Abstract:
Altimeters correct themselves by analysing pressure data to identify underlying climatic changes and modify sensed pressures accordingly to provide corrected altitude values. The detected underlying climatic changes are used to provide a barometer function independent of altitude changes. The climatic changes can be tropical or temperate. Various locations can be stored in the altimeter. A plot of the modified pressures can be displayed.

Description:
FIELD OF THE INVENTION 
   The present invention relates to correction of altimeters. 
   BACKGROUND TO THE INVENTION 
   Electronic and mechanical pressure-sensing altimeters are well-known. However, these devices all suffer from calibration problems when used in a mobile context. 
   Ambient air pressure changes with altitude and this phenomenon is the basis of the operation of pressure-sensing altimeters. However, this causes calibration problems for barometers which are mobile. 
   Air pressure changes by about 1 mbar per 10 m change in altitude. Air pressure changes of a few mbars per hour can also occur as a result of the movement of weather fronts. Consequently, there is a problem in distinguishing between pressure changes caused by changes in altitude and those caused by weather conditions. 
   In aviation applications, altimeters are calibrated from time to time by the aircrew using local mean sea-level pressure values received from air traffic control. However, there is no similar infrastructure for providing reference pressure values for personal devices. 
   SUMMARY OF THE INVENTION 
   It is an object of the present invention to provide an altimeter that can correct for non-height related air pressure changes. 
   According to the present invention, there is provided an altimeter, which may be implemented in a portable electronic apparatus or a personal communication device, such as a mobile phone, comprising:
         pressure sensing means;   user input means; and   processing means,   wherein the processing means is configured to:
           (a) respond to a user input by means of the user input means to start recording pressures, sensed by the pressure sensing means, together with the respective times thereof at intervals; and   (b) respond to a subsequent user input by means of the user input means to modify the recorded pressures in dependence on the difference between first and last of said recorded pressures.   
               

   Thus, the present invention corrects for changes in sensed air pressured due to factors other than altitude, wherein the initial and subsequent user inputs are performed at the same location, or at least at locations known to be at the same altitude. 
   The processing means may be configured to adjust said recorded pressures to take account of a daily pressure cycle characteristic of a tropical location before said difference is determined. This daily pressure cycle results in significant pressure changes over a relatively short time scale. The changes may be in one direction at a first time and a second direction at a time shortly afterwards. Therefore, correction in addition to a simple linear correction, based on the start and finish pressures, is required. 
   The processing means may be configured such that said modification is carried out in accordance with: 
               p   1     ⁡     (   t   )       =       p   ⁡     (   t   )       -       Δ   p   t     T             
where p′(t) is the corrected pressure at time t, p(t) is the actually or tropical-location-adjusted recorded pressure at time t and T is the total elapsed time between the initial and final pressure readings.
 
   The processing means may be responsive to the user input means to select between a tropical or a temperate mode. A memory may be included and store a list of locations and associated with respective temperate/tropical markers. The processing means may be responsive to the user input means to select between said a tropical and temperate modes on the basis of an input selecting one of the locations stored in said memory. 
   A display may be included and the processing means may be configured to respond to operation of the user input means by displaying a plot in dependence on said modified pressures. 
   According to the present invention, there is also provided a method of obtaining a record of altitude with time, the method comprising:
         starting to record air pressure and time at a start location;   continuing to record air pressure and time while moving to further locations;   returning to the start location and recording air pressure and time at the start location again;   modifying the recorded air pressures in dependence on the difference between the initial and final recorded air pressures.       

   The recorded pressures may adjusted to take account of a daily pressure cycle characteristic of a tropical location before said difference is determined. 
   The modification may be carried out in accordance with: 
               p   1     ⁡     (   t   )       =       p   ⁡     (   t   )       -       Δ   p   t     T             
where p′(t) is the corrected pressure at time t, p(t) is the actual or tropical-location-adjusted recorded pressure at time t and T is the total elapsed time between the initial and final pressure readings.
 
