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 .
Status of Claims
Claims 1-6, 9, and 12-22 are currently pending and are being hereby examined herein. Claims 7-8 and 10-11 have been canceled.
Response to Amendment / Remarks
Any reference to the prior office action refers to the non-final rejection dated 28 May 2025.
The rejections from the prior office action under 35 U.S.C. 112(b) are not fully resolved in view of the amendments and arguments. In view of amendments and persuasive arguments, Examiner is withdrawing the rejections listed under Claim 1, Claim 3, Claim 4, Claim 5, Claim 6, Claim 7, and Claim 9 from the prior action. Some rejections listed under Claim 2, specifically (b) and (c) on the prior office action, (note: these rejections also apply to Claims 3-5 because they are dependent on Claim 2) were not fully overcome by amendment or arguments, see current rejections under 35 U.S.C. 112(b) below (note: the lettering on the current office action is different from the prior office action).
Applicant’s arguments with respect to the prior art rejections under 35 U.S.C. 103 in the prior office action have been considered but are moot because the new ground of rejection does not rely on any reference applied in the prior rejection of record for any teaching or matter specifically challenged in the argument. The new grounds of rejection were necessitated by amendment.
Applicant’s arguments with respect to the rejection under 35 U.S.C. 101 with respect to Claims 1-13 have been considered, but are not persuasive. Applicant did not provide any examples of “additional limitations” in this Application that would be considered integration into a practical application. Examiner did not find any persuasive arguments indicating Claims 1-13 are an improvement to the existing technology as the claims only recite abstract ideas and computer implementation / displaying of such. Applicant cites overcoming prior art as a reason for eligibility, however, as noted above, Examiner has issued a new means of rejection using prior art. Applicant argues that aircraft collision systems can be patent eligible, Examiner does not disagree that aircraft collision systems can be patent eligible and notes that currently presented Claim 22 does overcome the rejection under 35 U.S.C. 101, see below.
In response to amendment, Examiner has withdrawn some objections to the specification from the prior office action. To clarify one specific example for the objection about altitude and height, the equation for PZ(SZ) would be consistent with the equation for Px(Sx) and Py(Sy) if D3, currently listed as “altitude” was “height”. Many objections were partially addressed by Applicant, but the specification was only partially resolved of issues (e.g., changing one reference to an equation but not others) and now has new internal inconsistencies and has introduced new matter, see updated objections below.
The objection to the drawings from the prior office action is withdrawn in view of the claim amendments.
All claim objections from the prior office action are withdrawn in view of the claim amendments.
Drawings
The drawings are objected to under 37 CFR 1.83(a). The drawings must show every feature of the invention specified in the claims. Therefore, the system of Claim 19, the system of Claim 20, and the method of Claim 22 must be shown or the features canceled from the claims. No new matter should be entered. Corrected drawing sheets in compliance with 37 CFR 1.121(d) are required in reply to the Office action to avoid abandonment of the application. Any amended replacement drawing sheet should include all of the figures appearing on the immediate prior version of the sheet, even if only one figure is being amended. The figure or figure number of an amended drawing should not be labeled as “amended.” If a drawing figure is to be canceled, the appropriate figure must be removed from the replacement sheet, and where necessary, the remaining figures must be renumbered and appropriate changes made to the brief description of the several views of the drawings for consistency. Additional replacement sheets may be necessary to show the renumbering of the remaining figures. Each drawing sheet submitted after the filing date of an application must be labeled in the top margin as either “Replacement Sheet” or “New Sheet” pursuant to 37 CFR 1.121(d). If the changes are not accepted by the examiner, the applicant will be notified and informed of any required corrective action in the next Office action. The objection to the drawings will not be held in abeyance.
Specification
35 U.S.C. 112(a) requires the specification to be written in “full, clear, concise, and exact terms.” The specification is replete with terms which are not clear, concise and exact. The specification should be revised carefully in order to comply with 35 U.S.C. 112(a). Examples of some unclear, inexact or verbose terms used in the specification are:
The specification appears to use the term “altitude” to mean both a dimension of an aircraft and the height an aircraft is flying above ground.
