This is my code its working for my App. You can try it to fetch the Location.

 ro_gps_icon.setOnClickListener(new View.OnClickListener() {
        @Override
        public void onClick(View v) {

            LocationManager locationManager = (LocationManager) getSystemService(LOCATION_SERVICE);
            if (ActivityCompat.checkSelfPermission(RODetailsActivity.this, Manifest.permission.ACCESS_FINE_LOCATION) != PackageManager.PERMISSION_GRANTED && ActivityCompat.checkSelfPermission(RODetailsActivity.this, Manifest.permission.ACCESS_COARSE_LOCATION) != PackageManager.PERMISSION_GRANTED) {
                return;
            }           locationManager.requestLocationUpdates(LocationManager.GPS_PROVIDER, 30000, 0, (LocationListener) RODetailsActivity.this);
            Criteria criteria = new Criteria();
            String bestProvider = locationManager.getBestProvider(criteria, true);
            Location location = locationManager.getLastKnownLocation(bestProvider);

            if (location == null) {
                Toast.makeText(getApplicationContext(), "GPS signal not found", Toast.LENGTH_SHORT).show();
            }
            if (location != null) {
                Log.e("locatin", "location--" + location);

                Log.e("latitude at beginning",
                        "@@@@@@@@@@@@@@@" + location.getLatitude());
                onLocationChanged(location);
            }
        }
    });

and method for getting the data.

public void onLocationChanged(Location location) {
    Geocoder geocoder;
    List<Address> addresses;
    geocoder = new Geocoder(this, Locale.getDefault());

    double latitude = location.getLatitude();
    double longitude = location.getLongitude();

    Log.e("latitude", "latitude--" + latitude);
    try {
        Log.e("latitude", "inside latitude--" + latitude);
        addresses = geocoder.getFromLocation(latitude, longitude, 1);
        if (addresses != null && addresses.size() > 0) {
            String address = addresses.get(0).getAddressLine(0);
            String city = addresses.get(0).getLocality();
            String state = addresses.get(0).getAdminArea();
            String country = addresses.get(0).getCountryName();
            String postalCode = addresses.get(0).getPostalCode();
            String knownName = addresses.get(0).getFeatureName();

            ro_gps_location.setText(state + " , " + city + " , " + country);
            ro_address.setText(address + " , " + knownName + " , " + postalCode);
        }
    } catch (IOException e) {
        // TODO Auto-generated catch block
        e.printStackTrace();
    }
}

Just start a location Update listener on the click of that button. and when new location arrives move the camera in mapObject (got in OnMapReady() method) to that location with animations.

With a simple trick, you can replace the my location button with a custom one.

1. Customize the Layout of your new button.
2. Set my location enabled in maps api.
3. Hide default button of my location.
4. call click method of my location on your custom button click.

1. Customize the layout of your new button

add a new button to your desired location in layout file of map activity.

<?xml version="1.0" encoding="utf-8"?>
<RelativeLayout xmlns:android="http://schemas.android.com/apk/res/android"
     xmlns:map="http://schemas.android.com/apk/res-auto"
     xmlns:app="http://schemas.android.com/apk/res-auto"
     xmlns:tools="http://schemas.android.com/tools"
     android:layout_height="match_parent"
     android:layout_width="match_parent">

    <fragment
         android:id="@+id/map"
         android:name="com.google.android.gms.maps.SupportMapFragment"
         android:layout_width="match_parent"
         android:layout_height="match_parent"
         tools:context=".activities.MapsActivity" />

   <ImageView
        android:id="@+id/ic_location"
        android:layout_width="18dp"
        android:layout_height="18dp"
        android:src="@drawable/ic_location"
        android:layout_marginRight="8dp"
        android:layout_marginBottom="18dp"
        android:layout_alignParentRight="true"
        android:layout_alignParentBottom="true"/>
</RelativeLayout>

2. Set my location enabled in maps api

@Override
public void onMapReady(GoogleMap googleMap) {
    mMap = googleMap;
    // Enable My Location
    mMap.setMyLocationEnabled(true);
    /* and DON'T disable the default location button*/
 }

3. Hide default button of my location.

    //Create field for map button.
    private View locationButton;

    @Override
    public void onMapReady(GoogleMap googleMap) {
        mMap = googleMap;
        mMap.setMyLocationEnabled(true);

        // get your maps fragment
        SupportMapFragment mapFragment = (SupportMapFragment) getSupportFragmentManager().findFragmentById(R.id.map); 
        // Extract My Location View from maps fragment 
        locationButton = mapFragment.getView().findViewById(0x2);
        // Change the visibility of my location button
        if(locationButton != null)
            locationButton.setVisibility(View.GONE);
    }

4. call click method of my location on your custom button click.

findViewById(R.id.ic_location).setOnClickListener(new View.OnClickListener() {
        @Override
        public void onClick(View v) {
            if(mMap != null)
            {
                if(locationButton != null)
                    locationButton.callOnClick();

            }
         }
    });

