Leaflet marker position update from json

<!DOCTYPE html>
<html>
  <head>
    <link rel="stylesheet" href="//cdn.leafletjs.com/leaflet-0.7.5/leaflet.css" />
    <link rel="stylesheet" href="style.css" />
  </head>
  <body>
    <div id="leaflet"></div>
    <script type="text/javascript" src="//cdn.leafletjs.com/leaflet-0.7.5/leaflet.js"></script>
    <script type="text/javascript" src="script.js"></script>
  </body>
</html>

var map = L.map('leaflet', {
  'center': [0, 0],
  'zoom': 0,
  'layers': [
    L.tileLayer('http://{s}.basemaps.cartocdn.com/light_all/{z}/{x}/{y}.png', {
      attribution: '&copy; <a href="http://www.openstreetmap.org/copyright">OpenStreetMap</a> contributors, &copy; <a href="http://cartodb.com/attributions">CartoDB</a>'
    })
  ]
});

var markers = {};

function setMarkers(data) {
  data.BMS.forEach(function (obj) {
    if (!markers.hasOwnProperty(obj.id)) {
      markers[obj.id] = new L.Marker([obj.lat, obj.long]).addTo(map);
      markers[obj.id].previousLatLngs = [];
    } else {
      markers[obj.id].previousLatLngs.push(markers[obj.id].getLatLng());
      markers[obj.id].setLatLng([obj.lat, obj.long]);
    }
  });
}

var json = {
  "BMS":[{
    "id": 'A',
    "lat": -45,
    "long": -45
  },{
    "id": 'B',
    "lat": 45,
    "long": -45
  }]
}

setMarkers(json);

var updatedJson = {
  "BMS":[{
    "id": 'A',
    "lat": -45,
    "long": 45
  },{
    "id": 'B',
    "lat": 45,
    "long": 45
  }]
}

setTimeout(function () {
  setMarkers(updatedJson);
}, 3000);

console.log(markers);

body {
  margin: 0;
}
html, body, #leaflet {
  height: 100%;
}