transformation, which reorganizes correlated oversampled subsamples into uncorrelated multi-path whitened sample sequences, is a prerequisite for effectively reducing the estimated variance in cross-path averaging.

[0067] Several alternative approaches are given below. When the velocity and spectral width are constant, besides using horizontal polarization alone, the multi-hysteresis autocorrelation sequences of horizontal and vertical polarization can be weighted and combined according to their respective SNR ratios before fitting. This is more robust when the SNR is limited. The fitting itself can also be changed from equal-weighted least squares to least squares weighted by the variance of each hysteresis estimate, giving greater weight to hysteresis with better SNR (usually low hysteresis). The choice of hysteresis does not need to be fixed at 1, 2, or 3: when the spectrum is very wide, high hysteresis has sunk into noise, so only 1 or 2 can be used; when the spectrum is very narrow and the echo is strong, it can be extended to 4 or 5 to measure the tail of Gaussian decay more accurately. The limitation of a narrow unambiguous velocity can be resolved by using staggered pulse repetition periods, that is, alternating the interval between adjacent pulses between two coprime periods, so that the effective unambiguous velocity is determined by the difference between the two periods, which is much greater than the corresponding value of a single period. The multi-hysteresis framework in this step naturally accommodates non-uniform hysteresis. Regarding the selection of differential components, as previously mentioned, when inter-channel coupling is negligible, we can revert to zero-hysteresis cross-correlation, omitting the Doppler stripping step. In terms of absolute power calibration, if constrained whitening is used in step 2 to suppress noise amplification at low signal-to-noise ratios, the sum of the power normalization coefficients for each channel will be less than... The power of the cross-path average is suppressed by a known factor, which can be corrected by multiplying back by the factor (calculated from the eigenvalues ​​of the correlation structure and the constraint constants). Since the differential reflectivity is the ratio of the two power paths and both paths use the same whitening transform, this factor is automatically canceled out and remains unaffected. This is another convenience of sharing whitening between the two polarizations. Furthermore, this step estimates parameters using autocorrelation moments. If the dwell time is long, the frequency domain can be used instead: perform a Discrete Fourier Transform on the Doppler spectrum of each whitened sample sequence along slow time. After averaging the power spectrum across the cross-paths, take the 0th, 1st, and 2nd moments of the spectrum, which correspond to power, velocity, and spectral width, respectively. This achieves the same result as the moment method, but the spectral domain is more convenient when strong clutter requires removing ground object echoes according to a velocity threshold. Further down, the rate of change of the differential propagation phase along the distance gives the differential phase, and the distance accumulation of the differential propagation phase is used to attenuate and correct the power and differential reflectivity of the two paths. All of these unfold naturally from the output of this step. All these substitutions do not change the essence of this step: calculate the autocorrelation and cross-correlation at lags 1, 2, and 3 for each of the multi-path horizontally polarized whitened sample sequences and the multi-path vertically polarized whitened sample sequences, and average them across the paths to obtain the horizontally polarized multi-lag autocorrelation sequence, the vertically polarized multi-lag autocorrelation sequence, and the multi-lag cross-correlation sequence. Using Gaussian autocorrelation as a model, under the constraints of the same radial velocity and the same spectral width, solve the system simultaneously to output the horizontally polarized echo power, vertically polarized echo power, radial velocity, spectral width, differential reflectivity, differential propagation phase, and correlation coefficient.

[0068] Thus far, steps 1 to 3 have achieved the following process: solid-state transmission with intra-frame orthogonal polarization waveform encoding, matched filtering to separate two polarization echoes within the same pulse and obtain pulse compression gain, range oversampling to prepare multiple sample points for each resolution volume; the two polarizations share the same whitening recombination coefficient to recombine related sample points into uncorrelated multi-path whitening sample sequences, both doubling the samples and maintaining the difference components of each path; then, using multi-hysteresis autocorrelation spectrum estimation with shared velocity spectral width constraints, the seven meteorological parameters are robustly inverted.

