Recursive Least Squares Estimation
نویسنده
چکیده
We start with estimation of a constant based on several noisy measurements. Suppose we have a resistor but do not know its resistance. So we measure it several times using a cheap (and noisy) multimeter. How do we come up with a good estimate of the resistance based on these noisy measurements? More formally, suppose x = (x1, x2, . . . , xn) T is a constant but unknown vector, and y = (y1, y2, . . . , yl) T is an l-element noisy measurement vector. Our task is to find the “best” estimate x̃ of x. Here we look at perhaps the simplest case where each yi is a linear combination of xj , 1 ≤ j ≤ n, with addition of some measurement noise νi. Thus, we are working with the following linear system, y = Hx+ ν, where ν = (ν1, ν2, . . . , νl) T , and H is an l × n matrix; or with all terms listed,
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