DETAILED ACTION
Notice of Pre-AIA or AIA Status
The present application, filed on or after March 16, 2013, is being examined under the first inventor to file provisions of the AIA .
Information Disclosure Statement
The information disclosure statement (IDS) submitted on 11/26/2024 is in compliance with the provisions of 35 CFR 1.97. Accordingly, the IDS has been considered by the examiner.
Specification
The disclosure is objected to because of the following informalities:
The Brief Description of the Drawings section uses “FIG.” (all caps) for Figures 1–3 (see [0012-0015]) but switches to “Fig.” (mixed case) for Figures 4–6 (see [0016-0019]). Applicant should use a consistent form of reference to drawings throughout the specification. See 37 C.F.R. §1.84(p)(1). This inconsistency, while minor, should be corrected so that all figure references in the specification uniformly appear as “FIG.”
Paragraph [0009] recites: “a pseudo-random phase code that does not repeat during a period of at least 5 ms seconds.” The phrase “ms seconds” is duplicative and grammatically incorrect. Applicant should correct this to “at least 5 ms” to reflect the intended meaning, consistent with Claim 8.
Appropriate correction is required.
Claim Objections
Claims 18 objected to because of the following informalities:
Claims 1 and 14 recites: “scanning aperture radar (SAR)” while the SAR acronym is for synthetic aperture radar (SAR), see Spec. [0020].
The preamble of Claim 1 introduces “a multi-static formation,” but the body of Claim 1 subsequently refers to “the multi-static configuration.” These terms differ. Because the preamble never introduces “a multi-static configuration,” the body’s reference to “the multi-static configuration” lacks a proper antecedent but does not rise to the level of 35 U.S.C. 112(b). This objection is raised under 37 C.F.R. §1.75.
Claim 10 recites: “the transmitting and receiving platforms compensate between the CPIs for their movement relative to the ROI.” In a system (apparatus) claim, the indicative mood (“compensate”) introduces potential ambiguity as to whether this is a functional limitation or a structural/configured-to limitation. Compare Claim 1’s use of “configured to” language. While this is unlikely to rise to a 112(b) rejection in view of the claim as a whole (the limitation can reasonably be read as “configured to compensate” in context), applicant may wish to amend Claim 10 to use “are configured to compensate” for consistency with the drafting style of Claim 1.
Claim 18 recites: “the first transmitting platform,” but Claim 1o4, from which Claim 18 depends, introduces only “a transmitting platform” without a numbering term, and no second transmitting platform is ever recited in Claim 14 or any of its dependents (Claims 15-20). Because only one transmitting platform is ever in play in this claim set, this issue is treated as a claim-drafting objection rather than a 112(b) rejection.
Appropriate correction is required.
Claim Rejections - 35 USC § 112
The following is a quotation of 35 U.S.C. 112(b):
(b) CONCLUSION.—The specification shall conclude with one or more claims particularly pointing out and distinctly claiming the subject matter which the inventor or a joint inventor regards as the invention.
The following is a quotation of 35 U.S.C. 112 (pre-AIA ), second paragraph:
The specification shall conclude with one or more claims particularly pointing out and distinctly claiming the subject matter which the applicant regards as his invention.
Claims 1 rejected under 35 U.S.C. 112(b) or 35 U.S.C. 112 (pre-AIA ), second paragraph, as being indefinite for failing to particularly point out and distinctly claim the subject matter which the inventor or a joint inventor (or for applications subject to pre-AIA 35 U.S.C. 112, the applicant), regards as the invention.
The body of Claim 1 recites: “the processor group is configured to form a first two-dimensional (2D) vertical and along-track scanning aperture radar (SAR) image.” The preamble of Claim 14 recites “satellite tomography of a precipitation field via a synthetic aperture radar,” while the body of Claim 14 recites forming a “scanning aperture radar (SAR) image.” Throughout the specification, “SAR” is uniformly defined and used as “synthetic aperture RADAR”. See, e.g., [0020] (“The disclosed system and method implement synthetic aperture RADAR (SAR)”). “Synthetic aperture radar” and “scanning aperture radar” are distinct terms to a person having ordinary skills in the art (PHOSITA). Synthetic aperture radar forms a large effective antenna aperture by combining signals recorded at successive positions of a moving platform. “Scanning aperture radar” is not a recognized equivalent term. The claims, by defining SAR as “scanning aperture radar,” conflict with the specification’s definition, leaving the metes and bounds of what type of radar is claimed unclear under the broadest reasonable interpretation. The examiner cannot discern from the face of the claim whether the applicant intended a synthetic aperture technique, a beam-scanning technique, or both.
