Patent Publication Number: US-8120530-B2

Title: Method and device for using GNSS satellite trajectory extension data in mobile apparatus

Description:
CROSS REFERENCE TO RELATED APPLICATION 
     The present application is a continuation-in-part of U.S. patent application Ser. No. 12/103,387, entitled “Method and device for predicting GNSS satellite trajectory extension data used in mobile apparatus”, filed on Apr. 15, 2008, which is entirely incorporated by reference herein. 
    
    
     TECHNICAL FIELD OF THE INVENTION 
     The present application relates to GNSS (Global Navigation Satellite System) trajectory prediction. 
     BACKGROUND OF THE INVENTION 
     For a GNSS (e.g. GPS) receiver, sensitivity is a major performance criterion. TTFF (Time to First Fix) is a representative standard for receiver sensitivity. To speed up TTFF, a technique called AGPS (Assisted Global Positioning System) is developed to promote TTFF performance. In an AGPS system, an assistant information is provided to a remote receiver so that the receiver can fix positions of satellites in a shortened period of time. An important portion of the assistant information is satellite navigation message, such as ephemeris, or satellite trajectory prediction data. The orbit determination technology and satellite trajectory prediction can be implemented by using a plenty of ranging observations from reference ground network stations, which can be simply referred to as ground observations. Practically, the processing of ground observations is complicated, thus strong calculation capability is required to execute the processing. As it is known, there must be some prediction errors existing in satellite trajectory extension, i.e. satellite trajectory predication, due to imperfect satellite trajectory prediction models. Therefore, prediction of the satellite trajectory cannot be extended unlimitedly. Currently, it is possible to predict the satellite trajectory for the up-coming 7 to 14 days. 
     For the reason mentioned above, only a device with high calculation capability such as a server is sufficient to support the satellite trajectory prediction. The server calculates the predicted satellite trajectory and passes the calculated satellite trajectory or equivalent data set to an AGPS server. Then the AGPS server provides the satellite trajectory prediction or equivalent data set to users through connection. According to the conventional schemes, it is difficult to execute the satellite trajectory prediction on a mobile apparatus such as a PDA (Personal Digital Assistant), a smart phone, a GPS apparatus or the like. Therefore, it is an object of the present invention to provide a method and a device for using GNSS satellite trajectory prediction that can be implemented and resided on a host processor, which can be embedded in a mobile apparatus. 
       FIG. 10  is a flow chart showing a conventional process of obtaining and using acquisition assistance (AA) data to acquire satellite signals. As shown, estimated time (S 1002 ), rough user position (S 1004 ) of a remote receiver and an estimated satellite position (S 1006 ) are computed based on satellite trajectory prediction such as long term orbit data at a server or obtained from the broadcast ephemeris, which is valid in two hours in general. The remote receiver then computes the AA data according to the position and time information in step S 1010 . For example, the remote receiver predicts possible Doppler shifts for the satellite in view of the remote receiver. That is, the AA data at least comprises predicted Doppler shifts for the satellite in view of the remote receiver. In GPS, each satellite has its satellite signal leave the satellite at a frequency of 1575.42 MHz. As known, the frequency of the satellite signal observed at the remote receiver will be shifted about ±4.5 KHz due to relative satellite motion. This is known as a Doppler shift. Then, a window of uncertainly range s provided for the satellite based on the AA data in step S 1020 . This window defines a certain range of the Doppler shift and a range of code phase (i.e. certain code chips of the satellite signal) for the satellite. The size of the window is determined depending on the accuracy of the estimated position and time. In step S 1030 , the remote receiver acquires the satellite signals using the AA data within the range of the window so as to avoid from searching the satellite in the widest range (i.e. all the Doppler shifts and all the code phases), which is referred to as “open sky searching”. In step S 1040 , a pseudorange, which is the time for the satellite signal flying from the satellite to the remote receiver multiplied by the speed of light, in time domain and a Doppler shift in frequency domain are computed from the acquired satellite signal. In step S 1050 , it is determined whether the number of the acquired satellites has been exceeded four. As well known in this field, to fix a position, at least four satellites must be required. If so, then the user position (i.e. the position of the remote receiver) can be fixed in step S 1060 . Otherwise, the remote receiver keeps searching (step S 1070 ), and the process goes back to step S 1020 . 
