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Texas A&M Senses New RFID Apps

A university research facility is hoping to deploy wireless sensors networks combined with RFID tags.
By Mary Catherine O'Connor
Feb 01, 2006Student researchers and professors in the Engineering Technology & Industrial Distribution (ETID) department of Texas A&M University are working with companies as diverse as a nursing home and a manufacturer of precast concrete to develop RFID applications, many of which combine RFID tags with environmental sensors.

The projects are being conceived and designed in the department's Sensors and RFID Technologies Laboratory, a 2,000-square-foot facility opened last fall with financial support from the university and with tags, interrogators and sensors provided by several RFID equipment manufacturers, including Alien Technology, Axcess, Crossbow Technology, Dust Networks, Escort Memory Service, Intermec Technologies and TAGSys.

Professor Ben Zoghi
"In establishing the lab, our goal is to converge the sensor network technologies with RFID networks," says Ben Zoghi, a professor and the lab's director. "We used to use sensors in our labs just to control things, but until we added RFID, we never had a way to track the movement of the things we were sensing. We never had sensors that could communicate an ID. RFID adds real-time visibility to wireless sensor networks."

The lab serves as a classroom for some of Zoghi's courses on control systems that are part of the school's Electrical Engineering Technology program. Working with two other faculty members and five student researchers in the five months since the lab's opening, Zoghi has initiated a number of projects with businesses near the university and throughout Texas.

One of these projects involves a Houston-based distributor of hazardous chemicals used in the semiconductor and photo development industries. Zoghi and his team are designing a monitoring system utilizing active RFID tags, interrogators and exciters from Carrollton, Texas-based Axcess, combined with temperature and chemical sensors. The team plans to attach the tags and sensor devices to barrels of the distributor's chemicals, including hydrofluoric acid and potassium hydroxide. They will then monitor the movement of the items through RFID interrogators in storage areas and in doorways. If the barrels are removed without permission, the system will alert personnel. The tags will also trigger alerts if the sensors are exposed to temperatures outside a set range, or if they detect a chemical odor signifying a potential leak.

One project Zoghi hopes to deploy would assist the staff of a nursing home near the university in monitoring the whereabouts of patients, some of whom suffer from cognitive problems. Patients would wear active RFID tags designed to trigger RFID readers with attached sensors that could alert the staff if a patient neared a particular doorway. Zoghi says the system could be linked to a security system that could lock particular doors if a patient approached. The system could also be linked to surveillance cameras, so that an interrogator would turn on the nearest camera upon sensing an ID tag. The system would then alert a nurse's station.

However, Zoghi says, an application such as this could raise very serious concerns among the patients and their families, who may be uncomfortable with the notion of tracking patients' movements. "It's a matter of privacy, and also of conveying to the elderly patients what the system does and what it would be used for."

Zoghi and his colleagues are also discussing a project with a company that manufactures precast concrete forms, such as electrical vaults and barriers. The firm wants to keep a better record of where its inventory is located within its yard, so Zoghi proposed a system using passive RFID tags and GPS receivers. The forklifts used to move the forms in and out of the yard would be equipped with RFID interrogators able to read passive tags attached to the forms. Mobile computers inside the forklifts would then combine the RFID tag data with GPS coordinates from a mobile GPS receiver installed on the forklift. The company would use this combined data to track inventory movements.

In the wake of the Sago mining accident in West Virginia last month, a student working at the lab suggested a personnel badge combining an active RFID tag with a carbon monoxide sensor could be used both to locate miners and to send alerts when exposed to gas. Based on this idea, Zoghi says the lab offered a proposal to the state of West Virginia, but has not received a response. "We had mixed feelings about this," he says. "We don't want to look like we're being opportunistic [in the wake of a tragedy], but we feel like this could be a good application that could help locate miners."

