Extended object or group target tracking using random matrix with nonlinear measurements

For extended-object/group-target tracking (EOT/GTT), the random-matrix approach is appealing. This approach assumes that the measurements are linear in the state and in the noise with its covariance being a random matrix to represent the object extension or the target group. In practice, however, the measurements are nonlinear in the state and noise. This paper proposes a random-matrix approach for EOT/GTT using nonlinear measurements. First, a matched linearization (ML) is proposed to linearize the nonlinear measurements. The linearized form has two parts. The first is linear in the state, and it is optimized in the sense of minimum mean square error (MMSE). The second part is linear in the extension-related noise with a preserved second moment, which is important since the extension information is contained in the covariance of this noise. The linearized measurements can be incorporated into existing random-matrix algorithms after a simple conversion under certain conditions. Second, a variational Bayesian (VB) scheme is proposed for EOT/GTT using the linearized measurements. This approach can be generally applied no matter whether the linearized measurements are converted or not. The effectiveness of the proposed ML and VB approach is demonstrated by simulation results compared with existing random-matrix algorithms.