Filtering of Randomly Sampled Time-Stamped Measurements

This paper concerns the filtering of measurements that are taken by networked sensors at nonuniform intervals but that are accurately time stamped. Traditional digital filtering methods are difficult or impossible to use due to nonuniform sampling. Two filtering methods are described. Both are based on making an assumption about the signal behavior between measurements, such as the signal being constant between measurements. In the first method, a filter is formulated as an ordinary differential equation that is incrementally solved as measurements arrive. Such filtering is general; nonlinear and nontime invariant filters may be constructed. In the second method, signal convolution with a continuous-time finite impulse response filter is efficiently performed using a spline representation for the filter response. Such filters are ldquoFIR likerdquo in the sense that they have frequency-domain performance similar to FIR filters and have only slightly worse asymptotic computation time and memory requirements compared to FIR filters, yet have the advantage of being able to deal with nonuniformly sampled measurements. Examples of the operation of both sorts of filters are shown on actual measured data.