Calibration of positioning systems

• US 6,957,072 B2
• Filed: 05/03/2001
• Issued: 10/18/2005
• Est. Priority Date: 05/03/2000
• Status: Expired due to Fees

• Current Assignee: Telefonaktiebolaget LM Ericsson
• Original Assignee: Telefonaktiebolaget LM Ericsson
• Inventors: Fischer, Sven, Kangras, Ari
• Primary Examiner(s): Trinh, Sonny
• Assistant Examiner(s): Torres, Marcos L.
• Application Number:
  US09/847,357
• Publication Number:
  US 20020016172A1
• Time in Patent Office: 1,629 Days
• Field of Search: 455/456.1, 455/456.2, 455/456.5, 455/456.6, 342/450, 342/457, 342/350, 342/357.01, 342/357.02, 342/357.1
• US Class Current: 455/456.1
• CPC Class Codes: G01S 5/021 Calibration, monitoring or correction G01S5/0252 takes precedence
• CPC Class Codes: G01S 5/0242 Determining the position of transmitters to be subsequently used in positioning G01S5/0289 takes precedence
• CPC Class Codes: G01S 5/0244 Accuracy or reliability of position solution or of measurements contributing thereto
• CPC Class Codes: H04W 64/00 Locating users or terminals or network equipment for network management purposes, e.g. mobility management

Abstract

Mobile station positioning methods are calibrated using an error bias estimation for refining the determination of the mobile station location which does not require any added hardware to the telecommunications system. The position of the mobile station is calculated assuming no bias errors and a first order approximation of the mobile station position is derived as a function of the bias error. The bias error is then estimated and used to refine the previously calculated mobile station position.

Claims

1. A method of calibrating a mobile station location system in a cellular telecommunications network, the method comprising the steps of:

determining a position (z_k0) of a mobile station in the telecommunications network assuming no bias error;

deriving, concurrently, an approximation of the position (z_k) of a k_th mobile station as a function of an n-dimensional vector (b) of unknown biases according to a calibration bias estimation equation $\begin{array}{c}b=<br><br>b_0-\{\underset{k=1}{\overset{N}{\sum <br><br>}}<br><br>H_k^T<br><br>P_k^{-1}<br><br>H_k-\\ {<br><br>\underset{k=1}{\overset{N}{\sum <br><br>}}<br><br>\left(H_k^T<br><br>P_k^{-1}<br><br>{G_k<br><br>\left(G_k<br><br>P_k^{-1}<br><br>G_k\right)}^{-1}<br><br>G_k^T<br><br>P_k^{-1}<br><br>H_k\right)\}}^{-1}\\ <br><br>\left(\underset{k=1}{\overset{N}{\sum <br><br>}}<br><br>H_k^T<br><br>P_{k-1}<br><br>\left(Y_k-r<br><br>\left(z_{\mathrm{k0}},b_0\right)\right)\right)\end{array}$

wherein b is an updated estimate of b₀, b₀ is the apriori value of a bias vector, Y_k is a generic m-dimensional measurement related to the k_th mobile station, z_k is the position of the k_th mobile station represented by the column vector (xy), H_k is a derivative of r(z,b) with respect to bias and G_k is a derivative of the function of r(z,b) with respect to position; and

refining the position (z_k0) of the mobile station, using the updated estimate of b, according to the equation

Y_k=r(z_k,b)+e_k

where k=1, . . . ,N, and e_k is an additive noise term with covariance P_k.

2. The method of claim 1, wherein the step of deriving an approximation of the position (z_k) of a k_th mobile station as a function of an n-dimensional vector (b) of unknown biases further comprises the step of

selecting zhd k to minimize loss function V(z_k,b₀), wherein z_k0 satisfies V′

(z_k0,b₀)=0.

3. The method of claim 2 wherein the n-dimensional vector (b) is calculated for multiple mobile stations.

4. The method of claim 3, wherein the calculated value of b of the multiple mobile stations is fed to a position calculation function (PCF) for improving the accuracy of the bias parameters used for determining a refined position of a target mobile station.

5. The method of claim 4, further comprising the steps of

sending the calculated value of b of the multiple mobile stations to a timing calibration function and the position (z_k0) of the mobile station to the position calculation function;

the timing calibration function performing calibration bias estimation; and

forwarding the results to the position calculation function for inclusion in computing the refined position of the target mobile station.

6. The method of claim 1 wherein the mobile station location system is a time of arrival mobile station location system.

7. The method of claim 1 wherein the mobile station location system is an angle of arrival mobile station location system.

8. The method of claim 1, further comprising the step of the mobile station performing the necessary measurements for computing the original estimate of the position of the mobile station.

9. A system for calibrating a mobile station location system in a cellular telecommunications network, the system comprising:

means for determining a position (z_k0) of a mobile station in the telecommunications network assuming no bias error;

means for deriving, concurrently, an approximation of the position (z_k) of a k_th mobile station as a function of an n-dimensional vector (b) of unknown biases according to a calibration bias estimation equation $\begin{array}{c}b=<br><br>b_0-\{\underset{k=1}{\overset{N}{\sum <br><br>}}<br><br>H_k^T<br><br>P_k^{-1}<br><br>H_k-\\ {<br><br>\underset{k=1}{\overset{N}{\sum <br><br>}}<br><br>\left(H_k^T<br><br>P_k^{-1}<br><br>{G_k<br><br>\left(G_k<br><br>P_k^{-1}<br><br>G_k\right)}^{-1}<br><br>G_k^T<br><br>P_k^{-1}<br><br>H_k\right)\}}^{-1}\\ <br><br>\left(\underset{k=1}{\overset{N}{\sum <br><br>}}<br><br>H_k^T<br><br>P_{k-1}<br><br>\left(Y_k-r<br><br>\left(z_{\mathrm{k0}},b_0\right)\right)\right)\end{array}$

wherein b is an updated estimate of b₀,b₀ is the apriori value of a bias vector, Y_k is a generic m-dimensional measurement related to the k_th mobile station, z_k is the position of the k_th mobile station represented by the column vector (xy), H_k is a derivative of r(z,b) with respect to bias and G_k is a derivative of the function of r(z,b) with respect to position; and

means for refining the position (z_k0) of the mobile station using the updated estimate of b, according to the equation

Y_k=r(z_k,b)+e_k

where k=1, . . . ,N, and e_k is an additive noise term with covariance P_k.

10. The system of claim 9, wherein the means for deriving an approximation of the position (z_k) of a k_th mobile station as a function of an n-dimensional vector (b) of unknown biases further comprises

means for selecting z_k to minimize loss function designated V(z_bb₀), wherein z_k0 satisfies V′

(z_k0,b₀)=0.

11. The system of claim 10 wherein the n-dimensional vector (b) is calculated for multiple mobile stations.

12. The system of claim 11, further comprising means for sending the calculated value of b of the multiple mobile stations to

a position calculation function (PCF) for improving the accuracy of the bias parameters used for determining the refined position of a target mobile station.

13. The system of claim 12, further comprising:

means for sending the calculated value of b of the multiple mobile stations to a timing calibration function and for sending the position (z_k0) of the mobile station to the position calculation function;

the timing calibration function performing calibration bias estimation and forwarding the results to the position calculation function for inclusion in computing the refined position of the target mobile station.

14. The system of claim 9 wherein the mobile station location system is a time of arrival mobile station location system.

15. The system of claim 9 wherein the mobile station location system is an angle of arrival mobile station location system.

16. The system of claim 9, wherein the mobile station performs the necessary measurements for computing the original estimate of the position of the mobile station.