Method for velocity estimation of meteorological target by using terahertz cloud radar
By using frequency division polarization echo coherent processing and Doppler velocity correction methods, the problem of high-precision velocity estimation for spaceborne terahertz cloud-measuring radar was solved, achieving high-precision meteorological target velocity measurement, eliminating the ghosting problem, and improving the stability and adaptability of velocity measurement.
Patent Information
- Application Number
- PCT/CN2024/129677
- Authority / Receiving Office
- WO · WO
- Patent Type
- Applications
- Current Assignee / Owner
- Priority Date
- 2024-07-29
- Filing Date
- 2024-11-04
- Publication Date
- 2026-02-05
AI Technical Summary
Existing spaceborne cloud-measuring radars struggle to achieve high-precision velocity estimation in the terahertz band, and suffer from ghosting issues and velocity ambiguity due to low polarization isolation.
A high-precision velocity estimation method is achieved by employing frequency-division polarization echo coherent processing, frequency-division polarization echo phase extraction and velocity estimation, average Doppler velocity deviation correction based on land and sea surface echoes, and joint velocity correction based on radar reflectivity factor partial derivative and target velocity spatial continuity, combined with satellite platform auxiliary data.
It achieves high-precision meteorological target velocity estimation, eliminates the ghosting problem caused by low polarization isolation, solves the high-velocity ambiguity problem of spaceborne terahertz cloud-measuring radar, and has good platform adaptability and Doppler velocity extraction stability.
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Figure CN2024129677_05022026_PF_FP_ABST
Abstract
Description
A method for estimating the velocity of meteorological targets using terahertz cloud-measuring radar Technical Field
[0001] This invention relates to the field of active microwave atmospheric sounding, and more particularly to a method for estimating the velocity of meteorological targets using a terahertz cloud-measuring radar on a spaceborne platform. Background Technology
[0002] Clouds are an important component of the Earth-atmosphere system (water cycle, regulating Earth's energy radiation balance), a significant factor influencing weather and climate change, and the greatest source of uncertainty in current weather forecasting and climate change analysis. The Fifth Plenary Session of the Intergovernmental Panel on Climate Change (IPCC) report states that among the components of total radiative forcing, cloud radiative forcing exhibits the greatest uncertainty, making it the largest source of uncertainty in climate change analysis. Current spaceborne cloud-measuring radars have room for improvement in detection sensitivity and significant application needs in high-precision velocity measurement.
[0003] The high-speed motion of satellite platforms coupled with high-frequency Doppler signals to the echo, as well as the vertical convection of meteorological targets, results in a wide range of target velocity and a broad Doppler spectrum. This often causes phenomena such as velocity ambiguity and spectrum folding in the echo of terahertz frequency band meteorological radar. Existing spaceborne cloud-measuring radar technology is difficult to adapt to the terahertz frequency band.
[0004] The statements herein provide only background information in relation to this invention and do not necessarily constitute prior art. Disclosure of the invention
[0005] The purpose of this invention is to provide a method for estimating the velocity of meteorological targets by a terahertz cloud-measuring radar, which achieves high-precision velocity estimation, eliminates the ghosting problem caused by low polarization isolation, and solves the problem of high-velocity ambiguity in spaceborne terahertz cloud-measuring radar.
[0006] To achieve the above objectives, this invention provides a method for estimating the velocity of meteorological targets using a terahertz cloud-measuring radar, comprising:
[0007] Frequency-division polarization echo coherent processing;
[0008] Frequency-division polarization echo phase extraction and velocity estimation;
[0009] Correction based on mean Doppler velocity deviation of land and sea surface echoes;
[0010] Radar reflectivity factor partial derivative and target velocity spatial continuity combined velocity correction.
[0011] The frequency-division polarization echo coherent processing includes:
[0012] The frequency is obtained through two receiving channels. Horizontal polarization and frequency are Vertically polarized scattered echo signal:
[0013] (1)
[0014] (2)
[0015] In the formula, for Time Frequency Vertical polarization channel receiving range echo signal at that location, for Time Frequency Vertical polarization emission, frequency Vertical polarization receiving range The echo component at that location, for Time Frequency Vertical polarization emission, frequency Vertical polarization receiving range The echo component at that location, The distance from the target to the radar. This represents the distance from the target.
