The comments that Peter Shor and Dan Bron posted beneath the original question lay out the all-purpose option of replacing "I" or "we" with "the author" or "the authors." The most common place to encounter this tactic in action is in the acknowledgments section of a report or other text, where relying on passive voice would sound ludicrous, as in this example:
Colleagues at the Emmett Kelly Institute are thanked for their contributions to this report. The unflagging support of spouses and children is also gratefully acknowledged.
In such cases, assuming that first-person pronouns are thoroughly banned, the best you can do is to shift to active voice and the persona of "the authors":
The authors wish to thank their colleagues at the Emmett Kelly Institute for their contributions to this report. They also gratefully acknowledge the unflagging support provided by their spouses and children.
In the main text, authors tend to resort less often to "the author" or "the authors" as a dodge for "I" or "we"—but other evasions may come to hand, such as "the research team," "[institution name]," or even "the data" (as in "the data suggest that ..." rather than "We infer from the data that ...").
Of course, passive voice is itself the dodge par excellence for framing personal actions, interpretations, and conclusions as if they were arose spontaneously or from an unknown source. That's how you get paragraphs like this one from AES Ocean Express, LLC, "Ocean Express Pipeline Project: Environmental Impact Statement" (June 2003):
184.108.40.206 Existing Environment
A total of 3 unidentified magnetic anomalies and 35 side scan sonar targets were recorded in Federal Waters. All of the magnetic anomalies were interpreted as debris and were not recommended for avoidance by Ocean Express. Most acoustic targets also were interpreted as debris. Among the four exceptions, one acoustic target was considered a possible section of cable, and three were interpreted as shipwrecks (Sonar Targets 41, 42, and 43). Of the three possible shipwrecks located in the side scan survey area, no determination has been made as to their eligibility for listing on the NRHP.
Readers of this paragraph don't know (1) who recorded the magnetic anomalies and side scan sonar targets, (2) who interpreted the magnetic anomalies as being debris, (3) who decided not to recommend them for avoidance by Ocean Express (unless Ocean Express made that determination, in which case a less ambiguous wording for the relevant phrase would be "and were not recommended by Ocean Express for avoidance"), (4) who interpreted most of the acoustic targets as debris, (5) who considered one acoustic target a possible section of cable, (6) who interpreted three other acoustic targets as shipwrecks, and (7) who has declined to make a determination on the possible shipwrecks' eligibility for listing on the NRHP. That's quite a record of ambiguity—even if the same people or entity turns out to have been responsible for all seven listed actions.
Supposing that one operational team within AES Ocean Express, LLC, was responsible for all of the activities cast in passive voice in the quoted paragraph—and supposing, even more fancifully, that the report's authors wanted to be clear about who did what—it might have recast the paragraph as follows:
AES Ocean Express's oceanic research team recorded a total of 3 unidentified magnetic anomalies and 35 side scan sonar targets in Federal Waters. The team interpreted all of the magnetic anomalies as debris and decided not to recommend any of them for avoidance by Ocean Express. It also interpreted 31 of the acoustic targets as debris. In assessing the four exceptions, the team interpreted one acoustic target to be a possible section of cable and three (Sonar Targets 41, 42, and 43) to be shipwrecks. The team has not determined whether the three possible shipwrecks located in the side scan survey area are eligible for listing on the NRHP.
The revised paragraph goes from seven passive constructions to none, the number of first-person pronouns remains at zero, and the wording identifies the entity hypothetically responsible for each action throughout. Obviously, we would need to alter the wording in order to correctly attribute any actions that entities other than AES Ocean Express's oceanic research team performed—but that part of the task shouldn't be hard.
As for the OP's specific question, "If I want to refer to my supervisors, who are not co-authoring the report with me, how can I do that?" the answer depends on how stiff you are willing to be. It is certainly possible to refer to "the author's supervisors," "the author's advisors," "senior colleagues of the author," or some other formulation (as appropriate), but it might sound better if you identified each person by name and title, rather than by hierarchical relationship to you. That is:
Siegfried Roy, professor and chair of the Large Cat department at the Catamount Institute
Siegfried Roy, the author's supervisor at the Catamount Institute
Without more context, it is impossible to say what contortions may be necessary to avoid using first-person pronouns and still get your intended meaning across—but it is very likely that you will have to sacrifice some degree of naturalness in your voice in order to achieve a complete ban on such pronoun usage.