     Under a circumstance where the valid ephemeris is not available, the remote receiver needs the assistance of the server in AGPS. The server provides the necessary data about the position and time to the receiver so that the receiver can compute the AA data so as to promote the performance of TTFF. If the remote receiver fails to get in connection with the server in any manner, then the receiver cannot compute the AA data and must execute the open sky searching (ex, searching all the satellites in the open sky with all code phases and Doppler shifts.). As can be known, it takes a great period of time to do the open sky searching. This will adversely influence the TTFF. 
     SUMMARY OF THE INVENTION 
     In accordance with an aspect of the present invention, a method for using GNSS satellite trajectory in a mobile apparatus comprises steps of obtaining at least one satellite navigation message for a satellite; determining a propagating condition according to the obtained satellite navigation message; estimating a plurality of parameters of a satellite trajectory prediction model according to the propagating condition to establish an estimated satellite trajectory predication model; propagating a set of satellite trajectory extension data by using the estimated satellite trajectory prediction model, computing acquisition assistance data according to the satellite trajectory extension data; and acquiring signals of the satellite by using the acquisition assistance data. The satellite navigation message can be previously obtained from satellite broadcasting or from an external source such as a server. 
     The method of the present invention further comprises determining if a valid ephemeris for the satellite is available. The acquisition assistance data is computed according to the valid ephemeris if the valid ephemeris is available. If the valid ephemeris is not available, the acquisition assistance data is computed according to the satellite trajectory extension data as above. 
     In accordance with another aspect of the present invention, a device for using GNSS satellite trajectory in a mobile apparatus comprises an interface for obtaining at least one satellite navigation message for a satellite; and a microprocessor for determining a propagating condition according to the satellite navigation message, estimating a plurality of parameters of a satellite trajectory prediction model according to the propagating condition to establish an estimated satellite trajectory prediction model, propagating a set of satellite trajectory extension data by the estimated satellite trajectory prediction model, computing acquisition assistance data according to the satellite trajectory extension data; and acquiring signals of the satellite by using the acquisition assistance data. 
     The microprocessor further determines if a valid ephemeris for the satellite is available. The microprocessor computes the acquisition assistance data according to the valid ephemeris if the valid ephemeris is available, while computes the acquisition assistance data according to the satellite trajectory extension data if the valid ephemeris is not available. 
     The satellite trajectory predication model used in the present invention can be any proper model such as a compact force model or an adjusted orbit model. The satellite navigation message comprises broadcasting ephemeris and/or almanac as well as satellite position state vector information and/or satellite velocity vector state information. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic illustration showing a mobile apparatus having a device for predicting and using trajectory extension data in accordance with the present invention; 
         FIG. 2  is a flow chart showing a method for predicting trajectory extension data in accordance with the present invention; 
         FIG. 3  is a schematic illustration showing various satellite navigation message sources for the mobile apparatus having the device for predicting and using satellite trajectory extension data in accordance with the present invention; 
         FIG. 4  schematically shows satellite navigation message segments obtained by the host device of  FIG. 1 ; 
         FIG. 5  is a schematic diagram showing all satellite message segments of TOE( 2 ) to TOE( 2   n ) collected by the host device of  FIG. 3 ; 
         FIG. 6  is a schematic diagram showing satellite arc information obtained from satellite navigation messages such as the obtained broadcasting ephemeris of satellite PRN 01  in  FIG. 4 ; 
         FIG. 7  is a flow chart showing a compact force model scheme for propagating a set of trajectory extension data; 
         FIG. 8  is a flow chart showing an adjusted orbit model scheme for propagating a trajectory; 
         FIG. 9  is a flow chart showing a method for using satellite trajectory extension data to acquire satellite signals in accordance with the present invention; and 
         FIG. 10  is a flow chart showing a conventional process of obtaining and using acquisition assistance (AA) data to acquire satellite signals. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       FIG. 1 . is a schematic illustration showing a mobile apparatus  100  in accordance with the present invention. The mobile apparatus  100  includes an antenna or antenna set  10  for receiving GNSS satellite signals and a GNSS receiver  20  as widely known in this field. The mobile apparatus further includes a host device  30 , which can be a host part of a PDA, a mobile phone, a portable multimedia player, a GPS apparatus or the like. The host device  30  has an I/O interface  32 , an embedded microprocessor  35 , and a memory  37 . 