[0016] The echo is simplified to:
[0017] (3)
[0018] (4)
[0019] After multiple mixing stages, the frequency-polarization diversity pulse pair cross-correlation function Represented as:
[0020] (5)
[0021] (6)
[0022] In the formula, Indicates continuous sampling The number of frequency diversity polarization pulse pairs, " indicates taking the conjugate, Indicates the number of frequency diversity polarization pulse pairs. The distance corresponding to the time interval of the polarization pulse pair. The cross-correlation function with a time interval of zero, "For taking the mold, for The target's speed of movement, For the corresponding wavelength, for Channel to Channel fixed phase difference, for Channel to Channel fixed phase difference, The target is the Doppler velocity spectrum width.
[0023] The frequency-division polarization echo phase extraction and velocity estimation include:
[0024] The corresponding Doppler velocity is obtained by using two adjacent pulse pairs:
[0025] (7)
[0026] In the formula, To estimate the speed, "" indicates the phase function is being calculated.
[0027] The mean Doppler velocity deviation correction based on land and sea surface echoes includes:
[0028] The satellite platform moves forward at a speed of The angle between the radar beam elevation and the nadir point is... The angle between the azimuth and the sub-star is The satellite platform's velocity vector is decomposed into components parallel to and aligned with the beam illumination direction. and the vertical beam illumination direction component The quantity affecting the radar's estimation of the target velocity is the parallel component. Based on equation (7), the parallel component is estimated to be... ;
[0029] Therefore, the corrected meteorological echo velocity estimate for:
[0030] (8)
[0031] (9).
[0032] The joint velocity correction based on the partial derivative of the radar reflectivity factor and the spatial continuity of the target velocity includes:
[0033] The corresponding gradient value is calculated using the partial derivative of the radar reflectivity factor, and the velocity correction value is calculated as follows:
[0034] (10)
[0035] In the formula, This indicates a calculation speed correction. As a correction factor, usually Depending on the different operating conditions, the speed can be selected as 0.165 m / s or 0.219 m / s. This indicates the partial derivative or gradient of the radar reflectivity factor with respect to the nadir point direction;
[0036] The corrected velocity value obtained above is converted into a phase representation using the Doppler formula and system operating frequency band information:
[0037] (11)
[0038] In the formula, This indicates the phase change introduced by the above situation. The operating wavelength of the system;
[0039] Total phase echo Represented as:
[0040] (12)
[0041] Phase entanglement is resolved by using path integration along a certain distance library, i.e.:
[0042] (13)
[0043] in, and These are the phases before and after untangling, respectively.
[0044] Target speed The estimated value is expressed as:
[0045] (14)
[0046] In the formula, This represents the final estimated value of the target's velocity. This represents the phase of a certain distance after untangling.
[0047] The present invention has the following beneficial effects:
[0048] This invention utilizes the phase modulation characteristics of echoes from consecutively adjacent meteorological targets, and combines the spatial and velocity continuity of meteorological targets to compensate and correct the initially obtained meteorological target velocity, thereby achieving high-precision estimation.
[0049] This invention fully considers the significant decorrelation effect of satellite platforms and the problem of signal interference between adjacent pulse pairs. It employs a frequency-division polarized pulse pair operating system, which eliminates the ghosting problem caused by low polarization isolation and fully utilizes the wide Doppler velocity adaptability of adjacent pulses. This solves the high-velocity ambiguity problem of spaceborne terahertz cloud-measuring radar.
[0050] This invention relates to a method that correlates partial differential correction with the continuous distribution of cloud target velocity, which can adaptively adjust the velocity discontinuity caused by edge jumps, thereby enabling the terahertz cloud measurement radar to have good platform adaptability and stability of Doppler velocity extraction. Brief description of the attached figures
[0051] Figure 1 is a flowchart of the velocity estimation method for meteorological targets by terahertz cloud-measuring radar provided by the present invention.