Because Claims 11, 15, and 19 incorporate the “SAR” term by reference to their parent claims’ 2D SAR images, they are also indefinite for the same reason. Dependent claims also inherit the indefiniteness of the independent claims.
Claim Rejections - 35 USC § 103
The following is a quotation of 35 U.S.C. 103 which forms the basis for all obviousness rejections set forth in this Office action:
A patent for a claimed invention may not be obtained, notwithstanding that the claimed invention is not identically disclosed as set forth in section 102, if the differences between the claimed invention and the prior art are such that the claimed invention as a whole would have been obvious before the effective filing date of the claimed invention to a person having ordinary skill in the art to which the claimed invention pertains. Patentability shall not be negated by the manner in which the invention was made.
The factual inquiries for establishing a background for determining obviousness under 35 U.S.C. 103 are summarized as follows:
1. Determining the scope and contents of the prior art.
2. Ascertaining the differences between the prior art and the claims at issue.
3. Resolving the level of ordinary skill in the pertinent art.
4. Considering objective evidence present in the application indicating obviousness or nonobviousness.
Claims 1, 2, 3, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, and 20 are rejected under 35 U.S.C. 103 as being unpatentable over Maschhoff et al. (US 2020/0150268 A1) in view of Lovber et al. (US 2018/0095163 A1).
Regarding Claims 1 and 14, Claims 1 and 14 are independent claims directed to a system and a non-transitory computer program product (CRM), respectively, for satellite multi-static SAR-based determination of a three-dimensional reflectivity map of a precipitation field. The bodies of Claims 1 and 14 recite substantively identical functional elements, differing only in statutory format and preamble. Claims 1 and 14 are therefore grouped and the full analysis is presented for Claim 1. Claim 14 is rejected for the same reasons as Claim 1 and is addressed in further detail below.
Maschhoff et al. (’268) in view of Lovber et al. (’163) teaches:
Maschhoff et al. (’268) teaches: A system for determining a three-dimensional (3D) reflectivity map of a precipitation field in a region of interest (ROI), (Title: “SATELLITE TOMOGRAPHY OF RAIN AND MOTION VIA SYNTHETIC APERTURE”; [0008]: “to enable a multi-static spotlight mode three dimensional (3D) RADAR observation of the precipitation field”). The preamble is limiting as it defines the structural purpose of the system; Maschhoff et al. (’268) is explicitly directed to creating a three-dimensional map of a precipitation field in a targeted region of interest.
Maschhoff et al. (’268) teaches: the system comprising: a plurality of platforms configured to fly in a multi-static formation at an altitude that is higher than an altitude of the precipitation field, ([0008]: “the use of a formation of small spacecraft in low earth orbit”.
Maschhoff et al. (’268) teaches: the plurality of platforms comprising a first transmitting platform, and first and second receiving platforms, ([0008]: “the spacecraft payloads includes one or more radio frequency (RF) transmitters and two or more receivers, hosted on satellites at a common altitude”; [0041]: “a first and a second receiver (Rx₁, Rx₂) are shown with a transmitter (Tx)”).
Maschhoff et al. (’268) teaches: the first transmitting platform being configured to participate in a first bi-static pair with the first receiving platform, and to participate in a second bi-static pair with the second receiving platform; ([0040]: “One embodiment of the three-dimensional precipitation (multi-static) RADAR system employs separate transmitting and receiving microsatellites in low earth orbit”; [0043]: “Waves emitted by the transmitter, Tx, are scattered back to the receivers (in phase coherence with all of the receivers operating at a frequency of interest)”). FIG. 1 of Maschhoff et al. (’268) depicts transmitter Tx forming a first bi-static pair with Rx₁ and a second bi-static pair with Rx₂.
Maschhoff et al. (’268) teaches: a processor group comprising at least one processor; ([0081]: “the invention may be implemented as computer software”; FIG. 3 depicting a [0067]: “sensor control processing module 38” on the transmitter and a [0068]: “receiver process control module 44” on the receiver, each constituting at least one processor in the processor group).
