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A novel Kalman filter-based scheme is proposed to estimate the navigational states of a vehicle from the range measurements obtained using beacons (transmitter-receivers): at least three placed at known locations and one on the vehicle. The novelty of the scheme stems from 1) the use of pseudomeasurements which are some nonlinear function of the range measurements so that the measurement model is linear with the resulting Kalman filter globally convergent, 2) the measurements of the pair-wise sums and differences in the ranges so as to reduce the sensitivity to the measurement noise, and 3) the optimal location of the beacons to ensure that the state estimation error is minimised, resulting in the estimation accuracy being linear in the true states. Both the bias and the random errors are considered to account for the sources of errors such as the sensor bias, the faults, and the sensor noise. The proposed scheme is evaluated on a number of simulated examples.