[0052] Figure 2 is a waveform diagram of the frequency division-polarization pulse pair of the spaceborne terahertz cloud measurement radar.
[0053] Figure 3 is a schematic diagram of the pointing velocity coupling correction principle of the spaceborne terahertz cloud measuring radar platform.
[0054] Figure 4 is a schematic diagram of the principle of radar reflectivity factor partial derivative correction combined with cloud target velocity continuity correction. Best way to implement the present invention
[0055] The preferred embodiments of the present invention will be described in detail below with reference to Figures 1 to 4.
[0056] This invention provides a method for estimating the velocity of meteorological targets using a terahertz cloud-measuring radar. The method combines high-precision velocity estimation of meteorological targets in the terahertz band on a spaceborne platform with satellite-aided data. It improves the system's Doppler velocity adaptability range by using a terahertz band frequency-division polarization pulse operating mode. It corrects the average velocity measurement deviation introduced by beam pointing by extracting the Doppler velocity of ground and sea surface echoes under high signal-to-noise ratio conditions. Finally, it performs high-precision correction of measurement deviations within clouds by combining partial differential correction of radar reflectivity factor with spatial continuity of cloud target velocity, thereby achieving high-precision velocity measurement of meteorological targets in the terahertz band on a spaceborne platform.
[0057] Taking a one-dimensional scanning observation method as an example, the high-precision velocity estimation process of terahertz band meteorological targets on a spaceborne platform is broken down in detail. As shown in Figure 1, the velocity estimation method of meteorological targets by the terahertz cloud-measuring radar includes the following steps:
[0058] Step S1: The pulse waveform operation mode of frequency division combined with polarization modulation expands the Doppler adaptation velocity range of the radar system;
[0059] This invention leverages the strong isolation characteristics of frequency signals with a certain interval and the isolation characteristics of polarization information. Combining the advantages of both, it achieves wide velocity range measurement on the one hand, and reduces crosstalk in strong echo signals on the other. In other words, this invention proposes a waveform pulse operating mode that combines frequency division multiplexing with polarization modulation. By isolating frequency and polarization, it significantly reduces the ghosting problem in observations and uses continuous pulses to estimate the target velocity based on the obtained phase information.
[0060] The process mainly includes auxiliary data (including satellite flight speed, antenna beam pointing information, etc.) as shown in Figure 1, radar observation data (raw echoes received by radar), frequency division polarization echo coherent processing, and frequency division polarization echo phase extraction and velocity estimation.
[0061] Figure 2 shows the operating waveform of a frequency-polarization diversity pulse pair, which can eliminate the "ghosting" problem of a single-frequency polarization diversity pulse pair. This system obtains the frequency through two receiving channels. Horizontal polarization and frequency are The vertically polarized scattered echo signal is represented as:
[0062] (1)
[0063] (2)
[0064] In the formula, for Time Frequency Vertical polarization channel receiving range echo signal at that location, for Time Frequency Vertical polarization emission, frequency Vertical polarization receiving range The echo component at that location, for Time Frequency Vertical polarization emission, frequency Vertical polarization receiving range The echo component at that location, The distance from the target to the radar. This represents the distance from the target.
[0065] Considering that out-of-band signals of waveforms at different frequencies within the pulse time can be greatly suppressed by the filter, the echo can be simplified as follows:
[0066] (3)
[0067] (4)
[0068] Therefore, it can be seen from the above formula that the "ghosting" inherent in polarization systems can be eliminated through filtering.
[0069] After multiple mixing stages, the frequency-polarization diversity pulse pair cross-correlation function Represented as:
[0070] (5)
[0071] (6)
[0072] In the formula, Indicates continuous sampling The number of frequency diversity polarization pulse pairs, " indicates taking the conjugate, Indicates the number of frequency diversity polarization pulse pairs. The distance corresponding to the time interval of the polarization pulse pair. The cross-correlation function with a time interval of zero, "For taking the mold, for The target's speed of movement, For the corresponding wavelength, for Channel to Channel fixed phase difference, for Channel to Channel fixed phase difference, The target is the Doppler velocity spectrum width.