Maschhoff et al. (’268) does not explicitly teach transmitting a phase-encoded RADAR waveform at a constant transmission frequency. Maschhoff et al. (’268) instead discloses linear frequency modulated (LFM) pulses ([0056]: “Each linear frequency modulated (LFM) pulse was about 100 µs”), in which the carrier frequency is continuously swept across a bandwidth during each pulse rather than remaining constant. However, Lovber et al. (’163) teaches: the first transmitting platform is configured, while flying in the multi-static configuration, to transmit a phase-encoded RADAR waveform at a constant transmission frequency toward the ROI, (Title: “Phase-Modulated Continuous Wave Radar System (with PRBS Codes)”; [0004]: “phase modulated continuous wave radar (phase modulated CW radar)…employs binary-phase-shift-keyed (BPSK) carrier modulation using engineered cyclic codes for signal transmission”; FIG. 1, [0012]: “Bi-phase modulation of transmit tone using pseudo-noise (PN) sequence”). A continuous wave (CW) radar operates at a constant carrier frequency; Lovber et al. (’163) teaches that this constant-frequency carrier is phase-encoded using a pseudo-noise code, teaching a phase-encoded RADAR waveform transmitted at a constant transmission frequency.
It would have been obvious to a person having ordinary skill in the art (PHOSITA) before the effective filing date of the claimed invention to modify the multi-static satellite SAR system of Maschhoff et al. (’268) to transmit a constant-frequency, PRBS phase-encoded waveform as taught by Lovber et al. (’163) in place of the LFM waveform of Maschhoff et al. (’268). One would have been motivated to do so because Maschhoff et al. (’268) expressly identifies low hardware cost as a primary design objective ([0076]: “at a cost point more than ten times lower than other space-borne precipitation RADAR systems”), and Lovber et al. (’163) teaches precisely this advantage, disclosing that the phase modulated CW radar architecture eliminates the need for an expensive linear, broadband swept frequency source and high-performance digitizer in the radar front end, replacing these with low-cost CDMA-inspired BPSK modulation and lower-performance digitizers (Title: “Phase Modulated Continuous Wave Radar…” Background). A PHOSITA would recognize that substituting the LFM waveform of Maschhoff et al. (’268) with the constant-frequency PRBS phase-encoded waveform of Lovber et al. (’163) reduces transmitter hardware cost and complexity in the microsatellite design context of Maschhoff et al. (’268), directly advancing that reference’s stated cost objective. There is a reasonable expectation of success because both LFM and phase modulated CW radar waveforms achieve target range resolution through pulse compression — LFM through chirp matched filtering and phase modulated CW radar through code correlation — and Lovber et al. (’163) demonstrates that phase modulated CW radar with PRBS phase encoding successfully resolves target range using correlator-based pulse compression, providing a validated alternative to LFM. A PHOSITA would therefore have a reasonable expectation that substituting the LFM waveform of Maschhoff et al. (’268) with the phase modulated CW radar waveform of Lovber et al. (’163) preserves the range measurement and 3D precipitation field mapping capabilities required by the claims.
Maschhoff et al. (’268) teaches: the constant frequency, phase-encoded waveform being reflected by the precipitation field, thereby creating first and second reflected signals; ([0050]: “Waves emitted by the transmitter, Tx, are scattered back to the receivers”; FIG. 1, [0050]: “8 and 10 indicate the portions of the scattered wave directed toward Rx₁ and Rx₂ respectively, from a portion of the backscattering precipitation field”). In the combined system, the constant-frequency phase-encoded waveform is reflected by the precipitation field in the same manner, creating first and second reflected signals directed toward the first and second receiving platforms.
Maschhoff et al. (’268) teaches: the first receiving platform is configured to receive the first reflected signal during a first coherent processing interval (CPI), and the second receiving platform is configured to receive the second reflected signal during the first coherent processing interval (CPI); ([0034]: “It is known that a correlated time-series of hydrometeor field echoes will eventually de-correlate if the SAR coherent period of integration (T.sub.CPI) is extended too long. To avoid this decorrelation, T should be notably less than λ/σ.sub.Dop, where σ.sub.Dop is the standard deviation of hydrometeor velocities”; [0049]: “Coherent SAR 5 km (x 15 km vertical) image was collected in a 2.0 ms coherent processing interval (CPI)”; [0046]: “each of the two receivers, Rx₁ and Rx₂, separately collect the backscattered radiation”). Maschhoff et al. (’268) at [0046] confirms that both receivers operate within shared CPIs, as their signals are cross-correlated to form the cross-track interferogram requiring simultaneous reception.
Maschhoff et al. (’268) teaches: the processor group is configured to form a first two-dimensional (2D) vertical and along-track SAR image of the precipitation field according to range and Doppler information extracted from the first reflected signal; ([0046]: “each of the two receivers, Rx₁ and Rx₂, separately collect the backscattered radiation needed to reconstruct a 2D (Range-Doppler) SAR image of the precipitation field in which the spatial dimensions along the orbital track, and along the range axis are resolved in the reconstructed image”). The range axis corresponds to the vertical (altitude) dimension and the along-track axis is resolved from Doppler, constituting the first 2D vertical and along-track SAR image.
