Distributed and decentralized Kalman filtering for Cascaded Fractional order systems

Abstract

This paper presents a distributed Kalman filter algorithm for cascaded systems of fractional order. Certain conditions are introduced under which a division of a fractional system into cascaded subsystems is possible. A functional distribution of a large scale system and of the state estimation algorithm leads to smaller and scalable nodes with reduced memory and computational effort. Since each subsystem performs its calculations locally, a central processing node is not needed. All data which are required by subsequent nodes are communicated to them unidirectionally. Also a comparison between the Fractional Kalman Filter (FKF) and the Cascaded Fractional Kalman Filter (CFKF) is given by an example.

Cascaded Fractional Kalman Filtering for State and Current Estimation of Large-Scale Lithium-Ion Battery Packs

“…Because the binomial coefficient in (2) converges to zero for j → ∞, one can neglect very old values of x. Therefore, we consider a maximum number l of past values of x which is called short memory principle (SMP) [25,27]. The fractional, time-variant, and discrete-time state-space representation can be obtained from (2) following [23,28] whereby index k denotes the current time step t k in…”

“…. , α N,k ∈ R + denote the orders of the fractional derivative at time k [25,27]. The upper limit of the sum is denoted by the buffer length z = min(k + 1, l) due to the SMP.…”

“…For these states, in fact, an initialization function is needed [30], except one uses an infinite buffer z → ∞ which is not possible in practice. As discussed in [25], a fractional order Kalman filter can compensate a missing or wrong initialization of the system. Furthermore, it is discussed in [6] that the initialization of a fractional order state-space model has only a small influence on the SOC estimation of a single cell.…”

“…3.4 the model-based calculation of branch currents has been introduced and motivated. For a model-based branch current estimation, we propose the usage of (24) and (25) for each subsystem S a separately, because we want to calculate the estimations locally. As discussed, we need information about the states and the resistances of both subsystems S a and S a−1 .…”

“…Therefore, the communication effort compared to a common distributed system is reduced. This cascaded filtering approach has been extended in [25] for fractional order models.…”