Abstract:
In order to solve a conventional problem that precision deterioration that cannot be determined by only a DOP, a positioning system is provided which comprises: a receiver for receiving signals from a plurality of positioning satellites to output data received from satellites; a satellite selector for selecting a plurality of combinations of positioning satellites to be objects of positioning calculation based on the data received from satellites to output satellite combination data; a positioning calculator for performing positioning calculation based on the data received from satellites and the satellite combination data to output positioning results thereof; a velocity detector for detecting a velocity of the positioning system to output velocity data; and a positioning output determining unit for selecting a positioning result closest to a predicted position out of the positioning results to output the positioning result as a positioning output.

Description:
This application is based on Application No. 2001-207696, filed in Japan on Jul. 9, 2001, the contents of which are hereby incorporated by reference. 
   BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates to a positioning system for receiving signals from a positioning satellite or an apparatus similar to a positioning satellite to perform the positioning thereof, and in particular, to a positioning system for performing positioning with respect to a moving object. A positioning satellite or a satellite referred to in the following description shall include an apparatus similar to a positioning satellite unless specifically described. 
   2. Description of the Related Art 
   In positioning performed by receiving signals from a positioning satellite or from an apparatus similar to the positioning satellite, one of the factors which affects the precision thereof is a satellite arrangement. A degree of influence on the precision of the satellite arrangement is called “DOP: Dilution of Precision, ” which can be calculated using schematic trajectory information of the positioning satellite. In a conventional positioning system, the DOP is generally used as an index for selecting the positioning satellite in order to use it upon positioning. This is indicated, for example, on page 93 of “Revised “Basis of GPS surveying”, Jun Tsuchiya and Hiromichi Tsuji,” Japan Association of Surveyors. 
   A conventional positioning system will now be described with reference to a drawing.  FIG. 10  is a simplified block diagram showing an example of a configuration of an N channel receiver of positioning satellite signals that forms a part of the conventional positioning system. 
   In  FIG. 10 , reference numeral  1  denotes an N channel receiver of positioning satellite signals,  81  denotes an antenna,  82  denotes an amplifier,  83  denotes a mixer,  84  denotes an IF,  85  denotes an AD converter,  86  denotes correlation detecting DLLs and  87  denotes decoders. 
   Operations of the conventional positioning system will be described next with reference to a drawing. 
   Electric waves from each positioning satellite have a substantially identical frequency. However, the electric waves can be identified by a correlator because they are not CDMA converted by particular data. Since the frequency of electric waves from each satellite is fluctuated by the Doppler effect of the like, it is necessary to follow it by the DLL. Received data of each satellite is thereafter obtained by a decoder. 
   Since a detected part can be digitized, detection circuits normally in the order of 8 channels to 16 channels can operate simultaneously to follow signals from the individual positioning satellites. Since the number of positioning satellites is larger than the number of channels of a receiver, each channel does not always follow a particular positioning satellite. Therefore, an N channel output of a receiver includes an identification number of a positioning satellite. The received data further includes a pseudo distance ρ between the positioning satellite and the receiver, trajectory parameters of the positioning satellite or the like. 
     FIG. 11  shows a method of calculating a GDOP (Geometrical DOP) that is a kind of the DOP. 
   A matrix A shown in  FIG. 11  is generally called a design matrix. Each line of the matrix A corresponds to each positioning satellite i to be used in positioning. A first row is a partial differential coefficient α i  in the x direction of a pseudo distance ρ i  that can be calculated from a signal of the positioning satellite i. Second and third rows are partial differential coefficients β i  and γ i  in the y and z directions of the same. 
   In  FIG. 11 , the design matrix has four lines, which means that a positioning calculation is performed using four satellites. In the positioning calculation, the number of positioning satellites is not limited to four. 
   The GDOP is defined by a square root of a diagonal element sum of (A T ·A) −l . Here, A T  is a transposed matrix of the matrix A, A T ·A is a product of the transposed matrix A T  and the matrix A, and (A T ·A) −1  is an inverse matrix of the matrix (A T ·A). 
   While the precision of a positioning calculation has been conventionally grasped using such indexes, degradation of the precision that cannot be determined by the DOP occurs due to quality degradation of a signal received from the each of the positioning satellites, degradation of trajectory information of each of the positioning satellites or the like. 
   The quality degradation of a signal is exemplified by the case in which a signal is not directly received from the positioning satellite but is reflected by an obstacle around the positioning satellite to be received, and the case in which, if an angle of elevation of the positioning satellite in a positioning position is low, a propagation distance in the atmosphere becomes longer to make a propagation delay larger. 
   SUMMARY OF THE INVENTION 
   The present invention has been devised in order to solve the above-mentioned problem, and it is an object of the present invention to realize a positioning system that can determine precision of a positioning calculation using an index different from the DOP. 
