The phasor measurement units (PMU) are expected to enhance state estimation in the power grid by providing accurate and timely measurements. However, due to communication errors and equipment failures, some detrimental data can occur among the measurements. The largest residual removal (LRR) algorithm is commonly used for phasor state estimation with bad data. Here, we show that this method cannot guarantee correctness unless data redundancy is very abundant. We then establish the equivalence between the approaches of bad data removal and bad data estimation and subtraction. In addition, we propose two new algorithms by exploiting the sparsity of the bad data. All algorithms are tested by simulations and our projection and minimization (PM) algorithm provides the best performance.