The UnityActionFilterProvider class will build up custom filters in your web api project. The RegisterFilterProviders will call the buildup class.

RegisterFilterProvidersMethod.cs

private static void RegisterFilterProviders()
{
    var providers =
        GlobalConfiguration.Configuration.Services.GetFilterProviders().ToList();

    GlobalConfiguration.Configuration.Services.Add(
        typeof(System.Web.Http.Filters.IFilterProvider),
        new UnityActionFilterProvider(UnityConfig.GetConfiguredContainer()));

    var defaultprovider = providers.First(p => p is ActionDescriptorFilterProvider);

    GlobalConfiguration.Configuration.Services.Remove(
        typeof(System.Web.Http.Filters.IFilterProvider),
        defaultprovider);
}

UnityActionFilterProvider.cs

/// <summary>
/// Allows dependency injection to work with Web API Filters.
/// </summary>
public class UnityActionFilterProvider : ActionDescriptorFilterProvider, IFilterProvider
{
    private readonly IUnityContainer container;

    /// <summary>
    /// Constructor
    /// </summary>
    /// <param name="container">Unity container from UnityConfig.</param>
    public UnityActionFilterProvider(IUnityContainer container)
    {
        this.container = container;
    }

    /// <summary>
    /// 
    /// </summary>
    /// <param name="configuration"></param>
    /// <param name="actionDescriptor"></param>
    /// <returns></returns>
    public new IEnumerable<FilterInfo> GetFilters(
            HttpConfiguration configuration,
            HttpActionDescriptor actionDescriptor)
    {
        var filters = base.GetFilters(configuration, actionDescriptor);

        foreach (var filter in filters)
        {
            container.BuildUp(filter.Instance.GetType(), filter.Instance);
        }

        return filters;
    }
}