   A positionings system according to a first aspect of the invention comprises: a receiver for receiving signals from a plurality of positioning satellites to output data received from satellites; a satellite selector for selecting a plurality of combinations of positioning satellites to be objects of positioning calculation based on the data received from satellites to output satellite combination data; a positioning calculator for performing positioning calculation based on the data received from satellites and the satellite combination data to output positioning results thereof; and a positioning output determining unit for selecting a positioning result closest to a predicted position out of the positioning results to output the positioning result as a positioning output. As a result, there is an effect that the positioning becomes possible, which can also cope with precision degradation or the like not correlated to a DOP, and moreover, it becomes possible to generate a smooth positioning trajectory output result by performing trajectory prediction of a positioning system, whereby being capable of eliminating a sudden disturbance. 
   In a positioning system according to a second aspect of the present invention, the satellite selector includes: a satellite combination generator for generating second satellite combination data that combines the data received from satellites; a DOP calculator for calculating a DOP using the second satellite combination data based on the data received from satellites to output a DOP value; an aligning selector for aligning the plurality of DOP values to select a subset according to sizes of the values; and a combination data selecting and outputting unit for selecting a subset of outputs of the satellite combination generator using outputs of the aligning selector to output the satellite combination data. As a result, there is an effect that the positioning becomes possible, which can also cope with precision degradation or the like not correlated to a DOP, and moreover, it becomes possible to generate a smooth positioning trajectory output result by performing trajectory prediction of a positioning system, whereby being capable of eliminating a sudden disturbance. 
   In a positioning system according to a third aspect of the present invention, the positioning output determining unit includes: a positioning output selector for selecting a positioning result closest to a predicted position using the positioning results and a difference between the positioning results and the predicted position to output the positioning result as a positioning output; a trajectory predictor for predicting a trajectory of the positioning system using the positioning output to output the predicted position; and a difference calculation unit for calculating a difference between the positioning results and the predicted position. As a result, there is an effect that the positioning becomes possible, which can also cope with precision degradation or the like not correlated to a DOP, and moreover, it becomes possible to generate a smooth positioning trajectory output result by performing trajectory prediction of a positioning system, whereby being capable of eliminating a sudden disturbance. 
   In a positioning system according to a fourth aspect of the present invention, the trajectory predictor includes: a first coordinate converter for converting a coordinate system of the positioning output to a first coordinate system expressed by a latitude, a longitude and an altitude; an trajectory calculator for performing trajectory predicting calculation using a predetermined model based on the first coordinate system and outputting a predicted value of a second coordinate system expressed by a latitude, a longitude and an altitude; and a second coordinate converter for converting the predicted value of the second coordinate system to the coordinate system of the predicted position. As a result, there is an effect that the positioning becomes possible, which can also cope with precision degradation or the like not correlated to a DOP, and moreover, it becomes possible to generate a smooth positioning trajectory output result by performing trajectory prediction of a positioning system, whereby being capable of eliminating a sudden disturbance. 
   In a positioning system according to a fifth aspect of the present invention, the trajectory calculator performs trajectory predicting calculation on an assumption that the positioning system is taking a uniform acceleration motion. As a result, there is an effect that the positioning becomes possible, which can also cope with precision degradation or the like not correlated to a DOP, and moreover, it becomes possible to generate a smooth positioning trajectory output result by performing trajectory prediction of a positioning system, whereby being capable of eliminating a sudden disturbance. 
   In a positioning system according to a sixth aspect of the present invention, the positioning output determining unit includes: a plurality of positioning outputs selector for selecting a plurality of positioning results close to the predicted position using the positioning result and a difference between the positioning result and the predicted position to output them as selected outputs; a positioning output calculator for calculating a positioning position using a plurality of selected outputs of the plurality of positioning outputs selector to output it as a positioning output; a trajectory predictor for predicting a trajectory of the positioning system using the positioning output to output the predicted position; and a difference calculation unit for calculating a difference between the positioning result and the predicted position. As a result, it becomes possible to eliminate an error factor that is likely to be included in a selected one positioning result, and in addition, there is an effect that a more precise positioning result using information of a plurality of positioning satellites can be outputted by performing a calculation of a positioning output using a plurality of positioning results. 
   In a positioning system according to a seventh aspect of the present invention, the trajectory predictor includes: a first coordinate converter for converting a coordinate system of the positioning output to a first coordinate system expressed by a latitude, a longitude and an altitude; a trajectory calculator for performing a trajectory predicting calculation using a predetermined model based on the first coordinate system and outputting a predicted value of a second coordinate system expressed by a latitude, a longitude and an altitude, and at the same time outputting a predicted value of coordinate system fluctuation for predicting that a trajectory of the positioning system fluctuates from a coordinate system currently used; a second coordinate converter for converting the predicted value of the second coordinate system to the coordinate system of the predicted position; and a coordinate system updating unit for updating a coordinate system to be used in trajectory predicting calculation based on the predicted value of coordinate system fluctuation. As a result, there is an effect that a more precise positioning result using information of a plurality of positioning satellites can be outputted. 