The specification does not consistently use industry standard terms for the axes and does not clarify the coordinate system being used instead. The industry standard assumption would be: the longitudinal axis is from the nose to tail of the aircraft (rolling occurs around this axis, this would be the x-axis, the aircraft dimension following this axis is fuselage length), the lateral axis follows the wings of the aircraft (pitching occurs around this axis, this would be the y-axis, the aircraft dimension following this axis is wingspan), and the vertical (so called perpendicular in the specification) axis follows the fuselage height of the aircraft (yaw occurs around this axis, this would be the z-axis, the aircraft dimension following this axis is height).
Which axes are lateral and longitudinal is not consistent through-out the specification.
The specification uses the subscript “y” when referencing functions, variables, etc. of the X-axis (for example,
P
y
S
y
) without describing the reason (see at least equation (1)).
The specification uses the subscript “x” when referencing functions, variables, etc. of the Y-axis (for example,
P
x
S
x
) without describing the reason (see at least equation (5)).
There are functions that do not adhere with mathematical principles (see at least equation (6)).
Applicant uses the term “perpendicular axis”.
There are internally conflicting equations in view of the amendment (i.e., an equation was updated in one place of the specification without updating through-out).
Appropriate correction is required.
The amendment filed 7 July 2025 is objected to under 35 U.S.C. 132(a) because it introduces new matter into the disclosure. 35 U.S.C. 132(a) states that no amendment shall introduce new matter into the disclosure of the invention. The added material which is not supported by the original disclosure is as follows:
There was not an equation for probability of overlapping including both lateral distance and plane length in the original disclosure [middle of page 3 of 32].
The equation for fs(y) and its summary are changed in a way not supported by the original disclosure (multiple variables are redefined) [bottom of page 3 of 32].
The equations including GERh1, GERh2, and GERh3 and their summary are changed in a way not supported by the original disclosure, the terms U and V now relate to different dimensions than originally supported [top of page 4 of 32].
The amended example equation for GERh2 does not equal 7.6567*10^(-7) since “/1” in the denominator was replaced by “/60”, and there is no support for adding “/60” to this equation [top of page 32].
Applicant is required to cancel the new matter in the reply to this Office Action.
Claim Objections
Claim 1 is objected to because of the following informalities:
Oxford commas should be used to separate lists of three or more terms (e.g., “longitudinal, altitudinal and lateral” should be “longitudinal, altitudinal, and lateral”).
The limitation “standard deviations of a distance of the first aircraft in the longitudinal direction relative to a navigation station and an altitude and a lateral distance of the first aircraft after a flight time” should be “standard deviations of a distance of the first aircraft in the longitudinal direction relative to a navigation station, of the first aircraft after a flight time, and a lateral distance of the first aircraft after [[a]] the flight time”.
“compare probabilities of collision of the first aircraft…” should be “compare the probabilities of collision of the first aircraft…”.
“according to the loss interval frequencies per hour of the first aircraft in the longitudinal, altitudinal and lateral directions corresponding to the three dimensions” should be “according to the loss interval [[frequencies]] frequency per hour of the first aircraft in each of the longitudinal, altitudinal and lateral directions corresponding to the three dimensions”.
Appropriate correction are required.
Claim Rejections - 35 USC § 112
The following is a quotation of the first paragraph of 35 U.S.C. 112(a):
(a) IN GENERAL.—The specification shall contain a written description of the invention, and of the manner and process of making and using it, in such full, clear, concise, and exact terms as to enable any person skilled in the art to which it pertains, or with which it is most nearly connected, to make and use the same, and shall set forth the best mode contemplated by the inventor or joint inventor of carrying out the invention.
Claims 1-6, 9, and 12-22 are rejected under 35 U.S.C. 112(a) as failing to comply with the written description requirement. The claims contain subject matter which was not described in the specification in such a way as to reasonably convey to one skilled in the relevant art that the inventor or a joint inventor at the time the application was filed, had possession of the claimed invention.