     Also refer to  FIG. 2 , which is a flow chart showing a method for predicting satellite trajectory extension data in accordance with the present invention. The GNSS receiver  20  collects broadcasting GNSS satellite navigation messages such as broadcasting ephemeris and/or almanac information as well as satellite position state vectors and/or satellite velocity sate vectors via the antenna  10  in step S 201 . The receiver  20  transmits the satellite navigation messages to the host device  30 . The receiver  20  may just pass the satellite navigation messages to the host device  30 , and the microprocessor  35  embedded in the host device  30  decodes the satellite navigation messages. Alternatively, the receiver  20  decodes the satellite navigation messages and passes the decoded messages to the host device  30  directly. Then, the obtained and decoded satellite navigation messages are stored in the memory  37 . Other satellite related information such as satellite geometric information, earth orientation information, coordinates transformation information, the earth potential model information (e.g. JGM3, EGM96 . . . etc.), the solar system ephemerides (e.g. JPL DE200 or DE405) and tidal models are all pre-stored in the memory  37  of the host device  30 . 
       FIG. 3  is a schematic illustration showing various satellite navigation message sources for the mobile apparatus  100 . As shown, the mobile apparatus  100  also externally obtains satellite navigation messages. In addition to broadcast ephemeris and almanac received through the antenna  10 , the host device  30  obtains information for predicting satellite trajectory extension data from an external source such as an orbit database server  50  or another mobile apparatus  110  via network or wireless communication. It is noted that the host device  30  of the mobile apparatus  100  can also predict satellite trajectory extension data based on history information saved therein. The microprocessor  35  can also check consistency between the satellite navigation messages from different sources (e.g. broadcasting ephemeris received via the antenna  10  and information from another mobile apparatus  110 ) before executing satellite trajectory extension data prediction. 
       FIG. 4  shows schematically satellite navigation message segments obtained by the host device  30  of  FIG. 1 . In this drawing, the shadowed checks indicate that the satellite navigation message segments of the corresponding time intervals are obtained.  FIG. 4  shows the broadcast ephemeris being received by the device  30 . For example, as shown, for a satellite PRN 01 , the ephemeris segments of TOE( 2 ) (i.e. ephemeris of time t 2  to t 4 ) and TOE( 2   k ) (i.e. ephemeris of time t 2k  to t 2k+2 ) are obtained. That is, satellite messages of two discrete time intervals are known. For another satellite PRN 02 , the ephemeris segments of TOE( 2   k ) and TOE( 2   n ) are obtained. As generally known, orbit accuracy of ephemeris is better than an almanac. Accordingly, only the almanac in the vicinity of time of almanac (TOA) can be used. The microprocessor  35  then can use the known satellite navigation messages to predict the extended portion of satellite trajectory. Generally, multiple discrete ephemeris segments provide more complete data set of satellite navigation messages. However, even if only one ephemeris segment is obtained, it is also possible to predict the extended trajectory. In contrast, if all ephemeris segments and/or almanac segments are known, satellite trajectory prediction can be done for a very long period with high accuracy.  FIG. 5  is a diagram schematically showing that all satellite message segments of TOE( 2 ) to TOE( 2   n ) are collected by the host device  30  of the  FIG. 3 . It is difficult to collect all satellite message segments of TOE( 2 ) to TOE( 2   n ) by host device  30  shown in  FIG. 1 . However, through the help from the additional source such as another mobile apparatus  110  or the orbit database server  50 , the host device  30  as shown in  FIG. 3  can collect all satellite message segments easily. 
