Exploring Connections Between a Multiple Model Kalman Filter and Dynamic Fixed Share with Applications to Demand Response

Kalman filtering and online learning are two approaches to estimate the state of a system in the presence of inaccurate (e.g., noisy) measurements. While many online learning algorithms are model-free and data-driven, two recently developed online learning algorithms, Dynamic Mirror Descent (DMD) and Dynamic Fixed Share (DFS), incorporate dynamic models, similarly to Kalman filtering algorithms. Our previous work showed that DMD can be constructed to produce state estimates that are identical to those produced by a discrete-time Kalman filter. This work extends our previous work by exploring connections between a multiple model Kalman filter (MMKF) and DFS, which both incorporate a set of candidate models to address situations in which the underlying model is unknown. We show that the functions/parameters used within DFS can be constructed to produce the same estimates as a MMKF. We then modify DFS to include several heuristics that are used to improve the performance of a MMKF in order to assess whether they can also be used to improve the performance of DFS. Finally, we investigate the performance of the algorithms and their variations in a simulation study. Specifically, we seek to estimate the time-varying power consumption of an aggregation of electric loads, which could be used as the feedback signal within a demand response algorithm. The simulation results empirically show that DFS implementations generally perform better than comparable MMKF implementations since we are able to tune the functions/parameters used within DFS.