   A plot of the modified recorded pressure or the altitudes represented thereby may be presented. 
   A first device may be used to perform said air pressure recording and the recorded pressures transferred to a second device, which is used to modify said recorded air pressures. 
   The first device may be a personal communications device and the second device may be a computer. 
   The computer may display an image in dependence on the modified air pressures. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a block diagram of a mobile phone including a pressure sensor; 
       FIG. 2  is a state diagram representing part of the user interface of the mobile phone shown in  FIG. 1  for a first embodiment of the present invention; 
       FIGS. 3(   a ) to  3 ( h ) show the display and user interface navigation keys of the mobile phone shown in  FIG. 1  with the mobile phone in various of states shown in  FIG. 2 ; 
       FIG. 4  is a flowchart of an initial part of the sport altimeter function of the mobile phone shown in  FIG. 1  for the first embodiment of the present invention; 
       FIG. 5  is a flowchart of a timer task of the sport altimeter function of the mobile phone shown in  FIG. 1  for the first embodiment of the present invention; 
       FIG. 6  is a flowchart of an altimeter stop process of the sport altimeter function of the mobile phone in  FIG. 1  for the first embodiment of the present invention; 
       FIG. 7  shows a mobile phone communicatively connected to a computer; 
       FIG. 8  is a flowchart of an altimeter process of the mobile phone shown in  FIG. 7  for a second embodiment of the present invention; 
       FIG. 9  is a flowchart of the tropical processing step of the process shown in  FIG. 8 ; 
       FIG. 10  illustrates the daily atmospheric pressure change at a tropical location; 
       FIG. 11  is a flowchart of the temperate processing step of the process shown in  FIG. 8 ; 
       FIG. 12  is a state diagram representing part of the user interface of the mobile phone shown in  FIG. 1  for the second embodiment of the present invention; 
       FIGS. 13(   a ) to  13 ( j ) show the display and user interface navigation keys of the mobile phone shown in  FIG. 1  with the mobile phone in various of the states shown in  FIG. 12 ; 
       FIG. 14  is a flowchart of an initial part of the sport altimeter function of the mobile phone shown in  FIG. 1  for the second embodiment of the present invention; 
       FIG. 15  is a flowchart of a timer task of the sport altimeter function of the mobile phone shown in  FIG. 1  for the second embodiment of the present invention; and 
       FIG. 16  is a flowchart of an altimeter stop process of the sport altimeter function of the mobile phone in  FIG. 1  for the second embodiment of the present invention. 
   

