Sir Robert Peel, the so-called father of modern policing, was early to identify that public trust would be essential to his vision’s success. Both before and after Peel, political theorists have written piles of books and papers on the relationship between people with authority and the people willingly subject to it.
John Locke talked about this relationship using the concept "consent of the governed", specifically, “no one can be...subjected to the political power of another without his own consent." His was a revolutionary way of understanding how a free public actually helps to determine the reach and nature of those in authority. Ultimately, theorists and practitioners alike landed on legitimacy as the term of art.
Police legitimacy is the term used when describing whether or not an agency has the trust of its community. Legitimacy is a scalable concept that, depending on the person, can be used to refer to an individual officer or the entire policing profession.
Technology hasn't been obviously useful in addressing the scenarios and outcomes that affect police legitimacy until recently. By making it easier to be transparent, tools like body-worn cameras, enterprise-grade police force management software, and early intervention systems have added a new layer to police legitimacy.
Foundations of Police Legitimacy
Legitimacy is maintained when the group deciding and enforcing the rules plays by them as well. They must be
impartial and objective in upholding the law. If the rule-bound population detects special treatment or bias, especially the self-serving kind, its attitude changes from acceptance to resistance, resentment, and, occasionally, revolution. (Here's looking at you, King G.) Peel's nine principles of policing is a prescient work that demonstrates the fundamental link between successful policing and police legitimacy.
Another way to understand legitimacy is through the relationship children have with rules during their "formative" years.
If a kid’s mom says no eating ice cream before bed because “It’s bad for you,” but that kid subsequently catches her wrist-deep in a pint of Ben and Jerry’s, that kid’s opinion about the legitimacy of her authority will likely become less favorable. As will his likelihood to comply in the future.
It doesn’t matter whether or not ice cream before bed is actually harmful. What causes friction is the inconsistency. This is why police legitimacy is so tightly entwined with procedural justice: we want those enforcing the rules to do so objectively and consistently.
A Social Institution
Researchers approach police legitimacy as a “riverhead” of social psychology and institutional theory.
Social psychology helps researchers understand how the formation of a person’s perception or outlook might influence their behavior during an encounter with police.
Paired with institutional theory, which defines legitimacy as “a generalized perception or assumption that the actions of an entity are desirable, proper, or appropriate within some socially constructed system of norms, values, beliefs, and definitions.”
When legitimacy exists, an institution gets the benefit of the doubt. Remove legitimacy, and that support begins to erode. For police, legitimacy is the difference between compliance and non-compliance, respect and ridicule, support and criticism; the consequences are serious when an agency lacks the support of its community.
Normative and Empirical Legitimacy
Multiple types of legitimacy can exist at the same time. This fact complicates any understanding of police legitimacy, as an agency could be “normatively” legitimate without “empirical” legitimacy.
Researchers distinguish these two forms of legitimacy by their respective source; i.e., whether we're considering an an agency through the eyes of the government or the public.
Normative legitimacy exists when an agency satisfies an objective criterion determined by an organization higher up the authority food chain. If an agency lacks any obvious signs of corruption, then they satisfy one condition of normative legitimacy.
The presence of empirical legitimacy, however, depends on the perceptions of citizens. As you might have guessed, perception is subjective, which means your community might view your agency as illegitimate even if you qualify by normative standards, i.e., a lack of obvious corruption.
Technologies to Improve Community Perception
Just as technology makes it easier for law enforcement to connect with communities, and by extension to better gauge and positively influence empirical legitimacy, it also helps leadership more easily access information they can use to support officers.
Body-Worn Cameras
These devices serve a dual purpose: collecting evidence and increasing transparency between law enforcement agencies and their communities. By capturing video of arrests and other interactions, both leadership and civilians can literally see how officers conduct themselves. These devices are impartial by nature - a camera on its own can't operate with bias towards officers or civilians. BWC's help move a subjective experience into the realm of objective by opening a contested incident to the oversight of many, diverse reviews. 
Early Warning and Intervention Systems
According to CALEA, "the failure of [an] agency to develop a comprehensive [EIS] system can lead to the erosion of public confidence in the agency's ability to investigate itself, while putting the public and employees in greater risk of danger."
EIS's have existed since the 70s. These early solutions existed in agency-specific data silos, though the focus even then was on community perception and uses of force. Having an EIS in place lends itself to both normative and empirical legitimacy. Normative in that it signals your agency is actively monitoring itself, and empirical in that it publicly demonstrates consideration of the public’s experience with your officers.
Recently, advances in data science have allowed agencies to implement research-driven solutions that promote an evidence-based approach to how we configure technology to alert us to officers in need of support, as well as the intervention chosen to help that officer. Agencies can use advanced technologies like machine learning to prevent officers from having an adverse event that could diminish empirical legitimacy and ruin an officer's career.