Abstract : Firstly, the comprehensive comment of nonlinear least-squares algorithms used for TMA in bearings-only system is given. The classical nonlinear least-squares algorithms and several conventional algorithms such as Newton-Gauss iteration, Marquardt iteration and self-adaptive nonlinear least-square are presented. Then, four mathematic models of nonlinear least-squares algorithms used for TMA in bearings-only system are established as follows, high nonlinear model, weakened nonlinear model, weakened again nonlinear model and weakened further nonlinear model.

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