   DESCRIPTION OF EXEMPLARY EMBODIMENTS 
   Embodiments of the present invention will now be described, by way of example, with reference to the accompanying drawings. 
   Mobile Phone 
   Referring to  FIG. 1 , a mobile phone, according to the present invention, comprises an antenna  1 , an rf subsystem  2 , a baseband DSP (digital signal processing) subsystem  3 , an analog audio subsystem  4 , a loudspeaker  5 , a microphone  6 , a controller  7 , a liquid crystal display  8 , a keypad  9 , memory  10 , a battery  11 , a power supply circuit  12  and a SIM (subscriber identity module)  13  and a solid-state pressure sensor  14 . 
   The rf subsystem  2  contains the rf circuits of the mobile phone&#39;s transmitter and receiver and a frequency synthesizer for tuning the mobile phone&#39;s transmitter and receiver. The frequency synthesizer include a variable crystal oscillator which provides a reference for the generation of other frequencies within the frequency synthesizer. The antenna  1  is coupled to the rf subsystem  2  for the reception and transmission of radio waves. 
   The baseband DSP subsystem  3  is coupled to the rf subsystem  2  to receive baseband signals therefrom and for sending baseband modulation signals thereto. The baseband DSP subsystems  3  includes codec functions which are well-known in the art. 
   The analog audio subsystem  4  is coupled to the baseband D SP subsystem  3  and receives demodulated audio therefrom. The analog audio subsystem  4  amplifies the demodulated audio and applies it to the loudspeaker  5 . Acoustic signals, detected by the microphone  6 , are pre-amplified by the analog audio subsystem  4  and sent to the baseband DSP subsystem  4  for coding. 
   The controller  7  controls the operation of the mobile phone  2 . To this end, it is coupled to the rf subsystem  2  for supplying tuning instructions to the frequency synthesizer and to the baseband DSP subsystem for supplying control data and management data for transmission. The controller  7  operates according to a program stored in the memory  10  with reference to the contents of the SIM  13 . The memory  10  is shown separately from the controller  7 . However, it may be integrated with the controller  7 . 
   The display device  8  is connected to the controller  7  for receiving control data and the keypad  9  is connected to the controller  7  for supplying user input data signals thereto. 
   The output of the pressure sensor  14  is connected to an input of the controller  7 . 
   The memory  10  contains programs, which are run by the controller  7 , to control the operation of the mobile phone. Among these programs is a program providing a sport altimeter function. 
   First Embodiment 
   Referring to  FIGS. 2 and 3(   a ), in a standby state st 1 , the mobile phone displays a legend  31 , a signal strength indicator  32 , a battery life indication  33 , a first key mode function  34  and a second key function  35 . The mobile phone&#39;s key pad  9  includes a left function key  9   a , a right function key  9   b , an up key  9   c  and a down key  9   d  for enabling a user to navigate the user interface displays. In the standby state st 1 , the legend is the a network id or some other text, the first key mode function  34  is “Menu” and the second key mode function  35  is “Names”. 
   If the user presses the left function key  9   a , when the mobile phone is in the standby state st 1 , the mobile phone moves to a messages start state st 2  ( FIG. 3(   b )). In the messages start state st 2 , the legend  31  is “Messages”, the first key mode function  34  is “Select” and the second key mode function  35  is “Exit”. In this state, if the user presses the right function key  9   b , the mobile phone returns to the standby state st 1  and, if the user presses the left function key  9   a , the mobile phone enters a first message option state (not show). 
   If the user presses up key  9   c , the mobile phone moves to an applications start state st 3  ( FIG. 3(   c )). Similarly, if the user presses the down key  9   d , the mobile phone moves to a settings state st 4 . The settings start state st 4  can also be reached by pressing the up key  9   c  when the mobile phone is in the message start state st 2  and the applications start state st 3  from the settings start state st 4  by pressing the down key  9   d.    
   As in the case of the messages start state st 2 , it is possible to return to the standby state st 1  by pressing the right function key  9   b  when the mobile phone is in either of the applications and settings start states st 3 , st 4 . 
   If the user presses the left function key  9   a  when the mobile phone is in the applications start state st 3 , the mobile phone moves to an application selection state st 5  ( FIG. 3(   d )). Pressing the up and down keys  9   c ,  9   d  when the mobile phone is in the application selection state st 5  will select different ones of the listed applications. 
   Pressing the right function key  9   b  in the application selection state st 5  returns the mobile phone to the applications start state st 3 . 
   If the user presses the left function key  9   a  when the mobile phone is in the application selection state st 5  when the “sport altimeter” option is highlighted, the mobile phone moves to a sport altimeter state st 6  ( FIG. 3(   e )). If the user presses the left function key  9   a , an options menu will be displayed, enabling the user to start the altimeter function. When the altimeter function is in operation, the legend  31  includes the current altitude, relative to the altitude when the altimeter function was started and the first key mode function  34  is labelled “Stop”. 
   Referring to  FIG. 4 , when the sport altimeter function is activated an initial pressure reading is taken (step s 1 ) and then stored with the current time (step s 2 ) in the memory  10 . The current relative altitude, i.e. 0 m, is displayed (step s 3 ) and a 15 minute timer is instantiated (step s 4 ). 
   Referring to  FIG. 5 , the task triggered by the timer comprises reading the current air pressure (step s 11 ), storing the read pressure with the current time (step s 12 ), calculating the relative altitude (step s 13 ), using the newly stored pressure and the pressure stored in step s 2 , displaying the calculated altitude (step s 14 ) ( FIG. 3(   f )) and instantiating another instance of the timer (step s 15 ). The same task is performed when the new timer, created in step s 15 , times out. 
   Referring to  FIGS. 3(   g ) and  6 , when the user presses the left function key  9   a  while the sport altimeter function is in action, the current pressure is read (step s 21 ). Then the difference between the current pressure and the initial pressure, obtained in step  1  of  FIG. 4 , is calculated (step s 22 ). This difference (Δ p ) is then used (step  23 ) to correct the rest of the stored pressures according to: 
               p   1     ⁡     (   t   )       =       p   ⁡     (   t   )       -       Δ   p   t     T             
where t is the time when the left function key  9   a  was pressed, p′(t) is the corrected pressure at time t, p(t) is the actual pressure reading at time t and T is the total elapsed time between the initial and final pressure readings.
 
