Code

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TOA Localization by a Rigid Body Receiver (08/28/2024)

Reference:X. Ke and K. C. Ho, "Localization of a passive object in 3-D by propagation time delays to A rigid body receiver of unknown location," IEEE Signal Process. Lett., vol. 72, pp. 3470-3486, 2024.
Simulation: TOALocByRB_Sim
All: TOALocByRB.zip

Localization by DSF and DD (07/28/2024)

Reference:X. Ke and K. C. Ho, "Localization by Doppler derivatives and Doppler-shifted frequencies," IEEE Signal Process. Lett., vol. 72, pp. 2890-2904, 2024.
Simulation: DSFDDLoc_Sim
All: DSFDDLoc.zip

Multistatic Localization of a Moving Object without the Knowledge of Transmitter Position (11/02/2023)

Reference: J. Pei, G. Wang, K. C. Ho, and L. Huang, "Reducing bias for multistatic localization of a moving object by transmitter at unknown position," IEEE Trans. Aerosp. Electron. Syst., vol. 59, no. 5, pp. 5324-5341, Oct. 2023.
Simulation: MSLocUknTxPosMvgObj_Sim
All: MSLocUknTxPosMvgObj.zip

Doppler-Shifted Frequency (DSF) Localization without the Knowledge of Signal Propagation Speed (11/01/2023)

Reference: D. Lin, G. Wang, K. C. Ho, and L. Huang, "Source localization by frequency measurements in unknown signal propagation speed environments," IEEE Trans. Aerosp. Electron. Syst., vol. 59, no. 4, pp. 3953-3970, Aug. 2023.
Simulation: DSFLocUknPropSpdMvgSrc_Sim
Simulation: DSFLocUknPropSpdStnySrc_Sim
All: DSFLocUknPropSpdMvgSrc.zip
All: DSFLocUknPropSpdStnySrc.zip

TDOA Localization without the Knowledge of Signal Propagation Speed (10/22/2023)

Reference: Y. Sun, K. C. Ho, Y. Yang, and L. Chen, "An asymptotically optimal estimator for source location and propagation speed by TDOA," IEEE Signal Process. Lett., vol. 30, pp. 1037-1041, Aug. 2023.
Simulation: TDOALocUknPropSpd_Sim
All: TDOALocUknPropSpd.zip

Single and Coupled Ellipse Fittings by MCC-VC (07/20/2023)

Reference: Wei Wang, Gang Wang, Chenlong Hu, and K. C. Ho, “Robust ellipse fitting based on maximum correntropy criterion with variable center,” IEEE Trans. Image Process., vol. 32, pp. 2520-2535, Apr. 2023.
All: MCC-VC_ellipse_fitting.zip

Transmitters and Scatterers Localization by Single Receiver Using TDOAs and AOAs (06/28/2023)

Reference: Y. Zhang and K. C. Ho, "Localization of transmitters and scatterers by single receiver", IEEE Trans. Signal Process., vol. 71, pp. 2267-2282, 2023.
Simulation: TDOAAOALocSglRx_Sim
All: TDOAAOALocSglRx.zip

Objective Prior Bayesian Detector (02/25/2023)

Reference: M. H. Al-Ali and K. C. Ho, "Objective Bayesian approach for binary hypothesis testing of multivariate Gaussian observations," IEEE Trans. Inf. Theory, vol. 69, no. 2, pp. 1337-1354, Feb. 2023.
Pd vs SNR for RealData: PdSNR_RealData
Pd vs SNR for ComplexData: PdSNR_ComplexData
Pd vs Pfa: PdAnalyticalAndSimulation
Bayes Factor: BayesFactor
Simulation: ObjBayesianDtr_SimFig1
Simulation: ObjBayesianDtr_SimFig2
Simulation: ObjBayesianDtr_SimFig3
All: ObjBayesianDtr.zip

DSF TMA in 3-D (10/28/2022)

