Technology continues to change the way detecting Missile trajectory is done. The advancement in technology has led to massive growth in missile defense (Ender et al., 201?0). Missile defense began over decades ago with simple techniques, developed by countries like the US and Russia, which could detect offensive launch events and track inbound ballistic missiles, however, these technologies had limited capability for defense (Kumar et al., 2012). The popularity of the field has been increasing as years goes while many countries are playing their roles interesting in unraveling some of the mysteries of the trajectory of a ballistic missile and how it is launched. This gives room facilitation in using new technology for production of a new product of quantity and visualizes missile defense (Clemons and Chang. 2012).
However, little has been done in the examination on how to understand and how these new technology of Doppler radar works. It is s subset of the radar technology that gives particular attention to figuring out the speed of an object (Lee and Singh. 2010). The principle behind this technology is that the waves that are produced by an object would be squashed together should they be moving towards you or be spread further apart should they be running away from you. This is the reason behind the seeming decrease in the pitch of a police siren as the vehicle moves away from a person since as each of the waves is being produced; the car tends to push further and further. Doppler radar has been implemented in missile defense (Zhu et al., 2010?).
This research is meant to find out how “Trackman”- which is a golf tracker equipment can be used to find the Trajectory of a Missile. The Trackman golf tracker employs the psychology of Doppler radar to trail both the hits and pitches of balls via their trajectory in golf and baseball. The obtained data is very significant to the scouts, players, and statisticians to assess the baseball and golf games to measure the performance of the player. Elsewhere it is applied in the manufacture of equipment to determine the working of the clubs and balls (Nathan. 2015).
Trackman’s technology is a golf tracker equipment used in golf broadcasts and other major networks. Golfers rely on this technology for fine-tuning of the game and lessons. The idea of Trackman was conceived by a golfer by the name Dr. Klaus Eldrup-Jorgensen, when he realized that in spite of the advancement in technology, limited technological improvements had been made in the field of golf. Therefore, Jorgensen joined hands with Fredrik Tuxen, a radar engineer. Tuxen modified the Doppler radar technology used for bullets and missiles tracking for golf. To mention briefly how the trackman works, we will use the example of Trackman 4, which is the latest product of the company. It employs the use of dual radar technology to capture 27 data points about both the ball and the club. These include both simple parameters such as club head speed and carry yardage and complex statistics such as dynamic loft and smash factor (Leach., 2017?).
In essence, every detail of the golf swing is quantified and substantiated by a machine of equal size to a laptop, placed behind the golfer. This equipment does not use any extra attachments or equipment. The device incorporates a built-in HD camera for recording the swing of the player. The video can then be monitored from phones, tablets, and laptops that are connected to a device via Bluetooth technology (Tuxen. 2018).
Of late, the data obtained was used to determine the drag forces on a trajectory hit where balls are lifted. Because the method has been executed widely by the professionals in the sporting field to identify the player’s performance and manufacturers have also used it to find out the safety of their equipment, an evaluation of the technology is required. The assessment comprises investigating how data is recorded in the system for pitches and also the hits, the filtration and accuracy of the data, and finally how the information is affected by the noise. The demonstration requires the method used by the system to record data and theory of radar discussion. It will involve an explanation of the raw data, and the purpose of how angles and positions were obtained. It helps to precisely identify where noise significantly affected the data in the trajectory, Because sound is a limiting factor in all systems of radar, considering the time spent to clarify the various types of noise and its influence on the data. (Fast. 2010). The assessed data from the radar comprised of all the trajectories of the pitch and hit (Nathan. 2012). It was carried out by use of great speed video tracking situated near the outfield and inside the home plate. A second system which comprised of cameras that were infrared was used in the monitoring which allowed for comparison. The repeatability of the radar was obtained by the use of the Game data which measured the efficiency of using the detector to determine the aerodynamic forces of the hit balls. This evaluation would aid as a prototype for ballistic missile trajectory detection.
The trackman employs the technology of Doppler radar. Thus it is prudent to examine briefly the Doppler radar effect and how it is used in missile trajectory detection. This knowledge can then be used to figure out how trackman can be used to track missiles.