   In a positioning system according to an eighth aspect of the present invention, the trajectory calculator performs a trajectory predicting calculation on an assumption that the positioning system is moving on a predetermined straight line. As a result, there is an effect that a more precise positioning result using information of a plurality of positioning satellites can be outputted. 
   In a positioning system according to a ninth aspect of the present invention, the coordinate system updating unit includes: a generator of coordinate system updating conversion matrix for calculating an angle deviation between each coordinate axis and a predicted trajectory using the predicted value of coordinate system fluctuation to generate a coordinate system updating conversion matrix that rotates a coordinate conversion matrix in the direction for compensating for the angle deviation; and a conversion matrix updating unit for applying the coordinate system updating conversion matrix to a present conversion matrix to update the conversion matrix. As a result, there is an effect that a more precise positioning result using information of a plurality of positioning satellites can be outputted. 
   A positioning system according to a tenth aspect of the present invention comprises: a receiver for receiving signals from a plurality of positioning satellites to output data received from satellites; a satellite selector for selecting a plurality of combinations of positioning satellites to be objects of positioning calculation based on the data received from satellites to output satellite combination data; a positioning calculator for performing positioning calculation based on the data received from satellites and the satellite combination data to output positioning results thereof; a velocity detector for detecting a velocity of the positioning system to output velocity data; and a positioning output determining unit for selecting a positioning result closest to a predicted position out of the positioning results to output the positioning result as a positioning output using the velocity data. As a result, there is an effect that the positioning becomes possible, which can also cope with precision degradation or the like not correlated to a DOP, and moreover, it becomes possible to generate a smooth positioning trajectory output result by performing trajectory prediction of a positioning system, whereby being capable of eliminating a sudden disturbance. 
   In a positioning system according to an eleventh aspect of the present invention, the satellite selector includes: a satellite combination generator for generating second satellite combination data that combines the data received from satellites; a DOP calculator for calculating a DOP using the second satellite combination data based on the data received from satellites to output a DOP value; an aligning selector for aligning the plurality of DOP values, thereby selecting a subset according to sizes of the values; and a combination data selecting and outputting unit for selecting a subset of outputs of the satellite combination generator using outputs of the aligning selector to output the satellite combination data. As a result, there is an effect that the positioning becomes possible, which can also cope with precision degradation or the like not correlated to a DOP, and moreover, it becomes possible to generate a smooth positioning trajectory output result by performing orbit trajectory prediction of the positioning system, whereby being capable of eliminating a sudden disturbance. 
   In a positioning system according to a twelfth aspect of the present invention, the positioning output determining unit includes: a positioning output selector for selecting a positioning result closest to a predicted position using the positioning results and a difference between the positioning results and the predicted position to output the positioning result as a positioning output; an trajectory predictor for predicting a trajectory of a positioning system using the positioning output and the velocity data to output the predicted position; and a difference calculation unit for calculating a difference between the positioning results and the predicted position. As a result, there is an effect that the positioning becomes possible, which can also cope with precision degradation or the like not correlated to a DOP, and moreover, it becomes possible to generate a smooth positioning trajectory output result by performing trajectory prediction of a positioning system, whereby being capable of eliminating a sudden disturbance. 
   In a positioning system according to a thirteenth aspect of the present invention, the trajectory predictor includes: a first coordinate converter for converting a coordinate system of the positioning output to a first coordinate system expressed by a latitude, a longitude and an altitude; a second coordinate converter for converting a coordinate system of the velocity data to a second coordinate system expressed by a latitude, a longitude and an altitude; a trajectory calculator for performing trajectory predicting calculation using a predetermined model based on the first and second systems of coordinates and outputting a predicted value of a third coordinate system expressed by a latitude, a longitude and an altitude; and a third coordinate converter for converting the predicted value of the third coordinate system to the coordinate system of the predicted position. As a result, there is an effect that the positioning becomes possible, which can also cope with precision degradation or the like not correlated to a DOP, and moreover, it becomes possible to generate a smooth positioning trajectory output result by performing trajectory prediction of a positioning system, whereby being capable of eliminating a sudden disturbance. 
   In a positioning system according to a fourteenth aspect of the present invention, the trajectory calculator performs the trajectory predicting calculation on an assumption that the positioning system is taking a uniform acceleration motion. As a result, there is an effect that the positioning becomes possible, which can also cope with precision degradation or the like not correlated to a DOP, and moreover, it becomes possible to generate a smooth positioning trajectory output result by performing trajectory prediction of a positioning system, whereby being capable of eliminating a sudden disturbance. 
   In a positioning system according to a fifteenth aspect of the present invention, the positioning output determining unit includes: a plurality of positioning outputs selector for selecting a plurality of positioning results close to the predicted position using the positioning result and a difference between the positioning result and a predicted position to output them as selected outputs; a positioning output calculator for calculating a positioning position using a plurality of selected outputs of the plurality of positioning outputs selector to output it as a positioning output; a trajectory predictor for predicting a trajectory of the positioning system using the positioning output and the velocity data to output the predicted position; and a difference calculation unit for calculating a difference between the positioning result and the predicted position. 