Maschhoff et al. (’268) teaches: the processor group is configured to form a second 2D vertical and along-track SAR image of the precipitation field according to range and Doppler information extracted from the second reflected signal; ([0046]: “each of the two receivers, Rx₁ and Rx₂, separately collect the backscattered radiation needed to reconstruct a 2D (Range-Doppler) SAR image”). Rx₂ separately collects the second reflected signal and independently forms its own 2D (Range-Doppler) SAR image, constituting the second 2D vertical and along-track SAR image.
Maschhoff et al. (’268) teaches: the processor group is configured to determine a 3D reflectivity map of the precipitation field according to the first and second 2D vertical and along-track SAR images. ([0040]: “Two of the three dimensions are provided by rather traditional “spotlight” mode synthetic aperture RADAR (SAR), using orbital velocity to sweep out a synthetic aperture”; [0054]: “A three dimensional image is then constructed using a tomographic approach, with the two dimensional P-SAR image as a constraint”; [0009]: “creating a three-dimensional precipitation field using the aggregated two-dimensional intensity images”).
Claim 14 is rejected for the same reasons as Claim 1. The preamble of Claim 14, “for satellite tomography of a precipitation field via a synthetic aperture radar,” is limiting and is taught by Maschhoff et al. (’268) (Title: “SATELLITE TOMOGRAPHY OF RAIN AND MOTION VIA SYNTHETIC APERTURE”). The one or more non-transitory machine-readable mediums encoded with instructions element of Claim 14 is taught by Maschhoff et al. (’268) ([0075]: “The computer readable medium as described herein can be a data storage device, or unit such as a magnetic disk, magneto-optical disk, an optical disk, or a flash drive”). Each functional step of Claim 14 — transmitting, receiving, forming the first and second 2D SAR images, and determining the 3D reflectivity map — is taught by Maschhoff et al. (’268) in view of Lovber et al. (’163) for the same reasons as the corresponding elements of Claim 1 set forth above.
Regarding Claims 2 and 15, Maschhoff et al. (’268) in view of Lovber et al. (’163) teaches the system according to Claim 1.
Maschhoff et al. (’268) teaches: determining the 3D reflectivity map comprises applying an amplitude-based or a power-based incoherent modeling algorithm to the first and second 2D vertical and along-track SAR images. ([0035]: “Multiple coherent field observations can then be aggregated in the image intensity domain (incoherent averaging) to increase the signal to noise ratio”; [0054]: “A three dimensional image is then constructed using a tomographic approach, with the two dimensional P-SAR image as a constraint”).
Regarding Claim 3, Maschhoff et al. (’268) in view of Lovber et al. (’163) teaches the system according to Claim 2.
Maschhoff et al. (’268) teaches: dividing the ROI into a plurality of voxels; ([0055]: “a single-pulse/single voxel had a signal to noise ratio of 10:1”). The system performs backscattering analysis on a per-voxel basis, which requires first partitioning the ROI into a grid of voxels, as taught by Maschhoff et al. (’268).
Maschhoff et al. (’268) teaches: for each of the voxels, computing a backscattered RF power; ([0055]: “In one embodiment of the observing system, a single-pulse back-scattered power (z=1) droplet field was assessed”). Maschhoff et al. (’268) computes the received backscattered power per voxel from the droplet number density and single-droplet RADAR cross section ([0055]), teaching per-voxel backscattered RF power computation.
Maschhoff et al. (’268) teaches: and interpreting each of the backscattered RF powers as a sum of contributions from scattering centers located in the voxel. ([0050]: “Such scatterers could include clouds, or fields of dust particles, or blowing sand, as well as fields of rain drops, snowflakes, hail, or sleet, which all have a three dimensional distribution of scattering centers”; [0055]: “Droplet Number Density: N(D) (1/m³ for Z=1), single droplet RADAR cross section: σ₀”). Maschhoff et al. (’268) computes per-voxel backscattered power from the number density and individual scattering cross section of hydrometeors within the voxel, embodying the physical model of interpreting total voxel backscattered RF power as a sum of contributions from individual scattering centers located in the voxel.
Regarding Claim 7, Maschhoff et al. (’268) in view of Lovber et al. (’163) teaches the system according to Claim 1.
Maschhoff et al. (’268) teaches: the platforms are orbiting satellites. ([0013]: “the use of a formation of small spacecraft in low earth orbit”.
Regarding Claims 8 and 9, Maschhoff et al. (’268) in view of Lovber et al. (’163) teaches the system according to Claim 1.