   Finally, the displayed relative altitude is set to 0 m (step s 24 ). 
   Thus, if the user presses the left function key  9   a  to stop the pressure readings when the user is at their initial altitude, e.g. when they have returned to the location where the pressure readings were started, the stored pressure readings are corrected for pressure changes due to factors other than altitude. The stored pressure readings may be overwritten by the corrected reading. Alternatively, the corrected pressure readings may be stored in different locations. 
   Referring to  FIG. 3(   g ), if the user presses the left function key  9   a  to reveal an options menu, after completing the above pressure recordal and correction, the user can select a plot option which causes the mobile phone to display a plot of the user&#39;s altitude with time using the corrected pressure readings. 
   Finally, referring again to  FIG. 2 , the user can return to the application selection state st 5  by pressing the right function key  9   b  when the mobile phone is in the sport altitude state st 6 . 
   Referring to  FIG. 7 , the actual and/or corrected pressure readings can also be transferred from the mobile phone  100  to a computer  101  using conventional techniques, e.g. infrared, Bluetooth, RS232 or USB. The computer  100  may be programmed to correct actual pressure readings, as described above, and to display a plot of altitude with time based on the corrected pressure readings. 
   It has been found that in temperate regions, this linear altitude correction method can extend the usefulness of altitude measurements from 2 hours to 6 to 24 hours. 
   Second Embodiment 
   In a second embodiment, the memory  10  of the mobile phone ( FIG. 1 ) also contains city data representing a table mapping city name onto altitude and one of two modes, for example: 
   
     
       
             
             
             
             
           
             
             
             
             
             
           
             
             
             
             
           
         
             
                 
                 
             
             
                 
               City 
               Altitude 
               Mode 
             
             
                 
                 
             
           
           
             
                 
             
           
        
         
             
                 
               London 
               14 
               m 
               Temperate 
             
             
                 
               New York 
               1 
               m 
               Temperate 
             
             
                 
               Beijing 
               63 
               m 
               Temperate 
             
             
                 
               Caracas 
               909 
               m 
               Tropical 
             
             
                 
               Rio De Janeiro 
               10 
               m 
               Tropical 
             
           
        
         
             
                 
               . . . 
               . . . 
               . . . 
             
             
                 
                 
             
           
        
       
     
   
   The user can select the city, where they are currently located, using a settings function of the mobile phone. 
   In order to provide the user with an altitude value, the mobile phone monitors the ambient air pressure using the pressure sensor  14  at hourly intervals. The timing of the pressure readings is effected by a pressure read timer implemented by the controller  7 . 
   Referring to  FIG. 8 , when the pressure read timer times out, the controller  7  reads the output of the pressure sensor  14 , step s 31 , and stores the read value in the memory  10 , step s 32 . The values are stored as a 72-hour moving window. 
   The controller  7  then looks up the mode associated with the currently set city, step s 33 . 
   The controller  7  first calculates, step s 34 , an uncorrected altitude value and displays the calculated altitude, step s 35 . The uncorrected altitude, a, value is calculated according to the formula:
 
 a=a   0   +k ( p   0   −p   t )
 
where a 0  is the altitude of the currently set city, p 0  is the air pressure stored when the current city was set, p t  is the most recent air pressure value, i.e. the most recent hourly pressure reading or p 0 , if the city was set less than one hour previously and k is a constant. k is approximately 10 when p 0  and p t  are in millibars.
 
   A tropical process, step s 37 , or temperate process, step s 38 , is then performed according to the mode associated with the currently set city, step s 36 . 
   In equatorial regions, ambient air pressure follows a daily cycle as the air heats up during the day and cools down during the night. This daily cycle results in a simple barometric altimeter giving a cyclically changing altitude. In tropical and sub-tropical regions, a similar daily pattern is evident but is combined with longer term seasonal patterns. However, in both cases, the daily cycle can be used as the basis of meaningful altitude correction. Consequently, the same mode, labelled “tropical”, is used for equatorial, tropical and sub-tropical regions. 
   Referring to  FIG. 9 , in the case of the tropical process s 37 , the stored hourly air pressure averages are used to correct for the daily pressure cycle. If pressure averages are available for 72 hours, step s 41 , a sinusoidal curve is fitted to the hourly pressure averages, step s 42 . The curve is of the form:
 
 p′   0 ( t )=π 0  sin(κ( t   0   +t−τ   0 ))
 
Referring to  FIG. 10 , τ 0  will generally be a point in time before the city was set at t 0 . As a result a corrected reference air pressure, p 0 ′ at the current time, t, will be:
 
 p′   0 ( t )=π 0  sin(κ( t   0   +t−τ   0 ))
 
 p′   0 ( t )=π 0  sin(κ( t   0   +t−τ   0 ))
 
