1. A computer implemented graph data visualization apparatus comprising:
a processor, for employing graph data to generate a graphics image that includes nodes and arcs that connect said nodes; and
a display unit, for displaying said graphics image generated by said processor on a display,
wherein said processor sequentially adds and arranges nodes in a display space provided by said display unit, said processor forming an arrangement of nodes in said display space, and
wherein, each time a node is added to the arrangement of nodes, said processor corrects the positioning of the individual nodes in the arrangement, by using a predetermined dynamic model employed only for a local area wherein said added node is located, and for correcting the positions of individual nodes in the local area previously arranged in said display space, wherein all said nodes and said arcs in said graphics image becoming arranged in the display space on the display provided by said display unit displaying the image resulting from all processing.
2. The graph data visualization apparatus according to claim 1, wherein said processor performs another position correction process to correct the positions of individual nodes by using said model for a node that is added to said display for nodes that are adjacent to said added node, and for other nodes that are located within a predetermined distance of said added node, without affecting the display in entirety.
3. A physical computer program product comprising a computer readable medium having computer readable program code means embodied therein for causing data visualization on a display, the computer readable program code means in said computer program product for causing a computer to effect the functions of claim 1.
The claims below are in addition to those above.
All refrences to claim(s) which appear below refer to the numbering after this setence.
1. A method for detecting a fault in a receiver for a satellite navigation system, the method comprising:
calculating a plurality of measurement residuals corresponding to a position solution;
combining the plurality of measurement residuals to form a test statistic;
calculating a threshold corresponding to the test statistic, wherein calculating the threshold includes selecting the threshold to be a value from a non-central chi squared distribution of possible test statistics that corresponds to a desired probability of false alarm;
comparing the test statistic to the threshold; and
if the test statistic is larger than the threshold, performing at least one of:
outputting an alarm indicative of a fault in the position solution and discarding the position solution.
2. The method of claim 1, wherein calculating a threshold includes integrating over potential values for a non-centrality parameter, the non-centrality parameter corresponding to the non-central chi squared distribution of possible test statistics.
3. The method of claim 1, wherein combining the plurality of measurement residuals includes squaring each measurement residual of the plurality of measurement residuals and summing the squared measurement residuals to form the test statistic.
4. The method of claim 1, wherein a measurement residual includes a difference between a predicted range based on the position solution and an actual pseudorange measurement used to calculate the position solution.
5. The method of claim 1, wherein the threshold is selected by choosing a threshold that satisfies the equation, 1\u2212PFA=\u222b0\u221e x2 (\u03bb, N\u2212M, 0)\u222b0Tx2(x, N\u2212M,\u03bb)\u2202x\u2202\u03bb, where PFA corresponds to the probability of false alarm, \u03c7 corresponds to the distribution of possible test statistics, \u03bb corresponds to a non-centrality parameter, T corresponds to the threshold, x corresponds to the measurement residual, and M corresponds to the number of unknowns in the system.
6. The method of claim 5, wherein the equation takes into account that error in pseudorange measurements by the receiver are biased by a random amount.
7. The method of claim 1, comprising:
when the test statistic is smaller than the threshold, outputting the position solution as valid.
8. An apparatus for detecting a fault in a position solution for a satellite navigation system, the apparatus comprising:
at least one processing device;
an output device coupled to the at least one processing device;
a receiver for a satellite navigation system coupled to the at least one processing device; and
at least one memory device coupled to the at least one processing device, the at least one memory device having instructions thereon for execution by the at least one processing device, wherein the instructions, when executed by the at least one processing device, cause the at least one processing device to:
calculate a plurality of measurement residuals corresponding to a position solution of the receiver;
combine the plurality of measurement residuals to form a test statistic;
calculate a threshold corresponding to the test statistic, wherein calculate the threshold includes select the threshold to be a value from a non-central chi squared distribution of possible test statistics that corresponds to a desired probability of false alarm;
compare the test statistic to the threshold; and
if the test statistic is larger than the threshold, perform at least one of:
output an alarm from the output device, the alarm indicative of a fault in the position solution and discard the position solution.
9. The apparatus of claim 8, wherein calculate a threshold includes integrate over potential values for a non-centrality parameter, the non-centrality parameter corresponding to the non-central chi squared distribution of possible test statistics.
10. The apparatus of claim 8, wherein combine the plurality of measurement residuals includes square each measurement residual of the plurality of measurement residuals and sum the squared measurement residuals to form the test statistic.
11. The apparatus of claim 8, wherein a measurement residual includes a difference between a predicted range based on the position solution and an actual pseudorange measurement used to calculate the position solution.
12. The apparatus of claim 8, wherein the threshold is selected by choosing a threshold that satisfies the equation, 1\u2212PFA=\u222b0\u221e x2 (\u03bb, N\u2212M, 0) \u222b0T x2(x, N\u2212M,\u03bb)\u2202x\u2202\u03bb, where PFA corresponds to the probability of false alarm, \u03c7 corresponds to the distribution of possible test statistics, \u03bb corresponds to a non-centrality parameter, T corresponds to the threshold, x corresponds to the measurement residual, and M corresponds to the number of unknowns in the system.
13. The apparatus of claim 12, wherein the equation takes into account that error in pseudorange measurements by the receiver are biased by a random amount.
14. The apparatus of claim 8, wherein the instructions, when executed by the at least one processing device, cause the at least one processing device to:
when the test statistic is smaller than the threshold, output the position solution as valid from the output device.
15. A non-transitory processor-readable medium including instructions which, when executed by at least one processor, cause the at least one processor to:
calculate a plurality of measurement residuals corresponding to a position solution of the receiver;
combine the plurality of measurement residuals to form a test statistic;
calculate a threshold corresponding to the test statistic, wherein calculate the threshold includes select the threshold to be a value from a non-central chi squared distribution of possible test statistics that corresponds to a desired probability of false alarm;
compare the test statistic to the threshold; and
if the test statistic is larger than the threshold, perform at least one of: output an alarm from the output device, the alarm indicative of a fault in the position solution and discard the position solution.
16. The processor-readable medium of claim 15, wherein calculate a threshold includes integrate over potential values for a non-centrality parameter, the non-centrality parameter corresponding to the non-central chi squared distribution of possible test statistics.
17. The processor-readable medium of claim 15, wherein combine the plurality of measurement residuals includes square each measurement residual of the plurality of measurement residuals and sum the squared measurement residuals to form the test statistic.
18. The processor-readable medium of claim 15, wherein a measurement residual includes a difference between a predicted range based on the position solution and an actual pseudorange measurement used to calculate the position solution.
19. The processor-readable medium of claim 15, wherein the threshold is selected by choosing a threshold that satisfies the equation, 1\u2212PFA=\u222b0\u221e x2 (\u03bb, N\u2212M, 0) \u222b0T x2 (x, N\u2212M, \u03bb)\u2202x\u2202\u03bb, where PFA corresponds to the probability of false alarm, \u03c7 corresponds to the distribution of possible test statistics, \u03bb corresponds to a non-centrality parameter, T corresponds to the threshold, x corresponds to the measurement residual, and M corresponds to the number of unknowns in the system.
20. The processor-readable medium of claim 19, wherein the equation takes into account that error in pseudorange measurements by the receiver are biased by a random amount.