Maschhoff et al. (’268) does not explicitly teach a pseudo-random phase code with a specified minimum non-repeating period, but Lovber et al. (’163) teaches: the constant frequency, phase-encoded waveform is phase modulated according to a pseudo-random phase code that does not repeat during a period of at least 5 ms (Claim 8) and at least 1 second (Claim 9). (Section “Pseudo-Random Binary Sequence Codes”; [0021]: “we assume the use of a PRBS-31 code (i.e. 31 bits long), which repeats after 2,147,483,647 chips. We assume for purposes of discussion that the radar transmitter modulates its CW tone using this code at a chip rate of 1.58 Gcps”; Section “Range Aliasing”: [0022]: “The length of the PRBS31 code extends the ambiguous range out to over 2,000 kilometers, far beyond the operational range of the radar”). At 1.58 × 10⁹ chips per second, PRBS-31 repeats after approximately 2,147,483,647 ÷ 1,580,000,000 ≈ 1.36 seconds, satisfying both the ≥ 5 ms requirement of Claim 8 and the ≥ 1 second requirement of Claim 9.
It would have been obvious to a PHOSITA, for the same reasons and from the same motivation to combine Maschhoff et al. (’268) and Lovber et al. (’163) as discussed above with respect to Claim 1, to implement the PRBS phase code in the combined system using the PRBS-31 code of Lovber et al. (’163) with its inherent extended non-repeating period. One would have been further motivated to do so because Lovber et al. (’163) teaches that the extended code length is required to eliminate range aliasing, ensuring that reflected signals from the maximum radar range are not confused with signals from shorter ranges (Section “Range Aliasing”: “The use of a very long random sequence such as PRBS31 eliminates range aliasing in the radar”). Eliminating range aliasing is a fundamental requirement of the precipitation radar system of Maschhoff et al. (’268), which observes targets at ranges up to approximately 705 km, making the extended non-repeating period of PRBS-31 directly necessary in the combined system. There is a reasonable expectation of success because the non-repeating period of PRBS-31 at the stated chip rate is a deterministic property of the code structure as taught by Lovber et al. (’163), providing certain satisfaction of the code-period requirements of Claims 8 and 9.
Regarding Claim 10, Maschhoff et al. (’268) in view of Lovber et al. (’163) teaches the system according to Claim 1.
Maschhoff et al. (’268) teaches: the transmitting and receiving platforms are configured to implement a spotlight mode in which the first CPI is a first of a successive plurality of CPIs during each of which the first transmitting platform and the first and second receiving platforms are pointed at the ROI; ([0011]: “spotlight mode comprises a series of coherently linked echoes collected while the at least one receiver rotates around a target area during which period the precipitation field is effectively stationary”; [0032]: “a spacecraft formation targets a region, and executes a coordinated “back-scan” maneuver to point data collecting apertures at the region of interest for an extended period of a few minutes”; [0049]: “100 of these were averaged over a non-coherent processing interval (NCPI) of 200 ms”). Maschhoff et al. (’268) at [0049] confirms successive CPIs during which the platforms remain pointed at the ROI, with 100 coherent 2D SAR images collected across successive CPIs.
Maschhoff et al. (’268) teaches: the transmitting and receiving platforms compensate between the CPIs for their movement relative to the ROI by executing coordinated “back-scan” maneuvers that maintain the pointing of the transmitting and receiving platforms at the ROI. ([0032]: “a spacecraft formation targets a region, and executes a coordinated “back-scan” maneuver to point data collecting apertures at the region of interest for an extended period of a few minutes”; [0073]: “operating the at least two receiving low earth orbit satellites in spotlight synthetic aperture RADAR mode”).
Regarding Claim 11, Maschhoff et al. (’268) in view of Lovber et al. (’163) teaches the system according to Claim 10.
Maschhoff et al. (’268) teaches: the first 2D vertical and along-track SAR image is a first incoherent 2D SAR image formed by incoherently combining a first plurality of coherent 2D SAR images derived from measurements made by the first receiving platform during the successive plurality of CPIs; and the second 2D vertical and along-track SAR image is a second incoherent 2D SAR image formed by incoherently combining a second plurality of coherent 2D SAR images derived from measurements made by the second receiving platform during the successive plurality of CPIs. ([0046]: “each of the two receivers…separately collect the backscattered radiation… a series of these 2D images are collected within a series of coherent processing intervals…these 2D images are added (incoherently) to improve the signal to noise ratio”; [0049]: “100 of these were averaged over a non-coherent processing interval (NCPI) of 200 ms” - coherent SAR images). Each receiving platform independently forms multiple coherent 2D SAR images over successive CPIs and then incoherently combines them, as explicitly taught by Maschhoff et al. (’268).