     Referring to  FIG. 2 , the microprocessor  35  computes the satellite arcs one by one according to the satellite navigation messages in step S 203 . A satellite arc means a segment of the satellite trajectory within a time interval corresponding to one segment of ephemeris or almanac. As known, ephemeris is updated every two hours. If the receiver  20  is turned on at any time between time of ephemeris t 2k  to t 2k+2 , once the receiver  20  “hits” the satellite (i.e. the satellite is acquired), then the ephemeris during this period TOE( 2   k ) is obtained. That is, if ephemeris of time interval TOE( 2   k ) is received, then the satellite arc during t 2k  to t 2k+2  is obtained. 
       FIG. 6  is a schematic diagram showing satellite arc information obtained from satellite navigation messages such as obtained broadcasting ephemeris of satellite PRN 01  as shown in  FIG. 4 . Each of the solid curves indicates that the ephemeris and/or almanac during the corresponding intervals are obtained. This is called a satellite arc. The dashed curve indicates the approximated satellite trajectory. As shown, satellite arc information during intervals TOE( 2 ) (i.e. t 2  to t 4 ) and TOE( 2   k ) (i.e. t 2k  to t 2k+2 ) are known. Then, many schemes can be used to approach a set of trajectory extension data. For example, the satellite arcs of TOE( 2 ) and TOE( 2   k ) can be combined to simulate the corresponding portion of the dashed curve. A satellite arc between TOE( 2 ) and TOE( 2   k ) can be ignored here, or, if necessary, it can be extracted by an interpolation scheme. Then, by using the information, the extended satellite arc after TOE( 2   k ) can be predicted. 
     The satellite arc can be presented as PVT type (position, velocity, and time) or Keplerian element type. In orbit determination, an example taking elliptic orbits, which may be characterized by orbital elements including six Keplerian orbital elements, will be described as an example. The six Keplerian orbital elements are semi-major axis element “a” defining the size of the orbit; eccentricity element “e” defining the shape of the orbit; inclination element “i” defining the orientation of the orbit with respect to the earth equator; argument of perigee element “ω” defining where the low point, perigee, of the orbit is with respect to earth surface; right ascension of ascending node element “Ω” defining the location of the ascending and descending orbit locations with the earth&#39;s equatorial plane; and true/mean anomaly element “ν” defining where the satellite is with the orbit with respect to the perigee. Computing the Keplerian orbital elements from the position and velocity vectors can be done because there is a one-to-one correspondence between the position/velocity vectors and the Keplerian orbital elements. The present invention can use the satellite position and velocity at the epoch time or the six Keplerian orbital elements at the same epoch time for propagating the satellite trajectory extension data. 
     Referring to  FIG. 2  again, in step S 203 , the microprocessor  35  also determines a propagating condition of a satellite trajectory prediction model. Two kinds of satellite trajectory prediction models will be described as embodiments of the present invention. It is noted that the embodiments should not be taken as a limitation of the claim scope of the present invention. The first kind of satellite trajectory prediction model is called a compact force model, and the second kind is called an adjusted orbit model. 
     Equation of motion for describing a general orbit model of an artificial Earth satellite can be written as: 
                         r   ⇀     ¨     =         -   GM     ⁢       r   ⇀       r   3         +     a   ⇀         ,           (   1   )               
where the first term represents the central gravity term and {right arrow over (a)} is the total perturbing acceleration. GM is the product of the constant of gravity and the mass of the Earth, {right arrow over (r)} is position vector of the geocentric radius of the satellite. This second order differential equation system, in general, cannot be solved analytically, because the function of solution may be very complicated. Therefore, a compact perturbed force model or an adjusted orbit model with propagation algorithms have to be used. Equations for both the compact force model and the adjusted orbit model are derived from the equation (1).