For instance for the case of radar gun of the police, radar of the Doppler by releasing a beam of electromagnetic waves that are usually modified to a specified frequency at an object in motion. Upon hitting the moving object, the electromagnetic waves released would bounce back towards the source which is also the host of the receiver besides the original transmitter.
The wave would be shifted since it is reflected off the moving object. On return to the radar gun, this wave is assumed to be an entirely new wave and as it was emitted from the target on to which it bounced off. In this regard, the target acts as new wave source. This reflected wave has a frequency that is not the same as the frequency with which it was initially sent to the target from the source. Since the radiation that was used in the radar gun was at a precise velocity at the time of being sent out from the source and at a new frequency on its return journey to the radar gun, it is possible to estimate the velocity of the target object which would give the velocity of the moving object.
The Pulse-Doppler gun does not only allow for the calculation of the linear velocity of the radar gun but also allows estimation of the radial velocities. It is achievable by using pulses instead of radiations from the beam that only move in a linear direction. The shift there occurs both in the frequency and the carrier cycles thereby permitting the determination of the radial velocities.
It is essential to ensure careful control of the system to achieve the radial velocities of the system. The stability of the phases of the radiation pulses must be ensured, and this is possible through providing that the system is in a coherent state. The only disadvantage of this system is that the Pulse-Doppler system is such that there is maximum velocity beyond which the radar is not able to measure radial velocity.
A Doppler radar uses Doppler effects in a much-specialized way to determine the velocity of objects which are at a distance. It works by sending a microwave signal which bounces back after hitting the desired target. The impact which occurs on the signal as it bounces back is determined, and from it, the velocity of the moving object is defined and how far from the Doppler radar purpose is.
Doppler applies the usage of the narrow band receivers to be able to eliminate objects which are moving at a low velocity or the objects which are stationary in that way the Doppler radar can eliminate signals which are false which may be from the clouds, trees, and other environmental influences.
The Doppler radar system uses the timing technique to determine the range of the target which the missile is targeting. Similarly, it uses the Doppler effects of which the return signal is used to determine the velocity of the target object. Also, uses the features of the continuous-wave radar and the pulse radar which initially applied to work separately use the complexity of the electronics which were involved.
The Doppler radar system uses to scan and tracking techniques in the detection of missiles. The frequency filtering, ambiguity resolution, and amplitude thresholding are the main things which are determined in the scanning mode of detecting weapons. The moment the resolving and detection of the reflection have taken place, the Doppler radar transmits the thinking automatically to the tracking mode in the space volumes which surround the missile track.
Doppler signal processing excludes selectively all the low-velocity reflection with the primary objective of ensuring that there is no detection which occurs below the threshold velocity of the moving object this is done to ensure that the confusion which might be caused by terrain, weather, and biological factors does not occur. The signal from the target domain which is detected is converted back to the time domain from the frequency domain sounds from the track of the operator who is in some radar system. This operator uses this sounds to do the classifications of the targets.
Due to the nature of the Doppler radar special considerations are to be put in place in large missiles because the Doppler radar works like a locked loop. The audible signal which is produced is used for the identification of the kind of the missile which is flying and at what velocity is the missile flying. Once that has been identified the target which the rocket is sent to hint is determined and the necessary actions can be put in place to keep tracking the missile by using the Doppler radar.
The Doppler radar must have the ability to have the multi-mode which can be able to handle both the missile turning and crossing trajectory. Once the Doppler is in the track mode, it includes techniques which enable the Doppler filtering of the spaces which are surrounding the track and trying at all the points to ensure that the missile which might be crossing the path immediately can be found and identified
When the missile has been launched, and its spinning motion is of the same kind with the motion of the Micro Doppler motion. The modulation period of frequency is what is referred to as the micro-Doppler modulation frequency which is a very stable and efficient parameter in the radar tracking and target recognition.
First, the signal of the spinning missile during its flight is established by the radar, then the micro-Doppler modulation frequency is extracted through the analysis which is done periodically of the resulting spectrogram (STFT) which is the frequency distribution time. This is done to be used for the target of BM recognition.
The Received echo is down-converted by the homodyne sensor by the use of the transmit waveform which acts as the local oscillator and ensures that the receiver output is the Doppler radar which in return shifts the amplitude which is modulated by the radar range system and the antenna beam.