Regarding Claim 12, Maschhoff et al. (’268) in view of Lovber et al. (’163) teaches the system according to Claim 1.
Maschhoff et al. (’268) does not explicitly teach pulse compression demodulation using reference waveforms that have been shifted in frequency from the transmission frequency as applied to a constant-frequency phase-encoded waveform. Maschhoff et al. (’268) instead teaches de-ramp demodulation for its LFM waveform ([0046]: “Range compensation/de-ramp processing is applied to each echo yielding vertical structure”). However, Lovber et al. (’163) teaches: extracting the range and Doppler information from the first and second reflected signals comprises applying thereto a pulse compression demodulation using a reference waveform at the transmission frequency, while also applying pulse compression demodulations thereto using reference waveforms that have been shifted in frequency from the transmission frequency. (FIG. 1, [0012]: “receiver baseband digitized (ADC) and demodulated using same PN sequence shifted to discriminate range bins, correlator to detect and integrate target signals in each range bin” and “Fast Fourier Transform (FFT) to determine Doppler velocity of targets in each range bin”; Section “Pseudo-Random Binary Sequence Codes”: [0013]: “after one or more (M) cycles of random Gold sequences, the output of the correlator generates a single point input to a Doppler Fast Fourier Transform (FFT) processor. When a large number (e.g. 1024) of such points has filled the processor buffer, an FFT is computed to determine the Doppler velocity of targets detected by the radar”). The correlator demodulates the received signal using the reference phase code at the transmission frequency (range extraction by pulse compression), and the FFT evaluates the correlator output at each discrete frequency bin.
It would have been obvious to a PHOSITA, for the same reasons and from the same motivation to combine Maschhoff et al. (’268) and Lovber et al. (’163) as discussed with respect to Claim 1, to perform the pulse compression demodulation using both the reference waveform at the transmission frequency and frequency-shifted reference waveforms via FFT processing as taught by Lovber et al. (’163). One would have been further motivated to do so because extracting both range and Doppler information is a fundamental requirement of SAR image formation, explicitly confirmed by Maschhoff et al. (’268) at [0046] (“2D (Range-Doppler) SAR image”), and Lovber et al. (’163) provides the specific, validated mechanism for jointly extracting this information from a phase modulated CW radar signal through combined correlator and FFT processing. There is a reasonable expectation of success because the mathematical equivalence between FFT Doppler processing and frequency-shifted reference correlation is well established in signal processing, and Lovber et al. (’163) demonstrates that this processing chain successfully extracts both range and Doppler information from phase modulated CW radar returns.
Regarding Claim 13, Maschhoff et al. (’268) in view of Lovber et al. (’163) teaches the system according to Claim 1.
Maschhoff et al. (’268) teaches: a timing synchronization of 10 ns between internal time bases of the receiving platforms is sufficient for forming the 3D reflectivity map. ([0026]: “An improvement from the current 10 ns range to the less than 10 ps range of the present application would provide an important improvement in that capability, while simultaneously reducing cost”).
Regarding Claim 17, Maschhoff et al. (’268) in view of Lovber et al. (’163) teaches the computer program product according to Claim 14.
Maschhoff et al. (’268) does not explicitly teach a pseudo-random phase code with a non-repeating period of at least 5 seconds, but Lovber et al. (’163) teaches: the instructions are configured to cause the constant frequency, phase-encoded waveform to be phase modulated according to a pseudo-random phase code that does not repeat during a period of at least 5 seconds. (Section “Pseudo-Random Binary Sequence Codes”: [0021]: “we assume the use of a PRBS-31 code (i.e. 31 bits long), which repeats after 2,147,483,647 chips”). In the precipitation radar application of Maschhoff et al. (’268), the required range resolution is approximately 125 m ([0049]: “resolving 125 m layers over 15 km”). A phase modulated CW radar chip rate sufficient for 125 m range resolution is on the order of c ÷ (2 × 125 m) ≈ 1.2 MHz. At 1.2 MHz, PRBS-31 repeats after 2,147,483,647 ÷ 1,200,000 ≈ 1,789 seconds — far exceeding the 5-second non-repeating period of Claim 17.
It would have been obvious to a PHOSITA before the effective filing date of the claimed invention, for the same reasons and from the same motivation to combine Maschhoff et al. (’268) and Lovber et al. (’163) as discussed with respect to Claim 1, to adapt the chip rate of the PRBS code to match the 125 m range resolution required by Maschhoff et al. (’268) at [0056]. One would have been motivated to do so because achieving the specified 125 m range resolution is a primary design constraint of the combined system, and selecting the chip rate to satisfy that constraint is a routine engineering parameter selection that a PHOSITA would perform as a matter of course. There is a reasonable expectation of success because the relationship between chip rate and range resolution in phase modulated CW radar is a deterministic, well-defined relationship as taught by Lovber et al. (’163), and operating PRBS-31 at the chip rate needed for 125 m range resolution inherently yields a non-repeating period of approximately 1,789 seconds, satisfying the ≥ 5-second requirement of Claim 17.
