  We present optimal quadratic estimators for the Fourier analysis of
cosmological surveys that detect several different types of tracers of
large-scale structure. Our estimators can be used to simultaneously fit the
matter power spectrum and the biases of the tracers - as well as redshift-space
distortions (RSDs), non-Gaussianities (NGs), or any other effects that are
manifested through differences between the clusterings of distinct species of
tracers. Our estimators reduce to the one by Feldman, Kaiser & Peacock (ApJ
1994, FKP) in the case of a survey consisting of a single species of tracer. We
show that the multi-tracer estimators are unbiased, and that their covariance
is given by the inverse of the multi-tracer Fisher matrix (Abramo, MNRAS 2013;
Abramo & Leonard, MNRAS 2013). When the biases, RSDs and NGs are fixed to their
fiducial values, and one is only interested in measuring the underlying power
spectrum, our estimators are projected into the estimator found by Percival,
Verde & Peacock (MNRAS 2003). We have tested our estimators on simple
(lognormal) simulated galaxy maps, and we show that it performs as expected,
being either equivalent or superior to the FKP method in all cases we analyzed.
Finally, we have shown how to extend the multi-tracer technique to include the
1-halo term of the power spectrum.
