To solve the problem of high cost in updating the fingerprint database in terms of time and effort

the theory of compressed sensing and focus Lagrange interpolation algorithm are proposed in the offline phase. The process of fingerprint vector refactoring is transformed into the problem of minimum

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norm optimization by compressed sensing

and total variation is used to recover the original fingerprint vector. Focus Lagrange interpolation algorithm takes the advantage of spatial correlation of sample nodes

by which the fingerprint database can be rebuilt through measuring a small amount of fingerprints. Finally a practical experiment in real indoor environment shows that the theory of compressed sensing achieves higher accuracy than focus Lagrange interpolation algorithm.