Regarding Claim 18, Maschhoff et al. (’268) in view of Lovber et al. (’163) teaches the computer program product according to Claim 14.
Claim 18 recites the same spotlight mode and back-scan maneuver limitations as Claim 10 within the Claim 14 family. Claim 18 is substantially the same as claim 10 and thus, the same cited sections and rationale as corresponding apparatus claim 10 is applied.
Regarding Claim 19, Maschhoff et al. (’268) in view of Lovber et al. (’163) teaches the computer program product according to Claim 18.
Claim 19 recites the same incoherent combination of coherent 2D SAR images over successive CPIs as Claim 11 within the Claim 14 family. Claim 19 is substantially the same as claim 11 and thus, the same cited sections and rationale as corresponding apparatus claim 11 is applied.
Regarding Claim 20, Maschhoff et al. (’268) in view of Lovber et al. (’163) teaches the computer program product according to Claim 14.
Claim 20 recites the same pulse compression demodulation with frequency-shifted reference waveforms as Claim 12 within the Claim 14 family. Claim 20 is substantially the same as claim 12 and thus, the same cited sections and rationale as corresponding apparatus claim 12 is applied.
Claims 4 and 5 are rejected under 35 U.S.C. 103 as being unpatentable over Maschhoff et al. (US 2020/0150268 A1) in view of Lovber et al. (US 2018/0095163 A1), further in view of Madhow et al. (US 2018/0074209 A1).
Regarding Claim 4, Maschhoff et al. (’268) in view of Lovber et al. (’163), further in view of Madhow et al. (’209), teaches the system according to Claim 3.
Maschhoff et al. (’268) in view of Lovber et al. (’163) does not explicitly teach applying a non-linear least-squares process to determine the coefficients of the incoherent modeling algorithm. Maschhoff et al. (’268) teaches a tomographic reconstruction approach ([0054]: “A three dimensional image is then constructed using a tomographic approach”) without specifying the optimization technique used for coefficient determination. However, Madhow et al. (’209) teaches: applying the amplitude-based or power-based incoherent modeling algorithm comprises determining coefficients which relate the backscattered RF amplitude or power for each of the voxels to a reflectivity for each of a plurality of model elements in a 3D reflectivity field model using a non-linear least-squares process. ([0064]: “The non-linear least squares solver 606 then recalculates a distribution of clock bias based on the LOS pseudoranges, the hypothesized particle positions and the predicted distributions from the drift model 602”). Madhow et al. (’209) teaches a non-linear least-squares solver applied to a satellite-based signal processing inverse problem — determining unknown quantities (position, clock bias) from observed satellite signal measurements (pseudoranges) through a non-linear forward model — which is structurally identical to determining coefficients that relate observed 2D SAR image amplitudes or powers to 3D reflectivity model elements via a non-linear forward model.
It would have been obvious to a PHOSITA before the effective filing date of the claimed invention to apply the non-linear least-squares technique of Madhow et al. (’209) to the coefficient determination step of the tomographic reconstruction in the Maschhoff (’268)/Lovber (’163) combined system. One would have been motivated to do so because the coefficient determination in the 3D reflectivity inversion is a mathematical inverse problem in which the observed 2D SAR image amplitudes or powers are related to the unknown 3D reflectivity elements through a forward model that accounts for the geometry, propagation effects, and beam patterns of the bi-static SAR configuration — a model that is potentially non-linear in the unknown reflectivity values — making non-linear least-squares the appropriate and natural solution technique. Madhow et al. (’209) teaches at [0064] that non-linear least-squares is the established technique for precisely this class of satellite-based signal processing inverse problem, and a PHOSITA would directly recognize its applicability to the formally analogous inverse problem of Claim 4. There is a reasonable expectation of success because non-linear least-squares is a well-established optimization technique with known numerical implementations and convergence properties, and Madhow et al. (’209) demonstrates that the non-linear least-squares solver successfully resolves non-linear satellite-based inverse problems involving noisy observations and unknown state variables — the same conditions that characterize the coefficient determination problem of Claim 4.
Regarding Claim 5, Maschhoff et al. (’268) in view of Lovber et al. (’163), further in view of Madhow et al. (’209), teaches the system according to Claim 2.
