# US 2014/0195151 A1 · High fidelity horizontal position error estimation for vehicular gps/dr navigation > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 2014/0195151 A1 - Document ID: US20140195151A1 - Status: Published application - Kind: A1 - Application number: 13/734,523 - Filed: 2013-01-04 - Published: 2014-07-10 - Earliest claimed: 2013-01-04 - Assignees: General Motors Corporation - Applicants: General Motors LLC - Inventors: Debo Sun; Curtis L. Hay - Web page: https://patentgrep.com/patent/US20140195151A1 ## CPC - G01C 21/165: {combined with non-inertial navigation instruments} - G01C 21/28: with correlation of data from several navigational instruments - G01C 21/30: Map- or contour-matching - G01S 19/48: by combining or switching between position solutions derived from the satellite radio beacon positioning system and position solutions derived from a further system - G01C: MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY (measuring liquid level G01F; radio navigation, determining distance or velocity by use of propagation effects, e.g. Doppler effects, propagation time, of radio waves, analogous arrangements using other waves G01S) - G01S: RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES ## Abstract A method is provided for determining an Estimated Horizontal Position Error (EHPE) with respect to a navigation system onboard a telematics-equipped vehicle by utilizing a Global Navigation Satellite System (GNSS) navigation system in combination with a dead reckoning (DR) navigation system. The method includes: receiving GNSS positioning information from the GNSS navigation system; receiving DR positioning information from the DR navigation system; applying, by a telematics unit, a Kalman filter to the GNSS positioning information and the DR positioning information; calculating, by the telematics unit, the EHPE corresponding to the navigation system onboard the telematics-equipped vehicle based on the GNSS positioning information, the DR positioning information, and the Kalman filter. ## Claims ### Claim 1 A method for determining an Estimated Horizontal Position Error (EHPE) with respect to a navigation system onboard a telematics-equipped vehicle by utilizing a Global Navigation Satellite System (GNSS) navigation system in combination with a dead reckoning (DR) navigation system, the method comprising: receiving GNSS positioning information from the GNSS navigation system; receiving DR positioning information from the DR navigation system; applying, by a telematics unit, a Kalman filter to the GNSS positioning information and the DR positioning information; calculating, by the telematics unit, the EHPE corresponding to the navigation system onboard the telematics-equipped vehicle based on the GNSS positioning information, the DR positioning information, and the Kalman filter, wherein calculating the EHPE comprises: calculating a first root mean square (RMS) value associated with the GNSS positioning information in a first direction and a second RMS value associated with the GNSS positioning information in a second direction. ### Claim 2 (depends on 1) The method of claim 1, wherein calculating the EHPE further comprises: calculating a first difference between a GNSS measurement of the vehicle location and a DR propagation measurement of the vehicle location in a first direction and a second difference between the GNSS measurement of the vehicle location and the DR propagation measurement of the vehicle location in a second direction. ### Claim 3 (depends on 2) The method of claim 2, wherein calculating the first difference and the second difference is performed according to the following formulas: Δy=(DRLat−GLat)×(M+h); and Δx=(DRLong−GLong)×(N+h)×cos(DRLat); where M is meridian radius, N is prime vertical radius, Δy is the difference in the first direction, Δx is the difference in the second direction, DRLat is a DR propagation measurement in the first direction, GLat is a GNSS measurement in the first direction, h is a GNSS measurement of altitude, DRLong is a DR propagation measurement in the second direction, and GLong is a GNSS measurement in the second direction. ### Claim 4 (canceled) ### Claim 5 (depends on 1) The method of claim 1, wherein calculating the first RMS value associated with the GNSS positioning information in the first direction and the second RMS value associated with the GNSS positioning information in the second direction is performed according to the following formulas: RMS yGPS ≈ 1 n  ∑ i = 1 n  w ^ y 2  ( i ) + M ^ y 2 ; and RMS xGPS ≈ 1 n  ∑ i = 1 n  w ^ x 2  ( i ) + M ^ x 2 ; where RMSyGPS is the first RMS value associated with the GNSS positioning