The Sensors and RFID Technologies Laboratory is not the first RFID-related research center at the university. The school also opened the RFiD2 Lab, which focuses on passive RFID technology for supply chain and asset tracking applications (see Keeping Track of Cadets' Togs).
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MD Klanke 2006-07-03 11:39:30 PM
How GPS & RFID would best work and complemet each other I would enjoy talking about the use of RFID & GPS.. I have included a copy of my gps patent. If the RFID Information acts as a cpu, the systems would enjoy a useful marrage. many of the claims are a bit over the top, however the basic function would enjoy widespread use, United States Patent 6,313,791 Klanke November 6, 2001 -------------------------------------------------------------------------------- Automotive GPS control system Abstract This disclosure sets out a GPS receiver cooperative with a CPU having a memory. The memory enables inputting of data defining an electronic fence, i.e., a set of locations or a region where the vehicle is permitted to be operated. The electronic fence may be cooperative with a set of permitted driving instructions defining a delivery pathway for a set of stops, there being one or more delivery paths, which in conjunction with a clock, enables the vehicle to make delivery trips of a different nature at different times. Audio, visual and ignition control alarms are included to limit or stop vehicle operation outside the permitted locations. -------------------------------------------------------------------------------- Inventors: Klanke; Michael Dean (Katy, TX) Appl. No.: 321029 Filed: May 27, 1999 -------------------------------------------------------------------------------- Current U.S. Class: 342/357.17 ; 342/357.06; 701/210; 701/213 Field of Search: 342/357.06,357.13,357.17,457 701/213,208,210 -------------------------------------------------------------------------------- References Cited [Referenced By] -------------------------------------------------------------------------------- U.S. Patent Documents 5497149 March 1996 Fast 5504482 April 1996 Schreder 5532690 July 1996 Hertel 5550551 August 1996 Alesio 5729192 March 1998 Badger 5742227 April 1998 Escareno et al. 5790973 August 1998 Blaker et al. 5801618 September 1998 Jenkins Primary Examiner: Phan; Dao Attorney, Agent or Firm: Bracewell & Patterson LLP -------------------------------------------------------------------------------- Claims -------------------------------------------------------------------------------- What is claimed is: 1. A vehicle supported GPS system comprising: (a) a GPS receiver for receiving signals in determining the location of a vehicle supporting the GPS system; (b) a CPU with memory provided with vehicular permitted locations and permitted times, the CPU further receiving the GPS receiver generated location of the vehicle so that the CPU is enabled to compare vehicle location with vehicle permitted locations from memory and forming an indication that vehicle location is permitted; and (c) a clock providing a time signal to the CPU, wherein the CPU is enabled to compare the time signal with the permitted times, thereby forming an indication that vehicle time is permitted. 2. The apparatus of claim 1 wherein said CPU is provided with a first memory storing an electronic fence around a specific geographic area so that the vehicle is permitted within that area, and said CPU compares the vehicle location with the area inside the electronic fence to determine that the vehicle is permitted therein. 3. The system of claim 2 wherein said electronic fence is defined by permitted latitude and longitude designated locations, and said CPU compares vehicle location latitude and longitude to determine permitted locations thereof, and further including a circuit connected said CPU which stops vehicle operation on leaving the permitted location defined by the electronic fence. 4. The apparatus of claim 2 wherein said permitted vehicle location is defined by a route on streets, and said vehicle is permitted to drive the route on the streets, and said CPU forms a signal indicative of driving the routes thereby permitted. 5. The apparatus of claim 4 wherein said memory stores at least one route and said route begins with a home base location and extends down streets to return the vehicle to a designated return location at the conclusion of the route. 6. The system of claim 5 wherein said vehicle stores multiple routes and said routes are implemented at different but permitted times as defined by the clock connected to said CPU. 7. The system of claim 1 wherein said CPU with permitted location data from said memory determines that the vehicle has left a permitted area and forms a signal indicative thereof and which signal is provided to a vehicle ignition enabling circuit to stop operation of the vehicle. 8. The system of claim 2 wherein said vehicle system incorporates a cell phone to transmit or receive data relating to permitted vehicle locations, and said vehicle is equipped with vehicle sensors comprising an alarm system for the vehicle wherein said alarm system and sensors are armed selectively by said vehicle supported system. 9. The system of claim 8 wherein said phone handles electronic fence data. 10. The vehicle system of claim 1 including a cabinet enclosing said vehicle supported GPS system, and said cabinet connects with the vehicle ignition system to provide an enabling signal thereto for operation of the ignition system, and additionally connects to a vehicle supported I/O device for control of the vehicle supported system. 11. The system of claim 10 wherein said cabinet encloses a battery for said GPS system and comprising a battery separate from the vehicle battery. 