simple gyro auto calibration module

src/lib/mathlib/math/WelfordMean.hpp

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+/****************************************************************************
+ *
+ *   Copyright (c) 2021 PX4 Development Team. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
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+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in
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+ *    used to endorse or promote products derived from this software
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+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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+ ****************************************************************************/
+
+/**
+ * @file WelfordMean.hpp
+ *
+ * Welford's online algorithm for computing mean and variance.
+ */
+
+#pragma once
+
+namespace math
+{
+
+template<typename T>
+class WelfordMean
+{
+public:
+	// For a new value, compute the new count, new mean, the new M2.
+	void update(const T &new_value)
+	{
+		if (_count == 0) {
+			_mean = new_value;
+		}
+
+		_count++;
+
+		// mean accumulates the mean of the entire dataset
+		const T delta{new_value - _mean};
+		_mean += delta / _count;
+
+		// M2 aggregates the squared distance from the mean
+		// count aggregates the number of samples seen so far
+		_M2 += delta.emult(new_value - _mean);
+	}
+
+	bool valid() const { return _count > 2; }
+	unsigned count() const { return _count; }
+
+	void reset()
+	{
+		_count = 0;
+		_mean = {};
+		_M2 = {};
+	}
+
+	// Retrieve the mean, variance and sample variance
+	T mean() const { return _mean; }
+	T variance() const { return _M2 / _count; }
+	T sample_variance() const { return _M2 / (_count - 1); }
+private:
+	T _mean{};
+	T _M2{};
+	unsigned _count{0};
+};
+
+} // namespace math