Claim 1 is rejected for failing to comply with the written description requirement. Applicant has not pointed out where the amended claim language is supported nor does there appear to be a written description of the newly amended claim language in the original disclosure. Specifically, Examiner finds the limitation “standard deviations of a distance of the first aircraft in the longitudinal direction relative to a navigation station and an altitude and a lateral distance of the first aircraft after a flight time” is not supported by the original disclosure: the original disclosure instead states “a standard deviation of a lateral aircraft yaw distance when a distance from the aircraft to the navigation station is d”, “a standard deviation of a longitudinal distance of the aircraft after flight time T”, and “a standard deviation of an altitude distance of the aircraft after flight time T”. Therefore, the original disclosure does not support “standard deviations of a distance of the first aircraft in the longitudinal direction relative to a navigation station” and “standard deviations of…a lateral distance of the first aircraft after a flight time”. Claims 2-6, 9, and 12-22 are dependent on Claim 1, and accordingly also rejected. Appropriate corrections are required.
Claim 2 is further rejected for failing to comply with the written description requirement. Applicant has not pointed out where the amended claim is supported nor does there appear to be a written description of the newly amended claim language in the original disclosure. Specifically, Examiner finds the set of equations currently presented is not supported by the original disclosure: the original disclosure did not include the combination of a function representing a lateral distance and integrating that with respect to length of the aircraft (current equation for PYSY). Claims 3-5 are dependent on Claim 2, and accordingly also rejected.
Claim 3 is further rejected for failing to comply with the written description requirement. Applicant has not pointed out where the amended claim language is supported nor does there appear to be a written description of the newly amended claim language in the original disclosure. Specifically, Examiner finds the “
σ
d
is a standard deviation of the lateral distance of the first aircraft when a distance from the first aircraft to the navigation station is d” is not supported by the original disclosure.
Claim 5 is further rejected for failing to comply with the written description requirement. Applicant has not pointed out where the amended claim language is supported nor does there appear to be a written description of the newly amended claim language in the original disclosure. Specifically, Examiner finds there is no support in the original disclosure for the equation presented (there is no support for including lateral distances in the equation, the standard deviation definition as amended, and there is no support for the overall equation due to changes in the variables).
Claim 6 is rejected for failing to comply with the written description requirement. Applicant has not pointed out where the amended claim language is supported nor does there appear to be a written description of the newly amended claim language in the original disclosure. Specifically, Examiner finds there is no support in the original disclosure for the equations including GERh1 and GERh3 presented: in particular, the equations including GERh1 and GERh3 now include different variables (as one specific example, the equation including GERh1 in the original disclosure also included V and now includes U; the definitions of GERh1, V, and U have not changed in way that would have kept the meaning of the equation).
Claim 15 is rejected for failing to comply with the written description requirement. Applicant has not pointed out where the amended claim language is supported nor does there appear to be a written description of the newly amended claim language in the original disclosure. Specifically, Examiner finds there is no support in the original disclosure for the statement “operations of the first aircraft and the one or more second aircraft between layers with a difference in the flight level”.
Appropriate corrections are required.
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.
Claims 2-6 and 9 are rejected are rejected under 35 U.S.C. 112(b) as being indefinite for failing to particularly point out and distinctly claim the subject matter which the inventor or a joint inventor regards as the invention.
Claim 2 is rejected for being indefinite for the following additional reasons (Claims 3-5 depend from Claim 2, so they are accordingly also rejected):
The first equation is indefinite because it is unclear how one would integrate a longitudinal direction using lateral limits (wingspan). For the purposes of compact prosecution, Examiner will consider longitudinal or lateral distances. Appropriate correction is required.
The second equation is indefinite because it is unclear if “altitude” should be height of the aircraft above the ground or a dimension of the aircraft. For the purposes of compact prosecution, Examiner is interpreting this altitude to be an altitude or dimension of an aircraft. Appropriate correction is required.
The third equation is indefinite because it is unclear how one would integrate a lateral direction using longitudinal distances (length). For the purposes of compact prosecution, Examiner will assume longitudinal or lateral distances apply. Appropriate correction is required.