   In a positioning system according to a sixteenth aspect of the present invention, the trajectory predictor includes: a first coordinate converter for converting a coordinate system of the positioning output to a first coordinate system expressed by a latitude, a longitude and an altitude; a second coordinate converter for converting a coordinate system of the velocity data to a second coordinate system expressed by a latitude, a longitude and an altitude; a trajectory calculator for performing trajectory predicting calculation using a predetermined model based on the first and second systems of coordinates and outputting a predicted value of a third coordinate system expressed by a latitude, a longitude and an altitude, and at the same time outputting a predicted value of coordinate system fluctuation for predicting that a trajectory of the positioning system fluctuates from a coordinate system currently used; a third coordinate converter for converting the predicted value of the third coordinate system to the coordinate system of the predicted position; and a coordinate system updating unit for updating a coordinate system to be used in trajectory predicting calculation based on the predicted value of coordinate system fluctuation. As a result, there is an effect that a more precise positioning result using information of a plurality of positioning satellites can be outputted. 
   In a positioning system according to a seventeenth aspect of the present invention, the trajectory calculator performs trajectory predicting calculation on an assumption that the positioning system is moving on a predetermined straight line. As a result, there is an effect that a more precise positioning result using information of a plurality of positioning satellites can be outputted. 
   In a positioning system according to an eighteenth aspect of the present invention, the coordinate system updating unit includes: a generator of coordinate system updating conversion matrix for calculating an angle deviation between each coordinate axis and a predicted trajectory using the predicted value of coordinate system fluctuation to generate a coordinate system updating conversion matrix that rotates a coordinate conversion matrix in a direction for compensating for the angle deviation; and a conversion matrix updating unit for applying the coordinate system updating conversion matrix to a present conversion matrix to update the conversion matrix. As a result, there is an effect that a more precise positioning result using information of a plurality of positioning satellites can be outputted. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     In the accompanying drawings: 
       FIG. 1  is a block diagram showing a configuration of a positioning system in accordance with a first embodiment of the present invention; 
       FIG. 2  is a block diagram showing a configuration of a satellite selector of the positioning system in accordance with the first embodiment of the present invention; 
       FIG. 3  is a block diagram showing a configuration of a positioning output determining unit of the positioning system in accordance with the first embodiment of the present invention; 
       FIG. 4  is a block diagram showing a configuration of a trajectory predictor of the positioning output determining unit of the positioning system in accordance with the first embodiment of the present invention; 
       FIG. 5  is a diagram showing a configuration of a trajectory calculator of the trajectory predictor of the positioning output determining unit of the positioning system in accordance with the first embodiment of the present invention; 
       FIG. 6  is a block diagram showing a configuration of a trajectory predictor of a positioning output determining unit of a positioning system in accordance with a second embodiment of the present invention; 
       FIG. 7  is a diagram showing a configuration of an a trajectory calculator of the trajectory predictor of the positioning output determining unit of the positioning system in accordance with the second embodiment of the present invention; 
       FIG. 8  is a block diagram showing a configuration of a coordinate system updating unit of the trajectory predictor of the positioning output determining unit of the positioning system in accordance with the second embodiment of the present invention; 
       FIG. 9  is a block diagram showing a configuration of a positioning output determining unit of a positioning system in accordance with a third embodiment of the present invention; 
       FIG. 10  is a block diagram showing a configuration of a conventional N channel receiver of positioning satellite signals; and 
       FIG. 11  shows a method of calculating a GDOP. 
   

   DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
   First Embodiment 
   A positioning system in accordance with a first embodiment of the present invention will be described with reference to the accompanying drawings.  FIG. 1  is a block diagram showing a configuration of the positioning system in accordance with the first embodiment of the present invention. Note that, identical reference numerals denote identical or equivalent portions in each drawing. 
   In  FIG. 1 , reference numeral  1  denotes an N channel receiver of positioning satellite signals,  2  denotes a satellite selector,  3  denotes a positioning calculator,  4  denotes a velocity detector and  5  denotes a positioning output determining unit. 
   In this figure, reference numeral  6  denotes a positioning output that is an output of the positioning output determining unit  5 ,  7 - 1  to  7 -N denote pieces of data received from satellites that are N outputs of the N channel receiver of positioning satellite signals  1 ,  8 - 1  to  8 -M denote M pieces of satellite combination data selected by the satellite selector  2 ,  9  denotes velocity data that is an output of the velocity detector  4 , and  10 - 1  to  10 -M denote M positioning results corresponding to the inputs  8 - 1  to  8 -M to the positioning calculator  3 . 
     FIG. 2  is a block diagram showing a configuration of the satellite selector of the positioning system in accordance with the first embodiment. 
   In  FIG. 2 , reference numeral  11  denotes a satellite combination generator for generating pieces of satellite combination data  8  that are the data in which data received from satellites  7 - 1  to  7 -N are combined,  12  denotes a DOP calculator for calculating a DOP using the satellite combination data,  13  denotes an aligning selector for aligning a plurality of DOP values to thereby select a subset according to sizes of the values, and  14  denotes a combination data selecting and outputting unit for selecting and outputting a subset of an output of the satellite combination generator  11  using an output of the aligning selector  13 . 
