Datepicker altfield not populated after submit (onload)

Let's have an input field for a date using Datepicker, and an altfield populated from the said input, in a JSP.

<script type="text/javascript">
    $(function(){
            $("#datepicker").datepicker altField: '#altDate', altFormat: 'yy-mm-dd'});
</script>


<input type="text" id="datepicker" name="datepicker" value="${datepicker}"/>
<input type="text" id="altDate" name="altDate"/>

After a form using these inputs is submitted, the "datepicker" field is filled with the previously entered date, but the "altDate" is not. That means that submitting the form again calls the form with the "altDate" being empty.

A solution would be for the altfield to be loaded in a window.onload function which checks the content of the "datepicker" field.