Indoor Tracking With the Generalized $t$ -Distribution Noise Model

An indoor tracking system with forgetting factor and generalized
$t$
-distribution (GT) noise model is proposed in this paper. It consists of first using the weighted centroid formulas to give an estimate of the position and then a filter with GT noise model to improve on the estimate. A common problem with indoor tracking is the noisy disturbances and this paper uses the GT to model them. By being a superset encompassing Gaussian, uniform,
$t$
, Cauchy, and double exponential distributions, GT has the flexibility to characterize noise with Gaussian or non-Gaussian statistical properties. Because of the more accurate noise model, the filter with GT noise model can produce a better estimate than that of the Kalman filter which makes the usual assumption of Gaussian noise. An equation to compute the variance of the estimation error is also derived in this paper. For verification, 200 tracking experiments were conducted. The variance obtained from the experiments matched the variance calculated from the equation. The variance of the estimation error from the filter with GT noise model is smaller than that of the Kalman filter. Another experiment at the lift landing showed that the proposed filter with GT noise model is also less affected by outliers.