Basta verificar se as variáveis contêm um valor e, se tiverem, construa a consulta assim:
unset($sql);
if ($stationFilter) {
$sql[] = " STATION_NETWORK = '$stationFilter' ";
}
if ($verticalFilter) {
$sql[] = " VERTICAL = '$verticalFilter' ";
}
$query = "SELECT * FROM $tableName";
if (!empty($sql)) {
$query .= ' WHERE ' . implode(' AND ', $sql);
}
echo $query;
// mysql_query($query);