The Doppler radar consists of the Radar sensors, and also a data-multiplex/controller. The frequencies which are received are usually 10MHz apart from each other. The sensors which are in the Doppler system each of them consists of pairs of antenna mainly to receive and to transmit the signal.
To better understand how the trackman radar may fail to follow, an illustration using baseball game would be used. A trackman will be used to monitor the game to depict how the trackman may fail to track when used for missile trajectory tracking.
Apart from having an accurate range, the radar cannot frequently be able to track a pitch or more possible, follow a pitch. We have Numerous reasons which may contain an outcome. Foremost is that the ground ball is a hit. The radar aims to stop pursuing when the ball hits the ground which is shown by a radical variation in the trajectory. It is not necessary for the radar to track the shots since they hit the ground in time in their path. The other cause of a hit ball might not be pursued since it leaves the field of vision at the start of the path. It is distinctive for foul ball type hits. The field of view described is ± 45° in the azimuth angle and -15° and 45° in the elevation angle. Inclination of the 4° angle offers an improved elevation angle which is positive in the field of view. The amplitude of the frequency of the return signal failing to drop within the exposure threshold is a third reason of why a hit ball fails to be tracked. In this situation, the algorithm is postponed because the radar fails to establish whether the ball exists. It might be as a result of the surrounding noise or a weak signal which results from the vast distances or angles felt in the process of an infield fly ball, Whichever way, when the return signal fails to fall within a specified threshold the radar fails to track. Other cases where a fly ball that is well hit to the outfield fails to be followed and the predictable factors are linked to the operating system tasks like leveling. Communication losses have been periodically experienced between the radar and the laptop which result in the no tracking. The occurrences are occasional and almost ninety five percent of the time is used in monitoring the runs.
As per mentioned above, in the execution of other activities the radar fails to track, it comprises looking out for data from a formerly followed ball. Meaning, the element requires a reasonable time frame to complete its scheming before ensuring a tracked pitch or hit. The time to wait differs between hits and pitches which is significantly affected by the ball’s trajectory. 3 – 5 seconds is the usual wait time allowed between the consecutive pitches; we experience the rise of the wait time when a hit occurs. The estimated wait time of 5 -8 seconds happens when the ball is hit while in the midair for about 1 and 1 and half seconds. It takes 10 to 15 seconds when a fly ball is well hit in the outfield. It may vary marginally after the ball has left the field of view because it is upon the radar to wait for numerous seconds to decide whether the ball will go back to its original view field.
The benefit of using Radar is because of it’s of tracking which uses high-speed cameras where information is shown for both hits and pitches moments after the ball lands. It is advantageous because the unit is used for establishing the performance of equipment or to track games. The data measures and adequately describes the hit and the pitch. A set data for the pitch and hit user may comprise of statistics about the discharge speed and position of pitch, the final landing position of hit, the site, speed of the pitch and hit at home plate. Laterally with the information about the pitch and hit, the play data can also be entered. This information is cued in by the operator on an operator interface. The data for both the team and the player is also shown so that a full game can be tracked (?esi? et al., 2014).
Information about the pitch and it is recorded. This data together with operations input game data entirely describes the game and permits the tracking of the strikes by the system, the battings, and balls. If the initiation order is intact, the system will spontaneously cycle over the launches. After the tracking, the period has finished the data of the pitch, and it is allowed to be transferred to a .csv file for the purpose of editing. The real information taken by the radar, is called the Trackman raw data, which is accessible by means of the Trackman data file or .tmd file. The files are transferred to .xml format (by using a distinct program that is licensed which is called Workbench) which is edited and opened in Excel found in the Microsoft program. The Trackman information data file comprises more determined details about the whole trajectory of a single pitch and hits which includes filtered data that was unfiltered (Kalman 47 filter with an altered period stamp). It also displays where the radar misses track of a ball, usually at the end of a hit after the ball has moved far away from the radar. The data part in the .xml file used for this work was the velocity radial of the ball (Vr), the cosines directions (α, β, and γ) of Vr, and the initial range of the ball (R) (?Li et al., 2015?).