12. The vehicle supported system of claim 10 further comprising a visual alarm forming an output of the indication that vehicle location is permitted. 13. The vehicle supported system of claim 10 further comprising the audio alarm forming an output of the indication that vehicle location is permitted. 14. The vehicle supported system of claim 10 further comprising the vehicle ignition system enabling circuit forming an engine control signal while the vehicle location is permitted. 15. The vehicle supported system of claim 1 further comprising a receiver remote from the vehicle and a transmitter, wherein the transmitter is adapted to transmit a signal to the remote receiver forming an output of the indication that vehicle location is permitted. 16. The apparatus of claim 1 wherein a computer memory for said CPU receives a closed geometric pattern electronic fence data representation stored in memory and further wherein said CPU connects with a visual indicator for the driver to indicate vehicle location within said electronic fence, and said system further comprises a connected electronic communication link to an off vehicle receiver for transmission of permitted vehicle location to the receiver remote from the vehicle. 17. The apparatus of claim 16 wherein said receiver and CPU are continuously operative to determine vehicle location in response to the GPS determining signals, and further including a continuously operative vehicle connected ignition system enabling circuit provided with a signal from said CPU so that vehicle operation continues so long as the enabling signal permits, and said vehicle ignition system is constructed and arranged to interrupt operation of the vehicle engine. 18. The apparatus of claim 17 including a vehicle electrical system forming a current flow for said ignition system. 19. The apparatus of claim 18 including a vehicle mounted keypad to open the vehicle and an operator exposed ignition switch. -------------------------------------------------------------------------------- Description -------------------------------------------------------------------------------- BACKGROUND OF THE DISCLOSURE The term GPS refers to a global position system which provides data indicating these precise whereabouts of the GPS receiver. The GPS system is a 1990's extension of the old Loran system of World War II. That system was used to provide navigational data for ships at sea, especially those between the U.S. and Europe. In modern times, the GPS system has taken advantage of satellites which are stationed in synchronous orbits in space. Effectively, the satellite does not move with respect to a specific ground location on the earth so that it effectively has the operating advantages of a very tall antenna, indeed, an antenna extending about 20,000 miles up into space. A signal is transmitted from the GPS satellite and is received by a GPS receiver and data is processed which provides an indication of the location whereabouts of the receiver. GPS systems have recently been added to automobiles. They have common use in automobiles to especially provide the location of the automobile. Through the use of the GPS satellite, the on board GPS receiver and stored data, a screen can be presented to the driver which tells the driver the location of the vehicle with respect to a stored memory entry indicative of the map of a given city, to pick an example. The streets, buildings, and obstacles of a map in a given city are loaded into a CD ROM or other memory device and that data then is used to indicate to the driver the location or whereabouts with respect to the city. Sometimes, it can be used in a control or predictive fashion. This is exemplified by the patent of Blaker, which is U.S. Pat. No. 5,790,973. That helps determine the next freeway exit, thereby signaling to the driver what exit to take to arrive at a desired destination. As a further example, the recent patent of Schreder which is U.S. Pat. No. 5,504,482 uses GPS navigation to accomplish traffic routing around traffic jams and that sort of thing. Not withstanding the use of a GPS system as a 911 protection system regarding kidnapping, all as evidenced in the patent of Fast, which is U.S. Pat. No. 5,497,149. The present disclosure sets forth an improved and enhanced system which has GPS based responses. is U.S. Pat. No. 5,497,149. The present disclosure sets forth an improved and enhanced system which has GPS based responses. In particular, the present disclosure incorporates a memory which is adapted to receive a set of grid coordinates comparable to latitude and longitude for limiting mobility of the vehicle. This could be used to confine a vehicle to a specified region. Consider as an example a typical rectangular county in the midwest where all four sides of the county are laid out as straight line segments of specific latitude and longitude. A large number of counties are defined in that fashion stretching all the way from central Texas up to the Canadian border. Counties laid out in this rectangular pattern provide an easy example. The examples given below, while easily stated in terms of arithmetic, can be extended to more complicated geographic patterns. Suffice it to say, and taking into account examples which will be given, the GPS system is used to build or define an electronic fence around a given area. This has salutary effect in the use of the vehicle. First, it is a mechanism by which theft of the vehicle is limited. Secondly, it is a system by which an authorized driver is authorized for a given area, but not for another area. In the latter instance, this will occur for vehicles which are carrying dangerous cargoes which are permitted in some areas, but not others. As another example, this will apply to a vehicle which has insurance for one