The principle of inertial navigation is based on Newton's law of inertia, so inertial navigation can be understood to use an accelerometer to measure the acceleration of an object, then multiply it by time to get the speed, and then multiply it by time to get the displacement, thereby determining the position of the object. On the other hand, the angular velocity of the object is measured with a gyroscope, and then the angle is multiplied by the time to determine the direction of the object.

Inertial navigation system has the following advantages:
Good concealment, because it does not send out signals or receive external signals, so it is not easy to be found;
All-weather, the inertial navigation system does not require specific time or geographic factors, and can operate anytime, anywhere;
There are many parameters provided, such as GPS satellite navigation, which can only provide position, direction, and speed information, but inertial navigation can also provide attitude and heading information;
The navigation information update rate is high. The current common GPS update rate is 1 time per second, but inertial navigation can reach hundreds of updates per second or even higher.
However, due to its integral calculation method, inertial navigation has the following disadvantages:
Initial alignment is required, and the alignment is complicated, and the alignment time is long. If the accurate initial position and other information are not given, the calculation error will only become larger and larger;
Navigation error diverges with time. Because it is an integral (accumulation) operation, no matter how small the error is, the error will become larger and larger as time accumulates;
The price is expensive, of course, this is a very accurate inertial navigation system, usually the cost is between tens to several million.

So, how does the principle of inertial navigation work?
Assuming a three-axis accelerometer, the x-axis always points to the east, the y-axis always points to the north, and the z-axis always points to the sky, then the task of inertial navigation becomes particularly simple. The integral of the acceleration in the x-axis direction is the rate of change of longitude, y The integral of acceleration in the axial direction is the rate of change of latitude, and the integral of acceleration in the z-axis direction is the rate of change of altitude. With the change rate of latitude and longitude and the initial value of latitude and longitude, we can easily find the current location of the physics.
In this way, if you don't care about the orientation of the object, you can achieve inertial navigation with only the accelerometer. However, in fact, we still have to use a gyroscope. The simplest reason is how can you keep the direction of the three-axis accelerometer x, y, and z from east, north and sky without the help of a gyroscope?

Based on the above analysis of principles and ideas, people have designed a platform inertial navigation system (GINS). To put this system simpler, it is to design an inertial platform that will automatically adjust, no matter how the object rotates, the platform can always maintain the same posture.
This inertial platform needs to be realized with the help of a gyroscope. The schematic diagram of the platform inertial navigation is as follows:

First, the accelerometer measures the acceleration and transmits it to the navigation computer. The navigation computer resolves and separates harmful accelerations. The harmful accelerations include the acceleration caused by the movement of the carrier relative to the earth and the rotation of the earth, and the centripetal acceleration of the circular motion of the carrier on the surface of the earth. And the acceleration of gravity. The navigation computer calculates the command angular velocity according to the acceleration, and feeds it back to the gyroscope to compensate for the apparent movement of the gyroscope's rotation axis caused by the rotation of the earth. Then the gyroscope outputs the angular velocity. After being corrected by the correction loop, the output platform applies a moment to the inertial platform. The inertial platform adjusts its attitude and transmits its attitude parameters to the navigation computer. The navigation computer finally calculates the speed of the carrier And position as well as attitude and heading.
Adjust the inertial platform according to the measured values (accelerometer and gyroscope) to realize the isolation of the accelerometer and angular motion, and then use the acceleration integral to solve the velocity and even the position. Since the adjustment of the inertial platform is realized by hardware, the calculation amount of the whole system is very small compared with the strapdown inertial navigation mentioned later.

In the platform-type inertial navigation system, the inertial platform is a very critical component, and it mainly has the following functions:
Provide a measurement reference for the accelerometer, no matter how you move, the three axis directions of the accelerometer will not change;
Isolate the interference of the angular movement of the carrier. Since the platform is stable, the angular movement of the carrier will not affect the acceleration measurement;
Measuring the attitude and heading, the deflection angle of the carrier relative to the inertial platform, reflects the heading and attitude of the carrier.
However, due to the introduction of the inertial platform, this has led to the disadvantages of the platform inertial navigation system: complex structure, large volume, high production cost, and difficult maintenance. In fact, the platform-based inertial navigation system is a product of early inertial navigation. At that time, the calculation speed of the computer was far not as fast as it is now, which limited the realization of the inertial navigation system, and only the platform-based inertial navigation system could be used. But by the 1990s, more than 90% of the US had replaced strapdown inertial navigation systems.

What is strapdown inertial navigation system (SINS)? That is, the gyroscope and accelerometer are directly fixed on the carrier, and how the carrier moves, the gyroscope and accelerometer move. The structure of this system is very simple, but it will introduce several problems.
First of all, if you do inertial navigation on an airplane, since the angular motion speed of the airplane can reach more than 400 degrees per second, this requires the gyroscope to have a very large measurement range, which is difficult to achieve on the early mechanical gyroscopes. After the introduction of the laser gyroscope, this problem was solved.
In addition, because the three-axis of the accelerometer is pointed at any point, it is necessary to transform the acceleration value into the coordinate system of the northeast sky mentioned earlier in order to accurately calculate the position of the object. In this process, the amount of calculation is very large, and it is difficult for early computers to carry such a large amount of calculation, which makes it difficult to guarantee the real-time performance of early strapdown inertial navigation.