I solved this problem in my map fragment by re positioning my location button to the right bottom corner of view using code below, here is my MapsActivity.java :-

import android.support.v4.app.FragmentActivity;
import android.os.Bundle;
import android.view.View;
import android.view.ViewGroup;
import android.widget.RelativeLayout;

import com.google.android.gms.maps.CameraUpdateFactory;
import com.google.android.gms.maps.GoogleMap;
import com.google.android.gms.maps.OnMapReadyCallback;
import com.google.android.gms.maps.SupportMapFragment;
import com.google.android.gms.maps.model.LatLng;
import com.google.android.gms.maps.model.MarkerOptions;

public class MapsActivity extends FragmentActivity implements OnMapReadyCallback {

    private GoogleMap mMap;
    View mapView;

    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.fragment_map);
        // Obtain the SupportMapFragment and get notified when the map is ready to be used.
        SupportMapFragment mapFragment = (SupportMapFragment) getSupportFragmentManager()
                .findFragmentById(R.id.map);
        mapView = mapFragment.getView();
        mapFragment.getMapAsync(this);
            }

    /**
     * Manipulates the map once available.
     * This callback is triggered when the map is ready to be used.
     * This is where we can add markers or lines, add listeners or move the camera. In this case,
     * we just add a marker near Sydney, Australia.
     * If Google Play services is not installed on the device, the user will be prompted to install
     * it inside the SupportMapFragment. This method will only be triggered once the user has
     * installed Google Play services and returned to the app.
     */
    @Override
    public void onMapReady(GoogleMap googleMap) {
        mMap = googleMap;
        mMap.setMyLocationEnabled(true);

        // Add a marker in Sydney and move the camera
        LatLng sydney = new LatLng(-34, 151);
        mMap.addMarker(new MarkerOptions().position(sydney).title("Marker in Sydney"));
        mMap.moveCamera(CameraUpdateFactory.newLatLng(sydney));

        if (mapView != null &&
                mapView.findViewById(Integer.parseInt("1")) != null) {
            // Get the button view
            View locationButton = ((View) mapView.findViewById(Integer.parseInt("1")).getParent()).findViewById(Integer.parseInt("2"));
            // and next place it, on bottom right (as Google Maps app)
            RelativeLayout.LayoutParams layoutParams = (RelativeLayout.LayoutParams)
                    locationButton.getLayoutParams();
            // position on right bottom
            layoutParams.addRule(RelativeLayout.ALIGN_PARENT_TOP, 0);
            layoutParams.addRule(RelativeLayout.ALIGN_PARENT_BOTTOM, RelativeLayout.TRUE);
            layoutParams.setMargins(0, 0, 30, 30);
        }

    }
}

And here is layout of fragment :-

<FrameLayout xmlns:android="http://schemas.android.com/apk/res/android"
    xmlns:tools="http://schemas.android.com/tools"
    android:layout_width="match_parent"
    android:layout_height="match_parent"
    tools:context="com.infogird.www.location_button_reposition.MapFragment">

    <fragment xmlns:android="http://schemas.android.com/apk/res/android"
        xmlns:map="http://schemas.android.com/apk/res-auto"
        xmlns:tools="http://schemas.android.com/tools"
        android:id="@+id/map"
        android:name="com.google.android.gms.maps.SupportMapFragment"
        android:layout_width="match_parent"
        android:layout_height="match_parent"
        />
</FrameLayout>

I hope, this will solve your problem. Thanks.

Here is a simple way of programmatically enabling location like Maps app:

protected void enableLocationSettings() {
       LocationRequest locationRequest = LocationRequest.create()
             .setInterval(LOCATION_UPDATE_INTERVAL)
             .setFastestInterval(LOCATION_UPDATE_FASTEST_INTERVAL)
             .setPriority(LocationRequest.PRIORITY_HIGH_ACCURACY);

        LocationSettingsRequest.Builder builder = new LocationSettingsRequest.Builder()
                .addLocationRequest(locationRequest);

        LocationServices
                .getSettingsClient(this)
                .checkLocationSettings(builder.build())
                .addOnSuccessListener(this, (LocationSettingsResponse response) -> {
                    // startUpdatingLocation(...);
                })
                .addOnFailureListener(this, ex -> {
                    if (ex instanceof ResolvableApiException) {
                        // Location settings are NOT satisfied,  but this can be fixed  by showing the user a dialog.
                        try {
                            // Show the dialog by calling startResolutionForResult(),  and check the result in onActivityResult().
                            ResolvableApiException resolvable = (ResolvableApiException) ex;
                            resolvable.startResolutionForResult(TrackingListActivity.this, REQUEST_CODE_CHECK_SETTINGS);
                        } catch (IntentSender.SendIntentException sendEx) {
                            // Ignore the error.
                        }
                    }
                });
 }

And onActivityResult:

@Override
protected void onActivityResult(int requestCode, int resultCode, @Nullable Intent data) {
    if (REQUEST_CODE_CHECK_SETTINGS == requestCode) {
        if(Activity.RESULT_OK == resultCode){
            //user clicked OK, you can startUpdatingLocation(...);

        }else{
            //user clicked cancel: informUserImportanceOfLocationAndPresentRequestAgain();
        }
    }
}

You can see the documentation here: https://developer.android.com/training/location/change-location-settings