The route cosines, α, β, and γ, are determined per esteem to the axes that are well-demarcated by the radar. They consist of the -4° tilt of the radar around Zr and slightly turning around the Yo axis. The series of the ball is explained as the length from the ball to the radar as specified via the operator through the arrangement.
How the Trackman system gives the x, y, and z coordinates according to earth’s topology
The coordinate system of the Trackman for the golf ball applies the positive x-direction which usually points to the pitcher, which is at the same level with the ground, the positive coordinate which points upwards and the z coordinate which points to the catcher’s right. Hence the golf/pitched ball is mainly moving in the negative x-direction as shown in figure below.
Fig 1: The coordinate system of the Trackman and field
The coordinate field system can be seen in the diagram starting at the tip of the home plate with the X f , Y f , and Z f axis pointing which points in the same direction as the coordinate system of the radar. The position of the ball at any given time as reported by the user it is in respect with the field coordinate system.
The trackman radar uses a self-levelling system which enables it to keep the antennas pointed in an angle of 4o and tilted about the Z r axis. The optimal 4o tilt is an allowance to allow the radar to be pointed upwards slightly mainly for the purpose of optimization for tracking flying balls. There are two legs at the bottom of the radar which enable it to level about the X r axis such that the radar remains in level with the ground
Filtered and unfiltered statistics might be managed by the operator using the Workbench program which is responsible for permitting the scrutiny of individual data sets, offers drag and lift, and spectrums frequencies. It provides the capability of the operator to differentiate game aspects that comprises the distance of the calibration radar, weather conditions besides ball dimensions. This offers the capacity to find out the impacts they have on to change the environment or the informed data to replicate the existing situations of the game (Tuxen et al., 2018). It was much applied to alter .tmd files into files that can be read by Microsoft Excel. It permits for data together with the entire path of both the pitch and hit that will be evaluated. The tough signal realized at a zero frequency and maintains from the start to the end of the data because of the noise in the background. This sound is nonstop and doesn’t alter and hence has minimum influence on the signal of the balls. A strong negative frequency shows the pitch of the ball from time 0 to about 1.8 seconds. It begins with a fast peek in frequency at 0 second time, which is the movement of the pitcher as understood by the radar. The pitch then travels laterally until it is jammed by the bat, that is specified by a disturbance at roughly 1.8 seconds. Pitch’s signal doesn’t reduce along its track from the diving mound to home plate, because the ball is on the incoming the radar that is firming. We experience a great optimistic thorn in the frequency immediately after the disturbance produced by the bat and batter movements. The peak represents a begging of the tracked hit which lasts for four seconds until the time it is adjourned. The variation in the hit frequency exhibits that the signal starts to weaken as the ball moves more away of the radar. Other disturbances have been identified at lesser frequencies as the hit ball journeys laterally in its path. They are probable to be the moving players in the infield or any other object in the field of or the radar’s view. There is a presence of a feebler signal that trails the same frequency path as the pitch and hit but is reverse in sign. This is because of the looking glass in the frequency and is found out by the radar which has no influence on the precision of the information (Kagan and Nathan. 2017).
Frequencies that are a little lower or higher in greatness make it hard for the radar to measure the real signal which results in no tracking of the ball.
Research methodology is characterized as a deliberate methodology that guarantees the analyst to assemble appropriate data or to embrace examination relating to the topic of research by utilizing diverse research strategies. The aim of the proposed research is to evaluate how detect missile trajectory with GPS by use of trackman.
The objectives were set in order to assist in achieving the main aim of the study .Due to that, it was essential to have an overview of how to evaluate how detect missile trajectory with GPS by use of trackman. . It was of great importance to understand the main principles of detecting missile trajectory with GPS by use of trackman. Hence qualitative research method together with the literature review and quantitative approaches were employed for the research. This research methodology is appropriate to carry out this research because the literature reviews offer information that is detailed about the topic of research.
This research methodology gives an overview of the preliminary researches that have been carried out in the field and at the same time gives a short description of the topic of research. In short, the literature review that was conducted assists to find the research gap for the research topic.
Various mathematical models will be used in the used during the research regarding on various aspects detecting missile trajectory with GPS by use of trackman.
