In the distributed multi-sensor networks, in order to save the communication bandwidth, to quantize the point observations obtained by sensors into the interval measurements is required. However, the traditional filtering algorithm can not directly deal with the quantitative measurements. The box particle filter (Box-PF) as a "generalized particle filter" algorithm uses the box particles and the bounded error model to replace the traditional point particles and the error statistical model. Therefore, it is a powerful tool for processing interval measurements. Key advantages of the Box-PF against the standard particle filter (PF) are a smaller particle number, reduced computational complexity and a fast running speed. Therefore, to cope with the maneuvering target tracking with the quantitative measurements, this paper presents an interacting multiple model box particle filter (IMMBPF) algorithm. Simulation results show that under the condition of quantitative measurements IMMBPF and IMMPF are both able to accurately estimate the states of the maneuvering target. The IMMBPF, however, needs fewer particles, and computes more efficiently.