As a result, the approach of 1-D problem based on the proposed forward and one-step backward (FOSB-based) tracking scheme is illustrated in the following sections.
As compared with the KF-based tracking scheme, the speed estimate of the FOSB-based tracking scheme is based on the additional information contained in the future data.
In addition, for a fair comparison between the algorithms, the input observations of the KF-based tracking scheme is based on the location information extracted from positioning approaches, and the performance of the KF-based approach is also as a comparing bound for location tracking schemes.
Namely, the KF-based tracing scheme is based on the prediction and correction phases for location estimation; the proposed FOSB-based tracking scheme is to distribute and pass the reliable messages between the prediction and correction phases for location estimation.
However, for the linear Gaussian model, the KF-based tracking scheme is an optimal algorithm, and it gives the linear estimator in an MSE sense [27].
In Figure 5, for the linear trajectory in the first path, the FOSB-based tracking scheme is to delay the calculation of the speed estimate until one future observed location is obtained.
Furthermore, the shortage of the speed observation in recursive operations and non-causal nature can lead to a convergence bias if the proposed FOSB-based tracking scheme is used with an improper initial speed value.
Namely, the location accuracy of the proposed FOSB-based tracking scheme is weighted and dominated by the incoming messages having higher reliability information of the location and speed between the prediction and correction phases.
In addition, when the values of sampling times of the tracking algorithms are decreased from 4 to 0.01 s, not only is the accuracy of the estimated location increased, but also the performance of the KF-based tracking scheme is becoming more close to that of the FOSB-based tracking scheme.
For the purpose of increasing the execution speed, the lower computational complexity of the proposed FOSB-based tracking scheme is indeed a valuable improvement for estimating the location of an MT. The simulation results demonstrate that the proposed FOSB-based tracking scheme, in comparison with the traditional KF-based tracking scheme, achieves close location accuracy.
In terms of Figure 7, as the tracking scheme is based on a fixed-lag smoothing concept with faster sampling frequency, the phenomenon of the worse initial convergence can be reduced with selecting a more closer initial value or can be overcome with the times of the process cycle based on the inherent message-passing features to exchange information.