 
     The compact force model or adjusted orbit model has to be estimated for each subinterval arc and for each satellite individually. Thus, steps S 205  and S 207  are executed by a sequential scheme. In step S 205 , the microprocessor  35  uses the propagating condition and satellite related information to estimate a plurality of parameters of satellite trajectory prediction model. In compact force model, the model can be parameterized by the components of perturbation forces. However, in the adjusted orbit model, orbital parameters stand for a series of unknown parameters which define the orbital equation of motion. Both situations will be described later in detail. The satellite related information such as satellite geometric information, coordinate transformation information, weight and volume of the satellite stored in a memory  37 , can be also used to optimize the parameters. 
     In step S 207 , the microprocessor  35  uses a propagator (not shown), which can be implemented by a program built in the microprocessor  35 , to propagate a set of satellite trajectory extension data by using the propagating condition and the parameters of compact force model or the adjusted orbit model. In practice, the set of satellite trajectory extension data include data of a plurality of time periods. Each time period has a time length of at least one hour. 
     In step S 209 , the microprocessor  35  checks the validity of the propagated satellite trajectory extension data. If the propagated satellite trajectory extension data are valid, the microprocessor  35  sends the propagated satellite trajectory extension data to the receiver  20  for acquiring or tracking the satellite next time in step S 211 . The satellite trajectory extension data may be converted to equivalent data and stored first, and then the satellite trajectory extension data or the equivalent data are sent to the receiver  20  at subsequent start-ups. Another advantage relates to the elimination of any error due to the trajectory data being aged when relay to the satellite. Such error can cause the deviation and difference of the extension data and true orbit. This validity check avoids aging of trajectory extension data and limiting the growth of any error. 
       FIG. 7  is a flow chart showing a compact force model scheme for propagating a set of trajectory extension data. In an embodiment of the present invention, a closer look at the perturbation term {right arrow over (a)} in the equation (1) is made and the compact force model is used to summarize the various accelerations acting on the GNSS satellite. The compact force model approximates the forces influencing trajectory of a satellite so as to propagate the satellite trajectory. The forces includes earth gravity force component F Gravity , n-body force component F N-body , solar radiation pressure component F Srad , earth radiation pressure component F Erad , ocean tide attraction component F Ocen     —     tide , solid tide attraction component F Sold     —     tide  and relative gravity component F relat . In the compact force model, equation (1) is varied as: 
                       r   ⇀     ¨     =         -   GM     ⁢       r   ⇀       r   3         +       a   ⇀       N   -   bod       +       a   ⇀     Srad     +       a   ⇀     Erad     +       a   ⇀     Ocean_tide     +       a   ⇀     Sold_tide     +       a   ⇀     relat     +   …             (   2   )               
These force components are indicated by acceleration components in equation (2). For more precise numerical approximation, the entire propagating interval [t 0 , t f ] is divided into subintervals of a user-specified length. First in step S 702 , at least one satellite arc is computed from the obtained satellite navigation messages. Then, a propagating condition is determined according to the known satellite arc in step S 705 . That is, a satellite position is selected. In the first subinterval, the propagating condition is derived from one of the satellite positions selected from the computed satellite arcs, which are determined in step S 203  or S 702 . In any one of the subsequent intervals, the propagating condition is derived from the approximated solution of the previous subinterval. In another embodiment of the present invention, the microprocessor  35  can just only compute one satellite position from the collected satellite navigation messages as the propagating condition, instead of computing the entire satellite arc corresponding to the satellite navigation messages.