[0073] The corresponding Doppler velocity can be determined from two adjacent pulse pairs, expressed as:
[0074] (7)
[0075] In the formula, To estimate the speed, "" indicates the phase function is being calculated.
[0076] The alternating frequency-polarization diversity pulse pairs exhibit extremely high negative phase correlation, tending towards -1. Therefore, the variance of the alternating pulses tends towards 0, meaning they theoretically possess high measurement accuracy. Furthermore, the maximum Doppler ambiguity velocity of the alternating frequency-polarization diversity pulse pairs is... This allows for the acquisition of target velocity information over a wide range. Therefore, the alternating frequency-polarization diversity pulse pair used in this invention is both adaptable to high-speed target velocity measurement and has a low velocity variance.
[0077] Step S2, Average Doppler velocity deviation correction based on land and sea surface echoes: Based on land and sea clutter echo extraction to eliminate platform coupling velocity deviation caused by beam pointing;
[0078] The observation method of the spaceborne terahertz meteorological radar is shown in Figure 3. The angle between the radar beam elevation and the nadir point is... The angle between the azimuth and the sub-star is These two angle data and These are the two types of data in the auxiliary data in Figure 1. The radar can obtain both target echoes and surface clutter signals during its operation. The processing method of equation (7) is still effective for surface clutter data. Considering that the satellite's flight direction is perpendicular to the surface with zero pitch angle, i.e., the satellite's motion speed will not affect the echo speed of that surface, this compensation technique is mainly used to analyze the case where the pitch angle is not zero and azimuth scanning is not considered. The analysis of the velocity compensation amount involved in the average Doppler velocity deviation correction based on surface echoes is shown in Figure 4. The satellite platform's motion velocity vector is decomposed into components parallel to the beam illumination direction. and the vertical beam illumination direction component The quantity affecting the radar's estimation of target velocity is the parallel component. According to equation (7), the parallel component can be estimated as follows: Therefore, the corrected meteorological echo velocity estimate for:
[0079] (8)
[0080] (9)
[0081] Therefore, the present invention, by combining satellite-aided data and the Doppler velocity estimation mentioned in step S1, can effectively correct the velocity deviation introduced by the motion of the satellite platform.
[0082] Step S3: Velocity correction based on radar reflectivity factor partial derivative and cloud target velocity spatial continuity: Based on radar reflectivity factor partial derivative correction and cloud target velocity spatial continuity, the deviation caused by uneven beam illumination distribution is corrected while ensuring that the velocity is not blurred.
[0083] Because radar single-beam illumination areas are large and target boundaries may not completely fill the beam, a certain velocity error is often introduced, typically reaching several meters per second. Such an error is unacceptable for meteorological data applications. Fortunately, the above-mentioned effects of meteorological radar can be corrected by taking the first-order partial derivative of the radar reflectivity factor. However, for differences in movement velocity at boundaries or within a unit cloud, velocity anomalies often occur. This invention combines the continuity of cloud target spatial movement velocity with a joint processing method for radar reflectivity factor partial derivative velocity correction. The main operation method is as follows:
[0084] First, the corresponding gradient value is calculated using the partial derivative of the radar reflectivity factor, and then the velocity correction value is calculated, expressed as:
[0085] (10)
[0086] In the formula, This indicates a calculation speed correction. As a correction factor, usually Depending on the different operating conditions, the speed can be selected as 0.165 m / s or 0.219 m / s. This indicates the partial derivative or gradient of the radar reflectivity factor with respect to the direction of the nadir point.
[0087] Secondly, the corrected velocity values obtained above are converted into phase representations using the Doppler formula and system operating frequency band information:
[0088] (11)
[0089] In the formula, This indicates the phase change introduced by the above situation. This is the system's operating wavelength.
[0090] Finally, based on step S1 addressing the high-speed target adaptability requirements, the velocity-influencing factors here cause at most one level of velocity ambiguity. Therefore, the total echo phase... It can be represented as:
[0091] (12)
[0092] Considering the continuity of the target's motion velocity, the phase winding is resolved by using path integration along a certain distance library, i.e.:
[0093] (13)
[0094] in, and These are the phases before and after untangling, respectively.
