Robust interval-constrained H∞ filter

The conventional inequality-constrained H∞ filter needs checking whether each inequality is active or not, where the true but unknown state has to be approximated by its prediction in inequality check, and hence the prediction error unavoidably triggers decision risks and further causes the inequality mis-utilisation, implying the optimality loss. Here, the authors reformulate the interval constraints as equality constraints via the sine functions. However, the resultant equality constraints contain unknown parameters, i.e. the corresponding angles in the sine functions, and hence cannot be directly dealt within the framework of equality-constrained filtering. Through maximising the cost function with respect to the initial state, modelling errors, measurements and angles while minimising it with respect to state estimates, the interval-constrained H∞ filter is derived optimally and analytically, and validated via a road target tracking simulation.