 
     The force components corresponding to the selected satellite position are used to estimate a plurality of parameters of compact force model F(X*, t i ) in step S 710 , where the X* can be substituted by the six Keplerian elements, for example, at the reference epoch t k . In addition, the parameters of compact force model, such as force components, are estimated also with consideration of satellite related information including satellite geometric information and transformation information such as earth orientation factors and coordinates transforms between the celestial and terrestrial system. Then an equation of motion  {dot over (X)} *=F(X*, t) is generated in step S 730 . The equation of motion is propagated by a propagator (step S 740 ) to generate a segment of satellite trajectory extension data X*(t i+1 ) in step S 750 . The segment of satellite trajectory extension data X*(t i+1 ) indicates the trajectory from the time t i  to time t i+1 . Then the microprocessor  35  checks if the epoch t i+1  is the final epoch t f  of a predetermined period of time (step S 760 ). If not, the microprocessor  35  sets i=i+1 in step S 765 . That is, the microprocessor  35  is to compute the next segment of satellite trajectory extension data. After all segments of satellite trajectory extension data during the predetermined period of epoch to t 0  t f  are propagated, the entire extended satellite trajectory X*(t) is obtained (step S 770 ). The displacement equation of motion X*(t) in S 750  is an approximation of the satellites orbit or trajectory around the earth. Thus, the X*(t) is actually a reference trajectory. For a concern of fast computing, the reference trajectory is utilized in short-term trajectory extension. Otherwise, the reference trajectory is utilized to predict a longer and more accurate extension by adjusting the model algorithm. 
     The microprocessor  35  can start to compute the extended trajectory once the required information is sufficient. For example, if the receiver  20  receives the broadcast satellite navigation messages only for a while, the microprocessor  35  can compute the satellite trajectory extension data for an extended trajectory section even the receiver  20  loses connection with satellite signals later. If additional satellite information is input, the microprocessor  35  re-computes the extended trajectory. As mentioned, the microprocessor  35  may compute the satellite trajectory extension data base on old data stored therein. 
     As mentioned, in addition to compact force model, the adjusted orbit model may also be used to predict the satellite trajectories.  FIG. 8  is a flow chart showing an adjusted orbit model scheme for propagating a trajectory. An orbit in general sense is a unique (particular) solution of orbital equation of motion. The adjusted orbit model uses a series of unknown orbital parameters to define the satellite trajectory, which describes the motion of the satellite. The orbital parameters are defined as n parameters including the six Keplerian orbital elements of the orbits and additional dynamic parameters. In the adjusted orbit model, the additional dynamic parameters q m  describe the additional perturbed accelerations acting on the GNSS satellite. For the adjusted orbit model, equation (1) is varied as: 
                       r   ⇀     ¨     =         -   GM     ⁢       r   ⇀       r   3         +       a   ⇀     ⁡     (     a   ,   e   ,   i   ,   Ω   ,   w   ,   u   ,     q   1     ,     q   2     ,   …   ⁢           ,     q   m       )                 (   3   )               
where the unknown parameters {p i }={a, e, i, Ω, w, u, q 1 , q 2 , . . . , q m } may define the particular solution of orbit {right arrow over (r)}(t). The six Keplerian elements (or corresponding position and velocity state vectors) at time t 0  are defined from the propagating condition.
 
     As mentioned previously, the additional parameters q m  given in equation (3) are those dynamic parameters which have to be estimated for each arc and each individual satellite in order to obtain a reliable orbital fit. For example, in GNSS orbit determination, the additional dynamic parameters can be defined as the additional perturbed accelerations and/or harmonic periodic accelerations (sine and cosine terms) acting on the GNSS satellite. In advanced orbit determination, a user may wish to parameterize the orbits additionally with other stochastic parameters to improve the orbit quality. 
     As shown in  FIG. 8 , the satellite arc information is obtained from satellite navigation messages such as broadcasting ephemeris and/or almanac (step S 805 ). The microprocessor  35  then defines the propagating condition for the orbital parameters according to the satellite arc information (step S 810 ). In step S 820 , the microprocessor  35  executes orbit determination based on the propagating condition and solves the orbital parameters, which are derived from equation (3). The parameters of the satellite trajectory prediction model are estimated also with consideration of satellite related information including satellite geometric information and transformation information such as earth orientation factors and coordinates transforms between the celestial and terrestrial system. In step S 830 , the microprocessor  35  checks if the solved satellite arc fit the computed satellite arc from the obtained satellite navigation messages. If not, the procedure goes back to step S 810  to adjust the model, that is, to adjust the parameters. The above procedure runs again. If it is determined as good fit, then the propagation of the set of trajectory extension data is executed in step S 850  by the propagator (not shown). The propagation is implemented by numerical integration, for example. Then, the entire set of trajectory extension data X*(t 0 :t f ) is obtained in step S 860 . 