   In addition, in this figure, reference numerals  15 - 1  to  15 -P denote pieces of satellite combination data that are outputs of the satellite combination generator  11 ,  16 - 1  to  16 -P denote DOP values that are outputs of the DOP calculator  12 , and  17  denotes a selection signal that is an output of the aligning selector  13 . 
     FIG. 3  is a block diagram showing a configuration of the positioning output determining unit of the positioning system in accordance with the first embodiment. 
   In  FIG. 3 , reference numeral  18  denotes a positioning output selector for selecting an optimal result out of the positioning results  10 - 1  to  10 -M to output it as a positioning output  6 ,  19  denotes an trajectory predictor in which the positioning output  6  is inputted,  20  is a predicted position that is an output of the trajectory predictor  19 , reference numerals  21 - 1  to  21 -M denote difference calculation units for calculating differences between the positioning results  10 - 1  to  10 -M and the predicted position  20 , and  22 - 1  to  22 -M denote outputs of the difference calculation units  21 - 1  to  21 -M. 
     FIG. 4  is a block diagram showing a configuration of the trajectory predictor of the positioning output determining unit of the positioning system in accordance with the first embodiment. 
   In  FIG. 4 , reference numeral  23  denotes a coordinate converter for converting a coordinate system of the positioning output  6  to a coordinate system expressed by a latitude, a longitude and an altitude,  24 - 1  to  24 - 3  denote trajectory calculators to be applied to three components of a coordinate system to be used in the trajectory predictor  19 ,  25  denotes a coordinate converter for converting a coordinate system to which the trajectory calculators  24 - 1  to  24 - 3  are applied to a coordinate system of the predicted position  20 ,  26  denotes a coordinate converter for converting a coordinate system of the velocity data  9  to a coordinate system to be used in the trajectory predictor  19 ,  27 - 1  to  27 - 3  denote positioning outputs of each coordinate component that are outputs of the coordinate converter  23 ,  28 - 1  to  28 - 3  denote predicted values of each coordinate component of the trajectory calculators  24 - 1  to  24 - 3 , and  29 - 1  to  29 - 3  denote pieces of velocity data of each coordinate component that are outputs of the coordinate converter  26 . 
     FIG. 5  is a diagram showing a configuration of the trajectory calculator of the trajectory predictor of the positioning output determining unit of the positioning system in accordance with the first embodiment. 
   In  FIG. 5 , reference numerals  30 - 1  to  30 - 4  denote memories indicating a delay of one sample time,  31 - 1  to  31 - 7  denote adders,  32 - 1  to  32 - 7  denote coefficient multipliers,  33  denotes a coefficient multiplier, and  34  denotes a coefficient  32  regulator for regulating coefficients of the coefficient multipliers  32 - 1  to  32 - 7  according to an input value. 
   On a signal line of each figure, a slash is inserted to clearly indicate that a plurality of signal lines exist. 
   Operations of the positioning system in accordance with the first embodiment will now be described with reference to the drawings. 
   As shown in  FIG. 1 , the satellite selector  2  selects a plurality of combinations of the object satellites of positioning calculation out of the data received from satellites  7 - 1  to  7 -N, which the N channel receiver of positioning satellite signals  1  received, to output the satellite combination data  8 - 1  to  8 -M. 
   The positioning calculator  3  performs positioning calculation with a list of the above-mentioned pieces of data as an object, that is, based on the data received from satellites  7 - 1  to  7 -N and the satellite combination data  8 - 1  to  8 -M to output results of the positioning calculation as the positioning results  10 - 1  to  10 -M. 
   The positioning output determining unit  5  predicts a present position of the positioning system using the past positioning output  6  and the past and the present pieces of the velocity data  9  that are outputs of the velocity detector  4 . The positioning output determining unit  5  selects a measurement result closest to the predicted position  20  out of the measurement results  10 - 1  to  10 -M to output it. 
   Operations of the satellite selector  2  will now be described in detail. 
   As shown in  FIG. 2 , the satellite combination generator  11  outputs pieces of satellite combination data  15 - 1  to  15 -P, which generate combinations of the number of satellites required for the positioning measurement, using satellite numbers (identification numbers of positioning satellites) of the data received from satellites  7 - 1  to  7 -N. The signals of the satellite combination data  15 - 1  to  15 -P are, for example, “1, 2, 3, 4” if the combination is that of satellite numbers  1  to  4 . 
   The DOP calculator  12  calculates DOPs based on satellite position information (a pseudo distance ρ between a positioning satellite and a receiver, trajectory parameters of a positioning satellite, etc.) included in the data received from satellites  7 - 1  to  7 -N with respect to the combinations to output them as the DOP values  16 - 1  to  16 -P. 