[0069] The above-described embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for estimating the multi-hysteresis autocorrelation spectrum and jointly inverting meteorological parameters of a miniature dual-polarization weather radar, comprising the following steps: Step 1: The solid-state transmitter transmits a composite pulse in each pulse repetition period, consisting of the superposition of the first phase-coded waveform loaded on the horizontal polarization channel and the second phase-coded waveform loaded on the vertical polarization channel, forming an intra-frame orthogonal polarization waveform encoding. The first phase-coded waveform and the second phase-coded waveform are orthogonal to each other. The receiver performs matched filtering on the echoes from the horizontal polarization channel and the vertical polarization channel with the first phase-coded waveform and the second phase-coded waveform, respectively, to obtain the horizontal polarization echo and the vertical polarization echo, achieving simultaneous transmission and reception isolation. Range oversampling is performed on the horizontal polarization echo and the vertical polarization echo, resulting in a number of horizontal polarization oversampled subsamples and vertical polarization oversampled subsamples, each with an oversampling factor greater than 1, within each meteorological resolution volume. Step 2: Determine the whitening recombination coefficient based on the distance oversampling correlation structure. For each meteorological resolution volume, linearly combine the horizontally polarized oversampling subsamples and the vertically polarized oversampling subsamples with the same whitening recombination coefficient to obtain multiple horizontally polarized whitening sample sequences and multiple vertically polarized whitening sample sequences, which constitute whitening transformation and achieve sample multiplication. Each path of the horizontally polarized whitening sample sequence and the corresponding path of the vertically polarized whitening sample sequence maintain the same differential reflectance, differential propagation phase and correlation coefficient. Step 3: Perform multi-hysteresis autocorrelation spectrum estimation on the multi-path horizontally polarized whitened sample sequences and the multi-path vertically polarized whitened sample sequences to obtain the horizontally polarized multi-hysteresis autocorrelation sequence, the vertically polarized multi-hysteresis autocorrelation sequence, and the multi-hysteresis cross-correlation sequence. Under the constraints of the same radial velocity and the same spectral width, perform joint inversion of meteorological parameters to obtain and output the horizontally polarized echo power, vertically polarized echo power, radial velocity, spectral width, differential reflectivity, differential propagation phase, and correlation coefficient.

2. The method according to claim 1, characterized in that, The first and second phase-coded waveforms are each composed of multiple phase modulated sub-pulses sequentially spliced ​​together. The autocorrelation of the first phase-coded waveform exhibits a main peak at 0 range delay, as does the autocorrelation of the second phase-coded waveform. The cross-correlation between the first and second phase-coded waveforms at each range delay is lower than the main peak value of the autocorrelation of the first phase-coded waveform at 0 range delay. Using the first phase-coded waveform for matched filtering yields pulse compression gain along the range direction while obtaining the horizontally polarized echo, thus improving the detection capability of the miniature dual-polarization weather radar under low peak power conditions of the solid-state transmitter. When the first phase-coded waveform is used for matched filtering, the vertically polarized channel transmission component is suppressed in the horizontally polarized echo, and when the second phase-coded waveform is used for matched filtering, the horizontally polarized channel transmission component is suppressed in the vertically polarized echo.

3. The method according to claim 1, characterized in that, The receiver arranges the horizontal polarization channel and the vertical polarization channel in parallel, and simultaneously receives the echoes of the horizontal polarization channel and the vertical polarization channel within the same pulse repetition period. The sampling interval of the range oversampling is obtained by dividing the width of the matched filter resolution unit by the oversampling factor. The horizontal polarization oversampling sub-samples are arranged adjacent to each other along the range direction, and the vertical polarization oversampling sub-samples are arranged adjacent to each other along the range direction. Each oversampling sub-sample carries its own receiver thermal noise, and the horizontal polarization oversampling sub-samples and the vertical polarization oversampling sub-samples correspond one-to-one at the same range direction position.

4. The method according to claim 1, characterized in that, Determining the whitening recombination coefficient involves: selecting multiple adjacent meteorological volumes within the same distance range; using horizontally polarized oversampled subsamples and vertically polarized oversampled subsamples at each distance position of these adjacent meteorological volumes as statistical objects; statistically analyzing the correlation between the oversampled subsample values ​​at any two distance positions; and summarizing the correlation between each pair of distance positions to obtain a set of correlation quantities characterizing the distance oversampling correlation structure. The whitening recombination coefficient is then determined based on this set of correlation quantities. The distance oversampling correlation structure is introduced by a composite pulse and a matched filter between adjacent oversampled positions in the distance direction, maintaining consistency among meteorological volumes within the same distance range, and all meteorological volumes within the same distance range sharing the same whitening recombination coefficient.

5. The method according to claim 4, characterized in that, The whitening recombination coefficient matches the distance oversampling correlation structure, and the whitening transformation is a linear preconditioning of covariance matching. The whitening transformation reduces the pairwise correlation between multiple horizontally polarized whitened sample sequences and reduces the pairwise correlation between multiple vertically polarized whitened sample sequences, forming an oversampling equivalent observation space. The number of paths of both horizontally polarized and vertically polarized whitened sample sequences is equal to the oversampling factor, and the number of sample sequences that can be used for meteorological parameter estimation within a single pulse repetition period increases to several times the oversampling factor.

6. The method according to claim 1, characterized in that, Within the same meteorological resolution volume, the differential reflectance and differential propagation phase between the horizontal and vertical polarization channels are common to all range positions. The whitening transformation applies the same whitening recombination coefficient to the oversampled subsamples of the horizontal and vertical polarization channels at the same range position and then adds them together, so that each path of the horizontal polarization whitening sample sequence and the corresponding path of the vertical polarization whitening sample sequence maintain the same differential reflectance, differential propagation phase, and correlation coefficient as at each range position. The multiple horizontal polarization whitening sample sequences and the multiple vertical polarization whitening sample sequences carry differential reflectance, differential propagation phase, and correlation coefficient information in pairs.

