Traffic state estimation via a particle filter with compressive sensing and historical traffic data

In this paper we look at the problem of estimating traffic states within segments of road using a particle filter and traffic measurements at the segment boundaries. When there are missing measurements the estimation accuracy can decrease. We propose two methods of solving this problem by estimating the missing measurements by assuming the current measurements will approach the mean of the historical measurements from a suitable time period. The proposed solutions come in the form of an l
₁
norm minimisation and a relevance vector machine type optimisation. Test scenarios involving simulated and real data verify that an accurate estimate of the traffic measurements can be achieved. These estimated missing measurements can then be used to help to improve traffic state estimation accuracy of the particle filter without a significant increase in computation time. For the real data used this can be up to a 23.44% improvement in RMSE values.