information in the first direction, RMSxGPS is the second RMS value associated with the GNSS positioning information in the second direction, ŵ corresponds to noise originating from both the GNSS navigation system and the DR propagation system, {circumflex over (M)} corresponds to a constant including GNSS measurement bias and DR constant error, and n is a number of measurements. ### Claim 6 (depends on 1) The method of claim 1, wherein calculating the EHPE further comprises: calculating an error parameter in a first direction and a second direction based on the application of the Kalman filter. ### Claim 7 (depends on 6) The method of claim 6, wherein calculating the error parameter in the first direction and the second direction is performed according to the following formulas: δyk+1=(ŷk+1/k−ŷk)−(yGNSS,k+1−yGNSS,k); and δxk+1=({circumflex over (x)}k+1/k−{circumflex over (x)}k)−(xGNSS,k+1−xGNSS,k); where δyk+1 is the error parameter in the first direction, δxk+1 is the error parameter in the second direction, ŷk+1/k corresponds to a one-step prediction of position in the first direction from a step k to a step k+1, ŷk corresponds to a position estimate in the first direction at a step k, yGNSS,k+1 corresponds to a GNSS measurement of position in the first direction at a step k+1, yGNSS,k corresponds to a GNSS measurement of position in the first direction at a step k, {circumflex over (x)}k+1/k corresponds to a one-step prediction of position in the second direction, {circumflex over (x)}k corresponds to a position estimate in the second direction at a step k, xGNSS,k+1 corresponds to a GNSS measurement of position in the second direction at a step k+1, and xGNSS,k corresponds to a GNSS measurement of position in the second direction at a step k. ### Claim 8 (depends on 6) The method of claim 6, wherein calculating the EHPE further comprises: calculating a first RMS value associated with the DR positioning information in a first direction and a second RMS value associated with the DR positioning information in a second direction. ### Claim 9 (depends on 8) The method of claim 8, wherein calculating the first RMS value associated with the DR positioning information in the first direction and the second RMS value associated with the DR positioning information in the second direction is performed according to the following formulas: RMS yDR = 1 n - 1  ∑ i = 1 n - 1  δ   y i 2 ; and RMS xDR = 1 n - 1  ∑ i = 1 n - 1  δ   x i 2 ; where RMSyDR is the first RMS value associated with the DR positioning information in the first direction, RMSxDR is the second RMS value associated with the DR positioning information in the second direction, δy corresponds to the error parameter in the first direction, δx corresponds to the error parameter in the second direction, and n is a number of measurements. ### Claim 10 (depends on 8) The method of claim 8, wherein the calculated EHPE is based on the first and second RMS values associated with the DR positioning information in the first and second directions and the first and second RMS values associated with the GNSS positioning information in the first and second directions. ### Claim 11 A non-transitory computer-readable medium having computer-executable instructions stored thereon for determining an Estimated Horizontal Position Error (EHPE) with respect to a navigation system onboard a telematics-equipped vehicle by utilizing a Global Navigation Satellite System (GNSS) navigation system in combination with a dead reckoning (DR) navigation system, the computer-executable instructions, when executed by a processor, causing the following steps to be performed: receiving GNSS positioning information from the GNSS navigation system; receiving DR positioning information from the DR navigation system; applying a Kalman filter to the GNSS positioning information and the DR positioning information; calculating the EHPE corresponding to the navigation system onboard the telematics-equipped vehicle based on the GNSS positioning information, the DR positioning information, and the Kalman filter, wherein calculating the EHPE comprises: calculating a first root mean square (RMS) value associated with the GNSS positioning information in a first direction and a second RMS value associated with the GNSS positioning information in a second direction. ### Claim 12 (depends on 11) The non-transitory computer-readable medium of claim 11, wherein calculating the EHPE further comprises: calculating a first difference between a GNSS measurement of the vehicle location and a DR propagation measurement of the vehicle location in a first direction and a second difference between the GNSS measurement