Linear Likelihood Approximation Filter for Nonlinear State Estimation

In the nonlinear estimation problem, the direct evaluation of posterior density function (PDF) is always intractable due to the complex nonlinear integral. In this paper, we propose a linear likelihood approximation filter (LLAF), where the Variational Bayes (VB) framework was employed to indirectly calculate the posterior PDF. The key of achieving LLAF is to firstly use the linear Gaussian distribution with compensate parameters (CPs) to approximately express the measurement likelihood probability with the nonlinearity. Then, in VB framework, CPs identification and state estimation iterate, i.e. that CPs is identified for correcting the state while conversely, the state estimation is applied for identifying CPs. Compared with these existing nonlinear filters using the direct evaluation of PDF, LLAF improves the estimation accuracy with the simple computation complexity. Finally, the good performance of our proposed LLAF is demonstrated in the simulation of ballistic target tracking.