Some of the advantages of using mathematical models include:
Various computer programs and simulations will be carried out to determine the aspects of detecting missile trajectory with GPS by use of trackman.
By conducting the literature review, the author could pass the knowledge about the topic of research, and it would include the main features of a topic. This research approach is of great importance in achieving the objectives and aims of the research. This research approach is also very helpful in attaining all the objectives and aims of the research such as to have a summary of detecting missile trajectory with GPS by use of trackman, to evaluate the various principles behind detecting missile trajectory with GPS by use of trackman. The main reason behind the selection of this research methodology is to give detailed knowledge about detecting missile trajectory with GPS by use of trackman. This research methodology also gives the knowledge about the various scholars and who had previously carried research on the topic .The literature review that was carried out gave the detailed knowledge on detecting missile trajectory with GPS by use of trackman.
The research proposed is intended on utilizing literature reviews and use of various computer simulations investigation as a suitable system to carry out the research. Computer simulations and literature review encourages a researcher to keenly examine the information relating to a particular setting that is a specific topic of research. Additionally, literature review which is usually referred to as secondary sources allows a researcher to pick up top to bottom information and illustrate the aspects of a proposed research topic. For the given research project it is suitable carrying out various computer simulations
To successfully use Trackman to detect the trajectory and position of a missile, a system of a Trackman and a GPS receiver is required. The trackman uses a Doppler radar to detect missiles trajectory, while the GPS receiver will use the global positioning system and the Russian GLONASS satellites to achieve an accurate position of the missile along its path
Currently, the GPS system has a total of 31 satellites that are active and are inclined to the equator at an angle of 55 degrees. The GPS receiver can be an embedded gadget, or a GPS enabled phone or tablet (Ta. 2011). Trackman has a mobile app that can be installed in a GPS enabled phone then configured with the trackman kit to detect the position of a trajectory (Tomkiewicz et al., 2010). However, since the trackman uses the Doppler radar technology, the detection is short-ranged but effective due to the involvement of GPS system (Bjørneraas et al., 2010).
The GPS receiver device obtains a signal from each GPS satellite. The satellites transmit and communicate the actual time the signals are relayed. The GPS receiver then tells its length from the satellite by deducting the time the signal was sent from the time it was received by the GPS device (Logsdon. 2012). The GPS receiver can also tell the exact position of the satellites in the sky, at the instant the transmitted their signals. Thus, provided the location of the three satellites and the time of travel of GPS signals from the three satellites is known, the GPS receiver device will indicate its position in 3D that is east, north and altitude (Dubey. 2014).
The trackman device will be configured with the GPS device to detect the trajectory and position of a missile. As the trackman that uses the Doppler radar technology will be tracking the trajectory of a missile, the GPS device will be tracking the position of the missile along its trajectory (Miller et al., 2011).
The following sections will define functioning factors of the unit and correct setup processes to assist in minimizing the signal’s noise. It describes the interfaces of the user and demonstrates how they might be implemented to establish the system’s problem of calibration or setup. Lastly, details of various statistics sets taken by the radar are well-defined.
The boundary program was established by Trackman 4 and permits for all features of a missile to be launched and the cautious locations to be input by the user. The position of the launch can be tracked by the radar and then specified by the GPS device. Similarly, the position of the tracker is also input into the system. Once all the data are recorded, the radar needs elementary calibration to position himself within the operation field (Saito and Hideaki Kamata. 2017). The radar height between the ground and the mid of the “K” on the radar’s expression must be determined together with the length that separates the radar and the tip of the GPS. Lastly by use of the radar’s front camera, an image of the location is taken. At the left bottom of the screen, a zoom image is applied to precisely identify the tip of the GPS. This provides the radar a locus to establish its location in the arena of operation and permits the taken statistics to be converted to the points of the area. This means each distance should be measured as precisely as likely while also bring into line the radar in a straight-line pathway in the direction of the launch position (Li and Jilkov. 2010). However, in most cases, it is not probable to position the radar in a straight line with the target and launch position. Pre-assigned settings have been demarcated by Trackman 4 established on the kind of tracked game and must be particular by the user beforehand tracking starts. The situations vary the original range of the ball and are altered by the use of a hasty program found on the desktop.