Claim 6 is rejected for being indefinite for the following reason:
Claim 6 states “wherein the loss interval rates…are calculated, according to the formulas as follows…”; this lacks antecedent basis. Appropriate correction is required.
Claim 9 is rejected for being indefinite for the following reason:
Claim 9 states “the aircraft”, which is indefinite as one of ordinary skill would not know which aircraft this references. For the purposes of compact prosecution, Examiner does not believe the limitation “and the collision probability of the aircraft at the same flight level in the altitudinal direction is the collision probability of the first aircraft with the one or more second aircraft at the same flight level in the altitudinal direction” adds any limits beyond Claim 1, and this portion will be disregarded. Appropriate correction is required.
Claim Rejections - 35 USC § 101
35 U.S.C. 101 reads as follows:
Whoever invents or discovers any new and useful process, machine, manufacture, or composition of matter, or any new and useful improvement thereof, may obtain a patent therefor, subject to the conditions and requirements of this title.
Claims 1-6, 9, and 12-21 are rejected under 35 U.S.C 101 because the claimed invention is directed to an abstract idea without significantly more.
Step 1: Yes, the claims are drawn to one or more statutory categories. Claims 1-6, 9, and 14-17 are drawn to a non-transitory computer readable medium, Claims 12-13 and 18-21 are drawn to a system.
Step 2A Prong 1: Yes, the claims are drawn to an abstract idea. Specifically, the claims are drawn to mathematical concepts and mental processes.
The abstract ideas recited in Claim 1 (the independent claim) are as follows:
calculate probabilities of overlapping between a first aircraft and one or more second aircraft in three dimensions according to a length, a width, and a height of each of the first aircraft and the one or more second aircraft, distances between the first aircraft and the one or more second aircraft in longitudinal, altitudinal and lateral directions corresponding to the three dimensions, and [[a]] standard deviations of a of the first aircraft in the longitudinal direction relative to a navigation station and an altitude and a lateral distance of the first aircraft after a flight time
calculate a loss interval frequency per hour of the first aircraft in each of the longitudinal, altitudinal and lateral directions corresponding to the three dimensions according to the probabilities of overlapping between the first aircraft and the one or more second aircraft in the each of three dimensions, the length, the width and the height of each of the first aircraft and the one of the one or more second aircraft, and relative speeds in the longitudinal, lateral and altitudinal directions of the first aircraft and the one of the one or more second aircraft when flying in a same direction
obtain probabilities of collision between the first aircraft and the one of the one or more second aircraft in the directions corresponding to the three dimensions according to the loss interval frequencies longitudinal, altitudinal and lateral directions corresponding to the three dimensions, a model speed difference value between the first aircraft and the one of the one or more second of the first aircraft and the one or more second aircraft, first aircraft and the one of the one or more second aircraft at a same flight level in the altitudinal direction
compare probabilities of collision of the first aircraft with the one of the one or more second aircraft in the each of three dimensions to obtain a maximum probability and a dimension corresponding to the maximum probability in which the first aircraft and the one of the one or more second aircraft are most likely to have a collision
calculate a difference value by subtracting a safety standard value in the dimension corresponding to the maximum probability from the maximum probabilitythat indicates operation of the first aircraft and one of the one or more second aircraft is (i) safe when is less than or equal to 0, and (ii) unsafe when the difference value is greater than 0
Each of a, b, c, d, and e could be considered a mathematical concept or mental process depending on the complexity of the model. The dependent claims recite additional mental processes and/or mathematical concepts.