[0095] After the above processing, high-precision target velocity information can be obtained. Target movement velocity. The estimated value can be expressed as:
[0096] (14)
[0097] In the formula, This represents the final estimated value of the target's velocity. This represents the phase of a certain distance after untangling.
[0098] This invention proposes a method for high-precision velocity estimation of meteorological targets in the terahertz band on a spaceborne platform. This method is applicable to high-precision velocity estimation using spaceborne terahertz cloud-measuring radar, adaptable to a wide velocity measurement range, and provides high accuracy in estimating the target's average Doppler velocity. This invention primarily addresses the significant Doppler velocity effect of spaceborne platform terahertz cloud-measuring radar, platform velocity coupling, and the motion characteristics of meteorological targets. It employs a series of correlation measures to achieve high-precision velocity estimation of meteorological targets. First, the Doppler measurement velocity range is increased based on short-time adjacent phase differences to minimize measurement ambiguity. Second, a fixed-pointing echo to the sea surface is used as a beam pointing measurement reference to correct the overall Doppler velocity coupling deviation introduced by platform motion. Finally, the gradually varying velocity characteristics and phase periodicity of meteorological targets are utilized to eliminate the influence of non-uniform congestion caused by velocity reversal.
[0099] Compared with the prior art, the present invention has the following advantages:
[0100] 1. Publicly available spaceborne precipitation weather radars, based on actual data and definitions of the terminal velocity of raindrops falling in still atmosphere, and the definition of the radar reflectivity factor, directly calculate the corresponding velocity from the radar reflectivity factor through the empirical relationship between statistical velocity V and radar reflectivity factor Z, and approximate this value as the average Doppler velocity of the precipitation particles. This invention, however, utilizes the phase modulation characteristics of echoes from continuously adjacent meteorological targets, and combines the spatial and velocity continuity of meteorological targets, to compensate and correct for the initially obtained meteorological target velocities, thereby achieving high-precision estimation.
[0101] 2. Publicly available spaceborne Doppler cloud-measuring radars primarily employ conventional Doppler pulse systems, which have a limited range of adaptable target velocities. This invention, however, fully considers the significant decorrelation effect of satellite platforms and the problem of signal interference between adjacent pulse pairs. It adopts a frequency-division polarized pulse pair operating system, which eliminates the ghosting problem caused by low polarization isolation and fully utilizes the wide Doppler velocity adaptability of adjacent pulses. This solves the high-velocity ambiguity problem of spaceborne terahertz cloud-measuring radars.
[0102] 3. Publicly available spaceborne weather radar velocity correction techniques primarily address the problem of reduced Doppler velocity estimation under non-uniform distribution conditions using partial differential correction of radar reflectivity factors. However, this often leads to abrupt jumps in cloud edge distribution. This invention correlates partial differential correction with the continuous distribution of cloud target velocity, adaptively adjusting for velocity discontinuities caused by edge jumps. This results in terahertz cloud-measuring radar possessing good platform adaptability and stability in Doppler velocity extraction.
[0103] It should be noted that, in the embodiments of the present invention, the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," "counterclockwise," "axial," "radial," and "circumferential," etc., indicating the orientation or positional relationship, are based on the orientation or positional relationship shown in the accompanying drawings and are only for the convenience of describing the embodiments. They do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the present invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.
[0104] In this invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," "linking," and "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.
[0105] It should be understood that, when used in this specification and the appended claims, the term "comprising" indicates the presence of the described features, integrals, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.
[0106] It should also be understood that the terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the scope of the application. As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.
[0107] It should also be further understood that the term “and / or” as used in this application specification and the appended claims means any combination of one or more of the associated listed items and all possible combinations, and includes such combinations.
[0108] As used in this specification and the appended claims, the term "if" may be interpreted, depending on the context, as "when," "once," "in response to determination," or "in response to detection." Similarly, the phrases "if determined" or "if [described condition or event] is detected" may be interpreted, depending on the context, as "once determined," "in response to determination," "once [described condition or event] is detected," or "in response to detection of [described condition or event]."
