sMRT: Multi-Resident Tracking in Smart Homes With Sensor Vectorization

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Vectors01:30

Vectors

Vectors are mathematical entities characterized by both magnitude and direction. Unlike scalars, which are defined solely by magnitude, vectors represent quantities like displacement, velocity, and force, where direction is essential. Vectors are graphically represented as directed line segments, extending from an initial point to a terminal point, denoted with bold letters or arrows placed above the symbol. Two vectors are deemed equal if they share identical magnitudes and directions,...
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Position and Displacement Vectors01:00

Position and Displacement Vectors

To describe the motion of an object, one should first be able to describe its position (where it is at any particular time). More precisely, the position needs to be specified relative to a convenient frame of reference. A frame of reference is an arbitrary set of axes from which the position and motion of an object are described. Earth is often used as a frame of reference to describe the position of an object in relation to stationary objects on Earth.
Further, several important kinds of...
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Multi-input and Multi-variable systems01:22

Multi-input and Multi-variable systems

Cruise control systems in cars are designed as multi-input systems to maintain a driver's desired speed while compensating for external disturbances such as changes in terrain. The block diagram for a cruise control system typically includes two main inputs: the desired speed set by the driver and any external disturbances, such as the incline of the road. By adjusting the engine throttle, the system maintains the vehicle's speed as close to the desired value as possible.
In the absence of...
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Position Vectors01:29

Position Vectors

A position vector is a fundamental concept in mathematics that helps determine the position of one point with respect to another point in space. It is a vector that describes the direction and distance between two points. Position vectors are highly useful in the field of math and science, as they help represent spatial relationships and make calculations easier.
For instance, we want to locate a point P(x, y, z) relative to the origin of coordinates O. In that case, we can define a position...
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