   Thus, in step s 43 , the value of p 0 ′ is calculated and then used to calculate the corrected altitude, in accordance with:
 
 a=a   0   +k ( p   0   ′−p   t )
 
   Then the corrected altitude is stored, step s 44 . However, if there is insufficient data for curve fitting at step s 41 , no corrected altitude value is stored. 
   In temperate regions, the ambient air pressure does not follow clear cyclical patterns and a different approach must be applied to correction of altitude. 
   Referring to  FIG. 11 , in the case of the temperate process s 38 , the most recent three stored hourly air pressure averages are used to correct the altitude. If pressure averages are available for three hours, step s 51 , a straight line is fitted to the hourly pressure readings, step s 52 . 
   The slope of the fitted straight line is then used, in step s 53 , to calculate a new modified reference pressure p 0   n  is calculated according to:
 
 p   0   n   =m·t·p   0   n−1  
 
where p 0   n−1  is the previous modified reference pressure or the originally sensed pressure when no modifications have yet been made, m is the slope of the line and t is the time since p 0   n−1  was established.
 
   p 0   n  then used to calculate the corrected altitude, in accordance with:
 
 a=a   0   +k ( p   0   n   −p   t )
 
   Then the corrected altitude is stored, step s 54 . However, if there is insufficient data for the line fitting at step s 51 , no corrected altitude value is stored. 
   Referring to  FIGS. 12 and 13(   a ), in a standby state st 101 , the mobile phone displays a legend  31 , a signal strength indicator  32 , a battery life indication  33 , a first key mode function  34  and a second key function  35 . The mobile phone&#39;s key pad  9  includes a left function key  9   a , a right function key  9   b , an up key  9   c  and a down key  9   d  for enabling a user to navigate the user interface displays. In the standby state st 101 , the legend is the a network id or some other text, the first key mode function  34  is “Menu” and the second key mode function  35  is “Names”. 
   If the user presses the left function key  9   a , when the mobile phone is in the standby state st 101 , the mobile phone moves to a messages start state st 102  ( FIG. 13(   b )). In the messages start state st 102 , the legend  31  is “Messages”, the first key mode function  34  is “Select” and the second key mode function  35  is “Exit”. In this state, if the user presses the right function key  9   b , the mobile phone returns to the standby state st 101  and, if the user presses the left function key  9   a , the mobile phone enters a first message option state (not show). 
   If the user presses up key  9   c , the mobile phone moves to a settings start state st 103  ( FIG. 13(   c )). Similarly, if the user presses the down key  9   c , the mobile phone moves to an altimeter start state st 104 . The altimeter start state st 104  can also be reached by pressing the up key  9   c  when the mobile phone is in an applications start state st 108 . The applications start state st 108  can be reached from the messages start state st 102  by pressing the up key  9   c  and from the altimeter start state st 104  by pressing the down key  9   d.    
   As in the case of the messages start state st 102 , it is possible to return to the standby state st 101  by pressing the right function key  9   b  when the mobile phone is in any of the settings, altimeter and applications start states st 103 , st 104 , st 108 . 
   If the user presses the left function key  9   a  when the mobile phone is in the settings start state st 103 , the mobile phone moves to a city setting start state st 105  ( FIG. 13(   d )). Pressing the up and down keys  9   c ,  9   d , when the mobile phone is in the city setting start state st 105 , will take the mobile phone to other setting start states (not shown). 
   Pressing the right function key  9   b  in the city setting start state st 5  returns the mobile phone to the settings start state st 103 . 
   If the user presses the left function key  9   a  when the mobile phone is in the city setting start state st 105 , the mobile phone moves to a city setting state st 106  ( FIG. 13(   e )) in which the user can select a city from the city data stored in the memory  10 , using the up and down keys  9   c ,  9   d , and then pressing the left function key  9   a . If the user presses the right function key  9   b , the mobile phone returns to the city setting start state st 105  and the set city remains unchanged. 
   In response to pressing of the left function key  9   a  when the mobile phone is in the city setting state st 106 , the mobile phone moves to a city storing state st 107  in which the selected city and the current sensed pressure are stored in the memory  10 . When the selected city and current pressure have been stored, the mobile phone returns to the city setting start state st 105 . 
   If the user presses the left function key  9   a  when the mobile phone is in the altimeter start state st 104 , the mobile phone moves to an altimeter state st 109  ( FIG. 13(   f )) in which the stored corrected altitude, if available, and the stored uncorrected altitude are displayed. The displayed values are those obtained by the process shown in  FIG. 8 . 