[0109] Although the present invention has been described in detail through the preferred embodiments above, it should be understood that the above description should not be considered as a limitation of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without inventive effort are within the scope of protection of the present invention. After reading the above content, various modifications and substitutions to the present invention will be obvious to those skilled in the art. Therefore, the scope of protection of the present invention should be defined by the appended claims.
Claims
1. A method for velocity estimation of a meteorological target by a terahertz weather radar, characterized by, Comprising: Frequency division polarimetric echo phase correlation processing; Frequency division polarimetric echo phase extraction and velocity estimation; Mean Doppler velocity bias correction based on ground sea surface echo; Joint velocity correction of radar reflectivity factor gradient and target velocity spatial continuity.
2. The method of estimating the velocity of a meteorological target by a terahertz weather radar as claimed in claim 1, characterized by, The frequency division polarimetric echo phase correlation processing comprises: The frequency of is obtained by two receiving channels horizontal polarization and a frequency of 2.4 GHz The vertical polarization scattering echo signal of the target: (1) (2) In the formula, For Time frequency Vertical polarization channel receive distance a signal of the echo signal in the vicinity of the position of the object, For Time frequency vertical polarization transmission, frequency Vertical polarization reception distance the echo component of the backscatter, For Time frequency vertical polarization transmission, frequency Vertical polarization reception distance the echo component of the backscatter, for the target to the radar, is the distance of the target; The echo is simplified as: (3) (4) After multiple mixing stages, the cross-correlation function of the frequency-polarization diversity pulse pair is expressed as: (5) (6) In the formula, represents a continuous sampling a number of frequency diversity polarized pulse pairs, "denotes the taking of the conjugate, denotes the number of frequency diversity polarization pulse pairs, is the time interval corresponding to the distance of the polarized pulse pair, For the cross-correlation function with a time interval of zero, " "mod" for modulo, For speed of motion of the target, for the corresponding wavelength, For passage to Channel fixed phase difference, For passage to Channel fixed phase difference, is the Doppler velocity spectrum width of the target.
3. The method of estimating the velocity of a meteorological target by a terahertz weather radar as claimed in claim 2, characterized by, The frequency division polarimetric echo phase extraction and velocity estimation comprises: The corresponding Doppler velocity is calculated by two adjacent groups of pulses: (7) In the formula, To estimate the velocity, " " " represents the phase function.
4. The method of estimating the velocity of a meteorological target of a terahertz weather radar according to claim 3, characterized in that, The mean Doppler velocity bias correction based on ground sea surface echo comprises: The satellite platform moves forward at a speed of , the radar beam elevation angle is included between the radar beam elevation angle and the zenith angle , the angle between the azimuth direction and the subpoint is , the satellite platform motion velocity vector is decomposed into components parallel and perpendicular to the beam illumination direction and a vertical beam illumination direction component The quantity that affects the radar's estimate of the target's velocity is then the parallel component According to equation (7), the parallel component is estimated as ; Thus, the revised weather echo velocity estimate is: (8) (9)。 5. The method of estimating the velocity of a meteorological target of a terahertz weather radar according to claim 4, characterized in that, The joint velocity correction of radar reflectivity factor gradient and target velocity spatial continuity comprises: The corresponding gradient value is calculated by the radar reflectivity factor partial differentiation, and the velocity correction value is calculated as: (10) In the formulae, represents a calculation speed correction, For the correction factor, typically Depending on the working form, 0.165 m / s or 0.219 m / s can be selected, " " represents the partial differentiation or gradient of the radar reflectivity factor in the direction of the subspace point; The correction velocity value obtained above is converted into a phase representation by using the Doppler formula and system operating frequency band information: (11) In the formulae, represents the phase change introduced by the above situation, is the system operating wavelength; The total phase of the echo is represented as : (12) The phase unwrapping is solved by using the path integral method along a certain distance bin, that is: (13) wherein, and are the unwrapped and pre-unwrapped phases respectively; Target motion velocity The estimated value is expressed as: (14) In the formulae, a final estimate of the target motion velocity, " " represents the phase of a certain distance bin after unwrapping.
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