Maschhoff et al. (’268) in view of Lovber et al. (’163) does not explicitly teach applying a non-linear least-squares process for the element-wise coefficient determination of Claim 5, but Madhow et al. (’209) teaches: applying the amplitude-based or power-based incoherent modeling algorithm comprises, for each reflectivity element in the 3D reflectivity map, determining coefficients which relate amplitude or power elements in the first and second vertical and along-track 2D SAR images to the reflectivity element using a non-linear least-squares process. ([0064]: “The non-linear least squares solver 606 then recalculates a distribution of clock bias based on the LOS pseudoranges, the hypothesized particle positions and the predicted distributions from the drift model 602”). Madhow et al. (’209) teaches applying non-linear least-squares to determine the relationship between observed satellite signal measurements at a receiver and unknown state variables through a non-linear model, which is structurally identical to determining, for each individual 3D reflectivity element, the coefficients that relate the 2D SAR image amplitude or power elements to that reflectivity element via non-linear least-squares. Claim 5 is rejected for the same reasons and from the same motivation as Claim 4.
Claims 6 and 16 are rejected under 35 U.S.C. 103 as being unpatentable over Maschhoff et al. (US 2020/0150268 A1) in view of Lovber et al. (US 2018/0095163 A1), further in view of Przyboroski et al. (US 2025/0200404 A1).
Regarding Claim 6, Maschhoff et al. (’268) in view of Lovber et al. (’163), further in view of Przyboroski et al. (’404), teaches the system according to Claim 2.
Maschhoff et al. (’268) in view of Lovber et al. (’163) does not explicitly teach that the power-based incoherent modeling algorithm is a Gaussian Mixture Model, but Przyboroski et al. (’404) teaches: the power-based incoherent modeling algorithm is a Gaussian Mixture Model. ([0027]: “A probabilistic model such as a Gaussian Mixture Model (GMM) may assume that all data points within large data sets are generated from a mixture of a finite number of Gaussian distributions. The GMM may enable clustering of data points within the large data sets”; [0028]: “exemplary embodiments may take the result of a transformation…of a collection of images, video data and/or complex time-series (e.g., sensor) data, i.e., multi-dimensional numeric arrays…as input data and apply a GMM to approximate a distribution thereof”; [0029]: “GMM construction algorithm 190 may also be distinct from ML algorithm 160 and associated therewith) may be applied to input data 170 to generate a GMM distribution 180 (e.g., shown stored in memory 114.sub.1) that approximates input data 170”). Przyboroski et al. (’404) teaches that a GMM is an effective probabilistic modeling algorithm for approximating distributions of multi-dimensional array data derived from sensor measurements, constituting a power-based incoherent modeling algorithm when applied to power or amplitude measurement data.
It would have been obvious to a PHOSITA before the effective filing date of the claimed invention to implement the power-based incoherent modeling algorithm of the Maschhoff (’268)/Lovber (’163) combined system as a Gaussian Mixture Model as taught by Przyboroski et al. (’404). One would have been motivated to do so because the 3D precipitation reflectivity field consists of spatial clusters of hydrometeors — rain cells, storm cells, and gradient structures — whose reflectivity profiles naturally form a mixture of approximately Gaussian distributions corresponding to different precipitation intensities and spatial extents within the storm system. Przyboroski et al. (’404) teaches at [0028] that GMMs are effective for approximating distributions of multi-dimensional arrays derived from sensor data, and a PHOSITA would recognize that the 2D SAR image pixels — representing power measurements from voxels distributed through the 3D precipitation volume — constitute precisely the type of sensor-derived multi-dimensional array data for which Przyboroski et al. (’404) demonstrates GMM efficacy. Implementing the incoherent modeling algorithm as a GMM also provides a compact, computationally efficient probabilistic representation of the 3D reflectivity distribution, which is advantageous in the resource-constrained microsatellite computing environment of Maschhoff et al. (’268); Przyboroski et al. (’404) confirms this advantage at [0004] by teaching that GMM-based modeling enables “reducing a data footprint of the data set through the GMM distribution.” There is a reasonable expectation of success because Przyboroski et al. (’404) at [0033] demonstrates that the EM algorithm-based GMM construction converges reliably to a useful approximation of the underlying data distribution, and the same mathematical framework applies to approximating the distribution of backscattered power measurements across the 3D voxel grid of the precipitation radar tomographic problem. Claim 16 is rejected for the same reasons as Claim 6.
Regarding Claim 16, the claim is substantially the same as claim 6 and thus, the same cited sections and rationale as corresponding apparatus claim 6 is applied.
Conclusion
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/REMASH R GUYAH/Examiner, Art Unit 3648
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