of the vehicle location and the DR propagation measurement of the vehicle location in a second direction. ### Claim 13 (depends on 12) The non-transitory computer-readable medium of claim 12, wherein calculating the first difference and the second difference is performed according to the following formulas: Δy=(DRLat−GLat)×(M+h); and Δx=(DRLong−GLong)×(N+h)×cos(DRLat); where M is meridian radius, N is prime vertical radius, Δy is the difference in the first direction, Δx is the difference in the second direction, DRLat is a DR propagation measurement in the first direction, GLat is a GNSS measurement in the first direction, h is a GNSS measurement of altitude, DRLong is a DR propagation measurement in the second direction, and GLong is a GNSS measurement in the second direction. ### Claim 14 (canceled) ### Claim 15 (depends on 11) The non-transitory computer-readable medium of claim 11, wherein calculating the first RMS value associated with the GNSS positioning information in the first direction and the second RMS value associated with the GNSS positioning information in the second direction is performed according to the following formulas: RMS yGPS ≈ 1 n  ∑ i = 1 n  w ^ y 2  ( i ) + M ^ y 2 ; and RMS xGPS ≈ 1 n  ∑ i = 1 n  w ^ x 2  ( i ) + M ^ x 2 ; where RMSyGPS is the first RMS value associated with the GNSS positioning information in the first direction, RMSxGPS is the second RMS value associated with the GNSS positioning information in the second direction, ŵ corresponds to noise originating from both the GNSS navigation system and the DR propagation system, {circumflex over (M)} corresponds to a constant including GNSS measurement bias and DR constant error, and n is a number of measurements. ### Claim 16 (depends on 11) The non-transitory computer-readable medium of claim 11, wherein calculating the EHPE further comprises: calculating an error parameter in a first direction and a second direction based on the application of the Kalman filter. ### Claim 17 (depends on 16) The non-transitory computer-readable medium of claim 16, wherein calculating the error parameter in the first direction and the second direction is performed according to the following formulas: δyk+1=(ŷk+1/k−ŷk)−(yGNSS,k+1−yGNSS,k); and δxk+1=({circumflex over (x)}k+1/k−{circumflex over (x)}k)−(xGNSS,k+1−xGNSS,k); where δyk+1 is the error parameter in the first direction, δxk+1 is the error parameter in the second direction, ŷk+1/k corresponds to a one-step prediction of position in the first direction from a step k to a step k+1, ŷk corresponds to a position estimate in the first direction at a step k, yGNSS,k+1 corresponds to a GNSS measurement of position in the first direction at a step k+1, yGNSS,k corresponds to a GNSS measurement of position in the first direction at a step k, {circumflex over (x)}k+1/k corresponds to a one-step prediction of position in the second direction, {circumflex over (x)}k corresponds to a position estimate in the second direction at a step k, xGNSS,k+1 corresponds to a GNSS measurement of position in the second direction at a step k+1, and xGNSS,k corresponds to a GNSS measurement of position in the second direction at a step k. ### Claim 18 (depends on 16) The non-transitory computer-readable medium of claim 16, wherein calculating the EHPE further comprises: calculating a first RMS value associated with the DR positioning information in a first direction and a second RMS value associated with the DR positioning information in a second direction. ### Claim 19 (depends on 18) The non-transitory computer-readable medium of claim 18, wherein calculating the first RMS value associated with the DR positioning information in the first direction and the second RMS value associated with the DR positioning information in the second direction is performed according to the following formulas: RMS yDR = 1 n - 1  ∑ i = 1 n - 1  δ   y i 2 ; and RMS xDR = 1 n - 1  ∑ i = 1 n - 1  δ   x i 2 ; where RMSyDR is the first RMS value associated with the DR positioning information in the first direction, RMSxDR is the second RMS value associated with the DR positioning information in the second direction, δy corresponds to the error parameter in the first direction, δx corresponds to the error parameter in the second direction, and n is a number of measurements. ### Claim 20 (depends on 18) The non-transitory computer-readable medium of claim 18, wherein the calculated EHPE is based on the first and second RMS values associated with the DR positioning information in the first and second directions and the first and second RMS values associated with the GNSS positioning information in the first and second directions.