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Table 2 Relations between the general model (1) and the considered time-based and RSS-based localization modelsa

From: On a unified framework for linear nuisance parameters

General model (1)

y

H

x

G

u

TSE model (25)

δ (k−1)

Δ (k−1)

x t

1 N×1

r 0

SD-TOA model (31b)

D1′z 1

D1′A1′

x t

D1′A1″

\([||\mathbf {x}_{t}||_{2}^{2}-{r_{0}^{2}}, r_{0}]^{T}\)

SD-TDOA model (36b)

D2′z 2

D2′A2′

x t

D2′A2″

r j

SD-RSS model (43b)

D h

F

\([\mathbf {x}_{t}^{T}, ||\mathbf {x}_{t}||_{2}^{2}]^{T}\)

1 N×1

P0′

  1. aAll the considered models must be white or whitened, i.e., the covariance of the model noise should be a (scaled) identity