Apart from having an accurate range, the radar cannot frequently be able to track a pitch or more possible, follow a pitch. We have Numerous reasons which may contain an outcome. Foremost is that the ground ball is a hit. The radar aims to stop pursuing when the ball hits the ground which is shown by a radical variation in the trajectory. It is not necessary for the radar to track the shots since they hit the ground in time in their path. The other cause of a hit ball might not be pursued since it leaves the field of vision at the start of the path. It is distinctive for foul ball type hits. The field of view described is ± 45° in the azimuth angle and -15° and 45° in the elevation angle. Inclination of the 4° angle offers an improved elevation angle which is positive in the field of view. The amplitude of the frequency of the return signal failing to drop within the exposure threshold is a third reason of why a hit ball fails to be tracked. In this situation, the algorithm is postponed because the radar fails to establish whether the ball exists. It might be as a result of the surrounding noise or a weak signal which results from the vast distances or angles felt in the process of an infield fly ball, Whichever way, when the return signal fails to fall within a specified threshold the radar fails to track. Other cases where a fly ball that is well hit to the outfield fails to be followed and the predictable factors are linked to the operating system tasks like leveling. Communication losses have been periodically experienced between the radar and the laptop which result in the no tracking. The occurrences are occasional and almost ninety five percent of the time is used in monitoring the runs.
As per mentioned above, in the execution of other activities the radar fails to track, it comprises looking out for data from a formerly followed ball. Meaning, the element requires a reasonable time frame to complete its scheming before ensuring a tracked pitch or hit (Mattei and Monaco. 2014).
In this study, the projectile is a missile propelled by an armament (gun machine, handgun, missile, and grenade) or the like. Location launch may be a site from which it propels the projectile moreover by using a launch pad, like a tee setting the ball in advance before launch, a barrel of a weapon or an Outward on which the projectile relaxes before it’s launched. The unveiling location may be established in a number of ways. The first way is to dictate or assume that the launch occurs at a programmed location or within a prearranged zone. The other way of is to have the unveiling location also within the pictures, where a number of pictures are taken, and a change therein is recognized conforming to the launched projectile. This change may be the projectile being absent in a future image compared to one or more images taken before the launch. The real route of the projectile is the route of the projectile while in flight. The sequence may be derived from the actual path of the projectile. The track may be established in a prearranged plane, in that the track may differ in a 3-D setup, but where the most motivating track is that of the 3D path projected onto the ground plane (Szabo et al., 2011).
What is the cost and investment to be done to convert and install Trackman in detecting the missile trajectory?
The existing trackman kit is used for games. To modify the existing trackman kit for the missile detection extra cost in both hardware and software must be involved. The cost involved is hardware and the software costs as outlined below.
Equipment cost
Trackman 4 kit $19000
GPS device $74
Software $1000
Total $20074
Conclusion
A review of various research papers was done on this paper to study how trackman 4 used in golf can be transformed into a missile trajectory tracker. Various research papers are reviewed in the above section. It was determined from this review that guidance law for the missile, is considered as the major key factor that impacts the capacity of the missile in
This paper studied how the Trackman 4, used for this work, works and informs this data. The unit that was operated in the frequency of the x-band spectrum at approximately 10.5 GHz uses 4×4 array planar antennas where one emits and the other three are used for receiving. We had the definition of system of coordination accompanied with specific setups that are needed by the system to minimized multipath errors effects. There was the discussion of the user and the calibration interface and also the importance of the radar’s initial range. Three different launch distance settings were developed because of the unit used a fixed launch place in the process to determine the missiles initial range which was created by Trackman 4. Errors in the angle would have been experienced in the measurements made by the radar if the correct setting was not used for pursuing the outcome. Improper launch settings result in no tracking of the launch and the subsequent launches. There was an explanation of how the data was noted and exhibited by the radar which comprised of how the application of the Workbench will be applied to study the pitch and hit trajectories which an opportunity to establish noise experienced in the signal of the radar and helps in the provision of a confidential degree in the results. (Turetsky et al., 2014).
References
American journal of preventive medicine, 38?(2), pp.178-183.
