History of Multiple Subwoofer Optimization
This article discusses how multiple subwoofer optimization came about, and provides links to a number of articles that trace the development of the subject.
Bruno Korst-Fagundes Masters Thesis
The earliest known effective attempt to simultaneously fix frequency response errors at multiple listening positions can be found in the 1995 Master's thesis of Bruno Korst-Fagundes, and his paper with Xie and Snelgrove. He assumed multiple speakers with a mono source signal and didn't specifically mention subwoofers, but his concept applies equally well to subs. He split the mono signal into separate EQ for each speaker and found that if the number of speakers is equal to the number of listening positions at which their frequency response is measured, it's possible in theory to get perfectly flat response of the combined speaker outputs at multiple listening positions simultaneously. His approach works by solving a set of simultaneous linear equations at each frequency, based on measurements from each speaker to each listening position. The solution to each system of equations at a given frequency yields the required gain and phase of each sub's DSP filter at that frequency. A high-order finite-impulse-response (FIR) filter having the calculated gain and phase response at each frequency is then designed for each speaker. This approach requires special-purpose FIR filter hardware and has some practical problems related to the need for impractically high filter gains at some frequencies. The practical need to limit these gains places a limit on how flat the combined subwoofer responses can be in practice.
JBL used a variation of the approach originated by Korst-Fagundes on a product called the BassQ, which is no longer made. Its theory of operation is described in U.S. Patent 8355510.
Sound Field Management (SFM)
Harman also has a patented system called Sound Field Management (SFM). Its theory of operation from an engineering perspective is described in the article "Low-Frequency Optimization Using Multiple Subwoofers" by Todd Welti and Allan Devantier. This article was originally published in the Journal of the Audio Engineering Society (JAES) in May of 2006. Information about SFM from a consumer perspective can be found in the article by Floyd Toole on the Audioholics site titled "The Birth of Sound Field Management", which is part of a longer article called "History of Multi-Sub & Sound Field Management (SFM) for Small Room Acoustics". SFM works by minimizing a metric called the mean spatial variance (MSV). The goal of SFM is to first minimize the variation with listening position of the combined sub frequency responses (the MSV) without regard to the flatness of the response. A single separate PEQ, gain and delay per subwoofer are adjusted to minimize the MSV. After this step, EQ that's common to all subs is performed to flatten response. Finally, integration with the mains is performed in a third step. SFM is described in U.S. Patents 7526093, 8705755 and 8280076.
MSO works differently from SFM, as described in the tutorial introduction.
Dirac Live Bass Control (DLBC)
Dirac Live Bass Control is a fairly recent and much needed commercial development that's getting a lot of interest in the home theater community. Though there are no engineering-level articles about how its algorithm works, there is a white paper in PDF format called the "Dirac Live Bass Control User Guide" that has some interesting details. This user guide states that:
"...the present Bass Control solution provides a fine-tuning of the levels, delays and phase responses of individual subwoofers, under a criterion that the variations across space are minimized in a selected band of frequencies. Fig. 5 shows the result of such a fine-tuning, where a gain factor and two all-pass bi-quad filters have been applied to each subwoofer."
So it appears to use digital signal processing whose magnitude response is independent of frequency (delays, all-pass filters and attenuators) for each sub. Beginning in version 1.0.46, MSO can approximate this aspect of the DLBC behavior via the Neglect the MLP target curve option on the Method page of the Optimization Options property sheet. See the error calculations section in the reference manual for details.
One welcome feature introduced by DLBC is the ability to "optimize the splice" between the subs and all satellites in an automated way. If you have a miniDSP DDRC-88A with DDRC-88BM plugin, this can be done manually (and rather tediously) with MSO as described in the reference manual's theory and practice sections on this topic.
Earl Geddes Approach
Discussion of the Geddes approach in the DIY community seems to have begun in a thread at diyaudio.com that began in December of 2008, some two years and seven months after Welti and Devantier published their JAES article on Sound Field Management. Todd Welti was involved in discussions in that thread under the moniker "cap'n todd". Geddes' approach is intended to be used with DSP devices having simple infinite-impulse-response (IIR) filters, such as PEQ and shelving filters. An approach that uses low-cost DSP hardware makes a lot of practical sense. Despite discussion in that thread spanning thirteen years, he's never described specifics of how he computes the per-sub filter parameter values.