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In order to get a better understanding I used the method proposed in the paper to build the measurement function $y=h(x)$ using a Matrix $H$ and the state transition function $x_{n+1}=f(x_n)$ using a Matrix $A$. I did this for a practical example to get a feeling how it works. To be clear in the paper you cited they call the measurements $z$ instead of $y$. ...


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But what does the overall covariance matrix of the measurements look like where velocity is unmeasured? That's a meaningless question -- if you're really not measuring velocity, then by definition it has no immediate impact on the measurements. The covariance that matters is the filter's state covariance matrix $P$ in Wikipedia's notation. It encodes the ...


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This is exactly where the Dynamic Model comes into play. The whole idea of the Kalman Filter is that you have a model which connects between variables which are measured to those which are not measured (Estimation) or measured differently (Fusion). Since the velocity is the derivative of the location over time you have a model which connects them both. Once ...


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First of all, you're trying to evaluate the derivative of an exponential. If the base of the exponential is positive, the derivative exists. However, if the base is negative, the derivative does not exist. It would be pointless to use a Kalman filter when you have an exponential with a negative base. Secondly, your model of the echo envelope is $$ A(t) = ...


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Summary You can have only one (or no) primary sensor which is used in the prediction process. All other sensors are secondary and only used for corrections. Each correction takes the current state and a measurement from one of the secondary sensors and outputs the corrected state. You can run corrections as often as you want, typically each time one of the ...


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In my experience at the very least you need a nine or ten state Kalman (velocity, position, and angle -- that's nine states if you attempt to use Euler angles, ten if you use quaternions). Practically, you need to use IMU offset, so add six more states. If you use the IMU's compass function, add three more. It may not be a bad idea to monitor the ...


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