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An inertial measurement unit (IMU) is an electronic device that measures and reports a body's specific force, angular rate, and sometimes the orientation of the body, using a combination of accelerometers, gyroscopes, and sometimes magnetometers. When the magnetometer is included, IMUs are referred to as IMMUs.
If both are I(0), standard regression analysis will be valid. If they are integrated of a different order, e.g. one being I(1) and the other being I(0), one has to transform the model. If they are both integrated to the same order (commonly I(1)), we can estimate an ECM model of the form
The analysis of errors computed using the global positioning system is important for understanding how GPS works, and for knowing what magnitude errors should be expected.
Linear errors-in-variables models were studied first, probably because linear models were so widely used and they are easier than non-linear ones. Unlike standard least squares regression (OLS), extending errors in variables regression (EiV) from the simple to the multivariable case is not straightforward, unless one treats all variables in the same way i.e. assume equal reliability.
Naylor and Finger [1967] formulated a three-step approach to model validation that has been widely followed: [1] Step 1. Build a model that has high face validity. Step 2. Validate model assumptions. Step 3. Compare the model input-output transformations to corresponding input-output transformations for the real system. [5]
Any non-linear differentiable function, (,), of two variables, and , can be expanded as + +. If we take the variance on both sides and use the formula [11] for the variance of a linear combination of variables (+) = + + (,), then we obtain | | + | | +, where is the standard deviation of the function , is the standard deviation of , is the standard deviation of and = is the ...
The main steps in model-based design approach are: Plant modeling. Plant modeling can be data-driven or based on first principles. Data-driven plant modeling uses techniques such as System identification. With system identification, the plant model is identified by acquiring and processing raw data from a real-world system and choosing a ...
This algorithm is critical to modern iteratively-decoded error-correcting codes, including turbo codes and low-density parity-check codes. Steps involved [ edit ]