4 September 2009 Unbiased Kalman filter using converted measurements: revisit
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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.
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Wei Mei, Wei Mei, Yaakov Bar-Shalom, Yaakov Bar-Shalom, "Unbiased Kalman filter using converted measurements: revisit", Proc. SPIE 7445, Signal and Data Processing of Small Targets 2009, 74450U (4 September 2009); doi: 10.1117/12.831218; https://doi.org/10.1117/12.831218

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