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Added definition for plant.

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Roger Labbe 2015-11-29 14:41:34 -08:00
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01-g-h-filter.ipynb
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@ -996,11 +996,11 @@
"cell_type": "markdown",
"metadata": {},
"source": [
"Let me introduce some more formal terminology. The *system* is the object that we want to estimate. In this chapter the system is whatever we are trying to weigh. \n",
"Let me introduce some more formal terminology. The *system* is the object that we want to estimate. In this chapter the system is whatever we are trying to weigh. Some texts call this the *plant*. That terminology comes from control system theory. https://en.wikipedia.org/wiki/Plant_(control_theory%29\n",
"\n",
"The *state* of the system is the current configuration or values of that system that is of interest to us. If I put a 100 kg weight on the scale, its state is 100kg. We define the state based on what is relevant to us. The color, weight, and location of the scale is irrelevant to us so we do not include those values in the state. The *state estimate* is our filter's estimate of the state. For example, for the 100 kg weight weight our estimate might be 99.327 kg due to sensor errors and other factors.\n",
"The *state* of the system is the current configuration or values of that system that is of interest to us. We are interested only in the weight reading. If I put a 100 kg weight on the scale, the state is 100kg. We define the state based on what is relevant to us. The color of the scale is irrelevant to us so we do not include those values in the state. A QA engineer for the manufacturer might include color in the state so that she can track and control the manufacturing process. The *state estimate* is our filter's estimate of the state. For example, for the 100 kg weight weight our estimate might be 99.327 kg due to sensor errors.\n",
"\n",
"We use a *process model* to mathematically model the system. In this chapter our process model is the assumption that my weight today is yesterday's weight plus my weight gain for the last day. The process model does not model or otherwise account for the sensors. Another example would be a process model for an automobile. The process model might be \"distance equals velocity times time. This model is not perfect as the velocity of a car can vary over a non-zero amount of time, the tires can slip on the road, and so on. The *system error* or *process error* is the error in this model. We never know this value exactly; if we did we could refine our model to have zero error.\n",
"We use a *process model* to mathematically model the system. In this chapter our process model is the assumption that my weight today is yesterday's weight plus my weight gain for the last day. The process model does not model or otherwise account for the sensors. Another example would be a process model for an automobile. The process model might be \"distance equals velocity times time. This model is not perfect as the velocity of a car can vary over a non-zero amount of time, the tires can slip on the road, and so on. The *system error* or *process error* is the error in this model. We never know this value exactly; if we did we could refine our model to have zero error. Some texts use *plant model* and *plant error*. You may also see *system model*. They all mean the same thing.\n",
"\n",
"The predict step is known as *system propagation*. It uses the *process model* to form a new *state estimate*. Because of the *process error* this prediction is normally imperfect. Assuming we are tracking data over time, we say we *propogate* the state into the future. Some texts call this the *evolution*. \n",
"\n",