Reference: M. H. Ahmed, K. C. Ho, and G. Wang, "3-D target localization and motion analysis based on Doppler shifted frequencies," IEEE Trans. Aerosp. Electron. Syst., vol. 58, no. 2, pp. 815-833, Apr. 2022.
Closed-Form Solution: DSF3DTMA_CFS
SDP Solution: DSF3DTMA_SDP
MLE: DSF3DTMA_CFS_MLE
CRLB: DSF3DTMA_CRLB
Weight: DSF3DTMA_Weight
Simulation: DSF3DTMA_Sim
All: DSF3DTMA.zip

DSF localization in 3-D (10/28/2022)

Reference: M. H. Ahmed, K. C. Ho, and G. Wang, "3-D target localization and motion analysis based on Doppler shifted frequencies," IEEE Trans. Aerosp. Electron. Syst., vol. 58, no. 2, pp. 815-833, Apr. 2022.
Closed-Form Solution: DSF3DLoc_CFS
SDP Solution: DSF3DLoc_SDP
MLE: DSF3DLoc_CFS_MLE
CRLB: DSF3DLoc_CRLB
Weight: DSF3DLoc_Weight
Simulation: DSF3DLoc_Sim
All: DSF3DLoc.zip

DTDTDOA localization (10/18/2022)

Reference: Y. Zhang and K. C. Ho, "Localization by signals of opportunity in the absence of transmitter position," IEEE Trans. Signal Process., vol. 72, pp. 4602-4617, 2022. (Typo: the submatrix $\mathbf{I}_M$ on the left side of $\mathbf{R}$ in (93b) should be -$\mathbf{I}_M$)
Closed-Form Solution: DTDTDOALoc
Closed-Form Refinement Solution: DTDTDOALocRfn
MLE: DTDTDOALoc_MLE
CRLB: DTDTDOALoc_CRLB
Simulation: DTDTDOALoc_SimFig7Fig9
Simulation: DTDTDOALoc_SimFig11
All: DTDTDOALoc.zip

DTD localization (10/18/2022)

Reference: Y. Zhang and K. C. Ho, "Localization by signals of opportunity in the absence of transmitter position," IEEE Trans. Signal Process., vol. 72, pp. 4602-4617, 2022.
Closed-Form Solution: DTDLoc
Closed-Form Refinement Solution: DTDLocRfn
MLE: DTDLoc_MLE
CRLB: DTDLoc_CRLB
Simulation: DTDLoc_SimFig6Fig8
Simulation: DTDLoc_SimFig10
All: DTDLoc.zip

TOA localization by Moving Transceivers (8/28/2022)

Reference: K. C. Ho, "Localization through transceivers in unknown constant velocity trajectories," IEEE Trans. Signal Process., vol. 70, pp. 3011-3028, 2022. (Note: Both joint and sequential estimations require synchronization of receivers.)
Gauss-Newton MLE: XcvrTOALoc_GN_MLE
Sequential Estimation: XcvrTOALoc_GN_Seq
CRLB: XcvrTOALocCRLB
CRLB_SeqEst: XcvrTOALocSeqCRLB
Simulation: XcvrTOALoc_Sim
All: XcvrTOALoc.zip

Localization in 3-D by Space Angles from Linear Arrays (5/08/2022)

Reference: Y. Sun, K. C. Ho, L. Gao, J. Zou, Y. Yang, and L. Chen, "Three dimensional source localization using arrival angles from linear arrays: analytical investigation and optimal solution," IEEE Trans. Signal Process., vol. 70, pp. 1864-1879, 2022.
SDR Solution: SA3DLocLA_SDR
Gauss-Newton MLE: SA3DLocLA_MLE
CRLB: SA3DLocLACRLB
Example: Fig10to22
All: SA3DLocLA.zip

Computationally Efficient and Location Robust Estimator for IoT Device (4/12/2022)

