In the image plane of an optical sensor, the amplitude information (AI) is very reliable for distinguishing returns generated by actual targets or coming from clutter generators. However, the majority of recently derived multi-object filters based on Mahler's finite set statistics (FISST) theory have ignored utilizing this information. This paper proposes an approximate multi-object filter with additive AI applied for optical sensor systems. The algorithm is operated on an image plane generated by the optical sensor, which has been pre-processed. After each prediction step, we sample multiple particles to approximate the prior multi-object density. Moreover, at the update step, we employ the amplitude feature likelihood for situations where the signal-to-noise ratio (SNR) information of targets is known. The loopy belief propagation (LBP) method with sequentially updated initialization messages is designed to solve the data association problem involved in the update step of the multi-object particle filter. We analyze the convergence performance of the LBP algorithm with additive AI and sequentially updated initialization messages; an ad hoc method for improving the performance of the AI-aided LBP is designed.