So far I have done EKF Localization (known and unknown correspondences) and EKF SLAM for only known correspondences that are stated in Probabilistic Robotics. Now I moved to EKF SLAM with unknown correspondences. In the algorithm in page 322,
16. $\Psi_{k} = H^{k} \bar{\Sigma}[H^{k}]^{T} + Q$
17. $\pi_{k} = (z^{i} - \hat{z}^{k})^{T} \Psi^{-1}_{k}(z^{i} - \hat{z}^{k})$
18. $endfor$
19. $\pi_{N_{t+1}} = \alpha$
20. $j(i) = \underset{k}{argmin} \ \ \pi_{k}$
21. $N_{t} = max\{N_{t}, j(i)\}$
I don't understand the line 19. In the book page 323, The authors state
Line 19 sets the threshold for the creation of a new landmark: A new landmark is created if the Mahalanobis distance to all existing landmarks in the map exceeds the value $\alpha$. The ML correspondence is then selected in line 20.
what is $\alpha$ in line 19 and how is it computed? Also, what is the Mahalanobis distance? I did research about Mahalanobis distance but still I can't understand its role in EKF SLAM.
Edit: I found another book in my university's library Robotic Navigation and Mapping with Radar The authors state
The Mahalanobis distance measure in SLAM is define as $d^{2}_{M}(z^{j}_{k}, \hat{z}^{i}_{k})$, which provides a measure on the spatial difference between measurement $z^{j}_{k}$ and predicted feature measurement $\hat{z}^{i}_{k}$, given by $$ d^{2}_{M}(z^{j}_{k}, \hat{z}^{i}_{k}) = (z^{j}_{k} - \hat{z}^{i}_{k})^{T} S^{-1}_{k}(z^{j}_{k}, \hat{z}^{i}_{k}) $$ This value has to be calculated for all possible $(z^{j}_{k}, \hat{z}^{i}_{k})$ combinations, for which $$ d_{M}(z^{j}_{k},\hat{z}^{i}_{k}) \leq \alpha $$ Often referred to as a validation gate.
Leave me to the same question what is $\alpha$?