Reference: Y. Sun, K. C. Ho, G. Wang. J. Chen, Y. Yang, L. Chen, and Q. Wan, "Computationally attractive and location robust estimator for IoT device positioning," IEEE Internet Things J., to appear.
SCO Closed-Form Solution: TDOA_SCO_MPR
SUM Closed-Form Solution: TDOA_SUM_MPR
GTRS Closed-Form Solution: TDOA_GTRS_MPR
CRLB: ConsCRLB
Example: Fig2to9
Example: Fig10
Example: Fig20to23
Example: Fig24to27
All: TDOALocDeviceIoT.zip

Multistatic Localization of a Moving Object using a Stationary Transmitter at Unknown Location (11/28/2021)

Reference: Y. Zhang and K. C. Ho, "Multistatic localization in partially dynamic scenario with only sensor positions available," IEEE Trans. Aerosp. Electron. Syst., vol. 57, no. 5, pp. 3416-3432, Oct. 2021.
MOST Closed-Form Solution: MSLocMOST_CFS
MOMT Closed-Form Solution: MSLocMOMT_CFS
MOST Maximum Likelihood Estimator: MSLocMOST_MLE
MOST Maximum Likelihood Estimator (Object Emitting Signal): MSLocNoTxMOST_MLE
MOST CRLB: MSLocMOSTCRLB
MOMT CRLB: MSLocMOMTCRLB
Example: Example_MOST_Fig6to9
All: MOST.zip

Multistatic Localization of a Static Object using a Moving Transmitter at Unknown Location (11/28/2021)

Reference: Y. Zhang and K. C. Ho, "Multistatic localization in partially dynamic scenario with only sensor positions available," IEEE Trans. Aerosp. Electron. Syst., vol. 57, no. 5, pp. 3416-3432, Oct. 2021.
SOMT Closed-Form Solution: MSLocSOMT_CFS
MOMT Closed-Form Solution: MSLocMOMT_CFS
SOMT Maximum Likelihood Estimator: MSLocSOMT_MLE
SOMT Maximum Likelihood Estimator (Object Emitting Signal): MSLocNoTxSOMT_MLE
SOMT CRLB: MSLocSOMTCRLB
MOMT CRLB: MSLocMOMTCRLB
SOST CRLB: MSLocSOSTCRLB
Example: Example_SOMT_Fig2to5
All: SOMT.zip

2D Moving Object Localization by Doppler Shifted Frequencies, Multiple Time Instants (08/18/2021)

Reference: M. Ahmed, K. C. Ho, and G. Wang, "Localization of a moving source by frequency measurements," IEEE Trans. Signal Process., vol. 68, pp. 4839-4854, 2020.
CFS(Algebraic) Solution: DSF2DLocMtTm_CFS
SDP Solution: DSF2DLocMtTm_SDP
Localization Unknown fo: DSF2DLocFoUnkwnMtTm
CRLB: DSF2DLocMtTm_CRLB
CRLB Unknown fo: DSF2DLocFoUnkwnMtTm_CRLB
Example: Example_Fig6Fig7
All: DSF2DLocMtTm.zip

2D Moving Object Localization by Doppler Shifted Frequencies, Single Time Instant (08/18/2021)

Reference: M. Ahmed, K. C. Ho, and G. Wang, "Localization of a moving source by frequency measurements," IEEE Trans. Signal Process., vol. 68, pp. 4839-4854, 2020.
CFS(Algebraic) Solution: DSF2DLoc_CFS
SDP Solution: DSF2DLoc_SDP
Localization Unknown fo: DSF2DLocFoUnkwn
CRLB: DSF2DLoc_CRLB
CRLB Unknown fo: DSF2DLocFoUnkwn_CRLB
Example: Example_Fig2Fig3Fig4Fig5
All: DSF2DLoc.zip

3D Localization or Self-Localizaiton of Rigid Body by AOA (07/18/2021)