The additional elements recited in the currently pending claims are as follows:
A non-transitory computer-readable medium containing a set of instructions for a multi-dimensional aircraft collision risk evaluation system, wherein the set of instructions, when executed by [[the]] a processor, are adapted to:
A multi-dimensional aircraft collision risk calculation and safety evaluation system
At least one processor
A memory
A display and/or monitor and a graphics card of graphics processor configured to display object code
HF/VHF communication system or controller-pilot data link communications (CPDLC) system
Obtain a real-time speed and real-time altitude of the first aircraft and the one of the one or more second aircraft, and a real-time distance between the first aircraft and the one of the one or more second aircraft
a laptop, notebook or desktop computer
Step 2A Prong 2: No, the claims do not recite additional elements that integrate the judicial exception into a practical application. Additional elements a, b, c, d, and h individually and in combination fail to integrate the judicial exception into a practical application because they merely apply the abstract idea to one or more generic computing components (see MPEP 2106.05(d) and MPEP 2106.05(f)). Additional elements e and f fail to integrate the judicial exception into a practical application because they add insignificant extra solution activity of data output (see MPEP 2106.05(d) and MPEP 2106.05(g)). Additional element g fails to integrate the judicial exception into a practical application because it adds insignificant extra solution activity of data input (see MPEP 2106.05(d) and MPEP 2106.05(g)).
Step 2A Prong 2: No, the additional elements of these claims do not amount to significantly more than the judicial exception. Additional elements a, b, c, d, and h individually and in combination fail amount to significantly more than the judicial exception because the office takes official notice that they are describing well-understood, routine and conventional activities previously known to the industry (see MPEP 2106.05(d)). Additional elements e and f fail to amount to significantly more than the judicial exception because they are mere displaying / other insignificant extra- post-solutionary activity and additional element g fails to amount to significantly more than the judicial exception because it is mere insignificant extra-pre-solutionary activity (see Electric Power Group, LLC v. Alstom S.A., 830 F.3d 1350, 1354-55, 119 USPQ2d 1739, 1742 (Fed. Cir. 2016) and MPEP 2106.05(g)).
Examiner notes that Claim 22 does not have a rejection under 35 U.S.C 101 at this time and recommends making an independent method claim including the limitations of Claim 22 to overcome the rejections under 35 U.S.C 101.
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 1-6, 9, and 12-22 are rejected under 35 U.S.C. 103 as being unpatentable over IEEE Journal Article The Estimation of Collision Risk on Identical Airway (Long et al., hereinafter, Long) in view of U.S. Patent No. 5,714,948 (Farmakis et al., hereinafter, Farmakis).
Regarding Claim 1, Long discloses (see at least page 506: “a modeling method of collision risk model of air traffic are researched and discussed based on the actual needs of airspace planning.”):
calculate probabilities of overlapping between a first aircraft and one or more second aircraft in three dimensions according to a length, a width, and a height of each of the first aircraft and the one or more second aircraft, distances between the first aircraft and the one or more second aircraft in longitudinal, altitudinal and lateral directions corresponding to the three dimensions, and standard deviations of a distance of the first aircraft in the longitudinal direction relative to a navigation station and an altitude and a lateral distance of the first aircraft after a flight time (see at least pages 507-508: equation (8) is longitudinal overlap, equation (9) is lateral overlap, and equation (10) is vertical overlap; “Aircraft 1 is the leading aircraft whose type is i, and aircraft 2 is the trailing one, whose type is j”; average aircraft length, wingspan, and height are inputs to the equations; equation (7) shows how the standard deviations are defined);
calculate a loss interval frequency per hour of the first aircraft (see at least pages 506-508: equation (11) includes the length, the width, the height, the overlap probability in each of the three dimensions, and the relative speeds; equation (12) units are per hour based on the statement “the units of variables that haven’t been given are nautical mile for distance, hour for time, and knot for speed”);
obtain probabilities of collision between the first aircraft and the one of the one or more second aircraftthe one of the one or more second aircraft, model sizes of the first aircraft and the one or more second aircraft, and a collision probability of the first aircraft and the one of the one or more second aircraft at a same flight level in the altitudinal direction (see at least page 508: equation (13)).
