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Your state vector $x$ is correct. When you do bias estimation(look up IMU kalman filters) you assume that the bias is constant/slowly varying. So your $F$ matrix is just the identity(5x5). Your $H$ matrix converts the predicted state into the form of the measurement. So essentially convert this equation into matrix form $T_{est}−B_{x}$ which is just $[1,−1,0,...

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