   The aligning selector  13  outputs a selection signal  17  for selecting a subset of the satellite combination data  15 - 1  to  15 -P including satellite combination data capable of obtaining an optimal positioning result based on these DOP values. This is, for example, a number list having extracted numbers of combinations selected out of combination data of 1 to P. A method of selection is to select the DOP values  16 - 1  to  16 -P included in the range of the DOP in which positioning seems to be possible and select satellite combination data corresponding to these values. 
   The combination data selecting and outputting unit  14  outputs the satellite combination data selected out of the satellite combination data  15 - 1  to  15 -P as  8 - 1  to  8 -M. 
   Operations of the positioning output determining unit  5  will now be described in detail. 
   As shown in  FIG. 3 , the trajectory predictor  19  predicts a trajectory of the positioning system using the positioning output  6  and the velocity data  9 . The difference calculation units  21 - 1  to  21 -M calculate differences between the positioning results  10 - 1  to  10 -M and the predicted position  20  that is an output of the trajectory predictor  19  to output difference calculation unit outputs  22 - 1  to  22 -M. The positioning output selector  18  selects a positioning result closest to the predicted position  20  using these values to output it as the positioning output  6 . 
   Operations of the trajectory predictor  19  will now be described. 
   It is important to select an appropriate coordinate system in predicting a trajectory.  FIG. 4  shows, as an example, the trajectory predictor  19  in the case in which a coordinate system is selected in three direction of the latitude, the longitude and the altitude on the earth. It is obviously easy to change a coordinate system. The positioning output  6  and the velocity data  9  are subjected to coordinate conversion, respectively, and are inputted in the trajectory calculator  24 - 1  to  24 - 3  corresponding to each coordinate axis. The trajectory calculator  24  performs trajectory prediction calculation using a model that seems to be necessary. 
     FIG. 5  is a block diagram showing a configuration of a trajectory calculator assuming a uniform acceleration motion. 
   As shown in  FIG. 5 , respective coordinate components  27  are coordinate components of the positioning output  6 . The velocity data  29  of each coordinate component is added to a part where a velocity component is predicted, whereby it becomes possible to capture information that cannot be obtained only from the positioning output  6  and to increase precision of the prediction. 
   The coefficient  32  regulator  34  is capable of estimating precision of the prediction by inputting an integrated value of errors between respective coordinate components  27  and respective coordinate component prediction values  28 . It becomes possible to further increase the precision of the prediction by finely tuning the coefficients of the coefficient calculator  32  of the trajectory calculator  24  based on the input. 
   As shown in  FIG. 4 , the coordinate converter  25  of the orbit trajectory predictor  19  applies coordinate conversion to each coordinate component prediction value  28 - 1  to  28 - 3 , thereby generating and outputting the predicted position  20 . 
   Since the trajectory predictor  19  predicts and calculates a positioning position at the present time in accordance with a model using the past positioning output  6  and the past and the present pieces of velocity data  9 , it is not susceptible to influence of a sudden disturbance component included in received data of the present time. In addition, predicting calculation in accordance with a model can eliminate high frequency noises. With these effects, the trajectory predictor  19  can output a smooth positioning trajectory output result. This is preferable to a user. 
   As described above, positioning calculation is performed with respect to a plurality of candidates of a satellite combination, respectively, and the positioning results and a predicted position at the time of positioning by a trajectory predicting calculation are compared to select an optimal positioning result, with the result of which high precision positioning that can cope with precision degradation not correlated to a DOP becomes possible. Moreover, since trajectory prediction of a positioning system is performed, a smooth positioning trajectory output result can be generated and a sudden disturbance can be eliminated. 
   Further, in the above-mentioned first embodiment, the positioning output determining unit  5  predicts a present position of the positioning system using the past positioning output  6  and the past and the present pieces of velocity data  9  that are outputs of the velocity detector  4  to thereby increase precision of prediction. 
   However, the present position of the positioning system can be predicted with a positioning output determining unit that uses the past positioning output  6  only without using the velocity data  9 . In this positioning output determining unit, parts of the velocity detector  4 , the coordinate converter  26  and the trajectory calculator  24  that predict a velocity component for the velocity data  9  becomes unnecessary, which may be deleted, respectively. In addition, in the trajectory calculator  24  of the positioning output determining unit  5  shown in  FIG. 5 , the positioning output determining unit using the positioning output  6  only can be realized simply by setting the coefficient of the coefficient multiplier  32 - 7  in which the velocity data  29  is inputted at zero. In this case, positioning that can cope with precision degradation or the like not correlated to a DOP also becomes possible. Moreover, since trajectory prediction of a positioning system is performed, it becomes possible to generate a smooth positioning trajectory output result and to eliminate a sudden disturbance. 
   Second Embodiment 
   A positioning system in accordance with a second embodiment of the present invention will be described with reference to the accompanying drawings. 
     FIG. 6  is a block diagram showing a configuration of a trajectory predictor of a positioning system in accordance with the second embodiment of the present invention. Note that, configurations of other units are similar to those of the above-mentioned first embodiment. 