Long does not explicitly disclose A non-transitory computer-readable medium containing a set of instructions for a multi-dimensional aircraft collision risk evaluation system, wherein the set of instructions, when executed by a processor, are adapted to…,
calculate a loss interval frequency per hour of the first aircraft in each of the longitudinal, altitudinal and lateral directions corresponding to the three dimensions…,
obtain probabilities of collision between the first aircraft and the one of the one or more second aircraft in the directions corresponding to the three dimensions according to the loss interval frequencies per hour of the first aircraft in the longitudinal, altitudinal and lateral directions corresponding to the three dimensions…,
compare probabilities of collision of the first aircraft with the one of the one or more second aircraft in the each of three dimensions to obtain a maximum probability and a dimension corresponding to the maximum probability in which the first aircraft and the one of the one or more second aircraft are most likely to have a collision; and
calculate a difference value by subtracting a safety standard value in the dimension corresponding to the maximum probability from the maximum probability, and making or giving a safety evaluation that indicates operation of the first aircraft and one of the one or more second aircraft is (i) safe when the difference value is less than or equal to 0, and (ii) unsafe when the difference value is greater than 0.
Farmakis, in the same field of aircraft collision analysis, and therefore analogous art teaches A non-transitory computer-readable medium containing a set of instructions for a multi-dimensional aircraft collision risk evaluation system, wherein the set of instructions, when executed by a processor, are adapted to determine potential conflicts between aircraft (see at least column 11 lines 35-45, column 12 lines 10-30, and Fig. 2: “ATC computer 66 includes one or more processors (not shown) and a computer memory (not shown) for storing information and data received and other information.”; “ In accordance with the traffic separation alert functions, ATC computer 66 tracks each aircraft, monitors the location, tracking, speed altitude, status, and the relative location, altitude and tracking of each aircraft with respect to other aircraft. Based on GPS data for each aircraft, the received flight plan for each aircraft, and information on each type of aircraft regarding the aircraft's maximum and average speed, altitude, and flight characteristics, ATC computer 66 models the projected path and predicts possible (and even probable) separation standards violations, in addition to identifying existing separation standards violations. ATC computer 66 monitors the distance separating aircraft, identifies any possible conflicts or separation standards violations, and alerts or notifies the air traffic controller of these possible violations or conflicts so flights may be redirected.”).
It would have been obvious, before the effective filing date of the invention, with a reasonable expectation of success, to one having ordinary skill in the art, to combine the calculation steps of Long with the tracking and control of aircraft of Farmakis, because Farmakis states the purpose of tracking and control of aircraft is to “avoid separation standards violations and collisions” (see at least column 18 lines 1-5) and Long provides one model to calculate separate of aircrafts.
In view of Farmakis indicating separation requirements may be different from one another in different directions (see at least Long column 11 lines 60-67 and column 12 lines 1-15) and Long disclosing that one could calculate a loss interval frequency per hour of the first aircraft… and obtain probabilities of collision between the first aircraft and the one of the one or more second aircraft… according to the loss interval frequencies per hour of the first aircraft… as all three directions combined (as cited above), it would be obvious to try to separate the calculations of Long by dimension which would include to try among a finite list of possibilities to calculate a loss interval frequency per hour of the first aircraft in each of the longitudinal, altitudinal and lateral directions corresponding to the three dimensions…, obtain probabilities of collision between the first aircraft and the one of the one or more second aircraft in the directions corresponding to the three dimensions according to the loss interval frequencies per hour of the first aircraft in the longitudinal, altitudinal and lateral directions corresponding to the three dimensions… in order to solve the problem of previously comparing the combined risk of Long to a single threshold that does not account for possible higher / lower risk tolerances in different dimensions as taught by Farmakis. The motivation to combine would have been an improvement of separation alert functions (see at least Farmakis column 11 lines 65-67).