Reference: Y. Wang, G. Wang, S. Chen, K. C. Ho, and L. Huang, "An investigation and solution of angle based rigid body localization," IEEE Trans. Signal Process., vol. 68, pp. 5457-5472, 2020.
SDP Solution: AOARBL3D_SDR
BRPLE Solution: AOARBL3D_BRPLE
CRLB: AOARBL3D_CRLB
Plot Figure: AOARBL3D_PlotFig
Example: Example_Loc
All: AOARBLocSelfLoc3D.zip

3D Localization by AOA in MPR (04/03/2021)

Reference: Y. Sun, K. C. Ho, and Q. Wan, "Eigenspace solution for AOA localization in modified polar representation," IEEE Trans. Signal Process., vol. 68, pp. 2256-2271, 2020.
EV Closed-Form Solution: AOA3DLocMPR_EV
BR Closed-Form Solution: AOA3DLocMPR_BR
EV Solution Theoretical Performance: AOA3DLocMPR_CovEV
BR Solution Theoretical Performance: AOA3DLocMPR_CovBR
CRLB: AOA3DLocMPR_CCRLB
Example: Example_Figs
All: AOA3DLocMPR.zip

Time Delay or with Dopple Shift Localization Having Object and Sensor Motion Effects (11/12/2020)

Reference: T. Jia, K. C. Ho, H. Wang, and X. Shen, "Localization of a moving object with sensors in motion by time delays and Doppler shifts," IEEE Trans. Signal Process., vol. 68, pp. 5824-5841, 2020.
MLE Using Time by Gauss-Newton Iterations: TmLocObjSsrMtnEft_GN, TmLocObjMtnEft_CFS
MLE Using Time by Quasi-Newton Iterations: TmLocObjSsrMtnEft_QN, TmLocObjMtnEft_CFS
MLE Using Time & Doppler by Gauss-Newton Iterations: TmDpLocObjSsrMtnEft_GN, TmDpLocObjMtnEft_CFS
MLE Using Time & Doppler by Quasi-Newton Iterations: TmDpLocObjSsrMtnEft_QN, TmLocObjMtnEft_CFS
Time or/and Doppler Ignoring Object and Sensor Motion Effects: TmDpLocIgrObjSsrMtnEft_GN
Time or/and Doppler Ignoring Object Motion Effect: TmLocSsrMtnEft, TmDpLocSsrMtnEft
CRLB and Theoretical Performance: TmDpLocObjSsrMtnEftCRLB, TheoryMSE
Example: Example_Fig5Fig7
All: TmDpLocObjSsrMtnEft.zip

Time Delay or with Dopple Shift Localization Having Object Motion Effect (11/12/2020)

Reference: T. Jia, K. C. Ho, H. Wang, and X. Shen, "Localization of a moving object with sensors in motion by time delays and Doppler shifts," IEEE Trans. Signal Process., vol. 68, pp. 5824-5841, 2020.
Closed-Form Solution Using Time: TmLocObjMtnEft_CFS
Closed-Form Solution Using Time & Doppler: TmDpLocObjMtnEft_CFS
CRLB: TmDpLocObjMtnEftCRLB
Example: Example_Fig3Fig4
All: TmDpLocObjMtnEft.zip

Multistatic Localization of a moving object by a moving transmitter at unknown location having unknown time and frequency offsets (08/25/2020)

Reference: Y. Zhang and K. C. Ho, "Multistatic moving object localization by a moving transmitter of unknown location and offset," IEEE Trans. Signal Process., vol. 68, pp. 4438-4453, 2020.
Algebraic Closed-Form Solution: MSLocJntObjTxPosVel
Iterative MLE Solution: MSLocJntObjTxPosVel_MLE
Iterative MLE Solution by Indirect-path measurements: MSLocObjPosVelInd_MLE
CRLBs: MSLocObjPosVelCRLB
Example: Example_Fig4Fig7
All: MultiStaticMvgObjLocNoTxPosVelUnknOfsts.zip

Multistatic Localization of a stationary object by a stationary transmitter at unknown position having unknown time offset (08/25/2020)