Bjørneraas, K., Van Moorter, B., Rolandsen, C.M. and Herfindal, I., 2010. Screening global positioning system location data for errors using animal movement characteristics. ?Journal of Wildlife Management, 74?(6), pp.1361-1366.
?esi?, J., Markovi?, I., Juri?-Kavelj, S. and Petrovi?, I., 2014, September. Detection and tracking of dynamic objects using 3D laser range sensor on a mobile platform. In Informatics in Control, Automation and Robotics (ICINCO), 2014 11th International Conference on (Vol. 2, pp. 110-119). IEEE
Cooper, A.R., Page, A.S., Wheeler, B.W., Griew, P., Davis, L., Hillsdon, M. and Jago, R., 2010
Chu, K.H., Chen, Y. and Wang, X., Intellectual Fortress, LLC, 2017. ?Global positioning system. U.S. Patent 9,576,487
Dubey, A.K., 2014. Global positioning system. In Understanding an Orogenic Belt (pp.
215-230). Springer, Cham
Ender, T., Leurck, R.F., Weaver, B., Miceli, P., Blair, W.D., West, P. and Mavris, D., 2010. Systems-of-systems analysis of ballistic missile defense architecture effectiveness through surrogate modeling and simulation. ?IEEE Systems Journal, 4?(2), pp.156-166.
Fast, M., 2010. What the heck is PITCHf/x. ?The Hardball Times Annual, 2010, pp.153-158.
Hofmann-Wellenhof, B., Lichtenegger, H. and Collins, J., 2012. ?Global positioning system: theory and practice. Springer Science & Business Media.
Kagan, D. and Nathan, A.M., 2017. Statcast and the baseball trajectory calculator. ?The Physics
Teacher, 55?(3), pp.134-136.
Keitler, P., Pustka, D., Huber, M., Echtler, F. and Klinker, G., 2010. Management of tracking for mixed and augmented reality systems. In The Engineering of Mixed Reality Systems?(pp. 251-273). Springer, London.
Kumar, S.R., Rao, S. and Ghose, D., 2012. Sliding-mode guidance and control for all-aspect interceptors with terminal angle constraints. ?Journal of Guidance, Control, and Dynamics, 35?(4), pp.1230-1246.
Leach, R.J., 2017. ?The role of biomechanics in achieving different shot trajectories in golf
(Doctoral dissertation, Loughborough University)
Lee, K.W. and Singh, S.N., 2010. No certainty-equivalent adaptive missile control via
Immersion and invariance. ?Journal of guidance, control, and dynamics, 33?(3), pp.655-665. Clemons, T.M. and Chang, K.C., 2012. Sensor calibration using in-situ celestial observations to estimate bias in space-based missile tracking. ?IEEE Transactions on Aerospace and Electronic Systems, 48?(2), pp.1403-1427.
Li, B., Sun, B., Chen, C.F., Jiao, X.J., Zhang, S.Y. and Wang, Y., 2015. Simulation of Golf
Li, X.R. and Jilkov, V.P., 2010. Survey of maneuvering target tracking. Part II: Motion models of ballistic and space targets. ?IEEE Transactions on Aerospace and Electronic Systems, 46?(1).
Logsdon, T., 2012. ?The Navstar global positioning system. Springer Science & Business Media
Mapping the walk to school using accelerometer combined with a global positioning system
Miller, J.M. and Amin, H.S., KHI ACQUISTIONS LLC and KHI Acquisitions LLC, 2010
Nathan, A.M., Determining the 3D Spin Axis from Trackman Data (updated, March 31, 2015).
Nathan, A., 2010, March. The Flight of a Baseball. In APS March Meeting Abstracts.
Miller, J.M. and Amin, H.S., KHI ACQUISTIONS LLC and KHI Acquisitions LLC, 2011
Nathan, A.M., 2012. What New Technologies Are Teaching Us About the Game of Baseball?
Preliminary Temporal and Geometrical Camera Calibration
Real-time Tracking Based on Doppler radar. In Applied Mechanics and Materials (Vol. 743, pp. 828-835). Trans Tech Publications.
