We present new astrometric measurements from our ongoing monitoring campaign of the HR 8799 directly imaged planetary system. These new data points were obtained with NIRC2 on the W.M. Keck II 10 meter telescope between 2009 and 2014. In addition, we present updated astrometry from previously published observations in 2007 and 2008. All data were reduced using the SOSIE algorithm, which accounts for systematic biases present in previously published observations. This allows us to construct a self-consistent data set derived entirely from NIRC2 data alone. From this dataset, we detect acceleration for two of the planets (HR 8799b and e) at $>$3$sigma$. We also assess possible orbital parameters for each of the four planets independently. We find no statistically significant difference in the allowed inclinations of the planets. Fitting the astrometry while forcing coplanarity also returns $chi^2$ consistent to within 1$sigma$ of the best fit values, suggesting that if inclination offsets of $lesssim$20$^{o}$ are present, they are not detectable with current data. Our orbital fits also favor low eccentricities, consistent with predictions from dynamical modeling. We also find period distributions consistent to within 1$sigma$ with a 1:2:4:8 resonance between all planets. This analysis demonstrates the importance of minimizing astrometric systematics when fitting for solutions to highly undersampled orbits.
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