Unbiased Kalman filter using converted measurements: revisit
Wei Mei, Yaakov Bar‐Shalom · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2009
Existing unbiased converted measurement Kalman filters (CMKF) may still give biased estimates under some situations. The covariance of the converted measurement conditioned on the measurements is a noisy stochastic process with strong correlation with the measurement noise; therefore, the filter gain of the CMKF also becomes dependent on the measurement noise. Consequently the measurement noise weighted by the noise-dependent filter gain will no longer be zero mean, hence it can cause the CMKF to become biased. By using the converted measurement covariance at the previous time instead of the one at the current time, the filter gain of the CMKF is decorrelated from the measurement noise, which makes the weighted innovations zero mean. Simulation results show that the proposed CMKF with decorrelated measurement covariance runs with no bias in all situations.