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Multivariate Kalman Filter

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After reading the "Kalman Filter in one dimension" section, you should be familiar with the concepts of the Kalman Filter. In this section, we derive the multidimensional (multivariate) Kalman Filter equations. This tutorial section deals with a Linear Kalman Filter (LKF). The LKF assumes that the system dynamics are linear. Until now, we've dealt with one dimensional processes, like estimating the liquid temperature. But many dynamic processes have two, three, or even more dimensions. For instance, the state vector that describes the airplane's position in space is three-dimensional: ⎡ ⎣ ⎢ ⎢ x y z ⎤ ⎦ ⎥ ⎥ [ 𝑥 𝑦 𝑧 ] The state vector that describes the airplane position and velocity is six-dimensional: ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ x y z x ˙ y ˙ z ˙ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ [ 𝑥 𝑦 𝑧 𝑥 ˙ 𝑦 ˙ 𝑧 ˙ ] The state vector that describes the airplane position, velocity, and acceleration is nine-dimensional: ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ x y z x ˙ y ˙ z ˙ x ¨ y ¨ z ¨ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ [

Multivariate Kalman Filter After reading the "Kalman Filter in one dimension" section, you should be familiar with the concepts of the Kalman Filter. In this section, we derive the multidimensional (multivariate) Kalman Filter equations. This tutorial section deals with a Linear Kalman Filter (LKF). The LKF assumes that the system dynamics are linear. Until now, we've dealt with one dimensional processes, like estimating the liquid temperature. But many dynamic processes have two, three, or even more dimensions. For instance, the state vector that describes the airplane's position in…

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