# Reduced-Complexity Tracking Algorithms on Chip for Real-Time Location Estimation
## 4 The Proposed Filtering Algorithm Based on Chip
### Revise Covariance \(R\) and \(Q\) in Different Environments  
Due to the original algorithm, if the environment is different, the covariance \(\mathbb{R}_{k}\) and \(\mathbb{Q}_{k}\) cannot be corrected as the environment changes. The value of \(\mathbb{R}_{k}\) and \(\mathbb{Q}_{k}\) will be accessed by using the registers. Every one hundred points will be restored. In this way, real-time corrections can be made for different environmental variables, which not only reduces the computational complexity, but also increases the accuracy of tracking. The basic ideas of derivation processes for the KF algorithm are based on three distinctive features of the innovation approach which are linear, unbiased, and minimum-variance [30]. In terms of the prediction and correction steps, for the state space model with linear and Gaussian, a KF algorithm can be derived and applied to the recursive Bayesian estimation. As a result, the accuracy of KF-based approach depends on the variance of the model noise and the variance of measurement noise. In terms of the same model noise and measurement noise, for KF-based approach, the larger the sampling time is, the smoother the trajectory will be. Namely, the larger sampling time of a KF-based approach is not suitable for dramatic time variances in the corners of hallways. As illustrated in Equations (10), (11) and (20), the weight of the innovation is the KG. For forming a new estimate, the KG is the weight of the measurement and the weight of the previous estimate. For the state space model with same model noise and with a different variance of measurement noise, the closer the actual variance value is, the more accurate the localization approach is. When the measurement uncertainty is high, the KG is low. As illustrated in Figure 3, the convergence of the estimate uncertainty would be slow. In terms of the result in Ref. [32], the KG is close to zero when the measurement uncertainty is high and the estimate uncertainty is low. Namely, if the measurement uncertainty equals the estimate uncertainty, the KG equals to 0.5 [36].  
For applying to the simulation environment of linear systems in large KG, the measurement noise of the PKF-based approach is more closer to the actual variance value of the simulations. Namely, a low measurement uncertainty which is relative to the estimate uncertainty results in a high KG. The new estimate is close to the measurement. On the other hand, a high measurement uncertainty which is relative to the estimate uncertainty results in a low KG. The new estimate would be close to the previous estimate. The KG is the weight of the measurement and the weight of the previous estimate [36]. On the basis of Figure 5, the results illustrate the environment with the same large KG. In terms of PFK-based and DKF-based approaches, the results illustrate that a good choice at the right time can obtain a better result. Therefore, the appropriate judgment conditions should be chosen in different environmental factors. As illustrated in Figure 5, the PKF-based approach is suitable for a low measurement noise environments, and the DKF-based approach is suitable for a high measurement noise environments.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **DKF (Difference Kalman Filter)** & **PKF (Percentage Kalman Filter)** \\ \hline Method of judgment & Using differences to make judgment & Using percentages to make judgment \\ \hline Using situation & Smaller KG in the environment & Larger KG in the environment \\ \hline \hline \end{tabular}
\end{table}
Table 1: The difference between DKF and PKF.