Method and apparatus for transforming overbounds

• US 8,849,569 B2
• Filed: 03/07/2007
• Issued: 09/30/2014
• Est. Priority Date: 03/08/2006
• Status: Active Grant

• Current Assignee: Airbus Defence and Space GmbH
• Original Assignee: Eads Astrium GmbH
• Inventors: Trautenberg, Hans L., Frankenberger, Harald
• Primary Examiner(s): MANCHO, RONNIE M
• Application Number:
  US11/683,195
• Publication Number:
  US 20070222669A1
• Time in Patent Office: 2,764 Days
• Field of Search: 701/214, 701/469, 701/518, 701/470, 701/517, 701/468, 701/471, 701/500, 701/512, 701/478.5, 342/357.58, 342/126, 342/357.03, 342/357.2, 342/357.22, 342/357.23, 342/357.24, 342/127
• US Class Current: 701/518
• CPC Class Codes: G01S 19/08 providing integrity information, e.g. health of satellites or quality of ephemeris data
• CPC Class Codes: G01S 19/20 Integrity monitoring, fault detection or fault isolation of space segment

Abstract

A method for determining overbounds comprises the steps of determining conservative overbounds (q_i) of at least one error (ε_i) in a first phase space, multiplying the conservative overbounds (q_i) of errors (ε_i) in the first phase space by a first parameter (θ(−x)·2) and a second parameter (θ(x)·2), and determining an upper bound for the integrity risk at the alert limit (p_w,int(AL)) in a second phase space using overbounds (q_i) of errors (ε_i) in the first phase space by the first parameter (θ(−x)·2) and the second parameter (θ(x)·2).

Claims

1. A method for determining limiting overbounds in a satellite positioning system, said method comprising the steps of:

determining overbounds (q_i(x)) of at least one error (ε

_i) in a range domain, wherein the at least one error (ε

_i) in the range domain is an error in a determination of a distance between a satellite of the satellite positioning system and a user receiver in the satellite positioning system;

separately multiplying the overbounds (q_i(x)) of errors (ε

_i) in the range domain once by a first function θ

(−

x)·

2 and another time by a second function θ

(x)·

2, wherein θ

(x) is defined as follows;

θ

(x)=1 for x≧

0 and θ

(x)=0 for x<

0, to obtain a pair of overbounds (q_iL(x) and q_iR(x)) of errors (ε

_i) in the range domain;

determining an upper bound for an integrity risk at an alert limit (p_w,int(AL)) in a position domain using the pair of overbounds (q_iL(x) and q_iR(x)) of errors (ε

_i) in the range domain; and

determining whether an error in a calculation of a position of the user receiver exceeds the upper bound for the integrity risk at the alert limit,

wherein the steps are performed by a ground system in the satellite positioning system or the user receiver in the satellite positioning system for a plurality of satellites of the satellite positioning system.

2. A non-transitory computer readable medium encoded with a program for determining limiting overbounds in a satellite positioning system, by performing the following steps:

determining overbounds (q_i(x)) of at least one error (ε

_i) in a range domain, wherein the at least one error (ε

_i) in the range domain is an error in a determination of a distance between a satellite of the satellite positioning system and a user receiver in the satellite positioning system;

separately multiplying the overbounds (q_i(x)) of errors (ε

_i) in the range domain once by a first function θ

(−

x)·

2 and another time by a second function θ

(x)·

2, wherein θ

(x) is defined as follows;

θ

(x)=1 for x≧

0 and θ

(x)=0 for x<

0, to obtain a pair of overbounds (q_iL(x) and q_iR(x)) of errors (ε

_i) in the range domain;

determining an upper bound for an integrity risk at an alert limit (p_w,int(AL)) in a position domain using the pair of overbounds (q_iL(x) and q_iR(x)) of errors (ε

_i) in the range domain; and

determining whether an error in a calculation of a position of the user receiver exceeds the upper bound for the integrity risk at the alert limit,

wherein the steps are performed by a ground system in the satellite positioning system or by the user receiver in the satellite positioning system for a plurality of satellites of the satellite positioning system.