   In  FIG. 6 , reference numeral  40  denotes a coordinate converter for converting the positioning output  6  to a coordinate system to be used in trajectory calculators  41 - 1  to  41 - 3  (a coordinate system expressed by a latitude, a longitude and an altitude),  41 - 1  to  41 - 3  denote trajectory calculators for predicting and calculating a trajectory corresponding to each coordinate component,  42  denotes a coordinate converter for converting a predicted value of each coordinate component that is an output of the trajectory calculator  41  to the predicted position  20 ,  43  denotes a coordinate converter for converting the velocity data  9  to a coordinate system used in the trajectory calculators  41 - 1  to  41 - 3  (a coordinate system expressed by a latitude, a longitude and an altitude), and  44  denotes a coordinate system updating unit for updating a coordinate system used in predicting calculation using data for predicting that a trajectory of the positioning system fluctuates from a coordinate system currently used. 
   In addition, in the figure, reference numerals  45 - 1  to  45 - 3  denote coordinate components that are outputs of the coordinate converter  40 ,  46 - 1  to  46 - 3  denote predicted values of coordinate components that are outputs of the trajectory calculator  41 ,  47 - 1  to  47 - 3  denote coordinate components that are outputs of the coordinate converter  43 ,  48 - 1  to  48 - 3  denote outputs of the trajectory calculator  41  that are predicted values of coordinate system fluctuation for predicting that a trajectory of the positioning system fluctuates from a coordinate system currently used,  49  denotes a designated value for coordinate conversion that is coordinate conversion data of the coordinate converter  40 , the coordinate converter  42  and the coordinate converter  43 , and  50  denotes an initialization signal for, when the coordinate system updating unit  44  updates the designated value of coordinate conversion  49 , notifying the trajectory calculator  41  of timing for the update. 
     FIG. 7  is a diagram showing a configuration of the trajectory calculator of the positioning system in accordance with the second embodiment. 
   In  FIG. 7 , reference numerals  51 - 1  to  51 - 4  denote memories indicating a delay of one sample time,  52 - 1  to  52 - 7  denote adders,  53 - 1  to  53 - 7  denote coefficient multipliers,  54  denotes a coefficient multiplier,  55  denotes a coefficient  53  regulator for integrating errors between each coordinate component  45  and each predicted value of coordinate component  46 , thereby determining a state of the trajectory calculator  41  to regulate a coefficient of the coefficient multipliers  53 ,  56  denotes a coefficient multiplier,  57 - 1  to  57 -K denote K memories for accumulating in time series an error between each coordinate component  45  and each predicted value of coordinate component  46 , and  58  denotes a coordinate system fluctuation predictor for calculating a steady offset variation ratio of errors using an output of the coefficient multiplier  56  and outputs of the memories of  57 - 1  to  57 -K to predict deviation of a trajectory of the positioning system and a coordinate axis used in the trajectory calculation. 
     FIG. 8  is a block diagram showing a configuration of a coordinate system updating unit of the positioning system in accordance with the second embodiment. 
   In  FIG. 8 , reference numeral  60  denotes a generator of coordinate system updating conversion matrix,  61  denotes a conversion matrix updating unit, and  62  denotes a coordinate system updating conversion matrix. 
   Operations of the positioning system in accordance with the second embodiment will now be described with reference to the drawings. 
   The trajectory calculator  41  of the second embodiment shown in  FIG. 7  is different from the trajectory calculator  24  of the first embodiment shown in  FIG. 5  in that the initialization signal  50  is inputted in the coefficient  53  regulator  55  and the coordinate system fluctuation predictor  58  exists. 
   This coefficient  53  regulator  55  increases a coefficient of the coefficient multiplier  53  for a short period of time at the time when the initialization signal  50  is inputted in order to cause the internal state of the trajectory calculator  41  to follow each coordinate component  45  at a high speed. Thus, the states of the memories  51 - 1  to  51 - 3  can reflect each coordinate component  45 . 
   The coordinate system fluctuation predictor  58  calculates a steady offset variation ratio of errors using an output of the coefficient multiplier  56  and outputs of the memories  57 - 1  to  57 -K. An error following a steady variation ratio including errors indicates a possibility that each coordinate component  45  moves on a straight line different from an assumed trajectory, that is, a coordinate axis employed by the trajectory calculator  41 . It is possible to calculate an angle deviation between a present coordinate axis and an actual trajectory by calculating this variation ratio and then using a ratio between the calculated variation ratio and a distance moved or a predicted speed. The predicted values of a coordinate system variation  48 - 1  to  48 - 3  are calculated and outputted in this way. 
   The generator for coordinate system updating conversion matrix  60  shown in  FIG. 8  calculates an angle deviation between each coordinate axis and a predicted trajectory using the predicted values of coordinate system fluctuation  48 - 1  to  48 - 3  and generates the coordinate system updating conversion matrix  62  that rotates a coordinate conversion matrix in the direction to compensate for the angle deviation. In addition, the conversion matrix updating unit  61  applies the coordinate system updating conversion matrix  62  to a present conversion matrix to update the conversion matrix. 