     According to the present invention, the satellite trajectory prediction can be done in the microprocessor  35 , of which the calculation capability is not so strong as a PC, in the host device  30  even when the receiver  20  coupled to or incorporated with the host device  30  is disconnected with the satellite signals. 
       FIG. 9  is a flow chart showing a method for using satellite trajectory extension data to acquire satellites in accordance with an embodiment of the present invention. In this example, a mobile apparatus having the function of satellite predicting trajectory extension (e.g. the mobile apparatus  100  described above) may work in two modes. In a first mode, a valid broadcast ephemeris is received, and the ephemeris is used to compute acquisition assistance (AA) data. In a second mode, the valid ephemeris or other equivalent information is not available. Under such a circumstance, the mobile apparatus  100  uses satellite trajectory extension data created by the mobile apparatus  100  per se to compute the AA data. The details will be further described as follows. However, in another embodiment, the mobile apparatus  100  can always use satellite trajectory extension data created by the mobile apparatus  100  per se to compute the AA data even if the valid ephemeris data is available. 
     Please refer to  FIG. 9  and also  FIG. 1 . The mobile apparatus  100  shown in  FIG. 1  is described herein as an example. The mobile apparatus  100  attempts to fix the position thereof. If the mobile apparatus  100  is able to receive a broadcast ephemeris, which is usually valid within two hours, of a satellite, the received broadcast ephemeris is imported to the microprocessor  35  of the host device  30  (step S 910 ). In step S 915 , the received broadcast ephemeris is checked to see whether it is in the valid period or not. In general, the valid period of a broadcast ephemeris is two hours. If the ephemeris is valid, and then the ephemeris is used to determine estimated time and position (and velocity) of the satellite as well as a rough position of the mobile apparatus  100  in step S 940 . The data obtained in step S 940  are used to compute AA data in step S 950 . In step S 970 , the AA data is used to assist acquisition of satellite signals. 
     In step S 915 , if it is determined that the ephemeris is not valid (e.g. the broadcast ephemeris is expired) or even the ephemeris is not available, the satellite trajectory extension data, which is extended in the mobile apparatus  100  per se as described above or equivalent data are used. The process goes to step S 930 . The details will be further described as follows. 
     In step S 921 , satellite navigation messages are obtained. Herein the satellite navigation messages can be any kind of satellite navigation messages, such as almanac, ephemeris (expired or not) or relevant data received from other external sources. In this case, those data are previously received and stored in the mobile apparatus  100 . As mentioned, history information obtained from old acquisitions, for example, saved in the mobile apparatus  100  can also be used. In step S 923 , a propagating condition is determined according to the obtained satellite navigation messages. In step S 925 , a satellite trajectory prediction model is selected, and parameters of this model are estimated according to the propagating condition so as to establish an estimated satellite trajectory prediction model based on the selected satellite trajectory prediction model and the parameters. In step S 927 , the microprocessor  35  propagates a set of satellite trajectory extension data by using the estimated satellite trajectory prediction model. In step S 930 , the microprocessor  35  extracts the satellite trajectory extension data or equivalent data derived from the satellite trajectory extension data. In step S 935 , it is further checked whether those data are available and valid. If not, a flag indicates that the satellite trajectory extension data are not available is set in step S 960 . Otherwise, the satellite trajectory extension data propagated by the mobile apparatus  100  per se are used to determine the estimated time and position of the satellite as well as the user&#39;s rough position (i.e. the rough position of the mobile apparatus  100 ) (S 940 ). The data obtained in step S 940  are used to compute AA data in step S 950 . In step S 970 , the AA data is used to assist acquisition of satellite signals. 
     While the preferred embodiments of the present invention have been illustrated and described in detail, various modifications and alterations can be made by persons skilled in this art. The embodiment of the present invention is therefore described in an illustrative but not restrictive sense. It is intended that the present invention should not be limited to the particular forms as illustrated, and that all modifications and alterations which maintain the spirit and realm of the present invention are within the scope as defined in the appended claims.