geographic area, but the insurance policy is not effective for other areas. Finally, it is effective for particular drivers, for example, an older driver may be authorized for a larger area while a beginning teenager driver, will be authorized only for a specified area. The form of the electronic fence will be described in various examples given below, but it is a mechanism by which the vehicle operator is warned and subsequently the vehicle can then be shut down. The latter event is typically used to stop the vehicle as would occur on vehicle theft. In another aspect of the present disclosure, another memory is used for loading of a pattern of streets. This can be used to great advantage to keep certain vehicles off certain streets. Again, with a vehicle which is hauling a flammable cargo, certain routes are set aside for such vehicles. The GPS system of the present disclosure assists in keeping vehicles confined to the specified routes. Furthermore, it can be used for authorized delivery routes of any type of delivery vehicle. There might be a specified route for morning deliveries while a different route would be implemented for evening deliveries. Other variations can be implemented such as different delivery routes for different days of the week or for different products. After a route is driven, it may be hard to recall changes tied to the day of the week, etc. The present disclosure sets out a system which particularly enables route drivers to find their way with a variety of routes. This is also especially true when a route is changed, an example being the loss of one customer and the addition of another customer. This may change the pathway of the route significantly. This enables the route to be modified, looking at the map, thereby enabling a highly efficient route to be developed in light of distances on the map, difficulties with left turns, and so on. Moreover, the information which is provided for the driver is keyed to the date and time of day so that the route driver is assured of following the right route at the right time. Changes in routes can be accommodated dynamically during use. The present navigational system finds great benefit in a vehicle which is equipped with on board sensors to prevent burglary leading up to auto theft. While automotive alarm systems are old, the present disclosure cooperates with an alarm system which is a smart alarm system, i.e., one which shuts down the vehicle or otherwise provides alarm signals in the vehicle to protect the vehicle. The alarm system incorporated in the present disclosure provides two levels of protection. The first level of protection is protection against intrusion into the vehicle as might occur with night time theft. On the other side of the coin, the vehicle might be stolen in broad daylight, or at other times where the alarm system is not armed. This brings into play another aspect of the alarm system. If the vehicle is stolen and moved outside the permitted area, this requires transportation over the electronic fence. That can be used as a trigger to sound various and sundry alarms, giving a ten second warning, and then shutting off the ignition system. Also, it can be used to provide transmission of the vehicle whereabouts via cell phone. Examples of that will be developed below. In the alternative to that kind of interruption, an interruption using the audio and visual alarms can be implemented, forming a signal as an example to the operator to return to a specified road. Should the operator persist in driving on the wrong road or on the wrong route, then a warning can be given and the vehicle thereafter shut down after a ten or twenty second warning. The warnings have the value of shutting down the vehicle after forcing the driver to pull to the curb or to otherwise get out of the flow of traffic. This may still leave the vehicle parked illegally or obstructing traffic in some aspect, but at least it will give the vehicle driver enough time to pull to the side and get out of harm's way. There is an advantage to this, namely, that this kind of warning will enable the driver to pull to the side and to actually leave the vehicle. There is an advantage to this, should the vehicle operator be a thief, because it is desirable to let the thief pull over and get away from the vehicle. Alternately, the warning of ten seconds can be given at which time the vehicle pulls over and the doors are automatically locked, thereby holding the thief in the vehicle. The horn can then be sounded, or other warnings can be given to those in the near vicinity so that they will know that an illegal theft has occurred. Any number of steps can be undertaken depending on the on board audio and visual alarms provided with the present invention, and its cooperative connection to and triggering of door locks, window locks and so on. In another aspect of the present disclosure, the vehicle provided with the present system can be tracked. This kind of tracking system can be used to charge a mileage based depreciation account. In vehicles which are assigned to a pool, the various trips using vehicles out of the pool can be charged to individual drivers or departments involved in use of the vehicle. While this is done now commonly with company owned aircraft, it may be expedient to extend that to company owned automobiles. In another aspect of this disclosure, the system can be used to provide vehicle movement and tracking to thereby increment departmental charges for vehicle use and operation, or for insurance purposes. Some automobile leases are tied to mileage. This helps keep the driver informed of charges. This helps keep the home office informed of use, so that daily use charges can allocated if desired. These and other features and benefits result from the use of the