# What do the (+) and (-) symbols after variables mean?

This paper describing an Unscented Kalman Filter implementation uses notation that I am unfamiliar with nor can find on eg https://en.wikipedia.org/wiki/List_of_mathematical_symbols

Xu et al (2008)

An example line is:

$$\chi_{i,k-1}(+) = f(\chi_{i,k-1}), x_k(-)=\sum_{i=0}^{2n}\omega_i\chi_{i,k-1}(+)$$

This notation continues throughout the paper.

Could someone please tell me what the (+) and (-) indicate? At first I thought it was redundant information describing the post and prior versions of $x$ however one of them is $\chi$ and the other is $x$. I also thought it could be the positive and negative solutions of a square root but that isn't obvious to me as being correct either (why (+) of $\chi$ and (-) of $x$ and where are the other solutions).

• They seem to refer to the a priori and a posteriori estimate. Compare the equations with these, Wikipedia uses $x_{k\mid k-1}$ where your paper uses $x_k(-)$ and $x_{k\mid k}$ instead of $x_k(+)$. – N74 Feb 22 '16 at 10:38
• @N74. Thank you. That seems correct to me. (Although noting that they are using chi for the sigma points in the unscented version of the kalman filter.). It would be good if I could accept this as the answer. – David Feb 23 '16 at 12:54
• I copied it in the answer block, if you want. – N74 Feb 23 '16 at 13:29

They seem to refer to the a priori and a posteriori estimate. Compare the equations with these, Wikipedia uses $x_{k∣k−1}$ where your paper uses $x_k(−)$ and $x_{k∣k}$ instead of $x_k(+)$.