   If a trajectory of the positioning system is assumed to take a linear motion, it is possible to make a prediction of a trajectory more accurate by employing a coordinate system adapted to an actual trajectory. This can be explained from the fact that a difference between each coordinate component  45  and each predicted value of coordinate component  46  in the trajectory calculator  41  steadily becomes zero in the case where it is assumed that a positioning result without disturbance is obtained. When the trajectory calculator  41  employs a coordinate system different from trajectory the positioning system&#39;s trajectory, a steady error is generated on each coordinate axis. 
   Therefore, it can be expected that the trajectory predictor  19  of the second embodiment is more precise than the trajectory predictor  19  of the first embodiment. 
   As described above, since the trajectory predictor  19  performs an operation for sequentially adapting a coordinate system of trajectory calculation to an actual direction of the position system&#39;s trajectory, more precise positioning results using information of a plurality of positioning satellites can be outputted. In addition, it is also obvious that the trajectory predictor  19  of the second embodiment can be applied to the trajectory predictor  19  in a third embodiment to be described later. 
   Further, in the above-mentioned second embodiment, the positioning output determining unit  5  uses the past positioning output  6  and the past and the present pieces of velocity data  9  that are outputs of the velocity detector  4  to predict a present position of the positioning system, thereby improving precision of prediction. 
   However, a present position of the positioning system can be predicted with a positioning output determining unit that only uses the past positioning output  6  without using the velocity data  9 . In this positioning output determining unit, parts of the velocity detector  4 , the coordinate converter  43  and the trajectory calculator  41  that predict a velocity component for the velocity data  9  become unnecessary, which may be deleted, respectively. In addition, in the trajectory calculator  41  of the positioning output determining unit  5  shown in  FIG. 7 , the positioning output determining unit using the positioning output  6  only can be realized by simply setting the coefficient of the coefficient multiplier  53 - 7  in which the velocity data  47  is inputted at zero. In this case, there is an effect that positioning which can cope with precision degradation or the like not correlated to a DOP also becomes possible. Moreover, since trajectory prediction of a positioning system is performed, it becomes possible to generate a smooth positioning trajectory and to eliminate a sudden disturbance. 
   Third embodiment 
   A positioning system in accordance with the third embodiment of the present invention will be described with reference to the accompanying drawings. 
     FIG. 9  is a block diagram showing a configuration of a positioning output determining unit of the positioning system in accordance with the third embodiment of the present invention. Note that, configurations of other units are similar to those of the above-mentioned first embodiment. 
   In  FIG. 9 , reference numeral  70  denotes a plurality of positioning outputs selector for selecting a plurality of positioning results close to the predicted position  20  to output them,  71  denotes a positioning output calculator for calculating a positioning position using the plurality of selected outputs of the plurality of positioning outputs selector  70  to output it,  72 - 1  to  72 -L denote selected outputs of the plurality of positioning outputs selector  70 . 
   The third embodiment is different from the above-mentioned first embodiment in that a plurality of positioning results close to the predicted position  20  are selected instead of selecting one positioning result closest to the predicted position  20  to calculate the positioning output  6  using these values. 
   As a first example of the calculation, the positioning output calculator  71  calculates and outputs an average value of the selected outputs  72 - 1  to  72 -L. In addition, as a second example of the calculation, a root mean square value of the selected outputs  72 - 1  to  72 -L are calculated and outputted. 
   As described above, the positioning output  6  is calculated using a plurality of positioning results close to the predicted position  20 , whereby it becomes possible to eliminate an error factor that is likely to be included in a selected one positioning result. 
   In addition, since a positioning output is calculated using a plurality of positioning results, a more precise positioning result using information of a plurality of positioning satellites can be outputted. In addition, it is also obvious that the positioning output determining unit  5  of the third embodiment can be applied to the positioning output determining unit  5  of the above-mentioned second embodiment. 
   Further, in the above-mentioned third embodiment, the positioning output determining unit  5  uses the past positioning output  6  and the past and the present pieces of velocity data  9  that are outputs of the velocity detector  4  to predict a present position of the positioning system, thereby improving precision of the prediction. 
   However, a present position of the positioning system can be predicted with a positioning output determining unit that only uses the past positioning output  6  without using the velocity data  9 . In this positioning output determining unit, devices such as the velocity detector  4  relating to the velocity data become unnecessary, which may be deleted, respectively. Also in this case, as a result, there is an effect that the positioning becomes possible, which can also cope with precision degradation or the like not correlated to a DOP. Moreover, it becomes possible to generate a smooth positioning trajectory output result by performing trajectory prediction of a positioning system, whereby being capable of eliminating a sudden disturbance. 
   Thus, it is seen that a positioning system is provided. One skilled in the art will appreciate that the present invention can be practiced by other than the preferred embodiments which are presented for the purposes of illustration and not of limitation, and the present invention is limited only by the claims which follow.