Reference: Y. Zhang and K. C. Ho, "Multistatic moving object localization by a moving transmitter of unknown location and offset," IEEE Trans. Signal Process., vol. 68, pp. 4438-4453, 2020.
Algebraic Closed-Form Solution: MSLocJntObjTxPos
Iterative MLE Solution: MSLocJntObjTxPos_MLE
Iterative MLE Solution by Indirect-path measurements: MSLocObjPosInd_MLE
CRLBs: MSLocObjPosCRLB
Example: Example_Fig6Fig8
All: MultiStaticLocNoTxPosUnknOfst.zip

Ellptic or Hyperbolic Localization Using Minimum Measurement Solutions (03/31/2020)

Reference: Sanaa S. A. Al-Samahi, Yang Zhang, K. C. Ho, "Elliptic and hyperbolic localizations using minimum measurement solutions," Elsevier Signal Process., vol. 167, Feb. 2020.
Individual(MinMsr) Solution: IndvLocSol
Measurement Combinations for Individual Solutions: Config_Comb
Individual Solution Ambiguity Elimination: SolDetect
Individual Solution Selection for BLUE: IndvSolSel
Combining Individual Solutions by BLUE: BLUEest
Example (Ellpitic): Example_Fig12Fig13
Example (Hyperbolic): Example_Fig15Fig16
All: MinMsrSolElptHypb.zip

Rigid Body Localization by TOA Using Noisy Anchor Positions with a Calibration Emitter at Noisy Position (02/20/2020)

Reference: B. Hao, K. C. Ho, and Z. Li, "Range based rigid body localization with a calibration emitter for mitigating anchor position uncertainties," IEEE Trans. Wireless Commun., vol. 18, no. 12, pp. 5734-5748, Dec. 2019.
MLE1: TOARBLAncErrCalSrc_MLE1, TOARBLAncErrCalSrc_CostEval_MLE1
MLE2: TOARBLAncErrCalSrc_MLE2, TOARBLAncErrCalSrc_CostEval_MLE2
MLE3: TOARBLAncErrCalSrc_MLE3, TOARBLAncErrCalSrc_CostEval_MLE3
eDAC: TOARBLAncErrCalSrc_eDAC, TOAAncUpd_pNsy, TOALoc_pNsy, TOARBL_REF_aNsy
CRLB: TOARBLAncErrCalSrcCRLB
Example: Example_Figs
All: TOARBLAncErrCalSrc.zip

Time Delay or with Dopple Shift Localization Having Sensor Motion Effect (02/10/2020)

Reference: T. Jia, K. C. Ho, H. Wang, and X. Shen, "Effect of sensor motion on time delay and Doppler shift localization: analysis and solution," IEEE Trans. Signal Process., vol. 67, no. 22, pp. 5881-5895, Nov. 2019.
Closed-Form Solution Using Time (for Figs. 4 & 8): TmLocSenMtnEft
SDR Solution Using Time (for Figs. 4 & 8): TmLocSenMtnEft_SDR
MLE Using Time Ignoring Sensor Motion Effect (for Figs. 4 & 8): TmLocIgSenMtnEft_GN
Closed-Form Solution Using Time & Doppler (for Figs. 5 & 9): TmDpLocSenMtnEft
SDR Solution Using Time & Doppler (for Figs. 5 & 9): TmDpLocSenMtnEft_SDR
MLE Using Time & Doppler Ignoring Sensor Motion Effect (for Figs. 5 & 9): TmDpLocIgSenMtnEft_GN
CRLB (for Figs. 4, 5, 8 & 9): TmDpLocSenMtnEftCRLB
Example: Example_Fig4Fig5Fig8Fig9
All: TmDpLocSenMtnEft.zip

Multistatic Localization by Time Delay Measurements without Transmitter Position (02/10/2020)

