The definition of a trend is arbitrary and as a result, multiple definitions abound. There is no such thing as "defining the start and end of a trend without any ambiguity" because the sensitivity of the analysis tool or indicator may or may not pick up the noise (for example, the length of the moving average).
Conventional technical analysis defines that an uptrend consists of higher highs with higher lows as buyers keep buying the dips earlier and earlier. A downtrend is the opposite. Within a trend there may be noise or small periods of intermittent price oscillation. Larger ranges of oscillation may or may not be definitive of whether a trend remains intact.
There are a variety of tools used to identify trend. The most common are moving averages and trend lines. Renko and Point & Figure charts are used to remove noise from the data.
Numerous mathematical indicators also exist. Some examples are the Accumulation Distribution Indicator, Average Directional Index (ADX) and Directional Movement Indicator with possibly the MACD (Moving Average Convergence Divergence indicator) and Bollinger Bands being the most commonly used ones.
Market behavior is either trending, mean-reverting, or random (noise). A moving average works well when the market is trending, assuming that it's periodicity isn't too long or too short. If you lengthen the MA to reduce noise, the lag is increased and the trend is extended. If you shorten it to reduce lag, whipsaws may occur, making you question whether the trend has ended.
All indicators have major weaknesses. They are cannot function in both trending and ranging markets. Trending indicators work in trending markets and oscillators work well in oscillating markets. Since there is no way to know what type of market tomorrow will bring, there's no way to know which type of indicator will be the correct one to follow. But I digress.
Speaking of tomorrow, no indicator predicts the future. They are merely an analysis of historical data and a trend following indicator may identify the trend or lack thereof up until today. Any trade decision taken today that is based on past performance is made with the "hope" that the trend will continue. Whether it will is completely unknown. Stocks have no memory of yesterday and counter direction news will negate all mathematical dissection. The only thing that never lies is price action.