7. The method according to claim 5, characterized in that, Calculate the autocorrelation at lag 1, lag 2 and lag 3 along the pulse dimension on each horizontally polarized whitening sample sequence. Calculate the autocorrelation at the same lag along the pulse dimension on each vertically polarized whitening sample sequence. Calculate the cross-correlation at the same lag along the pulse dimension between each horizontally polarized whitening sample sequence and its corresponding vertically polarized whitening sample sequence. The autocorrelation correspondences of multiple horizontally polarized whitened sample sequences at the same lag are summed and averaged to obtain the horizontally polarized multi-lag autocorrelation sequence. Similarly, the autocorrelation correspondences of multiple vertically polarized whitened sample sequences at the same lag are summed and averaged to obtain the vertically polarized multi-lag autocorrelation sequence. Furthermore, the cross-correlation correspondences of multiple sequences at the same lag are summed and averaged to obtain the multi-lag cross-correlation sequence. The distance oversampling correlation structure reduces the statistical efficiency of meteorological parameter estimation obtained by directly averaging oversampling subsamples. Under the linear preconditioning effect of covariance matching, the estimate obtained by averaging the multiple lag moment estimates of multiple horizontally polarized whitened sample sequences and multiple vertically polarized whitened sample sequences approximates the linear estimate with the minimum variance under distance oversampling correlation observation conditions. This compensates for the reduced statistical efficiency caused by the distance oversampling correlation structure and reduces the estimated variance of horizontally polarized echo power, vertically polarized echo power, radial velocity, spectral width, differential reflectivity, differential propagation phase, and correlation coefficient.

8. The method according to claim 7, characterized in that, The horizontal and vertical polarization channels observe the same batch of hydrocondensate within the same meteorological resolution volume within the same pulse repetition period. The horizontal and vertical polarization echoes have the same radial velocity and the same spectral width. The Doppler spectrum of the meteorological echo is described by a Gaussian spectrum, and the autocorrelation corresponding to the Gaussian spectrum is a Gaussian autocorrelation. Based on the horizontal polarization multi-hysteresis autocorrelation sequence, a Gaussian autocorrelation model is fitted so that the values ​​of the Gaussian autocorrelation model at hysteresis 1, hysteresis 2, and hysteresis 3 are consistent with the values ​​of the horizontal polarization multi-hysteresis autocorrelation sequence at the same hysteresis, thus obtaining the horizontal polarization echo power, radial velocity, and spectral width. By fitting a Gaussian autocorrelation model to the vertically polarized multi-hysteresis autocorrelation sequence under the constraints of the same radial velocity and the same spectral width, the vertically polarized echo power is obtained; the differential reflectivity is obtained from the horizontally polarized echo power and the vertically polarized echo power.

9. The method according to claim 8, characterized in that, The phases of the multi-hysteresis cross-correlation sequence at hysteresis 1, hysteresis 2, and hysteresis 3 include the phase caused by radial velocity and the differential propagation phase between the horizontal polarization channel and the vertical polarization channel. Using the radial velocity obtained from the horizontal polarization multi-hysteresis autocorrelation sequence as a known quantity, the phase caused by radial velocity is separated from the phases of the multi-hysteresis cross-correlation sequence at each hysteresis to obtain the differential propagation phase. Using the spectral width obtained from the horizontally polarized multi-hysteresis autocorrelation sequence as a known quantity, the amplitude of the multi-hysteresis cross-correlation sequence at each hysteresis is normalized by the spectral width to obtain the correlation coefficient; The differential phase is obtained from the rate of change of the differential propagation phase along the distance direction.

10. The method according to claim 9, characterized in that, The differential propagation phase monotonically increases along the range direction from near to far. The differential propagation phase at each range direction position is used to attenuate and correct the horizontal polarization echo power, vertical polarization echo power, and differential reflectivity at the same range direction position along the range direction. The horizontal polarization echo power, vertical polarization echo power, radial velocity, spectral width, differential reflectivity, differential propagation phase, differential phase ratio, and correlation coefficient are solved simultaneously under the constraints of the same radial velocity and the same spectral width to achieve joint inversion of meteorological parameters. The horizontal polarization echo power, vertical polarization echo power, radial velocity, spectral width, differential reflectivity, differential propagation phase, differential phase ratio, and correlation coefficient of each meteorological resolution volume are output. The horizontal polarization echo power, vertical polarization echo power, radial velocity, spectral width, differential reflectivity, differential propagation phase, differential phase ratio, and correlation coefficient are used for precipitation estimation and water condensate phase identification.

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