   If the user presses the left function key  9   a  when the mobile phone is in the applications start state st 108 , the mobile phone moves to an application selection state st 109  ( FIG. 13(   g )). Pressing the up and down keys  9   c ,  9   d  when the mobile phone is in the application selection state st 109  will highlight different ones of the listed applications. 
   Pressing the right function key  9   b  in the application selection state st 109  returns the mobile phone to the applications start state st 108 . 
   If the user presses the left function key  9   a  when the mobile phone is in the application selection state st 109  with the “sport altimeter” option highlighted, the mobile phone moves to a sport altimeter state st 110  ( FIG. 13(   h )). If the user presses the left function key  9   a , an options menu will be displayed, enabling the user to start the altimeter function. When the sport altimeter function is in operation, the legend  31  includes the current altitude, relative to the altitude when the altimeter function was started and the first key mode function  34  is labelled “Stop”. 
   Referring to  FIG. 14 , when the sport altimeter function is activated an initial pressure reading is taken (step s 61 ) and then stored with the current time (step s 62 ) in the memory  10 . The current altitude, determined in step s 37  or step s 38  according to the currently set city, is displayed (step s 63 ) and a 15 minute timer is instantiated (step s 64 ). 
   Referring to  FIG. 15 , the task triggered by the 15 minute timer comprises reading the current air pressure (step s 71 ), storing the read pressure with the current time (step s 72 ), calculating the altitude (step s 73 ), using the newly stored pressure and the pressure stored in step s 62  and the initially displayed altitude, displaying the calculated altitude (step s 74 ) and instantiating another instance of the timer (step s 75 ). The same task is performed when the new timer, created in step s 75 , times out. 
   Referring to  FIGS. 13(   i ) and  16 , when the user presses the left function key  9   a  while the sport altimeter function is in action, the current pressure is read (step s 81 ). 
   If (step s 82 ) the currently selected city is temperate, the difference (Δ p ) between the current pressure and the initial pressure obtained in step s 61  of  FIG. 14  is calculated (step s 83 ) simply by subtracting the earlier from the latter. However, if (step s 82 ) the currently selected city is tropical, the difference (Δ p ) is calculated by correcting the all of the pressures according to the above Tropical Equation and then subtracting the earliest from the latest (step s 83 ). 
   The calculated difference (Δ p ) is then used (step  84 ) to correct the rest of the stored pressures according to: 
               p   1     ⁡     (   t   )       =       p   ⁡     (   t   )       -       Δ   p   t     T             
where p′(t) is the corrected pressure at time t, p(t) is the actual pressure reading at time t for temperate locations and the pressure reading, corrected for daily pressure cycling, for tropical locations and T is the total elapsed time between the initial and final pressure readings.
 
   Finally, the displayed altitude is set to the altitude corresponding to the corrected final pressure (step s 85 ). 
   Thus, if the user presses the left function key  9   a  to stop the pressure readings when the user is at their initial altitude, e.g. when they have returned to the location where the pressure readings were started, the stored pressure readings are corrected for pressure changes due to factors other than altitude. The stored pressure readings may be overwritten by the corrected reading. Alternatively, the corrected pressure readings may be stored in different locations. 
   Referring to  FIG. 13(   j ), if the user presses the left function key  9   a  to reveal an options menu, after completing the above pressure recordal and correction, the user can select a plot option which causes the mobile phone to display a plot of the user&#39;s altitude with time using the corrected pressure readings and the initial altitude. 
   It has been found that in temperate regions, the linear altitude correction method can extend the usefulness of altitude measurements from 2 hours to 6 to 24 hours and a similar extension can be obtained in tropical regions using the additional correction for cyclical daily pressure changes. 
   It will be appreciated that many modification may be made to the embodiments described above. For example, the recorded and plotted values may be in units of pressure or altitude or arbitrary units because the relationship between pressure and altitude is a simple linear relationship; in other words, pressure is converted to altitude by multiplication by a constant. Also, the pressure readings may be corrected for tropical locations before they are recorded, rather than in a batch after the final pressure reading has been stored.