程序中XXXX部分和//TODO部分根据具体项目进行修改和完善。

public class UpdateHelper {
    private static final String TAG = "UpdateHelper";
    private static final String FILE_PROVIDER_AUTHORITY = "XXXX";
    private static final String DATA_AND_TYPE = "application/vnd.android.package-archive";
    private static final String UPDATE_URL = "XXXX";

    public static boolean checkForUpdated(Context context) {
        boolean updated = false;
        try {
            int currentVersion = context.getPackageManager().getPackageInfo(context.getPackageName(), 0).versionCode;
        } catch (PackageManager.NameNotFoundException e) {
            e.printStackTrace();
        }
       //TODO 获取服务端最新版本号，与currentVersion做比较
        return updated;
    }

    public static void autoInstallUpdate(final Context context) {
        OkGo.<File>get(UPDATE_URL).tag(context).execute(new FileCallback() {
            @Override
            public void onSuccess(Response<File> response) {
                File file = response.body();
                setPermission(file.getPath());
                installApk(context, file.getPath());
            }

            @Override
            public void onError(Response<File> response) {
                super.onError(response);
                //TODO 网络请求出错
            }

            @Override
            public void onFinish() {
                super.onFinish();
                //TODO 网络请求结束
            }

            @Override
            public void downloadProgress(Progress progress) {
                super.downloadProgress(progress);
                int fraction = (int) (progress.fraction * 100);
                //TODO 下载中，显示下载进度
            }
        });
    }

    private static void installApk(Context context, String apkPath) {
        Intent intent = new Intent(Intent.ACTION_VIEW);
        intent.setFlags(Intent.FLAG_ACTIVITY_NEW_TASK);
        File file = new File(apkPath);
        if (Build.VERSION.SDK_INT > Build.VERSION_CODES.N) {
            Uri apkUri = FileProvider.getUriForFile(context, FILE_PROVIDER_AUTHORITY, file);
            intent.addFlags(Intent.FLAG_GRANT_READ_URI_PERMISSION);
            intent.setDataAndType(apkUri, DATA_AND_TYPE);
        } else {
            Uri apkUri = Uri.fromFile(file);
            intent.setDataAndType(apkUri, DATA_AND_TYPE);
        }
        context.startActivity(intent);
    }

    private static void setPermission(String filePath) {
        String command = "chmod " + "777" + " " + filePath;
        Runtime runtime = Runtime.getRuntime();
        try {
            runtime.exec(command);
        } catch (IOException e) {
            e.printStackTrace();
        }
    }
}