We consider a visible light positioning system in which a receiver performs position estimation based on signals emitted from a number of light emitting diode (LED) transmitters. Each LED transmitter can be malicious and transmit at an unknown power level with a certain probability. A maximum likelihood (ML) position estimator is derived based on the knowledge of probabilities that LED transmitters can be malicious. In addition, in the presence of training measurements, decision rules are designed for detection of malicious LED transmitters, and based on detection results, various ML based location estimators are proposed. To evaluate the performance of the proposed estimators, Cramér-Rao lower bounds (CRLBs) are derived for position estimation in scenarios with and without a training phase. Moreover, an ML estimator is derived when the probabilities that the LED transmitters can be malicious are unknown. The performances of all the proposed estimators are evaluated via numerical examples and compared against the CRLBs.