Full- and reduced-order distributed Bayesian estimation analytical performance bounds

Abstract

Motivated by the resource management problem in nonlinear multisensor tracking networks, the paper derives online, distributed estimation algorithms for computing the posterior Cramér-Rao lower bound (PCRLB) for full-order and reduced-order distributed Bayesian estimators without requiring a fusion center and with nodal communications limited to local neighborhoods. For both cases, Riccati-type recursions are derived that sequentially determine the global Fisher information matrix (FIM) from localizedFIMs of the distributed estimators. We use particle filter realizations for these bounds and quantify their performance for data fusion problems through Monte Carlo simulations. Manuscript

Consensus-based distributed dynamic sensor selection in decentralised sensor networks using the posterior Cramér–Rao lower bound

“…Matrix Jðxð0: kÞÞ is derived from the joint posterior distribution Pðxð0: kÞ; zð1: kÞÞ and is referred to as the Fisher information matrix (FIM). In this paper, the distributed computational algorithm proposed in [28], referred to as the dPCRLB, is used as the objective function for sensor selection. It has to be computed distributively and that too online as part of the sensor selection method.…”

“…The expressions for recursively computing J ðlÞ xðkÞ ð Þ and J ðlÞ xðkjk À 1Þ ð Þ are provided in Reference [28] and not reported here to save on space. The global FIM at the LPNs is computed in a distributed configuration using the dPCRLB expressions stated under the following theorem [28].…”

“…In the decentralised architecture [23], recall that there is no central fusion centre, no global knowledge of network topology is available locally, and estimation is performed in a distributed fashion across the system. Our previous work [24][25][26][27][28][29][30] and, likewise, the vast majority of the existing state-of-art distributed, non-linear estimation algorithms [31][32][33][34][35][36][37][38] for AN/SNs incorporate observations locally in a distributed fashion from all sensor nodes. The paper solves a more challenging distributed non-linear estimation problem with an additional constraint limiting the number of active sensors at each iteration.…”

“…Contributions: To summarise, the paper makes the following contributions: (i) Initially, the conventional (non-conditional) dPCRLB computational algorithm (introduced in [28]) is used as the objective function for distributed adaptive sensor selection. A combination of minimum and average consensus algorithms is then used to select a subset of sensor nodes in a distributed fashion resulting in the nonconditional PCRLB based sensor selector.…”

“…A combination of minimum and average consensus algorithms is then used to select a subset of sensor nodes in a distributed fashion resulting in the nonconditional PCRLB based sensor selector. (ii) The paper extends the non-conditional dPCRLB framework [28] to conditional dPCRLB [29] for adaptive non-linear sensor selection problems. The non-conditional PCRLB considers observations and state variables as random, consequently, it is determined primarily from the state model, observation model, and prior knowledge of the initial state of the system leading to an offline bound with actual observations averaged out over time.…”