present GPS based system. It is above all else a system which enables adaptability to be accomplished. The adaptability enables the vehicle to be protected while yet keeping track of the location of the vehicle when properly used, and especially enables interdiction of the vehicle when illegally used. The present apparatus is summarized an onboard GPS system incorporating a GPS receiver cooperative with a microprocessor or CPU. The CPU is provided with two separate memories. In typical circumstances, one memory comprises instructions defining an electronic fence. This memory is loaded with the electronic fence data so that the fence is made up of border segments which close to a defined geographic area and that fence is encoded in terms of latitude and longitude so that the GPS system can determine whether the vehicle is inside or outside the fence. A second memory is included and is preferably implemented cooperatively with a CD ROM so that a local map can be input, and specific streets are authorized on that map. While the choice may be all streets on the map, the streets also can be limited so that delivery routes are implemented, and different delivery routes can be implemented for different days or different products. The system incorporates a set of connections to door and window sensors to detect wrongful entry. This enables system control of the automobile in response to the sensors. Indeed, if a burglar attempts to enter the vehicle, an alarm can be initiated. Moreover, if a thief does get possession of the vehicle, it can be tracked and its whereabouts determined; in an interactive fashion, the vehicle can either be automatically or reactively stopped with or without warning and with or without an opportunity to lock the doors, thereby preventing the thief from escaping. The system cooperates with automobile engine and electrical ignition system, generator system and battery. This system enables proper storage of all the travels of the vehicle and whether or not they are authorized (or unauthorized) depending on the electronic fence implementation or the route implementation described above. BRIEF DESCRIPTION OF THE DRAWINGS So that the manner in which the above recited features, advantages and objects of the present invention are attained and can be understood in detail, a more particular description of the invention, briefly summarized above, may be had by reference to the embodiments thereof which are illustrated in the appended drawings. It is to be noted, however, that the appended drawings illustrate only typical embodiments of this invention and are therefore not to be. FIG. 1 is a schematic block diagram showing a GPS responsive system installed on board a car or truck to provide a display of vehicle position and to cooperate with an electronic fence or route map, or both, which are encoded into memory carried in the system of this disclosure; FIG. 2 is a side view showing a car and a tractor towing a trailer which can be equipped with the present invention; and FIG. 3 is a simplified schematic of a first route driven by the vehicle in conjunction with a second route which partly overlaps the first route, and which additionally shows the equipment available to the dispatcher including a CPU and I/O device. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT Attention is first directed to FIG. 1 of the drawings where the numeral 10 identifies the system which is located within the GPS cabinet of equipment mounted on a car, truck or other vehicle. A vehicle is represented by the line 12 as shown in FIG. 1 so that all the equipment to the left is located on or within the vehicle 12. The equipment to the right is located elsewhere and details of the locations will become more clear upon reading the present disclosure. For the moment, specific details of the vehicle including the size of the vehicle, the engine and other details regarding it will be introduced throughout the description of the GPS based system within the confines of the cabinet 10. A single cabinet is preferred, but the devices making up the present system can be scattered on the vehicle. Commonly, however, it has the form of a unified system so that it can be added as a unitized accessory. To the extent that some of the components in this apparatus have dual usage, they may be located elsewhere or they may be integrally constructed. An example of this is the cell phone which will be described in some detail hereinafter. That cell phone can be integrated in the structure or can be provided as a detachable component or can be remotely installed within the vehicle 12. The GPS system 10 of this disclosure comprises a first GPS receiver 14 and a second GPS receiver 16 which is otherwise identical. The function of the two will be noted. Effectively, both operate to receive signals from an overhead satellite which is maintained in a synchronous orbit, i.e., from the relative point of view of the Earth, the satellite stays over the same location. Several such GPS satellites are already in use and of the satellites around the Earth is controlled so that the satellites hold a steady position. They are viewed at the same latitude and longitude in the sky from a given point on the Earth. Multiple GPS satellites exist so that different regions of the Earth are illuminated by the antenna transmitted data from the GPS satellites. By various GPS satellites distributed appropriately around the world, the entire Earth is provided with GPS data which is therefore enabled to respond by locating the position of the GPS receiver. Such a receiver is incorporated at 14. Commonly, the output of the GPS receiver is defined by a coordinate system. That is normally the latitude and longitude of the target receiver. The accuracy of the GPS system is sufficient