I know that this question has an accepted answer but I thought I'd chip in with an alternative which uses array.reduce, seeing that summing an array is the canonical example for reduce:

Copy$scope.sum = function(items, prop){
    return items.reduce( function(a, b){
        return a + b[prop];
    }, 0);
};

$scope.travelerTotal = $scope.sum($scope.traveler, 'Amount');

Fiddle

Ecmascript5 solution:

var arr = [
        [{year:2015, value:23000, value1:1000},{year:2016,value:1000, value1:2000},{year:2017,value:400, value1:3000}],
        [{year:2015, value:10000, value1:1000},{year:2016,value:2000, value1:3000},{year:2017,value:500, value1:2000}]
    ],
    
    // summing up values for each `year`
    years = arr.reduce(function (r, a) {
        a.forEach(function (o) {
            y = o.year;
            if (Array.isArray(r[y])) {
                r[y][0] += o.value;
                r[y][1] += o.value1;
            } else {
                r[y] = [o.value, o.value1];
            }
        });
        return r;
    }, {}),

    // constructing the resulting array containing objects with `year` totals
    result = Object.keys(years).map(function (y) {
        return {year: y, value: years[y][0], value1: years[y][1]};
    });

console.log(result);

Use Array.prototype.reduce(), the reduce() method applies a function against an accumulator and each value of the array (from left-to-right) to reduce it to a single value.

var array = [{
  "adults": 2,
  "children": 3
}, {
  "adults": 2,
  "children": 1
}];

var val = array.reduce(function(previousValue, currentValue) {
  return {
    adults: previousValue.adults + currentValue.adults,
    children: previousValue.children + currentValue.children
  }
});
console.log(val);