TDOA Localization Using ClosedForm Solution

Reference: Y. T. Chan and K. C. Ho, "A simple and efficient estimator for hyperbolic location," IEEE Trans. Signal Process., vol. 42, pp. 19051915, Aug. 1994.
Solution: TDOALoc
CRLB: TDOALocCRLB
Example: Example
TDOA and FDOA Localization in ClosedForm, Moving Source and Sensors

Reference: K. C. Ho and W. Xu, "An accurate algebraic solution for moving source location using TDOA and FDOA measurements," IEEE Trans. Signal Process., vol. 52, pp. 24532463, Sept. 2004.
Solution: TDOAFDOALocMvgSrcSen
CRLB: TDOAFDOALocMvgSrcSenCRLB
Example: Example
TDOA Localization in ClosedForm With Sensor Position Errors, Stationary Source and Sensors

Reference: K. C. Ho, X. Lu and L. Kovavisaruch, "Source localization using TDOA and FDOA measurements in the presence of receiver location errors: analysis and solution," IEEE Trans. Signal Process., vol. 55, pp. 684696, Feb. 2007.
Solution: TDOALocStnySenPosErr
CRLB: TDOALocStnySenPosErrCRLB
Example: Example
TDOA and FDOA Localization in ClosedForm With Sensor Position Errors, Moving Source and Sensors

Reference: K. C. Ho, X. Lu and L. Kovavisaruch, "Source localization using TDOA and FDOA measurements in the presence of receiver location errors: analysis and solution," IEEE Trans. Signal Process., vol. 55, pp. 684696, Feb. 2007.
Solution: TDOAFDOALocMvgSenPosErr
CRLB: TDOAFDOALocMvgSenPosErrCRLB
Example: Example
TDOA Localization in ClosedForm With Sensor Position Errors and a Calibration Emitter

Reference: K. C. Ho and L. Yang, "On the use of a calibration emitter for source localization in the presence of sensor position uncertainty," IEEE Trans. Signal Process., vol. 56, pp. 57585772, Dec. 2008.
Solution: TDOALocSenPosErrCalEmtr
CRLB: TDOALocSenPosErrCalEmtrCRLB
Example: Example
TDOA Localization of Multiple Disjoint Sources in ClosedForm With Sensor Position Errors

Reference: L. Yang and K. C. Ho, "An approximately efficient TDOA localization algorithm in closedform for locating multiple disjoint sources with erroneous sensor positions," IEEE Trans. Signal Process., vol. 57, pp. 45984615, Dec. 2009.
Solution: TDOALocSenPosErrMultiDisjSrc
CRLB: TDOALocSenPosErrMultiDisjSrcCRLB
Example: Example

Reference: L. Yang and K. C. Ho, "Alleviating sensor position error in source localization using calibration emitters at inaccurate locations," IEEE Trans. Signal Process., vol. 58, pp. 6783, Jan. 2010.
Solution: TDOALocSenPosErrMultiCalEmtrIaccLoc
CRLB: TDOALocSenPosErrMultiCalEmtrIaccLocCRLB
Example: Example

Reference: M. Sun and K. C. Ho, "An asymptotically efficient estimator for TDOA and FDOA positioning of multiple disjoint sources in the presence of sensor location uncertainties," IEEE Trans. Signal Process., vol. 59, pp. 34343440, Jul. 2011.
Solution: TDOALocSenPosErrMultiDisjSrcSH
CRLB: TDOALocSenPosErrMultiDisjSrcCRLB
Example: Example, TDOALocSenPosErrMultiDisjSrc, TDOALocStnySenPosErr

Reference: M. Sun and K. C. Ho, "An asymptotically efficient estimator for TDOA and FDOA positioning of multiple disjoint sources in the presence of sensor location uncertainties," IEEE Trans. Signal Process., vol. 59, pp. 34343440, Jul. 2011.
Solution: TDOAFDOALocMultiDisjMvgSrcSenLocErrSH
CRLB: TDOAFDOALocMultiDisjMvgSrcSenLocErrCRLB
Example: ExampleOneSource, ExampleTwoSources, TDOAFDOALocMvgSenPosErr
TDOA Localization in ClosedForm With Reduced Bias

Reference: K. C. Ho, "Bias reduction for an explicit solution of source localization using TDOA," IEEE Trans. Signal Process., vol. 60, pp. 21012114, May 2012.
BiasRed Solution: TDOALoc_BiasRed
BiasSub Solution: TDOALoc_BiasSub, BiasTDOALoc
CRLB: TDOALocCRLB
Example: Example, TDOALoc
TDOA and FDOA Localization in ClosedForm With Reduced Bias

Reference: K. C. Ho, "Bias reduction for an explicit solution of source localization using TDOA," IEEE Trans. Signal Process., vol. 60, pp. 21012114, May 2012.
BiasRed Solution: TDOAFDOALoc_BiasRed, MinGenEigCmp
CRLB: TDOAFDOALocMvgSrcSenCRLB
Example: Example, TDOAFDOALocMvgSrcSen
AOA 3D Localization in ClosedForm With Reduced Bias

Reference: Y. Wang and K. C. Ho, "An asymptotically efficient estimator in closedForm for 3D AOA localization using a sensor network," IEEE Trans. Wireless Commun., vol. 14, no. 12, pp. 65246535, Dec. 2015.
Solution: AOA3DLoc_BRPLE
CRLB: AOA3DLocSenPosErrCRLB
Bias: AOA3DLocBias
Example: Example
3D Localization in ClosedForm by TDOA and AOA Measurements

Reference: J. Yin, Q. Wan, S. Yang, and K. C. Ho, "A simple and accurate TDOAAOA localization method using two stations," IEEE Signal Process. Lett., vol. 23, pp. 144148, Jan. 2016.
Solution, Performance: TDOAAOALoc
TDOA localization in LER Scenario

Reference: S. Li and K. C. Ho, “Accurate and effective localization of an object in large equal radius scenario,” IEEE Trans. Wireless Commun., vol. 15, no. 12, pp. 82738285, Dec. 2016.
Solution: TDOALoc_LER
CRLB: TDOALocCRLB
Example: Example_Fig2
Example: Example_Fig6, TDOALoc, Cov_TDOA, findCenter