Bearings-only tracking has been the focus of distinct research interest in the last few decades. To attack target maneuvering and measuring nonlinearity, most of the existing methods adopt an interactive multiple model (IMM) with a bank of nonlinear filtering recursions, such as an extended Kalman filter, an unscented Kalman filter (UKF), or a particle filter. However, these nine-state coupled-tracking methods usually suffer from low tracking accuracy due to inseparable model probability and high computational burden because of the calculating inverse of 9 x 9 matrices. This present work focuses on target tracking by two platforms's bearings-only measurements in an axial decoupled way. First, the passive ranging formula is derived with the conversion error proven to be Gaussian noises. Then to reduce the computational burden and maintain high tracking accuracy, the diagonal least upper bound for the covariance matrix of conversion error is given. This makes the decoupled tracking algorithm applicable. To attack the target maneuvering, the present decoupled IMM that uses a bank of passive-ranging-based Kalman filters is adopted along each axis separately. Finally, the decoupled tracking algorithm is compared with conventional coupled IMM in Cartesian coordinates by criterions such as tracking accuracy, model probability, and computational burden.