Reference: Y. Zhang and K. C. Ho, "Multistatic localization in the absence of transmitter position," IEEE Trans. Signal Process., vol. 67, no. 18, pp. 4745-4760, Sep. 2019.
Algebraic Closed-Form Solution for Single Transmitter (for Figs. 3 & 4): MSLocJntObjTx
Algebraic Closed-Form Solution for Multiple Trnasmitters (for Fig. 6): MSLocJntObjTxMulti
CRLB without Sensor Position Error (for Fig. 3): MSLocJntObjTxCRLB
CRLB with Sensor Position Error (for Fig. 4): MSLocJntObjTxCRLB_RxErr
CRLB for Multiple Transmitters with Sensor Position Error (for Fig. 6): MSLocJntObjTxMultiCRLB_RxErr
Example: Example_Fig3
Example: Example_Fig4
Example: Example_Fig6
All: MultiStaticLocNoTxPos.zip

Algebraic solution for TDOA localization in MPR (02/15/2020)

Reference: Y. Sun, K. C. Ho, and Q. Wan, “Solution and analysis of TDOA localization of a near or distant source in closed form,” IEEE Trans. Signal Process., vol. 67, no. 2, pp. 320-335, Jan. 2019.
SUM Solution: TDOA_SUM_MPR
GTRS Solution: TDOA_GTRS_MPR
CRLB: TDOALocCRLB_MPR
SUM Theoretical Performance: Cov_SUM_MPR, Bias_SUM_MPR
GTRS Theoretical Performance: Cov_GTRS_MPR, Bias_GTRS_MPR
Example: Example
All: TDOALoc_AlgbSolMPR.zip

Refinement of TDOAs in Multi-Source Scenario Using Rank Properties

Reference: T.-K. Le, K. C. Ho, and T.-H. Le, “Rank properties for matrices constructed by time differences of arrival,” IEEE Trans. Signal Process., vol. 66, no. 13, pp. 3491-3503, Jul. 2018.
TDOA Refinement: Refine_TDOA_distance_matrix
Example: Example_Fig4Fig5
All: TDOARefinement.zip

AOA localization Using MLE in MPR Formulation

Reference: Y. Wang and K. C. Ho, “Unified near-field and far-field localization for AOA and hybrid AOA-TDOA positionings,” IEEE Trans. Wireless Commun., vol. 17, no. 2, pp. 1242-1254, Feb. 2018.
Iterative MLE Solution in MPR: AOA_MLEMPR
CVX Solution in MPR(for Iterative MLE Initialization): AOA_SDRMPR_3D
Iterative MLE Solution in Cartesian: AOA_MLECAR_3D
CRLB(HBB): AOALoc_HBB_3D
Example: Example_Fig5Fig6
Example: Example_Fig7
All: AOALoc_MLEMPR.zip

AOA and TDOA localization Using MLE in MPR Formulation

Reference: Y. Wang and K. C. Ho, “Unified near-field and far-field localization for AOA and hybrid AOA-TDOA positionings,” IEEE Trans. Wireless Commun., vol. 17, no. 2, pp. 1242-1254, Feb. 2018.
Iterative MLE Solution in MPR: AOATDOA_MLEMPR
CVX Solution in MPR(for Iterative MLE Initialization): AOATDOA_SDRMPR_3D
Iterative MLE Solution in Cartesian: AOATDOA_MLECAR_3D
CRLB(HBB): AOATDOALoc_HBB_3D
Example: Example_Fig8Fig9
Example: Example_Fig10Fig11
All: AOATDOALoc_MLEMPR.zip

TDOA localization Using MLE in MPR Formulation

Reference: Y. Wang and K. C. Ho, “TDOA positioning irrespective of source range,” IEEE Trans. Signal Process., vol. 65, no. 6, pp. 1447-1460, Mar. 2017.
Iterative MLE Solution: TDOA_MLEMPR
CVX Solution (for Iterative MLE Initialization): TDOA_SDRMPR_3D
CRLB: TDOALocCRLB_MPR
Example: Example_Fig3
Example: Example_Fig8
All: TDOALoc_MLEMPR.zip