that the precise location can be determined, and this determination is made in real time in repetitive operation so the pathway or the resting position of the receiver can be determined usually within about three meters. The present apparatus utilizes a CPU 20 which is appropriately provided with input instructions through a I/O device 18, and there is a vehicle located I/O device 22 for remote entry of data and instructions. For instance, the I/O device 22 can be an external keypad for easy operation by a person outside the vehicle to open the vehicle. Some access code is entered. Also, the access code, on entry, can be used to disarm a vehicle alarm system. The alarm system is operated through the I/O device 22 which simultaneously initiates operation of the GPS system through the CPU 20. The CPU 20 outputs position in the form of latitude and longitude to a pager 24. The use of that will be noted below. The CPU operates with a schedule storage memory 26 and a separate memory 28 which enables inputting of data establishing two or more separate confining perimeters for the vehicle. The first is a surrounding electronic fence. The electronic fencewill be discussed and defined below. The second is a set of permitted (versus forbidden) streets or locations within the fence. Examples of that will also be given below. The GPS system 10 is provided with electric power by a primary battery 30 which in turn is protected with a back up battery 32. A voltage regulator 34 is connected to the vehicle battery 36. The vehicle battery 36 is provided with electric power from the vehicle electric generator 38. The battery 36 and the generator 38 together cooperate with the vehicle ignition system 40. That system responds to operation of the starter switch 42 to operate the vehicle engine 44. The ignition system 40 is enabled by a signal from the GPS to operate. Indeed, the ignition system 40 is also enabled with a signal from the security system as will be explained. It is permissible, even recommended, that the vehicle security system connect through the CPU 20 to take advantage of its availability, and thereby provide the enable signal for the car ignition system. The enable signal is routed from the CPU 20 through an ignition enable circuit 48 and is delivered through the conductor 46 to the car ignition system 40. Conveniently, the car ignition system 40 is provided with an enable switch such as a relay held in the closed position to enable current from the electrical system for the ignition system. In the event of an alarm condition by the vehicle security system, that alarm condition is sensed and the vehicle can be shut down completely. Such a shut down simply involves depriving the ignition system of electric current. By doing that, the vehicle will be stopped without electrical power for operation of the engine. While it may appear to be something of an extraneous observation, in fact the vehicle security system has enhanced value when supplemented with the GPS system of this disclosure. The supplementation is achieved by incorporating the security or alarm system with the GPS system 10. To expand on this, note the incorporation of the several sensors 50 which are connected with the CPU 20. These sensors respond to intrusion through the door, or perhaps through a window, or through vehicle motion and thereby form an alarm condition transmitted to the CPU 20. After the data is processed, one result thereof may well be shutting down the automobile by switching off electric current to the ignition system 40 so that the engine 44 will not operate. Having noted that, that virtue is worked into the GPS triggered protocols described below so that vehicle shut down can be done readily. Another aspect of the present disclosure is the incorporation of a cell phone with a built in transmitter and receiver. The phone 52 can be used optionally with a modem 54 for transmission of digital data. As needed, the cell phone 50 can be provided with a microphone 56 remote from the cell phone which is provided with an enable signal from the CPU 20. Alternately, the microphone can receive synthesized speech prompted by the CPU. Specific recorded verbal messages stored in memory can be transmitted or the speech can be synthesized by other techniques through the voice synthesizer 58. Digital transmission can be two-way so that digital data is sent through the modem 54 or received through the digital decoder 60. All of these serve as inputs and outputs to the cell phone 52. The cell phone.52 operates with a vehicle mounted cell phone antenna 62. A second antenna is included for the GPS system. The antenna 64 is typically a small antenna like the telephone antenna. Because the frequencies are relatively high, the wave length is relatively short so that the antennas are not large and therefore they are relatively inconspicuous. VEHICLE OPERATION WITH AN ELECTRONIC FENCE The present disclosure sets out a method for confining a vehicle for operation within an electronic fence. The electronic fence is implemented by storing data indicative of a border around a permitted area. Going beyond that area is prevented. For easy representation, assume that the rectangular area where the vehicle is permitted to operate is defined by four straight line segments inscribing a rectangle where the lines extend precisely on latitude and longitude lines. It is not uncommon for many of the counties of the U.S. to be inscribed in this fashion. Especially, the central U.S. is formed by regular rectangular counties where the county lines are precisely drawn north and south or east and west. Because the arithmetic can be shown rather simply, the following two equations set out the implementation of this: 1) latitude.sub.1

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