For the problem that traditional filtering algorithms tend to deteriorate when the measurement noise covariance is very low, a spherical-radical filter based on Gaussian likelihood approximation(SRGLAF) is proposed. To solve the state estimation problem with unknown measurement noise, an adaptive spherical-radical filter based on Gaussian likelihood approximation(ASRGLAF) is proposed. The simulation results show that the SRGLAF can improve the estimation accuracy with low measurement noise, and the ASRGLAF is effective in the scenario with unknown measurement noise.