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. 8273-8285, Dec. 2016.
Solution: TDOALoc_LER
CRLB: TDOALocCRLB
Example: Example_Fig2
Example: Example_Fig6, TDOALoc, Cov_TDOA, findCenter
All: TDOA_LER.zip

Multistatic Sonar Localization in Closed-Form by Differential Delay and Doppler Shift Measurements

Reference: L. Yang, L. Yang, and K. C. Ho, "Moving target localization in multistatic sonar by differential delays and Doppler shifts," IEEE Signal Process. Lett., vol. 23, no. 9, pp. 1160-1164, Sep. 2016.
Solution: MultiStaticDfDlyDopplerLoc
CRLB(Differential Delay Only): MultiStaticDfDlyLocCRLB
CRLB: MultiStaticDfDlyDopplerLocCRLB
Example: MultiStaticDfDlyDopplerLocExample
All: MultiStaticDfDlyDopplerLoc.zip

3D Localization in Closed-Form by TDOA and AOA Measurements

Reference: J. Yin, Q. Wan, S. Yang, and K. C. Ho, "A simple and accurate TDOA-AOA localization method using two stations," IEEE Signal Process. Lett., vol. 23, pp. 144-148, Jan. 2016.
Solution, Performance: TDOAAOALoc
All: TDOAAOALoc.zip

DAC Method for Rigid Body Localization Using TOAs

Reference: S. Chen and K. C. Ho, "Accurate localization of a rigid body using multiple sensors and landmarks," IEEE Trans. Signal Process., vol. 63, no. 24, pp. 6459-6472, Dec. 2015.
Solution: TOARBL_DAC, TOARBL_REF, TOALoc
CRLB: TOARBL_CRLB
Example: Example_Fig2Fig3Fig4Fig5
All: TOALocRigidBody.zip

AOA 3D Localization in Closed-Form With Reduced Bias

Reference: Y. Wang and K. C. Ho, "An asymptotically efficient estimator in closed-Form for 3-D AOA localization using a sensor network," IEEE Trans. Wireless Commun., vol. 14, no. 12, pp. 6524-6535, Dec. 2015.
Solution: AOA3DLoc_BRPLE
CRLB: AOA3DLocSenPosErrCRLB
Bias: AOA3DLocBias
Example: Example
All: AOA3DLoc.zip

Multistatic Localization by Time Delay or with Bearing Measurements Having Unknown Signal Propagation Speed

Reference: L. Rui and K. C. Ho, “Efficient closed-form estimators for multistatic sonar localization,” IEEE Trans. Aerosp. Electron. Syst., vol. 51, no. 1, pp. 600-614, Jan. 2015.
Solution, Random Speed: EllpLocMultTxRxRdnC
CRLB, Random Speed: EllpLocMultTxRxRdnCCRLB
Solution, Fixed Unknown Speed: EllpLocMultTxRxUknC
CRLB, Fixed Unknown Speed: EllpLocMultTxRxUknCCRLB
Example: ExampleFig3
Example: ExampleFig5Fig6
All: EllpLocMultTxRxUknC.zip

TDOA and FDOA Localization in Closed-Form 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. 2101-2114, May 2012.
BiasRed Solution: TDOAFDOALoc_BiasRed, MinGenEigCmp
CRLB: TDOAFDOALocMvgSrcSenCRLB
Example: Example, TDOAFDOALocMvgSrcSen
All: TFDOALocBiasRed.zip

TDOA Localization in Closed-Form 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. 2101-2114, May 2012.
BiasRed Solution: TDOALoc_BiasRed
BiasSub Solution: TDOALoc_BiasSub, BiasTDOALoc
CRLB: TDOALocCRLB
Example: Example, TDOALoc
All: TDOALocBiasRed.zip

TDOA and FDOA Localization of Multiple Disjoint Sources in Closed-Form With Sensor Position and Velocity Errors