Saito, S.M.H. and HideakiKimata, K.D.M., 2017. Ball 3D Trajectory Reconstruction without
Tuxen, F., Trackman AS, 2018. ?Device, System, and Method for Tracking Multiple Projectiles. U.S. Patent Application 15/206,996.
Tuxen, F., Trackman AS, 2018. ?Method and a sensor for determining a direction-of-arrival of impingent radiation. U.S. Accounting 9,958,527.
Tuxen, F. and Brink, F.E., Trackman AS, 2011. ?Assembly comprising a radar and an imaging element. U.S. Patent Application 13/138,167.
Tuxen, F., Trackman AS, 2017. ?Determination of Spin Parameters of a Sports Ball. U.S. Patent Application 15/461,926.
Tuxen, F., Trackman AS, 2014. ?Method and an apparatus for determining a deviation between an actual direction of a launched projectile and a predetermined direction. U.S. Patent 8,912,945.
Tuxen, F., Trackman AS, 2016. ?Method and an Apparatus for Determining a Deviation between an Actual Direction of a Launched Projectile and a Predetermined Direction. U.S. Patent Application 15/077,319.
Tuxen, F., Trackman AS, 2014. ?Determination of spin parameters of a sports ball. U.S. Patent 8,845,442.
Tuxen, F. and BRASCH, J., Trackman AS, 2018. ?Skid and Roll Tracking System. U.S. Patent Application 15/339,356.
Tuxen, F. and Brink, F.E., Trackman AS, 2016. ?Systems and methods for coordinating radar data and image data to track a flight of a projectile. U.S. Patent Application 15/050,456. Mattie, G. and Monaco, S., 2014. Nonlinear autopilot design for an asymmetric missile using robust back stepping control. ?Journal of Guidance, Control, and Dynamics, 37?(5), pp.1462-1476. Szabo, R., Pedersen, C.E. and Cooper, W.E., Lockheed Martin Corp, 2011. ?Missile tracking with interceptor launch and control. U.S. Patent 7,875,837.
System for dynamically pushing information to a user utilizing global positioning system. U.S.
Patent 7,982,599
System for dynamically pushing information to a user utilizing global positioning system. U.S. Patent 7,843,331
Turetsky, V., Glazer, V.Y. and Shinar, J., 2014. Robust trajectory tracking: differential game/cheap control approach. ?International Journal of Systems Science, 45?(11), pp.2260-2274.
Tomkiewicz, S.M., Fuller, M.R., Kie, J.G. and Bates, K.K., 2010. Global positioning system and associated technologies in animal behavior and ecological research. ?Philosophical Transactions of the Royal Society B: Biological Sciences, 365?(1550), pp.2163-2176.
Ta, J.L., 2011. ?Global positioning system?(Doctoral dissertation).
Xia, Y., Zhu, Z. and Fu, M., 2011. Back-stepping sliding mode control for missile systems based on an extended state observer. ?IET control theory & applications, 5?(1), pp.93-102.
Zhu, K., Qi, N.M. and Qin, C.M., 2010. Adaptive sliding mode controller design for BTT missile based on back stepping control [J]. ?Journal of Astronautics, 3, p.026.
Essay Writing Service Features
Our Experience
No matter how complex your assignment is, we can find the right professional for your specific task. Contact Essay is an essay writing company that hires only the smartest minds to help you with your projects. Our expertise allows us to provide students with high-quality academic writing, editing & proofreading services.
Free Features
Free revision policy
$10Free bibliography & reference
$8Free title page
$8Free formatting
$8How Our Essay Writing Service Works
First, you will need to complete an order form. It's not difficult but, in case there is anything you find not to be clear, you may always call us so that we can guide you through it. On the order form, you will need to include some basic information concerning your order: subject, topic, number of pages, etc. We also encourage our clients to upload any relevant information or sources that will help.
Complete the order form
Once we have all the information and instructions that we need, we select the most suitable writer for your assignment. While everything seems to be clear, the writer, who has complete knowledge of the subject, may need clarification from you. It is at that point that you would receive a call or email from us.
Writer’s assignment
As soon as the writer has finished, it will be delivered both to the website and to your email address so that you will not miss it. If your deadline is close at hand, we will place a call to you to make sure that you receive the paper on time.
Completing the order and download