Finally, it is obvious in view of Farmakis to compare probabilities of collision of the first aircraft with the one of the one or more second aircraft in the each of three dimensions to obtain a maximum probability and a dimension corresponding to the maximum probability in which the first aircraft and the one of the one or more second aircraft are most likely to have a collision (see at least column 12 lines 1-35: “TC computer 66 monitors the distance separating aircraft, identifies any possible conflicts or separation standards violations, and alerts or notifies the air traffic controller of these possible violations or conflicts so flights may be redirected.”; “programmed with the minimum horizontal and vertical separation requirements between aircraft ("traffic separation standards")”; “automatically redirect an aircraft's course, heading, altitude, etc., by the computer 66 determining the appropriate new course and transmitting via data link (i.e., transmitter 61) information to the aircraft informing it of the mandatory (or, alternatively, suggested) new route, altitude, heading, etc.”); and calculate a difference value by subtracting a safety standard value in the dimension corresponding to the maximum probability from the maximum probability, and making or giving a safety evaluation that indicates operation of the first aircraft and one of the one or more second aircraft is (i) safe when the difference value is less than or equal to 0, and (ii) unsafe when the difference value is greater than 0 (see at least column 17 lines 65-67 and column 18 lines 1-5: “ATC computer 66 may automatically coordinate and control the occurrence of all events at the airport, and communicate with aircraft on the ground and in the air to ensure that all aircraft movement on the ground and in the air, including landings, take-offs, etc. occurs in an orderly and efficient manner while maintaining a safe predetermined distance or time separating each aircraft/event, so as to avoid separation standards violations and collisions.”). It would have been obvious, before the effective filing date of the invention, with a reasonable expectation of success, to one having ordinary skill in the art, to ascertain that both of these limitations in view of Farmakis are obvious because it is well-known for comparisons to completed by subtraction and there are only finite number of options to try (i.e., “calculate a difference value by subtracting a safety standard value in the dimension corresponding to the maximum probability from the maximum probability, and making or giving a safety evaluation that indicates operation of the first aircraft and one of the one or more second aircraft is (i) safe when the difference value is less than or equal to 0, and (ii) unsafe when the difference value is greater than 0”, or calculate a difference value by subtracting the maximum probability from a safety standard value in the dimension corresponding to the maximum probability, and making or giving a safety evaluation that indicates operation of the first aircraft and one of the one or more second aircraft is (i) safe when the difference value is greater than 0, and (ii) unsafe when the difference value is less than or equal to 0, or other slightly modified options with “equal than” moved between safe and unsafe) and given that Farmakis teaches suggestions of new routes, etc. to reduce risk, it would be important to know where the highest risk is, so that the aircraft does not turn towards the risk / makes a maneuver that actually reduces the risk. The motivations are to ensure safe air travel.
Regarding Claim 2, the Long and Farmakis combination teaches the limitations of Claim 1. Furthermore, Long further discloses wherein the probabilities of overlapping between the first aircraft and the one or more second aircraft in the three dimensions are calculated by the following formulas:
a formula of the probability of overlapping between the first aircraft and the one or more second aircraft in a longitudinal direction is
P
X
S
X
=
∫
-
D
1
+
D
1
f
s
x
d
x
wherein
D
1
=(wingspan of the first aircraft)/2 + (a wingspan of the one or more second aircraft)/2,
S
X
=
f
s
x
is a first probability density function that obeys a normal distribution and represents a distance between the first aircraft and the one or more second aircraft in the longitudinal direction (see at least page 508: equation (8));
a formula of the probability of overlapping between the first aircraft and the one or more second aircraft in an altitudinal direction is
P
Z
S
Z
=
∫
-
D
2
+
D
2
f
s
z
d
z
wherein
D
2
=(an altitude of the first aircraft)/2 + (an altitude of the one or more second aircraft)/2,
S
Z
=
f
s
z
is a second probability density function that obeys a normal distribution and represents a distance between the first aircraft and the one or more second aircraft in the altitudinal direction (see at least page 508: equation (10)); and
a formula of the probability of overlapping between the first aircraft and the one or more second aircraft in a lateral direction is
P
Y
S
Y
=
∫
-
D
3
+
D
3
f
s
y
d
y
wherein
D
3
=(a length of the first aircraft)/2 + (a length of the one or more second aircraft)/2,
S
Y
=
f
s
y
is a third probability density function that obeys a normal distribution and represents a (see at least page 508: equation (9)).
Regarding Claim 3, the Long and Farmakis combination teaches the limitations of Claim 2. Furthermore, Long further discloses wherein
f
s
x
is calculated as follows:
f
s
x
=
1
σ
d
2
π
e
-
(
x
-
a
2
-