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. 3434-3440, Jul. 2011.
Solution: TDOAFDOALocMultiDisjMvgSrcSenLocErrSH
CRLB: TDOAFDOALocMultiDisjMvgSrcSenLocErrCRLB
Example: ExampleOneSource, ExampleTwoSources, TDOAFDOALocMvgSenPosErr
All: TDOAFDOALocMultiDisjMvgSrcSenPosErrSH.zip

TDOA Localization of Multiple Disjoint Sources in Closed-Form With Sensor Position Errors, Without Requiring Hypothesized Source Positions

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. 3434-3440, Jul. 2011.
Solution: TDOALocSenPosErrMultiDisjSrcSH
CRLB: TDOALocSenPosErrMultiDisjSrcCRLB
Example: Example, TDOALocSenPosErrMultiDisjSrc, TDOALocStnySenPosErr
All: TDOALocSenPosErrMultiDisjSrcSH.zip

TDOA Localization in Closed-Form With Sensor Position Errors and Multiple Calibration Emitters at Inaccurate Locations

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. 67-83, Jan. 2010.
Solution: TDOALocSenPosErrMultiCalEmtrIaccLoc
CRLB: TDOALocSenPosErrMultiCalEmtrIaccLocCRLB
Example: Example
All: TDOALocSenPosErrMultiCalEmtrIaccLoc.zip

TDOA Localization of Multiple Disjoint Sources in Closed-Form With Sensor Position Errors

Reference: L. Yang and K. C. Ho, "An approximately efficient TDOA localization algorithm in closed-form for locating multiple disjoint sources with erroneous sensor positions," IEEE Trans. Signal Process., vol. 57, pp. 4598-4615, Dec. 2009.
Solution: TDOALocSenPosErrMultiDisjSrc
CRLB: TDOALocSenPosErrMultiDisjSrcCRLB
Example: Example
All: TDOALocSenPosErrMultiDisjSrc.zip

TDOA Localization in Closed-Form 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. 5758-5772, Dec. 2008.
Solution: TDOALocSenPosErrCalEmtr
CRLB: TDOALocSenPosErrCalEmtrCRLB
Example: Example
All: TDOALocSenPosErrCalEmtr.zip

TDOA and FDOA Localization in Closed-Form 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. 684-696, Feb. 2007.
Solution: TDOAFDOALocMvgSenPosErr
CRLB: TDOAFDOALocMvgSenPosErrCRLB
Example: Example
All: TDOAFDOALocMvgSenPosErr.zip

TDOA Localization in Closed-Form 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. 684-696, Feb. 2007.
Solution: TDOALocStnySenPosErr
CRLB: TDOALocStnySenPosErrCRLB
Example: Example
All: TDOALocStnySenPosErr.zip

TDOA and FDOA Localization in Closed-Form, 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. 2453-2463, Sept. 2004.
Solution: TDOAFDOALocMvgSrcSen
CRLB: TDOAFDOALocMvgSrcSenCRLB
Example: Example
All: TDOAFDOALocMvgSrcSen.zip

Geolocation Using TDOA and FDOA

Reference: K. C. Ho and Y. T. Chan, “Geolocation of a known altitude object from TDOA and FDOA measurements," IEEE Trans. Aerosp. Electron. Syst., vol. 33, no. 3, pp. 770-783, Jul. 1997.
Solution: GeoTDOAFDOA_EmitterOnEarth, lamda2_GeoTDOAFDOA, poly2coeff
CRLB: GeoTDOAFDOA_CRLB
Example: Example_Fig6
All: GeoTDOAFDOA_AltCnstt.zip

TDOA Localization Using Closed-Form Solution

Reference: Y. T. Chan and K. C. Ho, "A simple and efficient estimator for hyperbolic location," IEEE Trans. Signal Process., vol. 42, pp. 1905-1915, Aug. 1994.
Solution: TDOALoc
CRLB: TDOALocCRLB
Example: Example
All: TDOALoc.zip