Algorithm I. Ideal Inertial-Based Shifting Trilateration.

Input: Asynchronous readers’ detections, raw inertial sensor data

Output: Updated Absolute Tag Location (ATL)

1: initialize tag memory: empty Detections, IS, TDV, and ATL tables

2: while (tag is not detected)

3:   Do   record data from inertial sensors in IS table

4: End While

5: Read Detections and IS tables // a tag is detected

6: Update Detections table with $l_k^n$

7: If (Detections table has k > 0 entries)

8:  Calculate displacement vector(s) $v_{\left(k-1\right)\to k}$ based on IS table

9: End If

10: If (Detections table has k = 2)  // check for enough detections to perform trilateration

11:  $C_0$ = Circle around $AT{L}_0$ coordinates in $l_0^n$ by a radius of $\Vert v_{0\to 1}+v_{1\to 2}\Vert$

12:  $C_1$ = Circle around $AT{L}_1$ coordinates in $l_1^n$ by a radius of $\Vert v_{1\to 2}\Vert$

13:  $C_2$ = the circle around the current reader by a radius of RSSI mapped detection range

14:  Calculate the current absolute tag location by trilateration of $C_0,C_1,$ and $C_2$

15:  Delete $l_0^n$ and $v_{0\to 1}$; // delete first entry in Detections and TDV tables

16:  If (solution is unique)

17:   Report current ATL (ATLi) to a central database server

18:   Update ATL table; go to 2  // add the new ATL to previous ATL entries

19:  Else

20:   go to 2

21:  End If

22: Else (Detections table has k = 1)

23:   $C_1$ = Circle around $L_2$ coordinates in $l_2^n$ by a radius of $\Vert v_{1\to 2}\Vert$

24:   $C_2$ = the circle around the current reader by a radius of RSSI mapped detection range

25:   Calculate the current absolute tag location(s) by intersecting $C_1$ and $C_2$

26: Else

27:  Update Detections table with $l_k^n$ and TDV table with $v_{\left(k-1\right)\to k}$, go to 2

28: End If