Unable to redirect to the child state with the Nested States

Unable to redirect to the child state from the Controller using $state.go.

I can navigate to the child state using ui-sref but when I am doing the same using controller, I am always going to the default state which is in redirection.

$stateProvider.state('my-profile', {
        url: "/my-profile",
        redirectTo: 'my-profile.a',
        templateUrl: 'template-path'
    }).state('my-profile.a', {
        url: '/a',
        templateUrl: 'template-path'
    }).state('my-profile.b', {
        url: '/b',
        templateUrl: 'template-path'
    })
this.$state.go("my-profile","b"); Redirects to a
this.$state.go("my-profile/b);   Redirects to a
this.$state.go("my-profile.b);    Redirects to a

I need to go to “b” Route

Source: AngularJS