# TZD Process Noise

In precise point positioning (PPP) solutions, the wet part of the tropospheric zenith delay (TZD) is usually estimated along with position and receiver clock parameters. The residual TZD effect varies over time, but the magnitude of its variation is predictable to some extent. For this reason, process noise is added to the TZD variance at each epoch. But how should the process noise value be selected?

A value of 5 mm/sqrt(hour) has often been recommended to model typical TZD variations. This means that, over a period of one hour, the variance of the TZD parameter will increase by 25 mm^2. While this notion is quite straightforward, we have to keep in mind that process noise alone is not the only factor influencing how the filter will track this effect. In reality, the ratio between carrier-phase variance and TZD process noise defines the filter's behavior.

For example, the following figure shows TZD estimates at station UNBJ, located at the University of New Brunswick (UNB), on 14 June 2015. Three PPP solutions were computed using the suggested process noise value of 5 mm/sqrt(hour). What distinguishes the three solutions is the carrier-phase standard deviation, selected as either: 1) 3 mm for the ionosphere-free (IF) combination; 2) 3 mm for uncombined (UC) signals; or 3) 1 cm for UC signals (not uncommon if you consider orbit/clock errors in your model).

As we can see, the smaller the input standard deviation (3 mm for IF), the more the filter will follow the measurements, leading to noisier TZD estimates. Specifying a larger input noise for the carrier phases will put more “weight” on the process noise value and smooth the TZD estimates (see the black curve). This is something to keep in mind before changing either the TZD process noise value or the carrier-phase precision in your filter.

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